Mehta, Madan Lal
1990-01-01
Since the publication of Random Matrices (Academic Press, 1967) so many new results have emerged both in theory and in applications, that this edition is almost completely revised to reflect the developments. For example, the theory of matrices with quaternion elements was developed to compute certain multiple integrals, and the inverse scattering theory was used to derive asymptotic results. The discovery of Selberg's 1944 paper on a multiple integral also gave rise to hundreds of recent publications. This book presents a coherent and detailed analytical treatment of random matrices, leading
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.
Conservation constraints on random matrices
Ma Wen Jong; Hsieh, J
2003-01-01
We study the random matrices constrained by the summation rules that are present in the Hessian of the potential energy surface in the instantaneous normal mode calculations, as a result of momentum conservation. In this paper, we analyse the properties related to such conservation constraints in two classes of real symmetric matrices: one with purely row-wise summation rules and the other with the constraints on the blocks of each matrix, which underscores partially the spatial dimension. We show explicitly that the constraints are removable by separating the degrees of freedom of the zero-eigenvalue modes. The non-spectral degrees of freedom under the constraints can be realized in terms of the ordinary constraint-free orthogonal symmetry but with the rank deducted by the block dimension. We propose that the ensemble of real symmetric matrices with full randomness, constrained by the summation rules, is equivalent to the Gaussian orthogonal ensemble (GOE) with lowered rank. Independent of the joint probabil...
Random matrices, random processes and integrable systems
2011-01-01
This book explores the remarkable connections between two domains that, a priori, seem unrelated: Random matrices (together with associated random processes) and integrable systems. The relations between random matrix models and the theory of classical integrable systems have long been studied. These appear mainly in the deformation theory, when parameters characterizing the measures or the domain of localization of the eigenvalues are varied. The resulting differential equations determining the partition function and correlation functions are, remarkably, of the same type as certain equations appearing in the theory of integrable systems. They may be analyzed effectively through methods based upon the Riemann-Hilbert problem of analytic function theory and by related approaches to the study of nonlinear asymptotics in the large N limit. Associated with studies of matrix models are certain stochastic processes, the "Dyson processes", and their continuum diffusion limits, which govern the spectrum in random ma...
Black holes and random matrices
Cotler, Jordan S.; Gur-Ari, Guy; Hanada, Masanori; Polchinski, Joseph; Saad, Phil; Shenker, Stephen H.; Stanford, Douglas; Streicher, Alexandre; Tezuka, Masaki
2017-05-01
We argue that the late time behavior of horizon fluctuations in large anti-de Sitter (AdS) black holes is governed by the random matrix dynamics characteristic of quantum chaotic systems. Our main tool is the Sachdev-Ye-Kitaev (SYK) model, which we use as a simple model of a black hole. We use an analytically continued partition function | Z( β + it)|2 as well as correlation functions as diagnostics. Using numerical techniques we establish random matrix behavior at late times. We determine the early time behavior exactly in a double scaling limit, giving us a plausible estimate for the crossover time to random matrix behavior. We use these ideas to formulate a conjecture about general large AdS black holes, like those dual to 4D super-Yang-Mills theory, giving a provisional estimate of the crossover time. We make some preliminary comments about challenges to understanding the late time dynamics from a bulk point of view.
Chaos, complexity, and random matrices
Cotler, Jordan; Hunter-Jones, Nicholas; Liu, Junyu; Yoshida, Beni
2017-11-01
Chaos and complexity entail an entropic and computational obstruction to describing a system, and thus are intrinsically difficult to characterize. In this paper, we consider time evolution by Gaussian Unitary Ensemble (GUE) Hamiltonians and analytically compute out-of-time-ordered correlation functions (OTOCs) and frame potentials to quantify scrambling, Haar-randomness, and circuit complexity. While our random matrix analysis gives a qualitatively correct prediction of the late-time behavior of chaotic systems, we find unphysical behavior at early times including an O(1) scrambling time and the apparent breakdown of spatial and temporal locality. The salient feature of GUE Hamiltonians which gives us computational traction is the Haar-invariance of the ensemble, meaning that the ensemble-averaged dynamics look the same in any basis. Motivated by this property of the GUE, we introduce k-invariance as a precise definition of what it means for the dynamics of a quantum system to be described by random matrix theory. We envision that the dynamical onset of approximate k-invariance will be a useful tool for capturing the transition from early-time chaos, as seen by OTOCs, to late-time chaos, as seen by random matrix theory.
Probabilistic Signal Recovery and Random Matrices
2016-12-08
is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources , gathering and...a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ORGANIZATION...proved a sharp invertibility result for sparse random matrices, showed how to improve the norm of a general random matrix by removing a small submatrix
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.
Spectral properties of random triangular matrices
Basu, Riddhipratim; Bose, Arup; Ganguly, Shirshendu; Hazra, Rajat Subhra
2011-01-01
We prove the existence of the limiting spectral distribution (LSD) of symmetric triangular patterned matrices and also establish the joint convergence of sequences of such matrices. For the particular case of the symmetric triangular Wigner matrix, we derive expression for the moments of the LSD using properties of Catalan words. The problem of deriving explicit formulae for the moments of the LSD does not seem to be easy to solve for other patterned matrices. The LSD of the non-symmetric tri...
Random matrices as models for the statistics of quantum mechanics
Casati, Giulio; Guarneri, Italo; Mantica, Giorgio
1986-05-01
Random matrices from the Gaussian unitary ensemble generate in a natural way unitary groups of evolution in finite-dimensional spaces. The statistical properties of this time evolution can be investigated by studying the time autocorrelation functions of dynamical variables. We prove general results on the decay properties of such autocorrelation functions in the limit of infinite-dimensional matrices. We discuss the relevance of random matrices as models for the dynamics of quantum systems that are chaotic in the classical limit. Permanent address: Dipartimento di Fisica, Via Celoria 16, 20133 Milano, Italy.
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
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...... in the system....
Randomness in resting state functional connectivity matrices.
Vergara, Victor M; Calhoun, Vince
2016-08-01
Separate brain regions exhibit synchronous intrinsic activity used to assess connectivity patterns known to appear among brain areas. Connectivity is evaluated from functional magnetic resonance imaging (fMRI) measuring the blood oxygen level dependent signal (BOLD) signal. Extensive research has revealed a distinctive pattern of connectivity among brain areas that can be visualized through a functional connectivity matrix (FCM) matrix. As in any measurement, BOLD signals are subject to contamination from noise and nuisances unrelated to brain's intrinsic activity. Up until now, little work has been developed to determine if patterns observed in FCMs occurred by chance or were driven by a more deterministic process. This work proposes a mathematical framework to test the randomness of FCM connectivity patterns in a systematic and statistical way. A cohort of 121 healthy controls is used to demonstrate the usefulness of the proposed framework. Results indicate that particular parts of the brain might exhibit decreasing randomness with age and gender. Results also show the framework's effectiveness in assessing FCM randomness.
Random matrices, Frobenius eigenvalues, and monodromy
Katz, Nicholas M
1998-01-01
The main topic of this book is the deep relation between the spacings between zeros of zeta and L-functions and spacings between eigenvalues of random elements of large compact classical groups. This relation, the Montgomery-Odlyzko law, is shown to hold for wide classes of zeta and L-functions over finite fields. The book draws on and gives accessible accounts of many disparate areas of mathematics, from algebraic geometry, moduli spaces, monodromy, equidistribution, and the Weil conjectures, to probability theory on the compact classical groups in the limit as their dimension goes to infinit
User-Friendly Tools for Random Matrices: An Introduction
2012-12-03
independent random matrices. We might even dream that the classical methods for studying the scalar concentration problem (1.6.1) extend to (1.6.2...matrix Gaussian series exhibit the behavior described in Theo- rem 4.1.1. Afterward, we show how to adapt the argument to address matrix Rademacher...bound. This behavior emerges from the next theorem, which closely parallels the scalar Chernoff theo- rem . Theorem 5.1.1 (Matrix Chernoff). Consider a
Some properties of fuzzy real numbers
Directory of Open Access Journals (Sweden)
Bayaz Daraby
2016-02-01
In this study, we try to prove Bernoulli's inequality in fuzzy real numbers with some of its applications. Also, we prove two other theorems in fuzzy real numbers which are proved before, for real numbers.
Products of rectangular random matrices: Singular values and progressive scattering
Akemann, Gernot; Ipsen, Jesper R.; Kieburg, Mario
2013-11-01
We discuss the product of M rectangular random matrices with independent Gaussian entries, which have several applications, including wireless telecommunication and econophysics. For complex matrices an explicit expression for the joint probability density function is obtained using the Harish-Chandra-Itzykson-Zuber integration formula. Explicit expressions for all correlation functions and moments for finite matrix sizes are obtained using a two-matrix model and the method of biorthogonal polynomials. This generalizes the classical result for the so-called Wishart-Laguerre Gaussian unitary ensemble (or chiral unitary ensemble) at M=1, and previous results for the product of square matrices. The correlation functions are given by a determinantal point process, where the kernel can be expressed in terms of Meijer G-functions. We compare the results with numerical simulations and known results for the macroscopic level density in the limit of large matrices. The location of the end points of support for the latter are analyzed in detail for general M. Finally, we consider the so-called ergodic mutual information, which gives an upper bound for the spectral efficiency of a MIMO communication channel with multifold scattering.
Cleaning large correlation matrices: Tools from Random Matrix Theory
Bun, Joël; Bouchaud, Jean-Philippe; Potters, Marc
2017-01-01
This review covers recent results concerning the estimation of large covariance matrices using tools from Random Matrix Theory (RMT). We introduce several RMT methods and analytical techniques, such as the Replica formalism and Free Probability, with an emphasis on the Marčenko-Pastur equation that provides information on the resolvent of multiplicatively corrupted noisy matrices. Special care is devoted to the statistics of the eigenvectors of the empirical correlation matrix, which turn out to be crucial for many applications. We show in particular how these results can be used to build consistent "Rotationally Invariant" estimators (RIE) for large correlation matrices when there is no prior on the structure of the underlying process. The last part of this review is dedicated to some real-world applications within financial markets as a case in point. We establish empirically the efficacy of the RIE framework, which is found to be superior in this case to all previously proposed methods. The case of additively (rather than multiplicatively) corrupted noisy matrices is also dealt with in a special Appendix. Several open problems and interesting technical developments are discussed throughout the paper.
CMV matrices in random matrix theory and integrable systems: a survey
Energy Technology Data Exchange (ETDEWEB)
Nenciu, Irina [Courant Institute, 251 Mercer St, New York, NY 10012 (United States)
2006-07-14
We present a survey of recent results concerning a remarkable class of unitary matrices, the CMV matrices. We are particularly interested in the role they play in the theory of random matrices and integrable systems. Throughout the paper we also emphasize the analogies and connections to Jacobi matrices.
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.
Universality of Wigner random matrices: a survey of recent results
Energy Technology Data Exchange (ETDEWEB)
Erdos, Laszlo [Ludwig-Maximilians-University of Munich (Germany)
2011-06-30
This is a study of the universality of spectral statistics for large random matrices. Considered are NxN symmetric, Hermitian, or quaternion self-dual random matrices with independent identically distributed entries (Wigner matrices), where the probability distribution of each matrix element is given by a measure {nu} with zero expectation and with subexponential decay. The main result is that the correlation functions of the local eigenvalue statistics in the bulk of the spectrum coincide with those of the Gaussian Orthogonal Ensemble (GOE), the Gaussian Unitary Ensemble (GUE), and the Gaussian Symplectic Ensemble (GSE), respectively, in the limit as N {yields} {infinity}. This approach is based on a study of the Dyson Brownian motion via a related new dynamics, the local relaxation flow. As a main input, it is established that the density of the eigenvalues converges to the Wigner semicircle law, and this holds even down to the smallest possible scale. Moreover, it is shown that the eigenvectors are completely delocalized. These results hold even without the condition that the matrix elements are identically distributed: only independence is used. In fact, for the matrix elements of the Green function strong estimates are given that imply that the local statistics of any two ensembles in the bulk are identical if the first four moments of the matrix elements match. Universality at the spectral edges requires matching only two moments. A Wigner-type estimate is also proved, and it is shown that the eigenvalues repel each other on arbitrarily small scales. Bibliography: 108 titles.
Delocalization at Small Energy for Heavy-Tailed Random Matrices
Bordenave, Charles; Guionnet, Alice
2017-08-01
We prove that the eigenvectors associated to small enough eigenvalues of a heavy-tailed symmetric random matrix are delocalized with probability tending to one as the size of the matrix grows to infinity. The delocalization is measured thanks to a simple criterion related to the inverse participation ratio which computes an average ratio of {L^4} and {L^2}-norms of vectors. In contrast, as a consequence of a previous result, for random matrices with sufficiently heavy tails, the eigenvectors associated to large enough eigenvalues are localized according to the same criterion. The proof is based on a new analysis of the fixed point equation satisfied asymptotically by the law of a diagonal entry of the resolvent of this matrix.
Random sampling and validation of covariance matrices of resonance parameters
Plevnik, Lucijan; Zerovnik, Gašper
2017-09-01
Analytically exact methods for random sampling of arbitrary correlated parameters are presented. Emphasis is given on one hand on the possible inconsistencies in the covariance data, concentrating on the positive semi-definiteness and consistent sampling of correlated inherently positive parameters, and on the other hand on optimization of the implementation of the methods itself. The methods have been applied in the program ENDSAM, written in the Fortran language, which from a file from a nuclear data library of a chosen isotope in ENDF-6 format produces an arbitrary number of new files in ENDF-6 format which contain values of random samples of resonance parameters (in accordance with corresponding covariance matrices) in places of original values. The source code for the program ENDSAM is available from the OECD/NEA Data Bank. The program works in the following steps: reads resonance parameters and their covariance data from nuclear data library, checks whether the covariance data is consistent, and produces random samples of resonance parameters. The code has been validated with both realistic and artificial data to show that the produced samples are statistically consistent. Additionally, the code was used to validate covariance data in existing nuclear data libraries. A list of inconsistencies, observed in covariance data of resonance parameters in ENDF-VII.1, JEFF-3.2 and JENDL-4.0 is presented. For now, the work has been limited to resonance parameters, however the methods presented are general and can in principle be extended to sampling and validation of any nuclear data.
Random sampling and validation of covariance matrices of resonance parameters
Directory of Open Access Journals (Sweden)
Plevnik Lucijan
2017-01-01
Full Text Available Analytically exact methods for random sampling of arbitrary correlated parameters are presented. Emphasis is given on one hand on the possible inconsistencies in the covariance data, concentrating on the positive semi-definiteness and consistent sampling of correlated inherently positive parameters, and on the other hand on optimization of the implementation of the methods itself. The methods have been applied in the program ENDSAM, written in the Fortran language, which from a file from a nuclear data library of a chosen isotope in ENDF-6 format produces an arbitrary number of new files in ENDF-6 format which contain values of random samples of resonance parameters (in accordance with corresponding covariance matrices in places of original values. The source code for the program ENDSAM is available from the OECD/NEA Data Bank. The program works in the following steps: reads resonance parameters and their covariance data from nuclear data library, checks whether the covariance data is consistent, and produces random samples of resonance parameters. The code has been validated with both realistic and artificial data to show that the produced samples are statistically consistent. Additionally, the code was used to validate covariance data in existing nuclear data libraries. A list of inconsistencies, observed in covariance data of resonance parameters in ENDF-VII.1, JEFF-3.2 and JENDL-4.0 is presented. For now, the work has been limited to resonance parameters, however the methods presented are general and can in principle be extended to sampling and validation of any nuclear data.
Weak commutation relations and eigenvalue statistics for products of rectangular random matrices.
Ipsen, Jesper R; Kieburg, Mario
2014-03-01
We study the joint probability density of the eigenvalues of a product of rectangular real, complex, or quaternion random matrices in a unified way. The random matrices are distributed according to arbitrary probability densities, whose only restriction is the invariance under left and right multiplication by orthogonal, unitary, or unitary symplectic matrices, respectively. We show that a product of rectangular matrices is statistically equivalent to a product of square matrices. Hereby we prove a weak commutation relation of the random matrices at finite matrix sizes, which previously has been discussed for infinite matrix size. Moreover, we derive the joint probability densities of the eigenvalues. To illustrate our results, we apply them to a product of random matrices drawn from Ginibre ensembles and Jacobi ensembles as well as a mixed version thereof. For these weights, we show that the product of complex random matrices yields a determinantal point process, while the real and quaternion matrix ensembles correspond to Pfaffian point processes. Our results are visualized by numerical simulations. Furthermore, we present an application to a transport on a closed, disordered chain coupled to a particle bath.
Limit distributions of random walks on stochastic matrices
Indian Academy of Sciences (India)
... then it is well known that the weak limit of the sequence n exists whose support is contained in the set of all 2 × 2 rank one stochastic matrices. We show that S ( ) , the support of , consists of the end points of a countable number of disjoint open intervals and we have calculated the -measure of each such point.
Exact Distributions of Finite Random Matrices and Their Applications to Spectrum Sensing.
Zhang, Wensheng; Wang, Cheng-Xiang; Tao, Xiaofeng; Patcharamaneepakorn, Piya
2016-07-29
The exact and simple distributions of finite random matrix theory (FRMT) are critically important for cognitive radio networks (CRNs). In this paper, we unify some existing distributions of the FRMT with the proposed coefficient matrices (vectors) and represent the distributions with the coefficient-based formulations. A coefficient reuse mechanism is studied, i.e., the same coefficient matrices (vectors) can be exploited to formulate different distributions. For instance, the same coefficient matrices can be used by the largest eigenvalue (LE) and the scaled largest eigenvalue (SLE); the same coefficient vectors can be used by the smallest eigenvalue (SE) and the Demmel condition number (DCN). A new and simple cumulative distribution function (CDF) of the DCN is also deduced. In particular, the dimension boundary between the infinite random matrix theory (IRMT) and the FRMT is initially defined. The dimension boundary provides a theoretical way to divide random matrices into infinite random matrices and finite random matrices. The FRMT-based spectrum sensing (SS) schemes are studied for CRNs. The SLE-based scheme can be considered as an asymptotically-optimal SS scheme when the dimension K is larger than two. Moreover, the standard condition number (SCN)-based scheme achieves the same sensing performance as the SLE-based scheme for dual covariance matrix K = 2 . The simulation results verify that the coefficient-based distributions can fit the empirical results very well, and the FRMT-based schemes outperform the IRMT-based schemes and the conventional SS schemes.
On the limit of extreme eigenvalues of large dimensional random quaternion matrices
Energy Technology Data Exchange (ETDEWEB)
Yin, Yanqing, E-mail: yinyq799@nenu.edu.cn; Bai, Zhidong, E-mail: baizd@nenu.edu.cn; Hu, Jiang, E-mail: huj156@nenu.edu.cn
2014-03-01
Since E.P. Wigner (1958) established his famous semicircle law, lots of attention has been paid by physicists, probabilists and statisticians to study the asymptotic properties of the largest eigenvalues for random matrices. Bai and Yin (1988) obtained the necessary and sufficient conditions for the strong convergence of the extreme eigenvalues of a Wigner matrix. In this paper, we consider the case of quaternion self-dual Hermitian matrices. We prove the necessary and sufficient conditions for the strong convergence of extreme eigenvalues of quaternion self-dual Hermitian matrices corresponding to the Wigner case.
Spectra of large time-lagged correlation matrices from random matrix theory
Nowak, Maciej A.; Tarnowski, Wojciech
2017-06-01
We analyze the spectral properties of large, time-lagged correlation matrices using the tools of random matrix theory. We compare predictions of the one-dimensional spectra, based on approaches already proposed in the literature. Employing the methods of free random variables and diagrammatic techniques, we solve a general random matrix problem, namely the spectrum of a matrix \\frac{1}{T}XA{{X}\\dagger} , where X is an N× T Gaussian random matrix and A is any T× T , not necessarily symmetric (Hermitian) matrix. Using this result, we study the spectral features of the large lagged correlation matrices as a function of the depth of the time-lag. We also analyze the properties of left and right eigenvector correlations for the time-lagged matrices. We positively verify our results by the numerical simulations.
Effect of Polydispersity on Diffusion in Random Obstacle Matrices
Cho, Hyun Woo; Kwon, Gyemin; Sung, Bong June; Yethiraj, Arun
2012-10-01
The dynamics of tracers in disordered matrices is of interest in a number of diverse areas of physics such as the biophysics of crowding in cells and cell membranes, and the diffusion of fluids in porous media. To a good approximation the matrices can be modeled as a collection of spatially frozen particles. In this Letter, we consider the effect of polydispersity (in size) of the matrix particles on the dynamics of tracers. We study a two dimensional system of hard disks diffusing in a sea of hard disk obstacles, for different values of the polydispersity of the matrix. We find that for a given average size and area fraction, the diffusion of tracers is very sensitive to the polydispersity. We calculate the pore percolation threshold using Apollonius diagrams. The diffusion constant, D, follows a scaling relation D˜(ϕc-ϕm)μ-β for all values of the polydispersity, where ϕm is the area fraction and ϕc is the value of ϕm at the percolation threshold.
A theory of solving TAP equations for Ising models with general invariant random matrices
DEFF Research Database (Denmark)
Opper, Manfred; Çakmak, Burak; Winther, Ole
2016-01-01
We consider the problem of solving TAP mean field equations by iteration for Ising models with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical functional approach that in the thermodynamic limit yields...... the iteration dependent on a Gaussian distributed field only. The TAP magnetizations are stable fixed points if a de Almeida–Thouless stability criterion is fulfilled. We illustrate our method explicitly for coupling matrices drawn from the random orthogonal ensemble....
Numerically Stable Evaluation of Moments of Random Gram Matrices With Applications
Elkhalil, Khalil
2017-07-31
This paper focuses on the computation of the positive moments of one-side correlated random Gram matrices. Closed-form expressions for the moments can be obtained easily, but numerical evaluation thereof is prone to numerical stability, especially in high-dimensional settings. This letter provides a numerically stable method that efficiently computes the positive moments in closed-form. The developed expressions are more accurate and can lead to higher accuracy levels when fed to moment based-approaches. As an application, we show how the obtained moments can be used to approximate the marginal distribution of the eigenvalues of random Gram matrices.
Two conjectures about spectral density of diluted sparse Bernoulli random matrices
Nechaev, S. K.
2014-01-01
We consider the ensemble of $N\\times N$ ($N\\gg 1$) symmetric random matrices with the bimodal independent distribution of matrix elements: each element could be either "1" with the probability $p$, or "0" otherwise. We pay attention to the "diluted" sparse regime, taking $p=1/N +\\epsilon$, where $0
Zeta function for the Lyapunov exponent of a product of random matrices
Energy Technology Data Exchange (ETDEWEB)
Mainieri, R. (Neils Bohr Institute, Blegdamsvej 17, Copenhagen O, 2100 (Denmark) Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States))
1992-03-30
A cycle expansion for the Lyapunov exponent of a product of random matrices is derived. The formula is nonperturbative and numerically effective, which allows the Lyapunov exponent to be computed to high accuracy. In particular, the free energy and heat capacity are computed for the one-dimensional Ising model with quenched disorder. The formula is derived by using a Bernoulli dynamical system to mimic the randomness.
NEW SPECTRAL STATISTICS FOR ENSEMBLES OF 2 × 2 REAL SYMMETRIC RANDOM MATRICES
Directory of Open Access Journals (Sweden)
Sachin Kumar
2017-12-01
Full Text Available We investigate spacing statistics for ensembles of various real random matrices where the matrix-elements have various Probability Distribution Function (PDF: f(x including Gaussian. For two modifications of 2 × 2 matrices with various PDFs, we derive the spacing distributions p(s of adjacent energy eigenvalues. Nevertheless, they show the linear level repulsion near s = 0 as αs where α depends on the choice of the PDF. More interestingly when f(x = xe−x2 (f(0 = 0, we get cubic level repulsion near s = 0: p(s ~ s3e−s2.We also derive the distribution of eigenvalues D(ε for these matrices.
Kazakov, Vladimir; Serban, Didina; Wiegmann, Paul; Zabrodin, Anton
2006-01-01
Random matrices are widely and successfully used in physics for almost 60-70 years, beginning with the works of Dyson and Wigner. Although it is an old subject, it is constantly developing into new areas of physics and mathematics. It constitutes now a part of the general culture of a theoretical physicist. Mathematical methods inspired by random matrix theory become more powerful, sophisticated and enjoy rapidly growing applications in physics. Recent examples include the calculation of universal correlations in the mesoscopic system, new applications in disordered and quantum chaotic systems, in combinatorial and growth models, as well as the recent breakthrough, due to the matrix models, in two dimensional gravity and string theory and the non-abelian gauge theories. The book consists of the lectures of the leading specialists and covers rather systematically many of these topics. It can be useful to the specialists in various subjects using random matrices, from PhD students to confirmed scientists.
Random matrices and the six-vertex model
Bleher, Pavel
2013-01-01
This book provides a detailed description of the Riemann-Hilbert approach (RH approach) to the asymptotic analysis of both continuous and discrete orthogonal polynomials, and applications to random matrix models as well as to the six-vertex model. The RH approach was an important ingredient in the proofs of universality in unitary matrix models. This book gives an introduction to the unitary matrix models and discusses bulk and edge universality. The six-vertex model is an exactly solvable two-dimensional model in statistical physics, and thanks to the Izergin-Korepin formula for the model with domain wall boundary conditions, its partition function matches that of a unitary matrix model with nonpolynomial interaction. The authors introduce in this book the six-vertex model and include a proof of the Izergin-Korepin formula. Using the RH approach, they explicitly calculate the leading and subleading terms in the thermodynamic asymptotic behavior of the partition function of the six-vertex model with domain wa...
Finite size effects in the averaged eigenvalue density of Wigner random-sign real symmetric matrices
Dhesi, G. S.; Ausloos, M.
2016-06-01
Nowadays, strict finite size effects must be taken into account in condensed matter problems when treated through models based on lattices or graphs. On the other hand, the cases of directed bonds or links are known to be highly relevant in topics ranging from ferroelectrics to quotation networks. Combining these two points leads us to examine finite size random matrices. To obtain basic materials properties, the Green's function associated with the matrix has to be calculated. To obtain the first finite size correction, a perturbative scheme is hereby developed within the framework of the replica method. The averaged eigenvalue spectrum and the corresponding Green's function of Wigner random sign real symmetric N ×N matrices to order 1 /N are finally obtained analytically. Related simulation results are also presented. The agreement is excellent between the analytical formulas and finite size matrix numerical diagonalization results, confirming the correctness of the first-order finite size expression.
Realistic Many-Body Quantum Systems vs. Full Random Matrices: Static and Dynamical Properties
Directory of Open Access Journals (Sweden)
Eduardo Jonathan Torres-Herrera
2016-10-01
Full Text Available We study the static and dynamical properties of isolated many-body quantum systems and compare them with the results for full random matrices. In doing so, we link concepts from quantum information theory with those from quantum chaos. In particular, we relate the von Neumann entanglement entropy with the Shannon information entropy and discuss their relevance for the analysis of the degree of complexity of the eigenstates, the behavior of the system at different time scales and the conditions for thermalization. A main advantage of full random matrices is that they enable the derivation of analytical expressions that agree extremely well with the numerics and provide bounds for realistic many-body quantum systems.
Finite size effects in the averaged eigenvalue density of Wigner random-sign real symmetric matrices
Dhesi, G; Ausloos, M.
2016-01-01
© 2016 American Physical Society.Nowadays, strict finite size effects must be taken into account in condensed matter problems when treated through models based on lattices or graphs. On the other hand, the cases of directed bonds or links are known to be highly relevant in topics ranging from ferroelectrics to quotation networks. Combining these two points leads us to examine finite size random matrices. To obtain basic materials properties, the Green's function associated with the matrix has...
Emergence of a spectral gap in a class of random matrices associated with split graphs
Bassler, Kevin E.; Zia, R. K. P.
2018-01-01
Motivated by the intriguing behavior displayed in a dynamic network that models a population of extreme introverts and extroverts (XIE), we consider the spectral properties of ensembles of random split graph adjacency matrices. We discover that, in general, a gap emerges in the bulk spectrum between -1 and 0 that contains a single eigenvalue. An analytic expression for the bulk distribution is derived and verified with numerical analysis. We also examine their relation to chiral ensembles, which are associated with bipartite graphs.
Directory of Open Access Journals (Sweden)
Hjalmar Rosengren
2006-12-01
Full Text Available We study multivariable Christoffel-Darboux kernels, which may be viewed as reproducing kernels for antisymmetric orthogonal polynomials, and also as correlation functions for products of characteristic polynomials of random Hermitian matrices. Using their interpretation as reproducing kernels, we obtain simple proofs of Pfaffian and determinant formulas, as well as Schur polynomial expansions, for such kernels. In subsequent work, these results are applied in combinatorics (enumeration of marked shifted tableaux and number theory (representation of integers as sums of squares.
Invertibility of some circulant matrices
Bustomi; Barra, A.
2017-10-01
We consider several cases of circulant matrices and determine the invertibility of these matrices. We give a criterion of the invertibility of matrices of the form circ(a, b, c, …, c) and circ(a, b, c, …, c, a) where a; b and c are real numbers. By using a different approach, we are able to generalize the result of Carmona.
Pseudosymmetric random matrices: Semi-Poisson and sub-Wigner statistics
Kumar, Sachin; Ahmed, Zafar
2017-08-01
Real nonsymmetric matrices may have either real or complex conjugate eigenvalues. These matrices can be seen to be pseudosymmetric as η M η-1=Mt , where the metric η could be secular (a constant matrix) or depending upon the matrix elements of M . Here we construct ensembles of a large number N of pseudosymmetric n ×n (n large) matrices using N [n (n +1 ) /2 ≤N ≤n2] independent and identically distributed random numbers as their elements. Based on our numerical calculations, we conjecture that for these ensembles the nearest level spacing distributions [NLSDs, p (s )] are sub-Wigner as pa b c(s ) =a s e-b sc(0 topological transitions in a Josephson junction. Interestingly, p (s ) for c =1 is called semi-Poisson, and we show that it lies close to the form p (s ) =0.59 s K0(0.45 s2) derived for the case of 2 ×2 pseudosymmetric matrix where the eigenvalues are most aptly conditionally real, E1 ,2=a ±√{b2-c2 } , which represent characteristic coalescing of eigenvalues in parity-time (PT) -symmetric systems.
Pseudosymmetric random matrices: Semi-Poisson and sub-Wigner statistics.
Kumar, Sachin; Ahmed, Zafar
2017-08-01
Real nonsymmetric matrices may have either real or complex conjugate eigenvalues. These matrices can be seen to be pseudosymmetric as ηMη^{-1}=M^{t}, where the metric η could be secular (a constant matrix) or depending upon the matrix elements of M. Here we construct ensembles of a large number N of pseudosymmetric n×n (n large) matrices using N[n(n+1)/2≤N≤n^{2}] independent and identically distributed random numbers as their elements. Based on our numerical calculations, we conjecture that for these ensembles the nearest level spacing distributions [NLSDs, p(s)] are sub-Wigner as p_{abc}(s)=ase^{-bs^{c}}(0distributions of their eigenvalues fit well to D(ε)=A[tanh{(ε+B)/C}-tanh{(ε-B)/C}] (exceptions also discussed). These sub-Wigner NLSDs are encountered in Anderson metal-insulator transition and topological transitions in a Josephson junction. Interestingly, p(s) for c=1 is called semi-Poisson, and we show that it lies close to the form p(s)=0.59sK_{0}(0.45s^{2}) derived for the case of 2×2 pseudosymmetric matrix where the eigenvalues are most aptly conditionally real, E_{1,2}=a±sqrt[b^{2}-c^{2}], which represent characteristic coalescing of eigenvalues in parity-time (PT) -symmetric systems.
A theory of solving TAP equations for Ising models with general invariant random matrices
DEFF Research Database (Denmark)
Opper, Manfred; Çakmak, Burak; Winther, Ole
2016-01-01
We consider the problem of solving TAP mean field equations by iteration for Ising models with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical functional approach that in the thermodynamic limit yields...... an effective dynamics of a single variable trajectory. Our main novel contribution is the expression for the implicit memory term of the dynamics for general invariant ensembles. By subtracting these terms, that depend on magnetizations at previous time steps, the implicit memory terms cancel making...
Energy Technology Data Exchange (ETDEWEB)
Cummings, A. [Physics Department, University College Dublin, Dublin (Ireland); Department of Mathematical Physics, National University of Ireland Maynooth, Kildare (Ireland); O' Sullivan, G. [Physics Department, University College Dublin, Dublin (Ireland); Heffernan, D.M. [Department of Mathematical Physics, National University of Ireland Maynooth, Kildare (Ireland); School of Theoretical Physics, Dublin Institute for Advanced Studies, Dublin (Ireland)
2001-09-14
Using the relativistic configuration interaction Hartree-Fock method the Hamiltonian matrices of Ce I, J=4{sup {+-}}, and Pr I, J=11/2{sup {+-}}, are studied. These matrices can be characterized as sparse, banded matrices, with a leading diagonal. Diagonalization of the Hamiltonian results in a set of energy eigenvalues and corresponding eigenvectors and the purpose of this investigation will be to characterize the Hamiltonian matrices and coupling matrices of Ce I and Pr I, for both ls and jj coupling representations, using various statistical predictions of Random Matrix Theory. (author)
Non-Newtonian Comment of Lebesgue Measure in Real Numbers
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Cenap Duyar
2017-01-01
Full Text Available We would like to generalize to non-Newtonian real numbers the usual Lebesgue measure in real numbers. For this purpose, we introduce the Lebesgue measure on open and closed sets in non-Newtonian sense and examine their basic properties.
Non-Newtonian Comment of Lebesgue Measure in Real Numbers
Duyar, Cenap; Sağır, Birsen
2017-01-01
We would like to generalize to non-Newtonian real numbers the usual Lebesgue measure in real numbers. For this purpose, we introduce the Lebesgue measure on open and closed sets in non-Newtonian sense and examine their basic properties.
A golden ratio notation for the real numbers
P. di Gianantonio (Pietro)
1996-01-01
textabstractSeveral methods to perform exact computations on real numbers have been proposed in the literature. In some of these methods real numbers are represented by infinite (lazy) strings of digits. It is a well known fact that, when this approach is taken, the standard digit notation cannot
Rocca, Dario; Bai, Zhaojun; Li, Ren-Cang; Galli, Giulia
2012-01-21
We present a technique for the iterative diagonalization of random-phase approximation (RPA) matrices, which are encountered in the framework of time-dependent density-functional theory (TDDFT) and the Bethe-Salpeter equation. The non-Hermitian character of these matrices does not permit a straightforward application of standard iterative techniques used, i.e., for the diagonalization of ground state Hamiltonians. We first introduce a new block variational principle for RPA matrices. We then develop an algorithm for the simultaneous calculation of multiple eigenvalues and eigenvectors, with convergence and stability properties similar to techniques used to iteratively diagonalize Hermitian matrices. The algorithm is validated for simple systems (Na(2) and Na(4)) and then used to compute multiple low-lying TDDFT excitation energies of the benzene molecule. © 2012 American Institute of Physics
Energy Technology Data Exchange (ETDEWEB)
Kasiviswanathan, Shiva [Los Alamos National Laboratory; Rudelson, Mark [UNIV OF MISSOURI; Smith, Adam [PENNSYLVANIA STATE U
2009-01-01
Contingency tables are the method of choice of government agencies for releasing statistical summaries of categorical data. In this paper, we consider lower bounds on how much distortion (noise) is necessary in these tables to provide privacy guarantees when the data being summarized is sensitive. We extend a line of recent work on lower bounds on noise for private data analysis [10, 13. 14, 15] to a natural and important class of functionalities. Our investigation also leads to new results on the spectra of random matrices with correlated rows. Consider a database D consisting of n rows (one per individual), each row comprising d binary attributes. For any subset of T attributes of size |T| = k, the marginal table for T has 2{sup k} entries; each entry counts how many times in the database a particular setting of these attributes occurs. Imagine an agency that wishes to release all (d/k) contingency tables for a given database. For constant k, previous work showed that distortion {tilde {Omicron}}(min{l_brace}n, (n{sup 2}d){sup 1/3}, {radical}d{sup k}{r_brace}) is sufficient for satisfying differential privacy, a rigorous definition of privacy that has received extensive recent study. Our main contributions are: (1) For {epsilon}- and ({epsilon}, {delta})-differential privacy (with {epsilon} constant and {delta} = 1/poly(n)), we give a lower bound of {tilde {Omega}}(min{l_brace}{radical}n, {radical}d{sup k}{r_brace}), which is tight for n = {tilde {Omega}}(d{sup k}). Moreover, for a natural and popular class of mechanisms based on additive noise, our bound can be strengthened to {Omega}({radical}d{sup k}), which is tight for all n. Our bounds extend even to non-constant k, losing roughly a factor of {radical}2{sup k} compared to the best known upper bounds for large n. (2) We give efficient polynomial time attacks which allow an adversary to reconstruct sensitive infonnation given insufficiently perturbed contingency table releases. For constant k, we obtain a
A new approach for inversion of large random matrices in massive MIMO systems.
Directory of Open Access Journals (Sweden)
Muhammad Ali Raza Anjum
Full Text Available We report a novel approach for inversion of large random matrices in massive Multiple-Input Multiple Output (MIMO systems. It is based on the concept of inverse vectors in which an inverse vector is defined for each column of the principal matrix. Such an inverse vector has to satisfy two constraints. Firstly, it has to be in the null-space of all the remaining columns. We call it the null-space problem. Secondly, it has to form a projection of value equal to one in the direction of selected column. We term it as the normalization problem. The process essentially decomposes the inversion problem and distributes it over columns. Each column can be thought of as a node in the network or a particle in a swarm seeking its own solution, the inverse vector, which lightens the computational load on it. Another benefit of this approach is its applicability to all three cases pertaining to a linear system: the fully-determined, the over-determined, and the under-determined case. It eliminates the need of forming the generalized inverse for the last two cases by providing a new way to solve the least squares problem and the Moore and Penrose's pseudoinverse problem. The approach makes no assumption regarding the size, structure or sparsity of the matrix. This makes it fully applicable to much in vogue large random matrices arising in massive MIMO systems. Also, the null-space problem opens the door for a plethora of methods available in literature for null-space computation to enter the realm of matrix inversion. There is even a flexibility of finding an exact or approximate inverse depending on the null-space method employed. We employ the Householder's null-space method for exact solution and present a complete exposition of the new approach. A detailed comparison with well-established matrix inversion methods in literature is also given.
A new approach for inversion of large random matrices in massive MIMO systems.
Anjum, Muhammad Ali Raza; Ahmed, Muhammad Mansoor
2014-01-01
We report a novel approach for inversion of large random matrices in massive Multiple-Input Multiple Output (MIMO) systems. It is based on the concept of inverse vectors in which an inverse vector is defined for each column of the principal matrix. Such an inverse vector has to satisfy two constraints. Firstly, it has to be in the null-space of all the remaining columns. We call it the null-space problem. Secondly, it has to form a projection of value equal to one in the direction of selected column. We term it as the normalization problem. The process essentially decomposes the inversion problem and distributes it over columns. Each column can be thought of as a node in the network or a particle in a swarm seeking its own solution, the inverse vector, which lightens the computational load on it. Another benefit of this approach is its applicability to all three cases pertaining to a linear system: the fully-determined, the over-determined, and the under-determined case. It eliminates the need of forming the generalized inverse for the last two cases by providing a new way to solve the least squares problem and the Moore and Penrose's pseudoinverse problem. The approach makes no assumption regarding the size, structure or sparsity of the matrix. This makes it fully applicable to much in vogue large random matrices arising in massive MIMO systems. Also, the null-space problem opens the door for a plethora of methods available in literature for null-space computation to enter the realm of matrix inversion. There is even a flexibility of finding an exact or approximate inverse depending on the null-space method employed. We employ the Householder's null-space method for exact solution and present a complete exposition of the new approach. A detailed comparison with well-established matrix inversion methods in literature is also given.
Directory of Open Access Journals (Sweden)
Raquel Caballero-Águila
2015-01-01
Full Text Available The distributed fusion state estimation problem is addressed for sensor network systems with random state transition matrix and random measurement matrices, which provide a unified framework to consider some network-induced random phenomena. The process noise and all the sensor measurement noises are assumed to be one-step autocorrelated and different sensor noises are one-step cross-correlated; also, the process noise and each sensor measurement noise are two-step cross-correlated. These correlation assumptions cover many practical situations, where the classical independence hypothesis is not realistic. Using an innovation methodology, local least-squares linear filtering estimators are recursively obtained at each sensor. The distributed fusion method is then used to form the optimal matrix-weighted sum of these local filters according to the mean squared error criterion. A numerical simulation example shows the accuracy of the proposed distributed fusion filtering algorithm and illustrates some of the network-induced stochastic uncertainties that can be dealt with in the current system model, such as sensor gain degradation, missing measurements, and multiplicative noise.
Truncated Linear Statistics Associated with the Top Eigenvalues of Random Matrices
Grabsch, Aurélien; Majumdar, Satya N.; Texier, Christophe
2017-04-01
Given a certain invariant random matrix ensemble characterised by the joint probability distribution of eigenvalues P(λ _1,\\ldots ,λ _N), many important questions have been related to the study of linear statistics of eigenvalues L=\\sum _{i=1}^Nf(λ _i), where f(λ ) is a known function. We study here truncated linear statistics where the sum is restricted to the N_1analysis of the statistical physics of fluctuating one-dimensional interfaces, we consider the case of the Laguerre ensemble of random matrices with f(λ )=√{λ }. Using the Coulomb gas technique, we study the N→ ∞ limit with N_1/N fixed. We show that the constraint that \\tilde{L}=\\sum _{i=1}^{N_1}f(λ _i) is fixed drives an infinite order phase transition in the underlying Coulomb gas. This transition corresponds to a change in the density of the gas, from a density defined on two disjoint intervals to a single interval. In this latter case the density presents a logarithmic divergence inside the bulk. Assuming that f(λ ) is monotonous, we show that these features arise for any random matrix ensemble and truncated linear statitics, which makes the scenario described here robust and universal.
Numerical Investigation of the Primety of Real numbers
DEFF Research Database (Denmark)
Jensen, Kristoffer
2011-01-01
The Farey sequences can be used [1] to create the Eulers totient function φ(n), by identifying the fractions for number n that did not occur in all Farey sequences up to n-1. This function creates, when divided by n-1, what is here called the Primety measure, which is a measure of how close to be......(n) is from n, the less n is a prime. φ(n) and P(n) is generalized to real numbers through the use of real numbered Farey sequences. The corresponding numerical sequences are shown to have interesting mathematical and artistic properties....
Fixed Points on the Real numbers without the Equality Test
DEFF Research Database (Denmark)
Korovina, Margarita
2002-01-01
In this paper we present a study of definability properties of fixed points of effective operators on the real numbers without the equality test. In particular we prove that Gandy theorem holds for the reals without the equality test. This provides a useful tool for dealing with recursive definit...
Gasbarra, Dario; Pajevic, Sinisa; Basser, Peter J.
2017-01-01
Tensor-valued and matrix-valued measurements of different physical properties are increasingly available in material sciences and medical imaging applications. The eigenvalues and eigenvectors of such multivariate data provide novel and unique information, but at the cost of requiring a more complex statistical analysis. In this work we derive the distributions of eigenvalues and eigenvectors in the special but important case of m×m symmetric random matrices, D, observed with isotropic matrix-variate Gaussian noise. The properties of these distributions depend strongly on the symmetries of the mean tensor/matrix, D̄. When D̄ has repeated eigenvalues, the eigenvalues of D are not asymptotically Gaussian, and repulsion is observed between the eigenvalues corresponding to the same D̄ eigenspaces. We apply these results to diffusion tensor imaging (DTI), with m = 3, addressing an important problem of detecting the symmetries of the diffusion tensor, and seeking an experimental design that could potentially yield an isotropic Gaussian distribution. In the 3-dimensional case, when the mean tensor is spherically symmetric and the noise is Gaussian and isotropic, the asymptotic distribution of the first three eigenvalue central moment statistics is simple and can be used to test for isotropy. In order to apply such tests, we use quadrature rules of order t ≥ 4 with constant weights on the unit sphere to design a DTI-experiment with the property that isotropy of the underlying true tensor implies isotropy of the Fisher information. We also explain the potential implications of the methods using simulated DTI data with a Rician noise model. PMID:28989561
Directory of Open Access Journals (Sweden)
P. Manfredi
2015-05-01
Full Text Available Cable bundles often exhibit random parameter variations due to uncertain or uncontrollable physical properties and wire positioning. Efficient tools, based on the so-called polynomial chaos, exist to rapidly assess the impact of such variations on the per-unit-length capacitance and inductance matrices, and on the pertinent cable response. Nevertheless, the state-of-the-art method for the statistical extraction of the per-unit-length capacitance and inductance matrices of cables suffers from several inefficiencies that hinder its applicability to large problems, in terms of number of random parameters and/or conductors. This paper presents an improved methodology that overcomes the aforementioned limitations by exploiting a recently-published, alternative approach to generate the pertinent polynomial chaos system of equations. A sparse and decoupled system is obtained that provides remarkable benefits in terms of speed, memory consumption and problem size that can be dealt with. The technique is thoroughly validated through the statistical analysis of two canonical structures, i.e. a ribbon cable and a shielded cable with random geometry and position.
Kougioumtzoglou, I. A.; Fragkoulis, V. C.; Pantelous, A. A.; Pirrotta, A.
2017-09-01
A frequency domain methodology is developed for stochastic response determination of multi-degree-of-freedom (MDOF) linear and nonlinear structural systems with singular matrices. This system modeling can arise when a greater than the minimum number of coordinates/DOFs is utilized, and can be advantageous, for instance, in cases of complex multibody systems where the explicit formulation of the equations of motion can be a nontrivial task. In such cases, the introduction of additional/redundant DOFs can facilitate the formulation of the equations of motion in a less labor intensive manner. Specifically, relying on the generalized matrix inverse theory, a Moore-Penrose (M-P) based frequency response function (FRF) is determined for a linear structural system with singular matrices. Next, relying on the M-P FRF a spectral input-output (excitation-response) relationship is derived in the frequency domain for determining the linear system response power spectrum. Further, the above methodology is extended via statistical linearization to account for nonlinear systems. This leads to an iterative determination of the system response mean vector and covariance matrix. Furthermore, to account for singular matrices, the generalization of a widely utilized formula that facilitates the application of statistical linearization is proved as well. The formula relates to the expectation of the derivatives of the system nonlinear function and is based on a Gaussian response assumption. Several linear and nonlinear MDOF structural systems with singular matrices are considered as numerical examples for demonstrating the validity and applicability of the developed frequency domain methodology.
Numerical Investigation of the Primety of Real numbers
DEFF Research Database (Denmark)
Jensen, Kristoffer
2011-01-01
The Farey sequences can be used [1] to create the Eulers totient function φ(n), by identifying the fractions for number n that did not occur in all Farey sequences up to n-1. This function creates, when divided by n-1, what is here called the Primety measure, which is a measure of how close to be......(n) is from n, the less n is a prime. φ(n) and P(n) is generalized to real numbers through the use of real numbered Farey sequences. The corresponding numerical sequences are shown to have interesting mathematical and artistic properties.......The Farey sequences can be used [1] to create the Eulers totient function φ(n), by identifying the fractions for number n that did not occur in all Farey sequences up to n-1. This function creates, when divided by n-1, what is here called the Primety measure, which is a measure of how close...... to being a prime number n is. P(n)=φ(n)/(n-1) has maximum 1 for all prime numbers and minimum that decreases non-uniformly with n. Thus P(n) is the Primety function, which permits to designate a value of Primety of a number n. If P(n)==1, then n is a prime. If P(n)
Random walks with long-range steps generated by functions of Laplacian matrices
Riascos, A. P.; Michelitsch, T. M.; Collet, B. A.; Nowakowski, A. F.; Nicolleau, F. C. G. A
2017-01-01
In this paper, we explore different Markovian random walk strategies on networks with transition probabilities between nodes defined in terms of functions of the Laplacian matrix. We generalize random walk strategies with local information in the Laplacian matrix, that describes the connections of a network, to a dynamics determined by functions of this matrix. The resulting processes is non-local allowing transitions of the random walker from one node to nodes beyond its nearest neighbors. I...
Spectra of empirical autocorrelation matrices: A random-matrix-theory-inspired perspective
Jamali, Tayeb; Jafari, G. R.
2015-07-01
We construct an autocorrelation matrix of a time series and analyze it based on the random-matrix theory (RMT) approach. The autocorrelation matrix is capable of extracting information which is not easily accessible by the direct analysis of the autocorrelation function. In order to provide a precise conclusion based on the information extracted from the autocorrelation matrix, the results must be first evaluated. In other words they need to be compared with some sort of criterion to provide a basis for the most suitable and applicable conclusions. In the context of the present study, the criterion is selected to be the well-known fractional Gaussian noise (fGn). We illustrate the applicability of our method in the context of stock markets. For the former, despite the non-Gaussianity in returns of the stock markets, a remarkable agreement with the fGn is achieved.
Ban, Ehsan; Barocas, Victor H; Shephard, Mark S; Picu, Catalin R
2016-04-01
Fiber networks are assemblies of one-dimensional elements representative of materials with fibrous microstructures such as collagen networks and synthetic nonwovens. The mechanics of random fiber networks has been the focus of numerous studies. However, fiber crimp has been explicitly represented only in few cases. In the present work, the mechanics of cross-linked networks with crimped athermal fibers, with and without an embedding elastic matrix, is studied. The dependence of the effective network stiffness on the fraction of nonstraight fibers and the relative crimp amplitude (or tortuosity) is studied using finite element simulations of networks with sinusoidally curved fibers. A semi-analytic model is developed to predict the dependence of network modulus on the crimp amplitude and the bounds of the stiffness reduction associated with the presence of crimp. The transition from the linear to the nonlinear elastic response of the network is rendered more gradual by the presence of crimp, and the effect of crimp on the network tangent stiffness decreases as strain increases. If the network is embedded in an elastic matrix, the effect of crimp becomes negligible even for very small, biologically relevant matrix stiffness values. However, the distribution of the maximum principal stress in the matrix becomes broader in the presence of crimp relative to the similar system with straight fibers, which indicates an increased probability of matrix failure.
Dynamic fair node spectrum allocation for ad hoc networks using random matrices
Rahmes, Mark; Lemieux, George; Chester, Dave; Sonnenberg, Jerry
2015-05-01
Dynamic Spectrum Access (DSA) is widely seen as a solution to the problem of limited spectrum, because of its ability to adapt the operating frequency of a radio. Mobile Ad Hoc Networks (MANETs) can extend high-capacity mobile communications over large areas where fixed and tethered-mobile systems are not available. In one use case with high potential impact, cognitive radio employs spectrum sensing to facilitate the identification of allocated frequencies not currently accessed by their primary users. Primary users own the rights to radiate at a specific frequency and geographic location, while secondary users opportunistically attempt to radiate at a specific frequency when the primary user is not using it. We populate a spatial radio environment map (REM) database with known information that can be leveraged in an ad hoc network to facilitate fair path use of the DSA-discovered links. Utilization of high-resolution geospatial data layers in RF propagation analysis is directly applicable. Random matrix theory (RMT) is useful in simulating network layer usage in nodes by a Wishart adjacency matrix. We use the Dijkstra algorithm for discovering ad hoc network node connection patterns. We present a method for analysts to dynamically allocate node-node path and link resources using fair division. User allocation of limited resources as a function of time must be dynamic and based on system fairness policies. The context of fair means that first available request for an asset is not envied as long as it is not yet allocated or tasked in order to prevent cycling of the system. This solution may also save money by offering a Pareto efficient repeatable process. We use a water fill queue algorithm to include Shapley value marginal contributions for allocation.
Some Double Sequence Spaces of Fuzzy Real Numbers of Paranormed Type
Directory of Open Access Journals (Sweden)
Bipul Sarma
2013-01-01
Full Text Available We study different properties of convergent, null, and bounded double sequence spaces of fuzzy real numbers like completeness, solidness, sequence algebra, symmetricity, convergence-free, and so forth. We prove some inclusion results too.
Some remarks on real numbers induced by first-order spectra
DEFF Research Database (Denmark)
Jakobsen, Sune; Simonsen, Jakob Grue
2016-01-01
The spectrum of a first-order sentence is the set of natural numbers occurring as the cardinalities of finite models of the sentence. In a recent survey, Durand et al. introduce a new class of real numbers, the spectral reals, induced by spectra and pose two open problems associated to this class...... may occur, and (iv) every right-computable real number between 0 and 1 occurs as the subword entropy of a spectral real. In addition, Durand et al. note that the set of spectral reals is not closed under addition or multiplication. We extend this result by showing that the class of spectral reals...
Rotationally invariant ensembles of integrable matrices.
Yuzbashyan, Emil A; Shastry, B Sriram; Scaramazza, Jasen A
2016-05-01
We construct ensembles of random integrable matrices with any prescribed number of nontrivial integrals and formulate integrable matrix theory (IMT)-a counterpart of random matrix theory (RMT) for quantum integrable models. A type-M family of integrable matrices consists of exactly N-M independent commuting N×N matrices linear in a real parameter. We first develop a rotationally invariant parametrization of such matrices, previously only constructed in a preferred basis. For example, an arbitrary choice of a vector and two commuting Hermitian matrices defines a type-1 family and vice versa. Higher types similarly involve a random vector and two matrices. The basis-independent formulation allows us to derive the joint probability density for integrable matrices, similar to the construction of Gaussian ensembles in the RMT.
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...
0011-0030.What is IEEE 754 StandardHow to convert real number ...
Indian Academy of Sciences (India)
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Some Classes of Difference Sequence Spaces of Fuzzy Real Numbers Defined by Orlicz Function
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Binod Chandra Tripathy
2011-01-01
Full Text Available We introduce the classes of generalized difference bounded, convergent, and null sequences of fuzzy real numbers defined by an Orlicz function. Some properties of these sequence spaces like solidness, symmetricity, and convergence-free are studied. We obtain some inclusion relations involving these sequence spaces.
Teaching of Real Numbers by Using the Archimedes-Cantor Approach and Computer Algebra Systems
Vorob'ev, Evgenii M.
2015-01-01
Computer technologies and especially computer algebra systems (CAS) allow students to overcome some of the difficulties they encounter in the study of real numbers. The teaching of calculus can be considerably more effective with the use of CAS provided the didactics of the discipline makes it possible to reveal the full computational potential of…
Infinite matrices and their recent applications
Shivakumar, P N; Zhang, Yang
2016-01-01
This monograph covers the theory of finite and infinite matrices over the fields of real numbers, complex numbers and over quaternions. Emphasizing topics such as sections or truncations and their relationship to the linear operator theory on certain specific separable and sequence spaces, the authors explore techniques like conformal mapping, iterations and truncations that are used to derive precise estimates in some cases and explicit lower and upper bounds for solutions in the other cases. Most of the matrices considered in this monograph have typically special structures like being diagonally dominated or tridiagonal, possess certain sign distributions and are frequently nonsingular. Such matrices arise, for instance, from solution methods for elliptic partial differential equations. The authors focus on both theoretical and computational aspects concerning infinite linear algebraic equations, differential systems and infinite linear programming, among others. Additionally, the authors cover topics such ...
Verification of Numerical Programs: From Real Numbers to Floating Point Numbers
Goodloe, Alwyn E.; Munoz, Cesar; Kirchner, Florent; Correnson, Loiec
2013-01-01
Numerical algorithms lie at the heart of many safety-critical aerospace systems. The complexity and hybrid nature of these systems often requires the use of interactive theorem provers to verify that these algorithms are logically correct. Usually, proofs involving numerical computations are conducted in the infinitely precise realm of the field of real numbers. However, numerical computations in these algorithms are often implemented using floating point numbers. The use of a finite representation of real numbers introduces uncertainties as to whether the properties veri ed in the theoretical setting hold in practice. This short paper describes work in progress aimed at addressing these concerns. Given a formally proven algorithm, written in the Program Verification System (PVS), the Frama-C suite of tools is used to identify sufficient conditions and verify that under such conditions the rounding errors arising in a C implementation of the algorithm do not affect its correctness. The technique is illustrated using an algorithm for detecting loss of separation among aircraft.
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.
A Compressed Sensing-Based Low-Density Parity-Check Real-Number Code
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Zaixing He
2013-09-01
Full Text Available In this paper, we propose a novel low-density parity-check real-number code, based on compressed sensing. A real-valued message is encoded by a coding matrix (with more rows than columns and transmitted over an erroneous channel, where sparse errors (impulsive noise corrupt the codeword. In the decoding procedure, we apply a structured sparse (low-density parity-check matrix, the Permuted Block Diagonal matrix, to the corrupted output, and the errors can be corrected by solving a compressed sensing problem. A compressed sensing algorithm, Cross Low-dimensional Pursuit, is used to decode the code by solving this compressed sensing problem. The proposed code has high error correction performance and decoding efficiency. The comparative experimental results demonstrate both advantages of our code. We also apply our code to cryptography.
Pole-placement Predictive Functional Control for under-damped systems with real numbers algebra.
Zabet, K; Rossiter, J A; Haber, R; Abdullah, M
2017-11-01
This paper presents the new algorithm of PP-PFC (Pole-placement Predictive Functional Control) for stable, linear under-damped higher-order processes. It is shown that while conventional PFC aims to get first-order exponential behavior, this is not always straightforward with significant under-damped modes and hence a pole-placement PFC algorithm is proposed which can be tuned more precisely to achieve the desired dynamics, but exploits complex number algebra and linear combinations in order to deliver guarantees of stability and performance. Nevertheless, practical implementation is easier by avoiding complex number algebra and hence a modified formulation of the PP-PFC algorithm is also presented which utilises just real numbers while retaining the key attributes of simple algebra, coding and tuning. The potential advantages are demonstrated with numerical examples and real-time control of a laboratory plant. Copyright © 2017 ISA. All rights reserved.
Fractal generalized Pascal matrices
Burlachenko, E.
2016-01-01
Set of generalized Pascal matrices whose elements are generalized binomial coefficients is considered as an integral object. The special system of generalized Pascal matrices, based on which we are building fractal generalized Pascal matrices, is introduced. Pascal matrix (Pascal triangle) is the Hadamard product of the fractal generalized Pascal matrices. The concept of zero generalized Pascal matrices, an example of which is the Pascal triangle modulo 2, arise in connection with the system ...
Grabsch, Aurélien; Texier, Christophe
2016-11-01
An invariant ensemble of N × N random matrices can be characterised by a joint distribution for eigenvalues P({λ }1,\\cdots ,{λ }N). The distribution of linear statistics, i.e. of quantities of the form L=(1/N){\\sum }if({λ }i) where f(x) is a given function, appears in many physical problems. In the N\\to ∞ limit, L scales as L˜ {N}η , where the scaling exponent η depends on the ensemble and the function f(x). Its distribution can be written in the form {P}N(s={N}-η L)≃ {A}N,β (s)\\exp \\{-(β {N}2/2){{Φ }}(s)\\}, where β \\in \\{1,2,4\\} is the Dyson index. The Coulomb gas technique naturally provides the large deviation function {{Φ }}(s), which can be efficiently obtained thanks to a ‘thermodynamic identity’ introduced earlier. We conjecture the pre-exponential function {A}N,β (s). We check our conjecture on several well controlled cases within the Laguerre and the Jacobi ensembles. Then we apply our main result to a situation where the large deviation function has no minimum (and L has infinite moments): this arises in the statistical analysis of the Wigner time delay for semi-infinite multichannel disordered wires (Laguerre ensemble). The statistical analysis of the Wigner time delay then crucially depends on the pre-exponential function {A}N,β (s), which ensures the decay of the distribution for large argument.
3-D decoupled inversion of complex conductivity data in the real number domain
Johnson, Timothy C.; Thomle, Jonathan
2018-01-01
Complex conductivity imaging (also called induced polarization imaging or spectral induced polarization imaging when conducted at multiple frequencies) involves estimating the frequency-dependent complex electrical conductivity distribution of the subsurface. The superior diagnostic capabilities provided by complex conductivity spectra have driven advancements in mechanistic understanding of complex conductivity as well as modelling and inversion approaches over the past several decades. In this work, we demonstrate the theory and application for an approach to 3-D modelling and inversion of complex conductivity data in the real number domain. Beginning from first principles, we demonstrate how the equations for the real and imaginary components of the complex potential may be decoupled. This leads to a description of the real and imaginary source current terms, and a corresponding assessment of error arising from an assumption necessary to complete the decoupled modelling. We show that for most earth materials, which exhibit relatively small phases (e.g. less than 0.2 radians) in complex conductivity, these errors become insignificant. For higher phase materials, the errors may be quantified and corrected through an iterative procedure. We demonstrate the accuracy of numerical forward solutions by direct comparison to corresponding analytic solutions. We demonstrate the inversion using both synthetic and field examples with data collected over a waste infiltration trench, at frequencies ranging from 0.5 to 7.5 Hz.
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.
Circulant conference matrices for new complex Hadamard matrices
Dita, Petre
2011-01-01
The circulant real and complex matrices are used to find new real and complex conference matrices. With them we construct Sylvester inverse orthogonal matrices by doubling the size of inverse complex conference matrices. When the free parameters take values on the unit circle the inverse orthogonal matrices transform into complex Hadamard matrices. The method is used for $n=6$ conference matrices and in this way we find new parametrisations of Hadamard matrices for dimension $ n=12$.
A Scientific Calculator for Exact Real Number Computation Based on LRT, GMP and FC++
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J. A. Hernández
2012-03-01
Full Text Available Language for Redundant Test (LRT is a programming language for exact real number computation. Its lazy evaluation mechanism (also called call-by-need and its infinite list requirement, make the language appropriate to be implemented in a functional programming language such as Haskell. However, a direction translation of the operational semantics of LRT into Haskell as well as the algorithms to implement basic operations (addition subtraction, multiplication, division and trigonometric functions (sin, cosine, tangent, etc. makes the resulting scientific calculator time consuming and so inefficient. In this paper, we present an alternative implementation of the scientific calculator using FC++ and GMP. FC++ is a functional C++ library while GMP is a GNU multiple presicion library. We show that a direct translation of LRT in FC++ results in a faster scientific calculator than the one presented in Haskell.El lenguaje de verificación redundante (LRT, por sus siglas en inglés es un lenguaje de programación para el cómputo con números reales exactos. Su método de evaluación lazy (o mejor conocido como llamada por necesidad y el manejo de listas infinitas requerido, hace que el lenguaje sea apropiado para su implementación en un lenguaje funcional como Haskell. Sin embargo, la implementación directa de la semántica operacional de LRT en Haskell así como los algoritmos para funciones básicas (suma, resta, multiplicación y división y funciones trigonométricas (seno, coseno, tangente, etc hace que la calculadora científica resultante sea ineficiente. En este artículo, presentamos una implementación alternativa de la calculadora científica usando FC++ y GMP. FC++ es una librería que utiliza el paradigma Funcional en C++ mientras que GMP es una librería GNU de múltiple precisión. En el artículo mostramos que la implementación directa de LRT en FC++ resulta en una librería más eficiente que la implementada en Haskell.
Deterministic sensing matrices in compressive sensing: a survey.
Nguyen, Thu L N; Shin, Yoan
2013-01-01
Compressive sensing is a sampling method which provides a new approach to efficient signal compression and recovery by exploiting the fact that a sparse signal can be suitably reconstructed from very few measurements. One of the most concerns in compressive sensing is the construction of the sensing matrices. While random sensing matrices have been widely studied, only a few deterministic sensing matrices have been considered. These matrices are highly desirable on structure which allows fast implementation with reduced storage requirements. In this paper, a survey of deterministic sensing matrices for compressive sensing is presented. We introduce a basic problem in compressive sensing and some disadvantage of the random sensing matrices. Some recent results on construction of the deterministic sensing matrices are discussed.
Allen, Frank B.; And Others
This is a supplementary unit to Mathematics for High School, Intermediate Mathematics, Part 1. In this publication, real numbers and rules for operating them are examined. The study begins by examining whole numbers and some of the properties of addition and multiplication of whole numbers. Most of the basic rules for algebra are developed from…
The Automorphism Group of the Lie Ring of Real Skew-Symmetric Matrices
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Jinli Xu
2013-01-01
Full Text Available Denote by n the set of all n×n skew-symmetric matrices over the field of real numbers, which forms a Lie ring under the usual matrix addition and the Lie multiplication as [A,B]=AB-BA, A,B∈n. In this paper, we characterize the automorphism group of the Lie ring n.
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.
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
On greedy and submodular matrices
Faigle, U.; Kern, Walter; Peis, Britta; Marchetti-Spaccamela, Alberto; Segal, Michael
2011-01-01
We characterize non-negative greedy matrices, i.e., 0-1 matrices $A$ such that max $\\{c^Tx|Ax \\le b,\\,x \\ge 0\\}$ can be solved greedily. We identify submodular matrices as a special subclass of greedy matrices. Finally, we extend the notion of greediness to $\\{-1,0,+1\\}$-matrices. We present
Justino, Júlia
2017-06-01
Matrices with coefficients having uncertainties of type o (.) or O (.), called flexible matrices, are studied from the point of view of nonstandard analysis. The uncertainties of the afore-mentioned kind will be given in the form of the so-called neutrices, for instance the set of all infinitesimals. Since flexible matrices have uncertainties in their coefficients, it is not possible to define the identity matrix in an unique way and so the notion of spectral identity matrix arises. Not all nonsingular flexible matrices can be turned into a spectral identity matrix using Gauss-Jordan elimination method, implying that that not all nonsingular flexible matrices have the inverse matrix. Under certain conditions upon the size of the uncertainties appearing in a nonsingular flexible matrix, a general theorem concerning the boundaries of its minors is presented which guarantees the existence of the inverse matrix of a nonsingular flexible matrix.
Fallat, Shaun M
2011-01-01
Totally nonnegative matrices arise in a remarkable variety of mathematical applications. This book is a comprehensive and self-contained study of the essential theory of totally nonnegative matrices, defined by the nonnegativity of all subdeterminants. It explores methodological background, historical highlights of key ideas, and specialized topics.The book uses classical and ad hoc tools, but a unifying theme is the elementary bidiagonal factorization, which has emerged as the single most important tool for this particular class of matrices. Recent work has shown that bidiagonal factorization
DEFF Research Database (Denmark)
Britz, Thomas
Bipartite graphs and digraphs are used to describe algebraic operations on a free matrix, including Moore-Penrose inversion, finding Schur complements, and normalized LU factorization. A description of the structural properties of a free matrix and its Moore-Penrose inverse is proved, and necessa...... and sufficient conditions are given for the Moore-Penrose inverse of a free matrix to be free. Several of these results are generalized with respect to a family of matrices that contains both the free matrices and the nearly reducible matrices....
Bolton, W
1995-01-01
This book is concerned with linear equations and matrices, with emphasis on the solution of simultaneous linear equations. The solution of simultaneous linear equations is applied to electric circuit analysis and structural analysis.
Michelitsch, T. M.; Collet, B. A.; Riascos, A. P.; Nowakowski, A. F.; Nicolleau, F. C. G. A.
2017-12-01
We analyze a Markovian random walk strategy on undirected regular networks involving power matrix functions of the type L\\frac{α{2}} where L indicates a ‘simple’ Laplacian matrix. We refer to such walks as ‘fractional random walks’ with admissible interval 0 α (recurrent for d≤slantα ) of the lattice. As a consequence, for 0global mean first passage times (Kemeny constant) for the fractional random walk. For an infinite 1D lattice (infinite ring) we obtain for the transient regime 0world properties with the emergence of Lévy flights on large (infinite) lattices.
Barcucci, E.; Bernini, A.; Bilotta, S.; Pinzani, R.
2016-01-01
Two matrices are said non-overlapping if one of them can not be put on the other one in a way such that the corresponding entries coincide. We provide a set of non-overlapping binary matrices and a formula to enumerate it which involves the k-generalized Fibonacci numbers. Moreover, the generating function for the enumerating sequence is easily seen to be rational.
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
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
Indian Academy of Sciences (India)
The way to think about matrices and understand matrix- multiplication is geometrically. When viewed properly, the reason for the validity of the example of the previous paragraph is this: if TA denotes the operation of 'coun- terclockwise rotation of the plane by 90°', and if T B de- notes 'projection onto the x-axis', then TAoTB, ...
Indian Academy of Sciences (India)
Abstract. Assuming a relation between the quark mass matrices of the two sectors a unique solution can be obtained for the CKM ﬂavor mixing matrix. A numerical example is worked out which is in excellent agreement with experimental data.
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.
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...
Indian Academy of Sciences (India)
IAS Admin
Her areas of interest are Lie groups and. Lie algebras and their representation theory, harmonic analysis and complex analysis, in particular, Clifford analysis. .... Its Jordan block structure can be expressed as either J0,3⊕Ji,2 ⊕Ji,2 ⊕J5,3 or, diag(J0,3,Ji,2,Ji,2,J5,3). 3. Nilpotent and Unipotent Matrices. DEFINITION 3.1.
Averaging operations on matrices
Indian Academy of Sciences (India)
2014-07-03
Jul 3, 2014 ... Arithmetic mean of objects in a space need not lie in the space. [Frechet; 1948] Finding mean of right-angled triangles. S = {(x,y,z) ∈ R+3 : x2 + y2 = z2}. = {. [ z x − ιy x + ιy z. ] : x,y,z > 0,z2 = x2 + y2}. Surface of right triangles : Arithmetic mean not on S. Tanvi Jain. Averaging operations on matrices ...
On some Toeplitz matrices and their inversions
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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.
Indian Academy of Sciences (India)
λj (BB∗) = λj (I − AA∗) = 1 − λj (AA∗). = 1 − λj (A∗A) = λj (I − A∗A) = λj (C∗C). Thus B and C have the same singular values, and again |||B||| = |||C||| for all unitarily invariant norms. This equality of norms does not persist when we go to arbitrary normal matrices, as we will soon see. From (2) and (4) we get a simple inequality.
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
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
Generalisations of Fisher Matrices
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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.
VanderLaan Circulant Type Matrices
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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.
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…
Kim, Seonghoon
2013-01-01
With known item response theory (IRT) item parameters, Lord and Wingersky provided a recursive algorithm for computing the conditional frequency distribution of number-correct test scores, given proficiency. This article presents a generalized algorithm for computing the conditional distribution of summed test scores involving real-number item…
Community Detection for Correlation Matrices
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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.
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 ...
Manin matrices and Talalaev's formula
Chervov, A.; Falqui, G.
2008-05-01
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: [Mij, Mkl] = [Mkj, Mil] (e.g. [M11, M22] = [M21, M12]). 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(\\partial_z-L_Gaudin(z)), \\det(1-e^{-\\partial_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(\\widehat{gl_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.
Hadamard Matrices and Their Applications
Horadam, K J
2011-01-01
In Hadamard Matrices and Their Applications, K. J. Horadam provides the first unified account of cocyclic Hadamard matrices and their applications in signal and data processing. This original work is based on the development of an algebraic link between Hadamard matrices and the cohomology of finite groups that was discovered fifteen years ago. The book translates physical applications into terms a pure mathematician will appreciate, and theoretical structures into ones an applied mathematician, computer scientist, or communications engineer can adapt and use. The first half of the book expl
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
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...
Directory of Open Access Journals (Sweden)
Irina Pchelintseva
2008-01-01
Full Text Available We consider self-adjoint unbounded Jacobi matrices with diagonal \\(q_n = b_{n}n\\ and off-diagonal entries \\(\\lambda_n = n\\, where \\(b_{n}\\ is a \\(2\\-periodical sequence of real numbers. The parameter space is decomposed into several separate regions, where the spectrum of the operator is either purely absolutely continuous or discrete. We study the situation where the spectral phase transition occurs, namely the case of \\(b_{1}b_{2} = 4\\. The main motive of the paper is the investigation of asymptotics of generalized eigenvectors of the Jacobi matrix. The pure point part of the spectrum is analyzed in detail.
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.
Immanant Conversion on Symmetric Matrices
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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.
Derivatives of triangular, Toeplitz, circulant matrices and matrices of other forms over semirings
Vladeva, Dimitrinka
2017-01-01
In this article we construct examples of derivations in matrix semirings. We study hereditary and inner derivations, derivatives of diagonal, triangular, Toeplitz, circulant matrices and of matrices of other forms and prove theorems for derivatives of matrices of these forms.
Iterative methods for Toeplitz-like matrices
Energy Technology Data Exchange (ETDEWEB)
Huckle, T. [Universitaet Wurzburg (Germany)
1994-12-31
In this paper the author will give a survey on iterative methods for solving linear equations with Toeplitz matrices, Block Toeplitz matrices, Toeplitz plus Hankel matrices, and matrices with low displacement rank. He will treat the following subjects: (1) optimal (w)-circulant preconditioners is a generalization of circulant preconditioners; (2) Optimal implementation of circulant-like preconditioners in the complex and real case; (3) preconditioning of near-singular matrices; what kind of preconditioners can be used in this case; (4) circulant preconditioning for more general classes of Toeplitz matrices; what can be said about matrices with coefficients that are not l{sub 1}-sequences; (5) preconditioners for Toeplitz least squares problems, for block Toeplitz matrices, and for Toeplitz plus Hankel matrices.
Sign pattern matrices that admit M-, N-, P- or inverse M-matrices
Araújo, C. Mendes; Juan R. Torregrosa
2009-01-01
In this paper we identify the sign pattern matrices that occur among the N–matrices, the P–matrices and the M–matrices. We also address to the class of inverse M–matrices and the related admissibility of sign pattern matrices problem. Fundação para a Ciência e a Tecnologia (FCT) Spanish DGI grant number MTM2007-64477
CHARACTERISTIC RADICALS OF STOCHASTIC MATRICES,
The paper investigates the distribution on a complex plane of characteristic radicals of stochastic matrices of the n-th order. The results obtained...can be interpreted as theorems on the relative distribution of characteristic radicals of an arbitrary matrix with non-negative elements. (Author)
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.
Some basic properties of block operator matrices
Jin, Guohai; Chen, Alatancang
2014-01-01
General approach to the multiplication or adjoint operation of $2\\times 2$ block operator matrices with unbounded entries are founded. Furthermore, criteria for self-adjointness of block operator matrices based on their entry operators are established.
Unbiased community detection for correlation matrices
MacMahon, Mel
2013-01-01
A challenging problem in the study of large 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 at identifying such modules and suffer from an unavoidable information loss. A promising alternative is that of employing community detection techniques developed in network theory. Unfortunately, the attempts made so far have merely replaced network data with correlation matrices, a procedure that we show to be fundamentally biased due to 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 unbiased correlation-based counterparts of the most popular community detection techniques. After successfully benchmarking our methods, we apply them to s...
Shin, Yong Cheol; Lee, Jong Ho; Jin, Linhua; Kim, Min Jeong; Kim, Yong-Joo; Hyun, Jung Keun; Jung, Tae-Gon; Hong, Suck Won; Han, Dong-Wook
2015-03-12
Electrospinning is a simple and effective method for fabricating micro- and nanofiber matrices. Electrospun fibre matrices have numerous advantages for use as tissue engineering scaffolds, such as high surface area-to-volume ratio, mass production capability and structural similarity to the natural extracellular matrix (ECM). Therefore, electrospun matrices, which are composed of biocompatible polymers and various biomaterials, have been developed as biomimetic scaffolds for the tissue engineering applications. In particular, graphene oxide (GO) has recently been considered as a novel biomaterial for skeletal muscle regeneration because it can promote the growth and differentiation of myoblasts. Therefore, the aim of the present study was to fabricate the hybrid fibre matrices that stimulate myoblasts differentiation for skeletal muscle regeneration. Hybrid fibre matrices composed of poly(lactic-co-glycolic acid, PLGA) and collagen (Col) impregnated with GO (GO-PLGA-Col) were successfully fabricated using an electrospinning process. Our results indicated that the GO-PLGA-Col hybrid matrices were comprised of randomly-oriented continuous fibres with a three-dimensional non-woven porous structure. Compositional analysis showed that GO was dispersed uniformly throughout the GO-PLGA-Col matrices. In addition, the hydrophilicity of the fabricated matrices was significantly increased by blending with a small amount of Col and GO. The attachment and proliferation of the C2C12 skeletal myoblasts were significantly enhanced on the GO-PLGA-Col hybrid matrices. Furthermore, the GO-PLGA-Col matrices stimulated the myogenic differentiation of C2C12 skeletal myoblasts, which was enhanced further under the culture conditions of the differentiation media. Taking our findings into consideration, it is suggested that the GO-PLGA-Col hybrid fibre matrices can be exploited as potential biomimetic scaffolds for skeletal tissue engineering and regeneration because these GO
Convertible Subspaces of Hessenberg-Type Matrices
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Henrique F. da Cruz
2017-12-01
Full Text Available We describe subspaces of generalized Hessenberg matrices where the determinant is convertible into the permanent by affixing ± signs. An explicit characterization of convertible Hessenberg-type matrices is presented. We conclude that convertible matrices with the maximum number of nonzero entries can be reduced to a basic set.
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
Genetic code, hamming distance and stochastic matrices.
He, Matthew X; Petoukhov, Sergei V; Ricci, Paolo E
2004-09-01
In this paper we use the Gray code representation of the genetic code C=00, U=10, G=11 and A=01 (C pairs with G, A pairs with U) to generate a sequence of genetic code-based matrices. In connection with these code-based matrices, we use the Hamming distance to generate a sequence of numerical matrices. We then further investigate the properties of the numerical matrices and show that they are doubly stochastic and symmetric. We determine the frequency distributions of the Hamming distances, building blocks of the matrices, decomposition and iterations of matrices. We present an explicit decomposition formula for the genetic code-based matrix in terms of permutation matrices, which provides a hypercube representation of the genetic code. It is also observed that there is a Hamiltonian cycle in a genetic code-based hypercube.
Non-hermitian random matrix theory: Method of hermitian reduction
Energy Technology Data Exchange (ETDEWEB)
Feinberg, J. [California Univ., Santa Barbara, CA (United States). Inst. for Theoretical Physics; Zee, A. [California Univ., Santa Barbara, CA (United States). Inst. for Theoretical Physics]|[Institute for Advanced Study, Olden Lane, Princeton, NJ 08540 (United States)
1997-11-03
We consider random non-hermitian matrices in the large-N limit. The power of analytic function theory cannot be brought to bear directly to analyze non-hermitian random matrices, in contrast to hermitian random matrices. To overcome this difficulty, we show that associated to each ensemble of non-hermitian matrices there is an auxiliary ensemble of random hermitian matrices which can be analyzed by the usual methods. We then extract the Green function and the density of eigenvalues of the non-hermitian ensemble from those of the auxiliary ensemble. We apply this ``method of hermitization`` to several examples, and discuss a number of related issues. (orig.). 25 refs.
Eigenspectrum bounds for semirandom matrices with modular and spatial structure for neural networks.
Muir, Dylan R; Mrsic-Flogel, Thomas
2015-04-01
The eigenvalue spectrum of the matrix of directed weights defining a neural network model is informative of several stability and dynamical properties of network activity. Existing results for eigenspectra of sparse asymmetric random matrices neglect spatial or other constraints in determining entries in these matrices, and so are of partial applicability to cortical-like architectures. Here we examine a parameterized class of networks that are defined by sparse connectivity, with connection weighting modulated by physical proximity (i.e., asymmetric Euclidean random matrices), modular network partitioning, and functional specificity within the excitatory population. We present a set of analytical constraints that apply to the eigenvalue spectra of associated weight matrices, highlighting the relationship between connectivity rules and classes of network dynamics.
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...
Directory of Open Access Journals (Sweden)
J. Qiang
2014-03-01
Full Text Available In this paper we report on start-to-end simulation of a next generation light source based on a high repetition rate free electron laser (FEL driven by a CW superconducting linac. The simulation integrated the entire system in a seamless start-to-end model, including birth of photoelectrons, transport of electron beam through 600 m of the accelerator beam delivery system, and generation of coherent x-ray radiation in a two-stage self-seeding undulator beam line. The entire simulation used the real number of electrons (∼2 billion electrons/bunch to capture the details of the physical shot noise without resorting to artificial filtering to suppress numerical noise. The simulation results shed light on several issues including the importance of space-charge effects near the laser heater and the reliability of x-ray radiation power predictions when using a smaller number of simulation particles. The results show that the microbunching instability in the linac can be controlled with 15 keV uncorrelated energy spread induced by a laser heater and demonstrate that high brightness and flux 1 nm x-ray radiation (∼10^{12} photons/pulse with fully spatial and temporal coherence is achievable.
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
Matrices with totally positive powers and their generalizations
Kushel, Olga Y.
2013-01-01
In this paper, eventually totally positive matrices (i.e. matrices all whose powers starting with some point are totally positive) are studied. We present a new approach to eventual total positivity which is based on the theory of eventually positive matrices. We mainly focus on the spectral properties of such matrices. We also study eventually J-sign-symmetric matrices and matrices, whose powers are P-matrices.
The lower bounds for the rank of matrices and some sufficient conditions for nonsingular matrices.
Wang, Dafei; Zhang, Xumei
2017-01-01
The paper mainly discusses the lower bounds for the rank of matrices and sufficient conditions for nonsingular matrices. We first present a new estimation for [Formula: see text] ([Formula: see text] is an eigenvalue of a matrix) by using the partitioned matrices. By using this estimation and inequality theory, the new and more accurate estimations for the lower bounds for the rank are deduced. Furthermore, based on the estimation for the rank, some sufficient conditions for nonsingular matrices are obtained.
Pathological rate matrices: from primates to pathogens
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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
A partial classification of primes in the positive matrices and in the doubly stochastic matrices
G. Picci; J.M. van den Hof; J.H. van Schuppen (Jan)
1995-01-01
textabstractThe algebraic structure of the set of square positive matrices is that of a semi-ring. The concept of a prime in the positive matrices has been introduced. A few examples of primes in the positive matrices are known but there is no general classification. In this paper a partial
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|... of reciprocal Fibonacci numbers called Filbert matrices. We find a formula for the entries of the inverse quantum Hilbert matrix....
Products of Generalized Stochastic Sarymsakov Matrices
Xia, Weiguo; Liu, Ji; Cao, Ming; Johansson, Karl; Basar, Tamer
2015-01-01
In the set of stochastic, indecomposable, aperiodic (SIA) matrices, the class of stochastic Sarymsakov matrices is the largest known subset (i) that is closed under matrix multiplication and (ii) the inﬁnitely long left-product of the elements from a compact subset converges to a rank-one matrix. In
The performance of the Congruence Among Distance Matrices (CADM) test in phylogenetic analysis
2011-01-01
Background CADM is a statistical test used to estimate the level of Congruence Among Distance Matrices. It has been shown in previous studies to have a correct rate of type I error and good power when applied to dissimilarity matrices and to ultrametric distance matrices. Contrary to most other tests of incongruence used in phylogenetic analysis, the null hypothesis of the CADM test assumes complete incongruence of the phylogenetic trees instead of congruence. In this study, we performed computer simulations to assess the type I error rate and power of the test. It was applied to additive distance matrices representing phylogenies and to genetic distance matrices obtained from nucleotide sequences of different lengths that were simulated on randomly generated trees of varying sizes, and under different evolutionary conditions. Results Our results showed that the test has an accurate type I error rate and good power. As expected, power increased with the number of objects (i.e., taxa), the number of partially or completely congruent matrices and the level of congruence among distance matrices. Conclusions Based on our results, we suggest that CADM is an excellent candidate to test for congruence and, when present, to estimate its level in phylogenomic studies where numerous genes are analysed simultaneously. PMID:21388552
Adhesion and metabolic activity of human corneal cells on PCL based nanofiber matrices.
Stafiej, Piotr; Küng, Florian; Thieme, Daniel; Czugala, Marta; Kruse, Friedrich E; Schubert, Dirk W; Fuchsluger, Thomas A
2017-02-01
In this work, polycaprolactone (PCL) was used as a basic polymer for electrospinning of random and aligned nanofiber matrices. Our aim was to develop a biocompatible substrate for ophthalmological application to improve wound closure in defects of the cornea as replacement for human amniotic membrane. We investigated whether blending the hydrophobic PCL with poly (glycerol sebacate) (PGS) or chitosan (CHI) improves the biocompatibility of the matrices for cell expansion. Human corneal epithelial cells (HCEp) and human corneal keratocytes (HCK) were used for in vitro biocompatibility studies. After optimization of the electrospinning parameters for all blends, scanning electron microscopy (SEM), attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR), and water contact angle were used to characterize the different matrices. Fluorescence staining of the F-actin cytoskeleton of the cells was performed to analyze the adherence of the cells to the different matrices. Metabolic activity of the cells was measured by cell counting kit-8 (CCK-8) for 20days to compare the biocompatibility of the materials. Our results show the feasibility of producing uniform nanofiber matrices with and without orientation for the used blends. All materials support adherence and proliferation of human corneal cell lines with oriented growth on aligned matrices. Although hydrophobicity of the materials was lowered by blending PCL, no increase in biocompatibility or proliferation, as was expected, could be measured. All tested matrices supported the expansion of human corneal cells, confirming their potential as substrates for biomedical applications. Copyright © 2016 Elsevier B.V. All rights reserved.
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.
Random walks on reductive groups
Benoist, Yves
2016-01-01
The classical theory of Random Walks describes the asymptotic behavior of sums of independent identically distributed random real variables. This book explains the generalization of this theory to products of independent identically distributed random matrices with real coefficients. Under the assumption that the action of the matrices is semisimple – or, equivalently, that the Zariski closure of the group generated by these matrices is reductive - and under suitable moment assumptions, it is shown that the norm of the products of such random matrices satisfies a number of classical probabilistic laws. This book includes necessary background on the theory of reductive algebraic groups, probability theory and operator theory, thereby providing a modern introduction to the topic.
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.
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.
Revisiting the texture zero neutrino mass matrices
Singh, Madan; Ahuja, Gulsheen; Gupta, Manmohan
2016-12-01
In the light of refined and large measurements of the reactor mixing angle θ, we have revisited the texture three- and two-zero neutrino mass matrices in the flavor basis. For Majorana neutrinos, it has been explicitly shown that all the texture three-zero mass matrices remain ruled out. Further, for both normal and inverted mass ordering, for the texture two-zero neutrino mass matrices one finds interesting constraints on the Dirac-like CP-violating phase δ and Majorana phases ρ and σ.
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.
A Euclidean algorithm for integer matrices
DEFF Research Database (Denmark)
Lauritzen, Niels; Thomsen, Jesper Funch
2015-01-01
We present a Euclidean algorithm for computing a greatest common right divisor of two integer matrices. The algorithm is derived from elementary properties of finitely generated modules over the ring of integers.......We present a Euclidean algorithm for computing a greatest common right divisor of two integer matrices. The algorithm is derived from elementary properties of finitely generated modules over the ring of integers....
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…
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
Condition number estimation of preconditioned matrices.
Kushida, Noriyuki
2015-01-01
The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results. The Lanczos connection based method provides the condition numbers of coefficient matrices of systems of linear equations with information obtained through the preconditioned conjugate gradient method. Estimating the condition number of preconditioned matrices is sometimes important when describing the effectiveness of new preconditionerers or selecting adequate preconditioners. Operating a preconditioner on a coefficient matrix is the simplest method of estimation. However, this is not possible for large-scale computing, especially if computation is performed on distributed memory parallel computers. This is because, the preconditioned matrices become dense, even if the original matrices are sparse. Although the Lanczos connection method can be used to calculate the condition number of preconditioned matrices, it is not considered to be applicable to large-scale problems because of its weakness with respect to numerical errors. Therefore, we have developed a robust and parallelizable method based on Hager's method. The feasibility studies are curried out for the diagonal scaling preconditioner and the SSOR preconditioner with a diagonal matrix, a tri-daigonal matrix and Pei's matrix. As a result, the Lanczos connection method contains around 10% error in the results even with a simple problem. On the other hand, the new method contains negligible errors. In addition, the newly developed method returns reasonable solutions when the Lanczos connection method fails with Pei's matrix, and matrices generated with the finite element method.
Condition number estimation of preconditioned matrices.
Directory of Open Access Journals (Sweden)
Noriyuki Kushida
Full Text Available The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results. The Lanczos connection based method provides the condition numbers of coefficient matrices of systems of linear equations with information obtained through the preconditioned conjugate gradient method. Estimating the condition number of preconditioned matrices is sometimes important when describing the effectiveness of new preconditionerers or selecting adequate preconditioners. Operating a preconditioner on a coefficient matrix is the simplest method of estimation. However, this is not possible for large-scale computing, especially if computation is performed on distributed memory parallel computers. This is because, the preconditioned matrices become dense, even if the original matrices are sparse. Although the Lanczos connection method can be used to calculate the condition number of preconditioned matrices, it is not considered to be applicable to large-scale problems because of its weakness with respect to numerical errors. Therefore, we have developed a robust and parallelizable method based on Hager's method. The feasibility studies are curried out for the diagonal scaling preconditioner and the SSOR preconditioner with a diagonal matrix, a tri-daigonal matrix and Pei's matrix. As a result, the Lanczos connection method contains around 10% error in the results even with a simple problem. On the other hand, the new method contains negligible errors. In addition, the newly developed method returns reasonable solutions when the Lanczos connection method fails with Pei's matrix, and matrices generated with the finite element method.
Experimental scattering matrices of clouds and randomly oriented particles
Muñoz, O.; Hovenier, J.W.; Kolokolova, L.; Hough, J.; Levasseur-Regourd, A.C.
2015-01-01
In the atmospheres of planets and satellites, liquid particles may occur in the form of clouds, hazes, fog, and rain. The liquid can be water as is the case in the atmosphere of the Earth but also other materials, like sulfuric acid that occurs in the atmosphere of Venus. These liquid particles can
Spectral Radii of Large Non-Hermitian Random Matrices
Jiang, Tiefeng; Qi, Yongcheng
2014-01-01
By using the independence structure of points following a determinantal point process, we study the radii of the spherical ensemble, the truncation of the circular unitary ensemble and the product ensemble with parameter n and k. The limiting distributions of the three radii are obtained. They are not the Tracy-Widom distribution. In particular, for the product ensemble, we show that the limiting distribution has a transition phenomenon: when k/n -> 0, k/n -> a in (0,infty) and k/n -> infty, ...
Communication Optimal Parallel Multiplication of Sparse Random Matrices
2013-02-21
ParLab affiliates National Instruments, Nokia , NVIDIA, Oracle and Samsung, as well as MathWorks. Research is also supported by DOE grants DE-SC0004938...DIG07-10227). Additional support comes from ParLab affiliates National Instruments, Nokia , NVIDIA, Oracle and Samsung, as well as MathWorks. Research is
Limit distributions of random walks on stochastic matrices
Indian Academy of Sciences (India)
(3). 4. = r − r3. In all these cases, the new points of positive λ-masses are generated according to the observation in the previous paragraph. Continuing this way, for every i, the 2i−1 polynomials in r of degree i with positive λ-masses in [0,r] can be generated and each such polynomial of degree i is of the form. ∑k j=1(−1)j−1.
Random normal matrices, Bergman kernel and projective embeddings
Klevtsov, Semyon
2014-01-01
We investigate the analogy between the large N expansion in normal matrix models and the asymptotic expansion of the determinant of the Hilb map, appearing in the study of critical metrics on complex manifolds via projective embeddings. This analogy helps to understand the geometric meaning of the expansion of matrix model free energy and its relation to gravitational effective actions in two dimensions. We compute the leading terms of the free energy expansion in the pure bulk case, and make some observations on the structure of the expansion to all orders. As an application of these results, we propose an asymptotic formula for the Liouville action, restricted to the space of the Bergman metrics.
Exact closed-form expression for the inverse moments of one-sided correlated Gram matrices
Elkhalil, Khalil
2016-08-15
In this paper, we derive a closed-form expression for the inverse moments of one sided-correlated random Gram matrices. Such a question is mainly motivated by applications in signal processing and wireless communications for which evaluating this quantity is a question of major interest. This is for instance the case of the best linear unbiased estimator, in which the average estimation error corresponds to the first inverse moment of a random Gram matrix.
Miszczak, Jarosław Adam
2013-01-01
numbers generated by quantum real number generator. Reasons for new version: Added support for the high-speed on-line quantum random number generator and improved methods for retrieving lists of random numbers. Summary of revisions: The presented version provides two signicant improvements. The first one is the ability to use the on-line Quantum Random Number Generation service developed by PicoQuant GmbH and the Nano-Optics groups at the Department of Physics of Humboldt University. The on-line service supported in the version 2.0 of the TRQS package provides faster access to true randomness sources constructed using the laws of quantum physics. The service is freely available at https://qrng.physik.hu-berlin.de/. The use of this service allows using the presented package with the need of a physical quantum random number generator. The second improvement introduced in this version is the ability to retrieve arrays of random data directly for the used source. This increases the speed of the random number generation, especially in the case of an on-line service, where it reduces the time necessary to establish the connection. Thanks to the speed improvement of the presented version, the package can now be used in simulations requiring larger amounts of random data. Moreover, the functions for generating random numbers provided by the current version of the package more closely follow the pattern of functions for generating pseudo- random numbers provided in Mathematica. Additional comments: Speed comparison: The implementation of the support for the QRNG on-line service provides a noticeable improvement in the speed of random number generation. For the samples of real numbers of size 101; 102,…,107 the times required to generate these samples using Quantis USB device and QRNG service are compared in Fig. 1. The presented results show that the use of the on-line service provides faster access to random numbers. One should note, however, that the speed gain can increase or
Analytical Derivation of the Inverse Moments of One-Sided Correlated Gram Matrices With Applications
Elkhalil, Khalil
2016-02-03
This paper addresses the development of analytical tools for the computation of the inverse moments of random Gram matrices with one side correlation. Such a question is mainly driven by applications in signal processing and wireless communications wherein such matrices naturally arise. In particular, we derive closed-form expressions for the inverse moments and show that the obtained results can help approximate several performance metrics such as the average estimation error corresponding to the Best Linear Unbiased Estimator (BLUE) and the Linear Minimum Mean Square Error (LMMSE) estimator or also other loss functions used to measure the accuracy of covariance matrix estimates.
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.
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...... matrix dynamics. Our empirical results show that the new mixing approach provides superior forecasts compared to multivariate volatility specifications using single sources of information....
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
Matricídio e transtorno bipolar
National Research Council Canada - National Science Library
Valença, Alexandre Martins; Mezzasalma, Marco André; Nascimento, Isabella; Nardi, Antonio Egidio
2009-01-01
.... Estudos de casos de matricídio têm revelado a presença de transtornos mentais, tais como esquizofrenia, transtorno bipolar, transtornos de personalidade e alcoolismo, assim como casos em que não há...
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 Impact factor: 1.857, year: 2016
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.
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.
Numerical Methods for Structured Matrices and Applications
Bini, Dario A; Olshevsky, Vadim; Tyrtsyhnikov, Eugene; van Barel, Marc
2010-01-01
This cross-disciplinary volume brings together theoretical mathematicians, engineers and numerical analysts and publishes surveys and research articles related to the topics where Georg Heinig had made outstanding achievements. In particular, this includes contributions from the fields of structured matrices, fast algorithms, operator theory, and applications to system theory and signal processing.
Matrices with high completely positive semidefinite rank
de Laat, David; Gribling, Sander; Laurent, Monique
2017-01-01
A real symmetric matrix M is completely positive semidefinite if it admits a Gram representation by (Hermitian) positive semidefinite matrices of any size d. The smallest such d is called the (complex) completely positive semidefinite rank of M , and it is an open question whether there exists an
Tissue integration of collagen-based matrices: an experimental study in mice.
Thoma, Daniel S; Villar, Cristina C; Cochran, David L; Hämmerle, Christoph H F; Jung, Ronald E
2012-12-01
To test whether or not tissue integration, biodegradation, and new blood vessel formation in two collagen-based matrices depend on the level of chemical cross-linking. Two collagen matrices with high (CM1) and low (CM2) levels of chemical cross-linking were randomly implanted in two pouches in 14 athymic nude mice. Three and 6 weeks later, the animals were euthanized. Histologic and histomorphometric measurements were performed on paraffin-embedded sections. Both collagen matrices integrated well into the surrounding soft tissues. The level of cross-linking and duration of implantation had an effect on the formation of new blood vessels. More blood vessels (n = in absolute numbers) were found in outer compartments compared to the central compartments of the matrices, reaching 5.6 (CM2) vs. 4.3 (CM1) at 3 weeks, and 5.3 (CM2) vs. 7.3 (CM1) at 6 weeks. Similarly, connective tissue formation increased for both matrices between 3 and 6 weeks, whereas the amount of remaining collagen network gradually decreased over time being more pronounced for CM1 (-50%) compared to CM2 (-15%). The degree of cross-linking was negatively correlated for all outcome measures resulting in improved tissue integration, superior matrix stability and enhanced angiogenic patterns for the less cross-linked collagen matrix (CM2) in this experimental study in mice. © 2011 John Wiley & Sons A/S.
Importance of randomness in biological networks: A random matrix ...
Indian Academy of Sciences (India)
2015-01-29
Jan 29, 2015 ... We show that in spite of huge differences these interaction networks, representing real-world systems, posses from random matrix models, the spectral properties of the underlying matrices of these networks follow random matrix theory bringing them into the same universality class. We further demonstrate ...
Cyclic monodromy matrices for sl(n) trigonometric R-matrices
Tarasov, Vitaly
1992-01-01
The algebra of monodromy matrices for sl(n) trigonometric R-matrices is studied. It is shown that a generic finite-dimensional polynomial irreducible representation of this algebra is equivalent to a tensor product of L-operators. Cocommutativity of representations is discussed. A special class of representations - factorizable representations is introduced and intertwiners for cocommuting factorizable representations are written through the Boltzmann weights of the sl(n) chiral Potts model. ...
On the Construction of Jointly Superregular Lower Triangular Toeplitz Matrices
DEFF Research Database (Denmark)
Hansen, Jonas; Østergaard, Jan; Kudahl, Johnny
2016-01-01
Superregular matrices have the property that all of their submatrices, which can be full rank are so. Lower triangular superregular matrices are useful for e.g., maximum distance separable convolutional codes as well as for (sequential) network codes. In this work, we provide an explicit design...... for all superregular lower triangular Toeplitz matrices in GF(2p) for the case of matrices with dimensions less than or equal to 5 × 5. For higher dimensional matrices, we present a greedy algorithm that find a solution provided the field size is sufficiently high. We also introduce the notions of jointly...... superregular and product preserving jointly superregular matrices, and extend our explicit constructions of superregular matrices to these cases. Jointly superregular matrices are necessary to achieve optimal decoding capabilities for the case of codes with a rate lower than 1/2, and the product preserving...
Eudragit E100 and Polysaccharide Polymer Blends as Matrices for ...
African Journals Online (AJOL)
Release Drug Delivery II: Swelling and Release Studies. ... Furthermore, in vivo absorption was predicted from the in vitro release data by convolution method. Results: E100 matrices exhibited little or no swelling while the matrices of SCMC and ...
Electrospun human keratin matrices as templates for tissue regeneration.
Sow, Wan Ting; Lui, Yuan Siang; Ng, Kee Woei
2013-04-01
The aim of this work was to study the feasibility of fabricating human hair keratin matrices through electrospinning and to evaluate the potential of these matrices for tissue regeneration. Keratin was extracted from human hair using Na2S and blended with poly(ethylene oxide) in the weight ratio of 60:1 for electrospinning. Physical morphology and chemical properties of the matrices were characterized using scanning electron microscopy and Fourier transform infrared spectroscopy, respectively. Cell viability and morphology of murine and human fibroblasts cultured on the matrices were evaluated through the Live/Dead(®) assay and scanning electron microscopy. Electrospun keratin matrices were successfully produced without affecting the chemical conformation of keratin. Fibroblasts cultured on keratin matrices showed healthy morphology and penetration into matrices at day 7. Electrospun human hair keratin matrices provide a bioinductive and structural environment for cell growth and are thus attractive as alternative templates for tissue regeneration.
Extreme eigenvalues of sample covariance and correlation matrices
DEFF Research Database (Denmark)
Heiny, Johannes
2017-01-01
This thesis is concerned with asymptotic properties of the eigenvalues of high-dimensional sample covariance and correlation matrices under an infinite fourth moment of the entries. In the first part, we study the joint distributional convergence of the largest eigenvalues of the sample covariance...... that the extreme eigenvalues are essentially determined by the extreme order statistics from an array of iid random variables. The asymptotic behavior of the extreme eigenvalues is then derived routinely from classical extreme value theory. The resulting approximations are strikingly simple considering the high...... dimension of the problem at hand. We develop a theory for the point process of the normalized eigenvalues of the sample covariance matrix in the case where rows and columns of the data are linearly dependent. Based on the weak convergence of this point process we derive the limit laws of various functionals...
Extreme eigenvalues of sample covariance and correlation matrices
DEFF Research Database (Denmark)
Heiny, Johannes
This thesis is concerned with asymptotic properties of the eigenvalues of high-dimensional sample covariance and correlation matrices under an infinite fourth moment of the entries. In the first part, we study the joint distributional convergence of the largest eigenvalues of the sample covariance...... eigenvalues are essentially determined by the extreme order statistics from an array of iid random variables. The asymptotic behavior of the extreme eigenvalues is then derived routinely from classical extreme value theory. The resulting approximations are strikingly simple considering the high dimension...... of the problem at hand. We develop a theory for the point process of the normalized eigenvalues of the sample covariance matrix in the case where rows and columns of the data are linearly dependent. Based on the weak convergence of this point process we derive the limit laws of various functionals...
A Construction of Lossy Source Code Using LDPC Matrices
Miyake, Shigeki; Muramatsu, Jun
Research into applying LDPC code theory, which is used for channel coding, to source coding has received a lot of attention in several research fields such as distributed source coding. In this paper, a source coding problem with a fidelity criterion is considered. Matsunaga et al. and Martinian et al. constructed a lossy code under the conditions of a binary alphabet, a uniform distribution, and a Hamming measure of fidelity criterion. We extend their results and construct a lossy code under the extended conditions of a binary alphabet, a distribution that is not necessarily uniform, and a fidelity measure that is bounded and additive and show that the code can achieve the optimal rate, rate-distortion function. By applying a formula for the random walk on lattice to the analysis of LDPC matrices on Zq, where q is a prime number, we show that results similar to those for the binary alphabet condition hold for Zq, the multiple alphabet condition.
Shin, Yong Cheol; Shin, Dong-Myeong; Lee, Eun Ji; Lee, Jong Ho; Kim, Ji Eun; Song, Sung Hwa; Hwang, Dae-Youn; Lee, Jun Jae; Kim, Bongju; Lim, Dohyung; Hyon, Suong-Hyu; Lim, Young-Jun; Han, Dong-Wook
2016-12-01
During the last few decades, considerable research on diabetic wound healing strategies has been performed, but complete diabetic wound healing remains an unsolved problem, which constitutes an enormous biomedical burden. Herein, hyaluronic acid (HA)/poly(lactic-co-glycolic acid, PLGA) core/shell fiber matrices loaded with epigallocatechin-3-O-gallate (EGCG) (HA/PLGA-E) are fabricated by coaxial electrospinning. HA/PLGA-E core/shell fiber matrices are composed of randomly-oriented sub-micrometer fibers and have a 3D porous network structure. EGCG is uniformly dispersed in the shell and sustainedly released from the matrices in a stepwise manner by controlled diffusion and PLGA degradation over four weeks. EGCG does not adversely affect the thermomechanical properties of HA/PLGA-E matrices. The number of human dermal fibroblasts attached on HA/PLGA-E matrices is appreciably higher than that on HA/PLGA counterparts, while their proliferation is steadily retained on HA/PLGA-E matrices. The wound healing activity of HA/PLGA-E matrices is evaluated in streptozotocin-induced diabetic rats. After two weeks of surgical treatment, the wound areas are significantly reduced by the coverage with HA/PLGA-E matrices resulting from enhanced re-epithelialization/neovascularization and increased collagen deposition, compared with no treatment or HA/PLGA. In conclusion, the HA/PLGA-E matrices can be potentially exploited to craft strategies for the acceleration of diabetic wound healing and skin regeneration. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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.
Meet and join matrices in the poset of exponential divisors
Indian Academy of Sciences (India)
exponential multiple (LCEM) do not always exist. In this paper we embed this poset in a lattice. As an application we study the GCED and LCEM matrices, analogues of GCD and LCM matrices, which are both special cases of meet and join matrices on lattices. Keywords. Exponential divisor; lattice; meet matrix; join matrix; ...
19 CFR 10.90 - Master records and metal matrices.
2010-04-01
... 19 Customs Duties 1 2010-04-01 2010-04-01 false Master records and metal matrices. 10.90 Section... Master Records, and Metal Matrices § 10.90 Master records and metal matrices. (a) Consumption entries... made, of each master record or metal matrix covered thereby. (c) A bond on Customs Form 301, containing...
Decision Matrices: Tools to Enhance Middle School Engineering Instruction
Gonczi, Amanda L.; Bergman, Brenda G.; Huntoon, Jackie; Allen, Robin; McIntyre, Barb; Turner, Sheri; Davis, Jen; Handler, Rob
2017-01-01
Decision matrices are valuable engineering tools. They allow engineers to objectively examine solution options. Decision matrices can be incorporated in K-12 classrooms to support authentic engineering instruction. In this article we provide examples of how decision matrices have been incorporated into 6th and 7th grade classrooms as part of an…
Approximate inverse preconditioners for general sparse matrices
Energy Technology Data Exchange (ETDEWEB)
Chow, E.; Saad, Y. [Univ. of Minnesota, Minneapolis, MN (United States)
1994-12-31
Preconditioned Krylov subspace methods are often very efficient in solving sparse linear matrices that arise from the discretization of elliptic partial differential equations. However, for general sparse indifinite matrices, the usual ILU preconditioners fail, often because of the fact that the resulting factors L and U give rise to unstable forward and backward sweeps. In such cases, alternative preconditioners based on approximate inverses may be attractive. We are currently developing a number of such preconditioners based on iterating on each column to get the approximate inverse. For this approach to be efficient, the iteration must be done in sparse mode, i.e., we must use sparse-matrix by sparse-vector type operatoins. We will discuss a few options and compare their performance on standard problems from the Harwell-Boeing collection.
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.
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
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
Index matrices towards an augmented matrix calculus
Atanassov, Krassimir T
2014-01-01
This book presents the very concept of an index matrix and its related augmented matrix calculus in a comprehensive form. It mostly illustrates the exposition with examples related to the generalized nets and intuitionistic fuzzy sets which are examples of an extremely wide array of possible application areas. The present book contains the basic results of the author over index matrices and some of its open problems with the aim to stimulating more researchers to start working in this area.
About the logarithm function over the matrices
Gerald, Bourgeois
2007-01-01
We prove the following results: let x,y be (n,n) complex matrices such that x,y,xy have no eigenvalue in ]-infinity,0] and log(xy)=log(x)+log(y). If n=2, or if n>2 and x,y are simultaneously triangularizable, then x,y commute. In both cases we reduce the problem to a result in complex analysis.
Octonions in random matrix theory
Forrester, Peter J.
2016-01-01
The octonions are one of the four normed division algebras, together with the real, complex and quaternion number systems. The latter three hold a primary place in random matrix theory, where in applications to quantum physics they are determined as the entries of ensembles of Hermitian random by symmetry considerations. Only for $N=2$ is there an existing analytic theory of Hermitian random matrices with octonion entries. We use a Jordan algebra viewpoint to provide an analytic theory for $N...
Maximal-entropy random walk unifies centrality measures
Ochab, J. K.
2012-01-01
In this paper analogies between different (dis)similarity matrices are derived. These matrices, which are connected to path enumeration and random walks, are used in community detection methods or in computation of centrality measures for complex networks. The focus is on a number of known centrality measures, which inherit the connections established for similarity matrices. These measures are based on the principal eigenvector of the adjacency matrix, path enumeration, as well as on the sta...
Classical perturbations for matrices of linear functionals
García Ardila, Juan Carlos
2017-01-01
Mención Internacional en el título de doctor El objetivo de esta Tesis es estudiar trasformaciones espectrales para matrices que tiene como entradas funcionales lineales. En particular estudiamos las transformaciones de Christoffel, Geronimus y Geronimus-Uvarov. Con el fin de que esta Tesis sea lo más autocontenida posible, la hemos dividido en siete capítulos. • En el Capítulo 1, introducimos algunos conceptos y fijamos la notación que será usada a lo largo de esta Tesis a ...
Deconvolution and Regularization with Toeplitz Matrices
DEFF Research Database (Denmark)
Hansen, Per Christian
2002-01-01
treatment requires the use of regularization methods. The corresponding computational problem takes the form of structured matrix problem with a Toeplitz or block Toeplitz coefficient matrix. The aim of this paper is to present a tutorial survey of numerical algorithms for the practical treatment...... of these discretized deconvolution problems, with emphasis on methods that take the special structure of the matrix into account. Wherever possible, analogies to classical DFT-based deconvolution problems are drawn. Among other things, we present direct methods for regularization with Toeplitz matrices, and we show...
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.
Analysis and synthesis of cascaded metasurfaces using wave matrices
Ranjbar, Amin; Grbic, Anthony
2017-05-01
Various matrix representations are used to analyze the propagation of electromagnetic waves through stratified (layered) media or cascaded circuit networks. These include ABCD matrices, scattering matrices, impedance matrices, and hybrid matrices. A less known network representation is the wave matrix. In this paper, a brief review of wave matrices is presented and their relation to other network representations derived. Wave matrices are found for common interfaces such as boundaries between dielectric media, dielectric slabs, as well as electric, magnetic, and magneto-electric sheet boundaries (generalized sheet transition conditions). These results are then used to develop an analytical synthesis approach for cascaded metasurfaces: metasurfaces consisting of a cascade of sheets separated by dielectric spacers. This is in contrast to earlier works which relied on numerical solvers or optimization methods to design such structures. A few design examples are presented to demonstrate the utility of the synthesis approach.
Effect of antioxidants on captopril floating matrices.
Jiménez-Martínez, Inéz; Domínguez-Ramírez, Adriana Miriam; Villafuerte-Robles, Leopoldo
2010-06-01
Stability of captopril in a controlled release formulation has been a challenge for some time. The sustained release of captopril from floating matrices has been studied varying the antioxidant load, the sodium bicarbonate proportion and the compaction pressure. Although in many cases the effect of compaction pressure remains hidden, actual results show that matrices compacted at 55 MPa have smaller density and float in the dissolution medium while those compacted at 165 MPa float only adding sodium bicarbonate. The increase of compaction pressure reduces the hydration volume and increases the time necessary to attain its maximum. These changes are attributed to lower matrix porosity and to the consequent diminution of water and drug transport. Increasing ascorbic acid proportions increase the matrix hydration volume and the drug released. The use of sodium ascorbate and the substitution of 15% polymer with sodium bicarbonate reduce the matrix hydration volume, shorten the matrix hydration process and increase the drug released. This is attributed to carbon dioxide bubbles that decrease the matrix coherence and expand the matrix volume, facilitating drug dissolution and only a limited further matrix expansion. The antioxidant protection provided by sodium ascorbate was lesser of that of ascorbic acid because of greater molecular mass and lesser release rate.
Bromination of selected pharmaceuticals in water matrices.
Benitez, F Javier; Acero, Juan L; Real, Francisco J; Roldan, Gloria; Casas, Francisco
2011-11-01
The bromination of five selected pharmaceuticals (metoprolol, naproxen, amoxicillin, phenacetin, and hydrochlorothiazide) was studied with these compounds individually dissolved in ultra-pure water. The apparent rate constants for the bromination reaction were determined as a function of the pH, obtaining the sequence amoxicillin>naproxen>hydrochlorothiazide≈phenacetin≈metoprolol. A kinetic mechanism specifying the dissociation reactions and the species formed for each compound according to its pK(a) value and the pH allowed the intrinsic rate constants to be determined for each elementary reaction. There was fairly good agreement between the experimental and calculated values of the apparent rate constants, confirming the goodness of the proposed reaction mechanism. In a second stage, the bromination of the selected pharmaceuticals simultaneously dissolved in three water matrices (a groundwater, a surface water from a public reservoir, and a secondary effluent from a WWTP) was investigated. The pharmaceutical elimination trend agreed with the previously determined rate constants. The influence of the main operating conditions (pH, initial bromine dose, and characteristics of the water matrix) on the degradation of the pharmaceuticals was established. An elimination concentration profile for each pharmaceutical in the water matrices was proposed based on the use of the previously evaluated apparent rate constants, and the theoretical results agreed satisfactorily with experiment. Finally, chlorination experiments performed in the presence of bromide showed that low bromide concentrations slightly accelerate the oxidation of the selected pharmaceuticals during chlorine disinfection. Copyright © 2011 Elsevier Ltd. All rights reserved.
Decomposition of Mueller matrices of scattering media: Theory and experiment
Directory of Open Access Journals (Sweden)
R. Ossikovski
2011-09-01
Full Text Available Algebraic decomposition of Mueller matrices is a particularly promising approach to the retrieval of the optical properties of the medium investigated in a polarized light scattering experiment. Various decompositions of generally depolarizing Mueller matrices are revisited and discussed. Both classic as well as recently proposed approaches are reviewed. Physical and mathematical aspects such as depolarization and limits of applicability are comparatively addressed. Experimental matrices of scattering media are decomposed by different methodologies and physically interpreted.
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.
Voiculescu, Dan; Nica, Alexandru
1992-01-01
This book presents the first comprehensive introduction to free probability theory, a highly noncommutative probability theory with independence based on free products instead of tensor products. Basic examples of this kind of theory are provided by convolution operators on free groups and by the asymptotic behavior of large Gaussian random matrices. The probabilistic approach to free products has led to a recent surge of new results on the von Neumann algebras of free groups. The book is ideally suited as a textbook for an advanced graduate course and could also provide material for a seminar. In addition to researchers and graduate students in mathematics, this book will be of interest to physicists and others who use random matrices.
Some properties of generalized K-centrosymmetric H-matrices
Liu, Zhongyun; Fa[Ss]Bender, H.
2008-05-01
Every nxn generalized K-centrosymmetric matrix A can be reduced into a 2x2 block diagonal matrix (see [Z. Liu, H. Cao, H. Chen, A note on computing matrix-vector products with generalized centrosymmetric (centrohermitian) matrices, Appl. Math. Comput. 169 (2) (2005) 1332-1345]). This block diagonal matrix is called the reduced form of the matrix A. In this paper we further investigate some properties of the reduced form of these matrices and discuss the square roots of these matrices. Finally exploiting these properties, the development of structure-preserving algorithms for certain computations for generalized K-centrosymmetric H-matrices is discussed.
Yi, Jiawang; Tan, Guanzheng
2015-12-20
Optical cryptosystems combined with compressed sensing can achieve compression and encryption simultaneously. But they usually use the same measurement matrix to sample all blocks of an image, which makes it easy to estimate the measurement matrix in the chosen plaintext attack. In this paper, we propose a robust scheme adopting multiple measurement matrices to overcome this shortcoming. The matrices can be efficiently derived by applying random row exchanging to a basic one, which is also encoded into the fractional Fourier transform (FrFT) domain to improve the visual effect of wrongly decrypted images. Chaos-based pixel scrambling is added into our double FrFT cryptosystem to guarantee its nonlinearity. Simulation results have shown the security and effectiveness of our scheme.
Medium-induced change of the optical response of metal clusters in rare-gas matrices
Xuan, Fengyuan; Guet, Claude
2017-10-01
Interaction with the surrounding medium modifies the optical response of embedded metal clusters. For clusters from about ten to a few hundreds of silver atoms, embedded in rare-gas matrices, we study the environment effect within the matrix random phase approximation with exact exchange (RPAE) quantum approach, which has proved successful for free silver clusters. The polarizable surrounding medium screens the residual two-body RPAE interaction, adds a polarization term to the one-body potential, and shifts the vacuum energy of the active delocalized valence electrons. Within this model, we calculate the dipole oscillator strength distribution for Ag clusters embedded in helium droplets, neon, argon, krypton, and xenon matrices. The main contribution to the dipole surface plasmon red shift originates from the rare-gas polarization screening of the two-body interaction. The large size limit of the dipole surface plasmon agrees well with the classical prediction.
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.
Drug delivery from ordered mesoporous matrices.
Manzano, Miguel; Colilla, Montserrat; Vallet-Regí, María
2009-12-01
Research interest in silica-based ordered mesoporous materials (SMMs) as drug delivery systems has grown drastically in the last few years owing to the great versatility and stability of these mesoporous matrices. This review aims to resume the work carried out in this area so far and the possible applications in biomedical technologies. The different SMMs can be designed and tailored using different chemical strategies according to the drug and clinical necessity. The available channels of SMMs that can be used to store drugs can be opened and closed by different systems, in the so-called stimuli-responsive release devices. These systems could improve the therapeutic efficacy compared with conventional sustained release systems. SMMs offer such a great versatility that can be used both for oral and for local drug delivery, with huge possible applications in different clinical areas.
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.
Quantum State Tomography via Reduced Density Matrices.
Xin, Tao; Lu, Dawei; Klassen, Joel; Yu, Nengkun; Ji, Zhengfeng; Chen, Jianxin; Ma, Xian; Long, Guilu; Zeng, Bei; Laflamme, Raymond
2017-01-13
Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However, it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this work, we demonstrate for the first time a class of states that are UD by their RDMs under the assumption that the global state is pure, but fail to be UD in the absence of that assumption. This discovery allows us to classify quantum states according to their UD properties, with the requirement that each class be treated distinctly in the practice of simplifying quantum state tomography. Additionally, we experimentally test the feasibility and stability of performing quantum state tomography via the measurement of local RDMs for each class. These theoretical and experimental results demonstrate the advantages and possible pitfalls of quantum state tomography with local measurements.
Equiangular tight frames and unistochastic matrices
Goyeneche, Dardo; Turek, Ondřej
2017-06-01
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.
Spirooxazine Photoisomerization and Relaxation in Polymer Matrices
Directory of Open Access Journals (Sweden)
Maria Larkowska
2011-01-01
Full Text Available 9′-Hydroxy-1,3,3-trimethylspiro[indoline-2,3′[3H]naphtha[2,1-b]-1,4oxazine] (SPO-7OH was used in studies of photochromic transformations in polymer matrices. Illumination with UV lamp caused opening the spirostructure of the oxazine with formation of open merocyanine species absorbing at ca. 610 nm. The kinetic studies of thermal relaxation of the open form showed that this process can be described with a biexponential function including both photochemical reaction and rheological behaviour of the polymeric environment. Basing on Arrhenius plot of the rate constant ascribed to the photochemical reaction, the activation energy was determined, which was 66.1 and 84.7 kJ/mole for poly(methyl methacrylate-co-butyl methacrylate and poly(vinylpyrrolidone matrix, respectively.
Viscous hydrophilic injection matrices for serial crystallography.
Kovácsová, Gabriela; Grünbein, Marie Luise; Kloos, Marco; Barends, Thomas R M; Schlesinger, Ramona; Heberle, Joachim; Kabsch, Wolfgang; Shoeman, Robert L; Doak, R Bruce; Schlichting, Ilme
2017-07-01
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 hydro-gels as viscous injection matrices is described, namely sodium carb-oxy-methyl 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 matrices afford
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
Octonions in random matrix theory
Forrester, Peter J.
2017-04-01
The octonions are one of the four normed division algebras, together with the real, complex and quaternion number systems. The latter three hold a primary place in random matrix theory, where in applications to quantum physics they are determined as the entries of ensembles of Hermitian random matrices by symmetry considerations. Only for N=2 is there an existing analytic theory of Hermitian random matrices with octonion entries. We use a Jordan algebra viewpoint to provide an analytic theory for N=3. We then proceed to consider the matrix structure X†X, when X has random octonion entries. Analytic results are obtained from N=2, but are observed to break down in the 3×3 case.
Computing Vibration-Mode Matrices From Finite-Element Output
Levy, Roy
1993-01-01
Postprocessing algorithms devised to facilitate vibrational-mode analyses of dynamics of complicated structures. Yields inertia matrices and elastic/rigid-coupling matrices. Such analyses important in simulation and control in active suppression of vibrations in large building or in precise aiming of large antenna.
A sparse flat extension theorem for moment matrices
M. Laurent (Monique); B. Mourrain
2008-01-01
htmlabstractIn this note we prove a generalization of the flat extension theorem of Curto and Fialkow [4] for truncated moment matrices. It applies to moment matrices indexed by an arbitrary set of monomials and its border, assuming that this set is connected to 1. When formulated in a basis-free
A generalized flat extension theorem for moment matrices
M. Laurent (Monique); B. Mourrain
2009-01-01
htmlabstractIn this note we prove a generalization of the flat extension theorem of Curto and Fialkow [4] for truncated moment matrices. It applies to moment matrices indexed by an arbitrary set of monomials and its border, assuming that this set is connected to 1. When formulated in a basis-free
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 ...
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...
Plant response to alternative matrices for in vitro root induction ...
African Journals Online (AJOL)
The advantage of alternative matrices raises the concomitant question of plant intelligence in sensing its environment. The present review apart from summarizing the works with alternative matrices, attempts to raise some issues related to plant sensitivity, which remain unanswered due to lack of present understanding in ...
Formation of complex anodic films on porous alumina matrices
Indian Academy of Sciences (India)
The kinetics of growth of complex anodic alumina films was investigated. These films were formed by filling porous oxide films (matrices) having deep pores. The porous films (matrices) were obtained voltastatically in (COOH)2 aqueous solution under various voltages. The filling was done by re-anodization in an electrolyte ...
A framework for medical diagnosis via fuzzy soft matrices
Directory of Open Access Journals (Sweden)
Yıldıray Çelik
2016-04-01
Full Text Available In this paper we introduce matrice represantation of fuzzy soft sets. By using the notion of fuzzy soft matrices, we apply fuzzy soft set technology through the well known Sanchez's [8] approach for medical diagnosis. Also we exhibit the technique with a hypothetical case study.
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…
Sarymsakov matrices and coordination tasks for multi-agent systems
Xia, Weiguo; Cao, Ming
2012-01-01
The convergence of products of stochastic matrices has proven to be critical in establishing the effectiveness of distributed coordination algorithms for multi-agent systems. After reviewing some classic and recent results on infinite backward products of stochastic matrices, we provide a new
Reprint of Testing scattering matrices: a compendium of recipes
Hovenier, J.W.; van der Mee, C.V.M.
2010-01-01
Scattering matrices describe the transformation of the Stokes parameters of a beam of radiation upon scattering of that beam. The problems of testing scattering matrices for scattering by one particle and for single scattering by an assembly of particles are addressed. The treatment concerns
Revisiting amino acid substitution matrices for identifying distantly related proteins.
Yamada, Kazunori; Tomii, Kentaro
2014-02-01
Although many amino acid substitution matrices have been developed, it has not been well understood which is the best for similarity searches, especially for remote homology detection. Therefore, we collected information related to existing matrices, condensed it and derived a novel matrix that can detect more remote homology than ever. Using principal component analysis with existing matrices and benchmarks, we developed a novel matrix, which we designate as MIQS. The detection performance of MIQS is validated and compared with that of existing general purpose matrices using SSEARCH with optimized gap penalties for each matrix. Results show that MIQS is able to detect more remote homology than the existing matrices on an independent dataset. In addition, the performance of our developed matrix was superior to that of CS-BLAST, which was a novel similarity search method with no amino acid matrix. We also evaluated the alignment quality of matrices and methods, which revealed that MIQS shows higher alignment sensitivity than that with the existing matrix series and CS-BLAST. Fundamentally, these results are expected to constitute good proof of the availability and/or importance of amino acid matrices in sequence analysis. Moreover, with our developed matrix, sophisticated similarity search methods such as sequence-profile and profile-profile comparison methods can be improved further. Newly developed matrices and datasets used for this study are available at http://csas.cbrc.jp/Ssearch/.
First-principles scattering matrices for spin transport
Xia, K.; Zwierzycki, M.; Talanana, M.; Bauer, G.E.W.; Kelly, Paul J.
2006-01-01
Details are presented of an efficient formalism for calculating transmission and reflection matrices from first principles in layered materials. Within the framework of spin density functional theory and using tight-binding muffin-tin orbitals, scattering matrices are determined by matching the wave
Can Public Health Risk Assessment Using Risk Matrices Be Misleading?
Vatanpour, Shabnam; Hrudey, Steve E; Dinu, Irina
2015-08-14
The risk assessment matrix is a widely accepted, semi-quantitative tool for assessing risks, and setting priorities in risk management. Although the method can be useful to promote discussion to distinguish high risks from low risks, a published critique described a problem when the frequency and severity of risks are negatively correlated. A theoretical analysis showed that risk predictions could be misleading. We evaluated a practical public health example because it provided experiential risk data that allowed us to assess the practical implications of the published concern that risk matrices would make predictions that are worse than random. We explored this predicted problem by constructing a risk assessment matrix using a public health risk scenario-Tainted blood transfusion infection risk-That provides negative correlation between harm frequency and severity. We estimated the risk from the experiential data and compared these estimates with those provided by the risk assessment matrix. Although we validated the theoretical concern, for these authentic experiential data, the practical scope of the problem was limited. The risk matrix has been widely used in risk assessment. This method should not be abandoned wholesale, but users must address the source of the problem, apply the risk matrix with a full understanding of this problem and use matrix predictions to inform, but not drive decision-making.
The semi-dynamical reflection equation: solutions and structure matrices
Energy Technology Data Exchange (ETDEWEB)
Avan, J; Zambon, C [Laboratoire de Physique Theorique et Modelisation, Universite de Cergy-Pontoise (CNRS UMR 8089), Saint-Martin 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex (France)], E-mail: avan@u-cergy.fr, E-mail: cristina.zambon@u-cergy.fr
2008-05-16
Explicit solutions of the non-constant semi-dynamical reflection equation are constructed, together with suitable parametrizations of their structure matrices. Considering the semi-dynamical reflection equation with rational non-constant Arutyunov-Chekhov-Frolov structure matrices, and a specific meromorphic ansatz, it is found that only two sets of the previously found constant solutions are extendible to the non-constant case. In order to simplify future constructions of spin-chain Hamiltonians, a parametrization procedure is applied explicitly to all elements of the semi-dynamical reflection equation available. Interesting expressions for 'twists' and R-matrices entering the parametrization procedure are found. In particular, some expressions for the R-matrices seem to appear here for the first time. In addition, a new set of consistent structure matrices for the semi-dynamical reflection equation is obtained.
Random discrete Schroedinger operators from random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Breuer, Jonathan [Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem 91904 (Israel); Forrester, Peter J [Department of Mathematics and Statistics, University of Melbourne, Parkville, Vic 3010 (Australia); Smilansky, Uzy [Department of Physics of Complex Systems, Weizmann Institute, Rehovot 76100 (Israel)
2007-02-02
We investigate random, discrete Schroedinger operators which arise naturally in the theory of random matrices, and depend parametrically on Dyson's Coulomb gas inverse temperature {beta}. They are similar to the class of 'critical' random Schroedinger operators with random potentials which diminish as vertical bar x vertical bar{sup -1/2}. We show that as a function of {beta} they undergo a transition from a regime of (power-law) localized eigenstates with a pure point spectrum for {beta} < 2 to a regime of extended states with a singular continuous spectrum for {beta} {>=} 2. (fast track communication)
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
Calculating scattering matrices by wave function matching
Energy Technology Data Exchange (ETDEWEB)
Zwierzycki, M. [Institute of Molecular Physics, Polish Academy of Sciences, Smoluchowskiego 17, 60-179 Poznan (Poland); Khomyakov, P.A.; Starikov, A.A.; Talanana, M.; Xu, P.X.; Karpan, V.M.; Marushchenko, I.; Brocks, G.; Kelly, P.J. [Faculty of Science and Technology and MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands); Xia, K. [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100080 (China); Turek, I. [Institute of Physics of Materials, Academy of Sciences of the Czech Republic, 616 62 Brno (Czech Republic); Bauer, G.E.W. [Kavli Institute of NanoScience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft (Netherlands)
2008-04-15
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.)
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.
Osteogenic signaling on silk-based matrices.
Midha, Swati; Murab, Sumit; Ghosh, Sourabh
2016-08-01
Bone tissue engineering has mainly focused on generating 3D grafts to repair bone defects. However, the underlying signaling mechanisms responsible for development of such 3D bone equivalents have largely been ignored. Here we describe the crucial aspects of embryonic osteogenesis and bone development including cell sources and general signaling cascades that guide mesenchymal progenitors towards osteogenic lineage. Drawing from the knowledge of developmental biology, we then review how silk biomaterial can regulate osteogenic signaling by focusing on the expression of cell surface markers, functional genomic information (mRNA) of stem cells cultured on silk matrices. In an attempt to recapitulate exact in vivo microenvironment of osteogenesis, role of scaffold architecture and material chemistry in regulating cellular differentiation is elaborated. The generated knowledge will not only improve our understanding of cell-material interactions but reveal newer strategies beyond a conventional tissue engineering paradigm and open new prospects for developing silk-based therapies against clinically relevant bone disorders. Copyright © 2016 Elsevier Ltd. All rights reserved.
Parameterization of orthonormal third-order matrices for linear calibration
Directory of Open Access Journals (Sweden)
Ivo Moll
2009-01-01
Full Text Available The paper derives a parametric definition of the set of third-order orthonormal real matrices.The derivation is done in several partial steps. First a generalized unit matrix is introduced as the simplest case of an orthonormal matrix along with some of its properties and, subsequently, the properties of orthonormal matrices are proved that will be needed.The derivation itself of a parametric definition of third-order orthonormal matrices is based on the numbers of zero entries that are theoretically possible. Therefore, it is first proved that a third-order square matrix with the number of non-zero entries different from nine, eight, five, or three cannot be orthonormal.The number of different ways in which the set of third-order orthonormal matrices can be parameterized is greater than one. The concepts of a rotation matrix and a flop-enabling rotation matrix are introduced to motivate the parameterization chosen.Given the product of two rotation matrices and one flop-enabling rotation matrix, it is first proved that it is a third-order orthonormal matrix. In the last part of the paper, it is then proved that such a product already includes, as special cases, all the third-order orthonormal matrices. It is thus a parametric definition of all third-order orthonormal matrices.
Wigner surmise for mixed symmetry classes in random matrix theory
Schierenberg, Sebastian; Bruckmann, Falk; Wettig, Tilo
2012-06-01
We consider the nearest-neighbor spacing distributions of mixed random matrix ensembles interpolating between different symmetry classes or between integrable and nonintegrable systems. We derive analytical formulas for the spacing distributions of 2×2 or 4×4 matrices and show numerically that they provide very good approximations for those of random matrices with large dimension. This generalizes the Wigner surmise, which is valid for pure ensembles that are recovered as limits of the mixed ensembles. We show how the coupling parameters of small and large matrices must be matched depending on the local eigenvalue density.
Integration of collagen matrices into the urethra when implanted as onlay graft
Directory of Open Access Journals (Sweden)
Kleber Sayeg
2013-06-01
Full Text Available Objective To assess the integration of decellularized heterologous collagen matrices into the urethra, when implanted with no cells or when seeded with autologous smooth muscle cells. Materials and Methods Eighteen New Zealand rabbits were randomly assigned to two groups: Group I (n = 9 - animals undergoing urethral segment resection with interposition of a patch of heterologous collagen matrix seeded with autologous smooth muscle cells; Group II (n = 9 - animals undergoing resection of a urethral segment with interposition of a decellularized heterologous collagen matrix patch. Two animals from each group were sacrificed on postoperative days seven, fourteen and twenty-eight; three animals from each group were sacrificed at the end of three postoperative months. At the end of the third month one animal from each group underwent urethroscopy for urethral integrity assessment and one animal from each group had its microcirculation image captured by a SDF device (Side-stream Dark Field - Microscan Analysis Software. One animal from each group in each euthanasia period underwent cystourethrography so as the urethra could be viewed at flow time. The matrices integration was assessed through histological examination using hematoxylin and eosin (H&E, Masson trichrome (MT, Picrosirius red and Von Willebrand staining. In a blind study with two pathologists all the slides were studied. Results The matrices whether seeded or not with autologous muscle cells were able to restore the architecture of the urethra, but were eliminated from the first week on, before incorporation. Microcirculation of the neourethra, at the end of the third month, showed the same characteristics as a normal urethra in both groups of animals. Conclusion Natural heterologous matrices implanted in the urethra as onlay graft were not incorporated into its walls but were able to fully restore the cell architecture of the organ, regardless of being seeded or not with autologous muscle
Flach, Joost; van der Waal, Mark B; van den Nieuwboer, Maurits; Claassen, Eric; Larsen, Olaf F A
2017-06-13
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, sensory properties, shelf-life and probiotic gastrointestinal tract (GIT) survival of these products are carefully balanced as they determine functionality and drive consumer acceptance. The strain-specific effects of probiotic species are imperative in this process but carrier matrices may play a pivotal role as well. This study therefore recapitulates the wealth of knowledge on carrier matrices and their interaction with probiotic strains. The most substantiated carrier matrices, factors that influence probiotic functionality and matrix effects on shelf-life, GIT survival and clinical efficacy are reviewed. Results indicate that carrier matrices have a significant impact on the quality of probiotic products. Matrix components, such as proteins, carbohydrates and flavoring agents are shown to alter probiotic efficacy and viability. In vivo studies furthermore revealed strain-dependent matrix effects on the GIT survival of probiotic bacteria. However, only a limited number of studies have specifically addressed the effects of carrier matrices on the aforementioned product-parameters; most studies seem to focus solely on the strain-specific effects of probiotic microorganisms. This hampers the innovation of probiotic products. More human studies, comparing not only different probiotic strains but different carrier matrices as well, are needed to drive the innovation cycle.
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.
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.
An investigation of proton conductivity of binary matrices sulfonated ...
Indian Academy of Sciences (India)
SPSU) and polyvinyl triazole were studied as binary matrices. The sulfonation of polysulfone was performed with trimethylsilylchlorosulfonate and high degree of sulfonation (140%) was obtained. Ion exchange capacity of SPSU was determined ...
Separation of traces of metal ions from sodium matrices
Korkisch, J.; Orlandini, K. A.
1969-01-01
Method for isolating metal ion traces from sodium matrices consists of two extractions and an ion exchange step. Extraction is accomplished by using 2-thenoyltrifluoracetone and dithizone followed by cation exchange.
Eudragit E100 and Polysaccharide Polymer Blends as Matrices for ...
African Journals Online (AJOL)
SCMC) as matrices. Methods: LB, SCMC and E100 were ... Keywords: Drug delivery, Polymer blend, Eudragit, Locust bean gum, Levodopa, Sodium carboxymethylcellulose ..... peaks and no unique peak different from those of the native polymers.
Automorphisms of sl(2) and dynamical r-matrices
Tsiganov, A V
1996-01-01
Two outer automorphisms of infinite-dimensional representations of $sl(2)$ algebra are considered. The similar constructions for the loop algebras and yangians are presented. The corresponding linear and quadratic $R$-brackets include the dynamical $r$-matrices.
On the extraction of weights from pairwise comparison matrices
Dijkstra, Theo K.
We study properties of weight extraction methods for pairwise comparison matrices that minimize suitable measures of inconsistency, 'average error gravity' measures, including one that leads to the geometric row means. The measures share essential global properties with the AHP inconsistency
Procrustes Problems for General, Triangular, and Symmetric Toeplitz Matrices
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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.
Preliminary Analysis on Matric Suction for Barren Soil
Azhar, A. T. S.; Fazlina, M. I. S.; Aziman, M.; Fairus, Y. M.; Azman, K.; Hazreek, Z. A. M.
2016-11-01
Most research conducted on slope failures can broadly be attributed to the convergence of three factors, i.e. rainfall, steepness of slope, and soil geological profile. The mechanism of the failures is mainly due to the loss of matric suction of soils by rainwater. When rainwater infiltrates into the slopes, it will start to saturate the soil, i.e., reduce the matric suction. A good understanding of landslide mechanisms and the characteristics of unsaturated soil and rock in tropical areas is crucial in landslide hazard formulation. Most of the slope failures in unsaturated tropical residual soil in Malaysia are mainly due to infiltration, especially during intense and prolonged rainfall, which reduces the soil matric suction and hence decreases the stability of the slope. Therefore, the aim of this research is to determine the matric suction for barren soil and to model an unsaturated slope with natural rainfall to evaluate the effects of matric suction on rainfall intensity. A field test was carried out using the Watermark Soil Moisture Sensor to determine the matric suction. The sensor was connected to a program called SpecWare 9 Basic which also used Data Logging Rain gauge Watermark 1120 to measure the intensity and duration of rainfall. This study was conducted at the Research Centre for Soft Soil which is a new Research and Development (R & D) initiative by Universiti Tun Hussein Onn Malaysia, Parit Raja. Field observation showed that the highest daily suction was recorded during noon while the lowest suction was obtained at night and early morning. The highest matric suction for loose condition was 31.0 kPa while the highest matric suction for compacted condition was 32.4 kPa. The results implied that the field suction variation was not only governed by the rainfall, but also the cyclic evaporation process. The findings clearly indicated that the changes in soil suction distribution patterns occurred due to different weather conditions.
Derivation of preliminary IBIS response matrices with the INTEGRAL simulator
Gotz, D.; Cremonesi, D. I.; Mereghetti, S
2001-01-01
We have used the IBIS Simulator to produce preliminary response matrices for the ISGRI and PICsIT detectors in order to help understanding their scientific performances before the calibration results are available. The derived matrices, in a format compatible with the XSPEC spectral analysis package, have been tested by fitting simple models and then used to analyze simulations of astrophysical sources with more complex spectra.
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.
Inner structure of vehicular ensembles and random matrix theory
Energy Technology Data Exchange (ETDEWEB)
Krbálek, Milan, E-mail: milan.krbalek@fjfi.cvut.cz; Hobza, Tomáš
2016-05-06
Highlights: • New class of random matrices (DUE) is proposed and analyzed in detail. • Approximation formula for level spacing distribution in DUE ensembles is analytically derived. • Connection between DUE and vehicular systems (analogical to a well-known link between GUE and Mexico buses) is presented. • It is shown that LS distribution of DUE matrices is the same as clearance distribution measured on expressways. - Abstract: We introduce a special class of random matrices (DUE) whose spectral statistics corresponds to statistics of microscopical quantities detected in vehicular flows. Comparing the level spacing distribution (for ordered eigenvalues in unfolded spectra of DUE matrices) with the time-clearance distribution extracted from various areas of the flux-density diagram (evaluated from original traffic data measured on Czech expressways with high occupancies) we demonstrate that the set of classical systems showing an universality associated with Random Matrix Ensembles can be extended by traffic systems.
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.
Inorganic Nanoparticle Nucleation on Polymer Matrices
Kosteleski, Adrian John
dressing applications. PAA's ability to nucleate nanoparticles in a solid matrix was displayed. Interestingly enough PAA retains its ability to nucleate nanoparticle even when its reactive functional groups are used in the crosslinking process. Silver nanoparticle composition and size on the solid polymer matrices was controlled by varying the composition of PAA. PAA and silver nanoparticles effect on the mechanical properties of the calcium alginate hydrogels were also studied. Physically crosslinking PAA with calcium alginate gels enables the development of intricate gel structures that are decorated with nucleated silver; yielding a composite biomaterial with improved and enhanced antimicrobial properties.
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.
Retinal pigment epithelium cell alignment on nanostructured collagen matrices.
Ulbrich, Stefan; Friedrichs, Jens; Valtink, Monika; Murovski, Simo; Franz, Clemens M; Müller, Daniel J; Funk, Richard H W; Engelmann, Katrin
2011-01-01
We investigated attachment and migration of human retinal pigment epithelial cells (primary, SV40-transfected and ARPE-19) on nanoscopically defined, two-dimensional matrices composed of parallel-aligned collagen type I fibrils. These matrices were used non-cross-linked (native) or after riboflavin/UV-A cross-linking to study cell attachment and migration by time-lapse video microscopy. Expression of collagen type I and IV, MMP-2 and of the collagen-binding integrin subunit α(2) were examined by immunofluorescence and Western blotting. SV40-RPE cells quickly attached to the nanostructured collagen matrices and aligned along the collagen fibrils. However, they disrupted both native and cross-linked collagen matrices within 5 h. Primary RPE cells aligned more slowly without destroying either native or cross-linked substrates. Compared to primary RPE cells, ARPE-19 cells showed reduced alignment but partially disrupted the matrices within 20 h after seeding. Expression of the collagen type I-binding integrin subunit α(2) was highest in SV40-RPE cells, lower in primary RPE cells and almost undetectable in ARPE-19 cells. Thus, integrin α(2) expression levels directly correlated with the degree of cell alignment in all examined RPE cell types. Specific integrin subunit α(2)-mediated matrix binding was verified by preincubation with an α(2)-function-blocking antibody, which impaired cell adhesion and alignment to varying degrees in primary and SV40-RPE cells. Since native matrices supported extended and directed primary RPE cell growth, optimizing the matrix production procedure may in the future yield nanostructured collagen matrices serving as transferable cell sheet carriers. Copyright © 2011 S. Karger AG, Basel.
An Algebraic Relation between Consimilarity and Similarity of Quaternion Matrices and Applications
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Tongsong Jiang
2014-01-01
Full Text Available This paper, by means of complex representation of a quaternion matrix, discusses the consimilarity of quaternion matrices, and obtains a relation between consimilarity and similarity of quaternion matrices. It sets up an algebraic bridge between consimilarity and similarity, and turns the theory of consimilarity of quaternion matrices into that of ordinary similarity of complex matrices. This paper also gives algebraic methods for finding coneigenvalues and coneigenvectors of quaternion matrices by means of complex representation of a quaternion matrix.
Macromolecular crowding for tailoring tissue-derived fibrillated matrices.
Magno, Valentina; Friedrichs, Jens; Weber, Heather M; Prewitz, Marina C; Tsurkan, Mikhail V; Werner, Carsten
2017-06-01
Tissue-derived fibrillated matrices can be instrumental for the in vitro reconstitution of multiphasic extracellular microenvironments. However, despite of several advantages, the obtained scaffolds so far offer a rather narrow range of materials characteristics only. In this work, we demonstrate how macromolecular crowding (MMC) - the supplementation of matrix reconstitution media with synthetic or natural macromolecules in ways to create excluded volume effects (EVE) - can be employed for tailoring important structural and biophysical characteristics of kidney-derived fibrillated matrices. Porcine kidneys were decellularized, ground and the obtained extracellular matrix (ECM) preparations were reconstituted under varied MMC conditions. We show that MMC strongly influences the fibrillogenesis kinetics and impacts the architecture and the elastic modulus of the reconstituted matrices, with diameters and relative alignment of fibrils increasing at elevated concentrations of the crowding agent Ficoll400, a nonionic synthetic polymer of sucrose. Furthermore, we demonstrate how MMC modulates the distribution of key ECM molecules within the reconstituted matrix scaffolds. As a proof of concept, we compared different variants of kidney-derived fibrillated matrices in cell culture experiments referring to specific requirements of kidney tissue engineering approaches. The results revealed that MMC-tailored matrices support the morphogenesis of human umbilical vein endothelial cells (HUVECs) into capillary networks and of murine kidney stem cells (KSCs) into highly branched aggregates. The established methodology is concluded to provide generally applicable new options for tailoring tissue-specific multiphasic matrices in vitro. Tissue-derived fibrillated matrices can be instrumental for the in vitro reconstitution of multiphasic extracellular microenvironments. However, despite of several advantages, the obtained scaffolds so far offer a rather narrow range of materials
Hypersymmetric functions and Pochhammers of 2×2 nonautonomous matrices
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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.
Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations
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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.
Osteocalcin/fibronectin-functionalized collagen matrices for bone tissue engineering.
Kim, S G; Lee, D S; Lee, S; Jang, J-H
2015-06-01
Collagen is the most abundant protein found in the extracellular matrix and is widely used to build scaffolds for biomedical applications which are the result of its biocompatibility and biodegradability. In the present study, we constructed a rhOCN/FNIII9-10 fusion protein and rhOCN/FNIII9-10-functionalized collagen matrices and investigated the potential value for bone tissue engineering. In vitro studies carried out with preosteoblastic MC3T3-E1 cells showed that rhOCN/FNIII9-10 fusion protein promoted cell adhesion and the mRNA levels of osteogenic markers including osteocalcin, runt-related transcription factor 2, alkaline phosphatase (ALP), and collagen type I. In addition, rhOCN/FNIII9-10-functionalized collagen matrices showed significant induction of the ALP activity more than rhFNIII9-10-functionalized collagen matrices or collagen matrices alone. These results suggested that rhOCN/FNIII9-10-functionalized collagen matrices have potential for bone tissue engineering. © 2014 Wiley Periodicals, Inc.
Recombinant spider silk matrices for neural stem cell cultures.
Lewicka, Michalina; Hermanson, Ola; Rising, Anna U
2012-11-01
Neural stem cells (NSCs) have the capacity to differentiate into neurons, astrocytes, and oligodendrocytes. Accordingly, NSCs hold great promise in drug screening and treatment of several common diseases. However, a major obstacle in applied stem cell research is the limitation of synthetic matrices for culturing stem cells. The objective of this study was to evaluate the suitability of recombinant spider silk (4RepCT) matrices for growth of NSCs. NSCs isolated from the cerebral cortices of mid-gestation rat embryos were cultured on either 4RepCT matrices or conventional poly-L-ornithine and fibronectin (P + F) coated polystyrene plates. From 48 h of culture, no significant differences in cell proliferation or viability were detected in NSC cultures on 4RepCT compared to control matrices (polystyrene plates coated with P + F). The NSCs retained an undifferentiated state, displaying low or no staining for markers of differentiated cells. Upon stimulation NSCs grown on 4RepCT differentiated efficiently into neuronal and astrocytic cells to virtually the same degree as control cultures, but a slightly less efficient oligodendrocyte differentiation was noted. We suggest that recombinant spider silk matrices provide a functional microenvironment and represent a useful tool for the development of new strategies in neural stem cell research. Copyright © 2012. Published by Elsevier Ltd.
What is the effect of matrices on cartilage repair? A systematic review.
Wylie, James D; Hartley, Melissa K; Kapron, Ashley L; Aoki, Stephen K; Maak, Travis G
2015-05-01
Articular cartilage has minimal endogenous ability to undergo repair. Multiple chondral restoration strategies have been attempted with varied results. The purpose of our review was to determine: (1) Does articular chondrocyte transplantation or matrix-assisted articular chondrocyte transplantation provide better patient-reported outcomes scores, MRI morphologic measurements, or histologic quality of repair tissue compared with microfracture in prospective comparative studies of articular cartilage repair; and (2) which available matrices for matrix-assisted articular chondrocyte transplantation show the best patient-reported outcomes scores, MRI morphologic measurements, or histologic quality of repair tissue? We conducted a systematic review of PubMed, CINAHL, and MEDLINE from March 2004 to February 2014 using keywords determined to be important for articular cartilage repair, including "cartilage", "chondral", "cell source", "chondrocyte", "matrix", "augment", "articular", "joint", "repair", "treatment", "regeneration", and "restoration" to find articles related to cell-based articular cartilage repair of the knee. The articles were reviewed by two authors (JDW, MKH), our study exclusion criteria were applied, and articles were determined to be relevant (or not) to the research questions. The Methodological Index for Nonrandomized Studies (MINORS) scale was used to judge the quality of nonrandomized manuscripts used in this review and the Jadad score was used to judge the quality of randomized trials. Seventeen articles were reviewed for the first research question and 83 articles were reviewed in the second research question from 301 articles identified in the original systematic search. The average MINORS score was 9.9 (62%) for noncomparative studies and 16.1 (67%) for comparative studies. The average Jadad score was 2.3 for the randomized studies. Articular chondrocyte transplantation shows better patient-reported outcomes at 5 years in patients without
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.
Parametric simulation of drug release from hydrogel-based matrices.
Lamberti, Gaetano
2012-01-01
In this work a model recently proposed to describe the drug release from hydrogel-based matrices was applied to describe the fractional drug release from matrices based on hydroxypropylmethylcellulose (HPMC) and diclofenac. The model, firstly proposed to describe the behaviour of systems based on HPMC and theophylline and a single set of preparation variables, is based on mass balances and transport phenomena evaluation and it was solved by an FEM-based numerical code. The experimental data on the HPMC-diclofenac matrices, taken from literature, have been obtained by varying the drug loading ratio, the compression force, the powder size of both the drug and the polymer. A good agreement between experimental data and model predictions, as calculated in the present work, was obtained without the use of any adjustable parameters. The predictive nature of the model has been confirmed, even changing the drug molecule and other preparative parameters. © 2011 The Author. JPP © 2011 Royal Pharmaceutical Society.
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...
Soluble organic matrices of aragonitic skeletons of Merulinidae (Cnidaria, Anthozoa).
Dauphin, Yannicke; Cuif, Jean-Pierre; Williams, C Terry
2008-05-01
Our interpretation of the overall taxonomy and evolution of the Scleractinia, the most important reef builders in tropical areas, has long depended exclusively on morphology of the calcareous skeletons. The reported series of physical and biochemical characterizations of skeletons and the mineralizing matrices extracted from the skeletons allow, for the first time, the level of biochemical diversity among corallites of the same family to be estimated. Similarities and differences observed in the micro- and nanostructures of the skeletons reflect those of the soluble organic matrices. Sulphur is mainly associated with sulphated acidic sugars. The role of sulphated sugars on the biomineralization processes is still underestimated. The resulting data suggest that environmental conditions may act on the mineralization process through the detailed compositions of the mineralizing matrices.
Microscale extraction method for HPLC carotenoid analysis in vegetable matrices
Directory of Open Access Journals (Sweden)
Sidney Pacheco
2014-10-01
Full Text Available In order to generate simple, efficient analytical methods that are also fast, clean, and economical, and are capable of producing reliable results for a large number of samples, a micro scale extraction method for analysis of carotenoids in vegetable matrices was developed. The efficiency of this adapted method was checked by comparing the results obtained from vegetable matrices, based on extraction equivalence, time required and reagents. Six matrices were used: tomato (Solanum lycopersicum L., carrot (Daucus carota L., sweet potato with orange pulp (Ipomoea batatas (L. Lam., pumpkin (Cucurbita moschata Duch., watermelon (Citrullus lanatus (Thunb. Matsum. & Nakai and sweet potato (Ipomoea batatas (L. Lam. flour. Quantification of the total carotenoids was made by spectrophotometry. Quantification and determination of carotenoid profiles were formulated by High Performance Liquid Chromatography with photodiode array detection. Microscale extraction was faster, cheaper and cleaner than the commonly used one, and advantageous for analytical laboratories.
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...
Computational Development of Jacobian Matrices for Complex Spatial Manipulators.
Goehler, Craig M; Murray, Wendy M
2012-05-01
Current methods for developing manipulator Jacobian matrices are based on traditional kinematic descriptions such as Denavit and Hartenberg parameters. The resulting symbolic equations for these matrices become cumbersome and computationally inefficient when dealing with more complex spatial manipulators, such as those seen in the field of biomechanics. This paper develops a modified method for Jacobian development based on generalized kinematic equations that incorporates partial derivatives of matrices with Leibniz's Law (the product rule). It is shown that a set of symbolic matrix functions can be derived that improve computational efficiency when used in MATLAB(®) M-Files and are applicable to any spatial manipulator. An articulated arm subassembly and a musculoskeletal model of the hand are used as examples.
Castillo-Oyagüe, Raquel; Milward, Paul J; Martín-Cerrato, Alicia; Lynch, Christopher D
2015-01-01
This study aimed to assess the reliability of the preoperative occlusal matrix technique in terms of the surface Vickers microhardness (VMH) of the underlying composite restorative material. Two hundred microhybrid composite cylinders were built up and light-cured in a single-layer step, forming two experimental groups (N = 100) according to their heights (1.5 mm/2 mm). Each group was divided into five subgroups (N = 20) depending on the matrix thickness (no matrix/0.5 mm/1 mm/2 mm/3 mm). Half the specimens per subgroup (N = 10) were randomly polymerized with a quartz-tungsten-halogen (QTH) light-curing unit (LCU). The remaining half were cured using a light-emitting diode lamp. The top and bottom samples' sides were tested for VMH at 1 hour and 24 hours post-curing using a universal VMH machine. A multiple analysis of variance with repeated measurements for the "surface" factor and the Student-Newman-Keuls test were run (α = 0.05). Bottom/top microhardness ratios were compared with the empirically accepted limit (0.8). Surface topography was analyzed under a scanning electron microscope. The thinnest matrices provided the significantly best VMH values. LCU, disc height, and time also contributed to VMH. At 24 hours, 2-mm high discs polymerized with QTH resulted in inadequate microhardness ratios when 1-mm thick to 3-mm thick matrices were used. The thinnest matrices are the most recommendable ones. The esthetics and occlusal reproducibility achieved with customized occlusal matrices fabricated before cavity preparation have been widely demonstrated. However, their effect on the physical properties of the restorations deserves further investigation. Although more studies are necessary, the thinnest matrices seem to be the most suitable to preserve the composite surface VMH and the curing depth. © 2015 Wiley Periodicals, Inc.
Parameter inference with estimated covariance matrices
Sellentin, Elena; Heavens, Alan F.
2016-02-01
When inferring parameters from a Gaussian-distributed data set by computing a likelihood, a covariance matrix is needed that describes the data errors and their correlations. If the covariance matrix is not known a priori, it may be estimated and thereby becomes a random object with some intrinsic uncertainty itself. We show how to infer parameters in the presence of such an estimated covariance matrix, by marginalizing over the true covariance matrix, conditioned on its estimated value. This leads to a likelihood function that is no longer Gaussian, but rather an adapted version of a multivariate t-distribution, which has the same numerical complexity as the multivariate Gaussian. As expected, marginalization over the true covariance matrix improves inference when compared with Hartlap et al.'s method, which uses an unbiased estimate of the inverse covariance matrix but still assumes that the likelihood is Gaussian.
Bioactive porcine matrices in heart valve tissue engineering.
Somers, Pamela; de Somer, Filip; Cornelissen, Maria; Thierens, Hubert; Van Nooten, Guido
2012-07-01
Platelet gel (PG), a storage vehicle of growth factors, can be considered for the application of growth factors in combination with mesenchymal stem cells (MSCs) to accelerate tissue regeneration. Moreover, the addition of bioactive factors to porcine aortic valves could result in a more rapid repopulation. The study aim was to load acellular porcine aortic valve matrices with the PG-rich growth factors and to evaluate the effect on MSC repopulation. Ovine mesenchymal stem cells (oMSCs) were isolated from sheep bone marrow. Acellular porcine heart valve matrices (n = 3) were preloaded with heparin and incubated with the PG for 2 h. A quantitative sandwich enzyme immunoassay was used to examine the release of basic fibroblast growth factor (bFGF) and transforming growth factor-beta (TGF-beta) from the matrices, oMSC repopulation was stimulated by static and dynamic culture. The immunoassays revealed that heparin-preloaded PG-incubated matrices showed a sustained release of 56.28 pg/ml bFGF and 30.66 ng/ml TGF-beta1 after 24 h. Dynamic culture induced oMSC invasion in growth factor-loaded matrices. Cell density results showed that dynamic culture significantly enhanced the repopulation of growth factor-loaded matrices (75 +/- 21 cells/mm2) when compared to static culture (26 +/- 10 cells/mm2). The incubation of a porcine aortic valve matrix with a PG concentrate creates a bioactive matrix. However, further fine-tuning of the PG concentration is necessary to take full advantage of platelet growth factor interaction between cells and the extracellular matrix in order to optimize cellular repopulation.
Synthesis of stiffness and mass matrices from experimental vibration modes.
Ross, R. G., Jr.
1971-01-01
With highly complex structures, it is sometimes desirable to derive a dynamic model of the system from experimental vibration data. This paper presents algorithms for synthesizing the mass and stiffness matrices from experimentally derived modal data in a way which preserves the physical significance of the individual mass and stiffness elements. The synthesizing procedures allow for the incorporation of other mass and stiffness data, whether empirical or based on the analyst's insight. The mass and stiffness matrices are derived for a cantilever beam example and are compared with those obtained using earlier techniques.
Limits on Estimating Autocorrelation Matrices from Mobile MIMO Measurements
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Tricia J. Willink
2013-01-01
Full Text Available On mobile radio links, data samples collected at successive time intervals and at closely spaced frequencies are correlated, so long data records are required to acquire sufficient independent samples for analysis. Statistical analysis of long data records is not reliable because the channel statistics remain wide-sense stationary only over short distances. This is a particular concern for MIMO systems when full autocorrelation matrices may be required for channel modelling or characterisation. MIMO channel responses from mobile measurements in an urban microcell have been used to investigate the limits on estimating autocorrelation matrices, and these are compared to those predicted by commonly used channel models.
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....
SIA matrices and non-negative stationary subdivision
Li, Xianjun
2012-01-01
This dissertation is concerned with SIA matrices and non-negative stationary subdivision, and is organized as follows: After an introducing chapter where some basic notation is given we describe, in Chapter 3, how non-negative subdivision is connected to a corresponding non-homogenous Markov process. The family of matrices A, built from the mask of the subdivision scheme, is introduced. Among other results, Lemma 3.1 and Lemma 3.2 relate the coefficients of the iterated masks to matrix produc...
Neoglucosylated collagen matrices drive neuronal cells to differentiate.
Russo, Laura; Sgambato, Antonella; Lecchi, Marzia; Pastori, Valentina; Raspanti, Mario; Natalello, Antonino; Doglia, Silvia M; Nicotra, Francesco; Cipolla, Laura
2014-04-16
Despite the relevance of carbohydrates as cues in eliciting specific biological responses, glycans have been rarely exploited in the study of neuronal physiology. We report thereby the study of the effect of neoglucosylated collagen matrices on neuroblastoma F11 cell line behavior. Morphological and functional analysis clearly showed that neoglucosylated collagen matrices were able to drive cells to differentiate. These data show for the first time that F11 cells can be driven from proliferation to differentiation without the use of chemical differentiating agents. Our work may offer to cell biologists new opportunities to study neuronal cell differentiation mechanisms in a cell environment closer to physiological conditions.
Matrices estructuradas y alta precisión relativa
Barreras Peral, Álvaro; Peña Ferrández, Juan Manuel
2014-01-01
Esta memoria se enmarca, dentro del Algebra Lineal Numérica, en el campo de estudio de métodos numéricos adaptados a clases de matrices con estructura especial, que es un campo que muestra una intensa y creciente actividad investigadora. Concretamente, considerará clases de matrices para las que se encontrarán métodos numéricos cuyo cálculo se podrá llevar a cabo con alta precisión relativa. Conseguir cálculos precisos es una propiedad muy deseable para cualquier método numérico. El ideal es ...
Taylor, Sandra L; Ruhaak, L Renee; Kelly, Karen; Weiss, Robert H; Kim, Kyoungmi
2017-03-01
With expanded access to, and decreased costs of, mass spectrometry, investigators are collecting and analyzing multiple biological matrices from the same subject such as serum, plasma, tissue and urine to enhance biomarker discoveries, understanding of disease processes and identification of therapeutic targets. Commonly, each biological matrix is analyzed separately, but multivariate methods such as MANOVAs that combine information from multiple biological matrices are potentially more powerful. However, mass spectrometric data typically contain large amounts of missing values, and imputation is often used to create complete data sets for analysis. The effects of imputation on multiple biological matrix analyses have not been studied. We investigated the effects of seven imputation methods (half minimum substitution, mean substitution, k-nearest neighbors, local least squares regression, Bayesian principal components analysis, singular value decomposition and random forest), on the within-subject correlation of compounds between biological matrices and its consequences on MANOVA results. Through analysis of three real omics data sets and simulation studies, we found the amount of missing data and imputation method to substantially change the between-matrix correlation structure. The magnitude of the correlations was generally reduced in imputed data sets, and this effect increased with the amount of missing data. Significant results from MANOVA testing also were substantially affected. In particular, the number of false positives increased with the level of missing data for all imputation methods. No one imputation method was universally the best, but the simple substitution methods (Half Minimum and Mean) consistently performed poorly. © The Author 2016. Published by Oxford University Press. For Permissions, please email: journals.permissions@oup.com.
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.
Random matrix theory for heavy-tailed time series
DEFF Research Database (Denmark)
Heiny, Johannes
2017-01-01
This paper is a review of recent results for large random matrices with heavy-tailed entries. First, we outline the development of and some classical results in random matrix theory. We focus on large sample covariance matrices, their limiting spectral distributions, the asymptotic behavior...... of their largest and smallest eigenvalues and their eigenvectors. The limits significantly depend on the finite or infiniteness of the fourth moment of the entries of the random matrix. We compare the results for these two regimes which give rise to completely different asymptotic theories. Finally, the limits...
Random matrix theory for pseudo-Hermitian systems: Cyclic blocks
Indian Academy of Sciences (India)
We discuss the relevance of random matrix theory for pseudo-Hermitian systems, and, for Hamiltonians that break parity and time-reversal invariance . In an attempt to understand the random Ising model, we present the treatment of cyclic asymmetric matrices with blocks and show that the nearest-neighbour spacing ...
Controlled growth factor release from synthetic extracellular matrices
Lee, Kuen Yong; Peters, Martin C.; Anderson, Kenneth W.; Mooney, David J.
2000-12-01
Polymeric matrices can be used to grow new tissues and organs, and the delivery of growth factors from these matrices is one method to regenerate tissues. A problem with engineering tissues that exist in a mechanically dynamic environment, such as bone, muscle and blood vessels, is that most drug delivery systems have been designed to operate under static conditions. We thought that polymeric matrices, which release growth factors in response to mechanical signals, might provide a new approach to guide tissue formation in mechanically stressed environments. Critical design features for this type of system include the ability to undergo repeated deformation, and a reversible binding of the protein growth factors to polymeric matrices to allow for responses to repeated stimuli. Here we report a model delivery system that can respond to mechanical signalling and upregulate the release of a growth factor to promote blood vessel formation. This approach may find a number of applications, including regeneration and engineering of new tissues and more general drug-delivery applications.
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.
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,…
A note on the statistical analysis of point judgment matrices
African Journals Online (AJOL)
There is scope for further research into statistical approaches for analyzing judgment matrices. In particular statistically based methods address rank reversal since standard errors are associated with estimates of the weights and thus the rankings are not stated with certainty. However, the weights are constrained to lie in a ...
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.
Nilpotent matrices and the minus partial order | Gareis | Quaestiones ...
African Journals Online (AJOL)
In this paper, {1}-inverses of a nilpotent matrix as well as matrices above a given nilpotent matrix under the minus partial order are characterized. Mathematics Subject Classication (2010): 15A09, 06A06. Key words: Generalized inverse, minus partial order, nilpotent matrix.
Investigation of drug release from carnauba wax matrices: a case ...
African Journals Online (AJOL)
A study was carried out to assess the effect of carnauba wax particle size on sustained release characteristics, the effect of drug loading on release and the kinetics of propranolol hydrochloride release from carnauba wax matrices. The results obtained showed that small particles (180 250 µ m) of carnauba wax had superior ...
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 ...
Information in Wrong Responses to the Raven Progressive Matrices
Thissen, David M.
1976-01-01
Where estimation of abilities in the lower half of the ability distribution for the Raven Progressive Matrices is important, or an increase in accuracy of ability estimation is needed, the multiple category latent trait estimation provides a rational procedure for realizing gains in accuracy from the use of information in wrong responses.…
The computation of linear triangular matrices in the finite element ...
African Journals Online (AJOL)
An algorithm is developed for generating the system matrices for the Finite Element Method of solving some classes of second order partial differential equations problems using the linear triangular elements. This algorithm reduces the complexity normally associated with the finite element approximation and makes the ...
Higgs-boson masses and mixing matrices in the NMSSM
DEFF Research Database (Denmark)
Drechsel, P.; Gröber, R.; Heinemeyer, S.
2017-01-01
We analyze the Higgs-boson masses and mixing matrices in the NMSSM based on an on-shell (OS) renormalization of the gauge-boson and Higgs-boson masses and the parameters of the top/scalar top sector. We compare the implementation of the OS calculations in the codes NMSSMCALC and NMSSM-FeynHiggs up...
A Kenya Standardization of the Raven's Coloured Progressive Matrices.
Costenbader, Virginia; Ngari, Stephen Mbugua
2001-01-01
Establishes a Kenyan standardization of the Raven's Coloured Progressive Matrices (RCPM), a nonverbal instrument widely used to assess academic aptitude in young children. Data was gathered from a sample of 1,370 children between the ages of 6 and 10 years. Using the current data, the RCPM appears to be a reliable and valid instrument for use in…
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) of locust bean gum with Eudragit® E100 and sodium carboxymethylcellulose on swelling and drug (levodopa) release from their tablet matrices. Methods: Sodium carboxymethylcellulose (SCMC), Eudragit® (E100) ...
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 ...
Technological optimization of manufacture of probiotic whey cheese matrices.
Madureira, Ana R; Brandão, Teresa; Gomes, Ana M; Pintado, Manuela E; Malcata, F Xavier
2011-03-01
In attempts to optimize their manufacture, whey cheese matrices obtained via thermal processing of whey (leading to protein precipitation) and inoculated with probiotic cultures were tested. A central composite, face-centered design was followed, so a total of 16 experiments were run using fractional addition of bovine milk to feedstock whey, homogenization time, and storage time of whey cheese as processing parameters. Probiotic whey cheese matrices were inoculated with Lactobacillus casei LAFTIL26 at 10% (v/v), whereas control whey cheese matrices were added with skim milk previously acidified with lactic acid to the same level. All whey cheeses were stored at 7 °C up to 14 d. Chemical and sensory analyses were carried out for all samples, as well as rheological characterization by oscillatory viscometry and textural profiling. As expected, differences were found between control and probiotic matrices: fractional addition of milk and storage time were the factors accounting for the most important effects. Estimation of the best operating parameters was via response surface analysis: milk addition at a rate of 10% to 15% (v/v), and homogenization for 5 min led to the best probiotic whey cheeses in terms of texture and organoleptic properties, whereas the best time for consumption was found to be by 9 d of storage following manufacture.
New r-Matrices for Lie Bialgebra Structures over Polynomials
Pop, Iulia; Yermolova-Magnusson, Julia
2010-08-01
For a finite dimensional simple complex Lie algebra {mathfrak{g}} , Lie bialgebra structures on {mathfrak{g}left[left[u right]right]} and {mathfrak{g}left[uright]} were classified by Montaner, Stolin and Zelmanov. In our paper, we provide an explicit algorithm to produce r-matrices which correspond to Lie bialgebra structures over polynomials.
More about unphysical zeroes in quark mass matrices
Directory of Open Access Journals (Sweden)
David Emmanuel-Costa
2017-01-01
Full Text Available 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.
Centrifugal seeding of mammalian cells in nonwoven fibrous matrices.
Ng, Robin; Gurm, Jesse Singh; Yang, Shang-Tian
2010-01-01
Three-dimensional (3D) cell cultures have many advantages over two-dimensional cultures. However, seeding cells in 3D scaffolds such as nonwoven fibrous polyethylene terephthalate (PET) matrices has been a challenge task in tissue engineering and cell culture bioprocessing. In this study, a centrifugal seeding method was investigated to improve the cell seeding efficiency in PET matrices with two different porosities (93% and 88%). Both the centrifugal force and centrifugation time were found to affect the seeding efficiency. With an appropriate centrifugation speed, a high 80-90% cell seeding efficiency was achieved and the time to reach this high seeding efficiency was less than 5 min. The seeding efficiency was similar for matrices with different porosities, although the optimal seeding time was significantly shorter for the low-porosity scaffold. Post seeding cell viability was demonstrated by culturing colon cancer cells seeded in PET matrices for over 5 days. The centrifugal seeding method developed in this work can be used to efficiently and uniformly seed small fibrous scaffolds for applications in 3D cell-based assays for high-throughput screening.
Rheology-Morphology Interrelationships for Nanocomposites based on Polymer Matrices
Kulichikhin, V.; Semakov, A.; Karbushev, V.; Makarova, V.; Mendes, E.; Fisher, H.; Picken, S.
2010-01-01
The main focus of this Chapter was targeted on novel approaches to compatibility of particles with polymer matrices and detail analysis of rheology-morphology interrelationships. Rather attractive method of mixing based on knowledge of rheological behavior of polymers at high shear rates was
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.
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.
A Hypothetical Learning Trajectory for Conceptualizing Matrices as Linear Transformations
Andrews-Larson, Christine; Wawro, Megan; Zandieh, Michelle
2017-01-01
In this paper, we present a hypothetical learning trajectory (HLT) aimed at supporting students in developing flexible ways of reasoning about matrices as linear transformations in the context of introductory linear algebra. In our HLT, we highlight the integral role of the instructor in this development. Our HLT is based on the "Italicizing…
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...
A simple procedure for the comparison of covariance matrices
2012-01-01
Background Comparing the covariation patterns of populations or species is a basic step in the evolutionary analysis of quantitative traits. Here I propose a new, simple method to make this comparison in two population samples that is based on comparing the variance explained in each sample by the eigenvectors of its own covariance matrix with that explained by the covariance matrix eigenvectors of the other sample. The rationale of this procedure is that the matrix eigenvectors of two similar samples would explain similar amounts of variance in the two samples. I use computer simulation and morphological covariance matrices from the two morphs in a marine snail hybrid zone to show how the proposed procedure can be used to measure the contribution of the matrices orientation and shape to the overall differentiation. Results I show how this procedure can detect even modest differences between matrices calculated with moderately sized samples, and how it can be used as the basis for more detailed analyses of the nature of these differences. Conclusions The new procedure constitutes a useful resource for the comparison of covariance matrices. It could fill the gap between procedures resulting in a single, overall measure of differentiation, and analytical methods based on multiple model comparison not providing such a measure. PMID:23171139
Convergence of GAOR Iterative Method with Strictly Diagonally Dominant Matrices
Directory of Open Access Journals (Sweden)
Guangbin Wang
2011-01-01
Full Text Available We discuss the convergence of GAOR method for linear systems with strictly diagonally dominant matrices. Moreover, we show that our results are better than ones of Darvishi and Hessari (2006, Tian et al. (2008 by using three numerical examples.
Vignati, Giulio; Chiecchio, Andrea; Osnaghi, Bianca; Giovanelli, Loredana; Meloncelli, Chiara
2008-01-01
The compatibility of immunoassay tests in different sample matrices is extremely important during the assay validation process. In this study, we investigated the interchangeability of some Access (and therefore all the UniCel Family platforms) assays between serum and plasma. We tested approximately 200 samples in parallel between serum and lithium heparin plasma for seven analytes: alpha-fetoprotein (AFP), carcino-embryonic antigen (CEA), total prostate specific antigen (tPSA), free prostate specific antigen (fPSA), digoxin, progesterone and unconjugated estriol (uE3). We used the Access2 Immunoassay System (Beckman Coulter), a fully automated random access system with a chemiluminescent signal. We performed statistical comparative analysis using two commercially available programs, Analyze-it from Microsoft Excel and MedCalc Software, and a dedicated statistical program. Firstly, we showed the results of the statistical tests performed on each population to verify their distribution. Analysis by several statistical tests (Passing and Bablok regression, Youden and Bland and Altman diagrams, the Mountain plot and multivariate analysis) showed that all the assays studied were valid in both serum and lithium heparin plasma matrices. As all Access and UniCel Family instruments use the same reagent packs, these results are transferable to all Beckman Coulter immunochemistry platforms, without a commutability problem between serum and plasma and without a need for establishment of a plasma reference interval.
Spectra of Adjacency Matrices in Networks with Extreme Introverts and Extroverts
Bassler, Kevin E.; Zia, Royce K. P.
In recent studies of networks with preferred degrees (suitable for describing social networks in which individuals tend to prefer a certain number of contacts), the XIE model of extreme introverts and extroverts was found to display remarkable collective behavior and to raise interesting theoretical issues. Though this system is defined through its dynamics, i.e., introverts/extroverts always cut/add links, the steady state turns out to be a Boltzmann-like distribution. While the intra-group links are static, the cross-links are dynamic and lead to an ensemble of bipartite graphs, with extraordinary long-ranged correlations between elements of the incidence matrix (details in JSTAT P07013, 2015). Here, we report simulation studies of a different perspective of networks, namely, the spectra associated with this ensemble of adjacency matrices. As a baseline, we first consider the spectra associated with (the adjacency matrices of) a simple random (Erdôs-Rènyi) ensemble of bipartite graphs, where simulation results can be understood analytically. Work supported by the NSF through Grants DMR-1206839 and DMR-1507371.
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.
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.
Biomimetism, biomimetic matrices and the induction of bone formation.
Ripamonti, Ugo
2009-09-01
the induction of bone formation, the emergence of the skeleton, of the vertebrates and of Homo species * Different strategies for the induction of bone formation. Biological significance of redundancy and synergistic induction of bone formation. Biomimetism and biomimetic matrices self-assembling the induction of bone formation The concavity: the shape of life and the induction of bone formation. Influence of geometry on the expression of the osteogenic phenotype. Conclusion and therapeutic perspectives on porous biomimetic matrices with intrinsic osteoinductivity Bone formation by induction initiates by invocation of osteogenic soluble molecular signals of the transforming growth factor-beta (TGF-beta) superfamily; when combined with insoluble signals or substrata, the osteogenic soluble signals trigger the ripple-like cascade of cell differentiation into osteoblastic cell lines secreting bone matrix at site of surgical implantation. A most exciting and novel strategy to initiate bone formation by induction is to carve smart self-inducing geometric concavities assembled within biomimetic constructs. The assembly of a series of repetitive concavities within the biomimetic constructs is endowed with the striking prerogative of differentiating osteoblast-like cells attached to the biomimetic matrices initiating the induction of bone formation as a secondary response. Importantly, the induction of bone formation is initiated without the exogenous application of the osteogenic soluble molecular signals of the TGF-beta superfamily. This manuscript reviews the available data on this fascinating phenomenon, i.e. biomimetic matrices that arouse and set into motion the mammalian natural ability to heal thus constructing biomimetic matrices that in their own right set into motion inductive regenerative phenomena initiating the cascade of bone differentiation by induction biomimetizing the remodelling cycle of the primate cortico-cancellous bone.
Preparation of extracellular matrices produced by cultured and primary fibroblasts
Franco-Barraza, Janusz; Beacham, Dorothy A.; Amatangelo, Michael D.; Cukierman, Edna
2016-01-01
Fibroblasts secrete and organize extracellular matrix (ECM), which provides structural support for their adhesion, migration, and tissue organization, besides regulating cellular functions such as growth and survival. Cell-to-matrix interactions are vital for vertebrate development. Disorders in these processes have been associated with fibrosis, developmental malformations, cancer, and other diseases. This unit describes a method for preparing a three-dimensional matrix derived from fibroblastic cells; the matrix is three-dimensional, cell and debris free, and attached to a two-dimensional culture surface. Cell adhesion and spreading are normal on these matrices. This matrix can also be compressed into a two-dimensional matrix and solubilized to study the matrix biochemically. Culturing fibroblasts on traditional two-dimensional (2-D) substrates induces an artificial polarity between lower and upper surfaces of these normally nonpolar cells. Not surprisingly, fibroblast morphology and migration differ once suspended in three-dimensional (3-D) collagen gels (Friedl and Brocker, 2000). However, the molecular composition of collagen gels does not mimic the natural fibroblast (i.e., mesenchymal) microenvironment. Fibroblasts secrete and organize ECM, which provides structural support for their adhesion, migration, and tissue organization, in addition to regulating cellular functions such as growth and survival (Buck and Horwitz, 1987; Hay, 1991; Hynes, 1999; Geiger et al., 2001). Cell-to-matrix interactions are vital for vertebrate development. Disorders in these processes have been associated with fibrosis, developmental malformations, cancer (i.e., desmoplastic tumor microenvironment), and other diseases (Rybinski et al., 2014). This unit describes methods for generating tissue culture surfaces coated with a fibroblast-derived 3-D ECM produced and deposited by both established and primary fibroblasts. The matrices closely resemble in vivo mesenchymal matrices and
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,
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.
Directory of Open Access Journals (Sweden)
Sun Deshu
2017-07-01
Full Text Available Some new error bounds for the linear complementarity problems are obtained when the involved matrices are weakly chained diagonally dominant B-matrices. Numerical examples are given to show the effectiveness of the proposed bounds.
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
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.
Recommendations on the use and design of risk matrices
DEFF Research Database (Denmark)
Duijm, Nijs Jan
2015-01-01
Risk matrices are widely used in risk management. They are a regular feature in various risk management standards and guidelines and are also used as formal corporate risk acceptance criteria. It is only recently, however, that scientific publications have appeared that discuss the weaknesses...... of the risk matrix. The objective of this paper is to explore these weaknesses, and provide recommendations for the use and design of risk matrices. The paper reviews the few relevant publications and adds some observations of its own in order to emphasize existing recommendations and add some suggestions...... of its own. The recommendations cover a range of issues, among them: the relation between coloring the risk matrix and the definition of risk and major hazard aversion; the qualitative, subjective assessment of likelihood and consequence; the scaling of the discrete likelihood and consequence categories...
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.
Optical detection of parasitic protozoa in sol-gel matrices
Livage, Jacques; Barreau, J. Y.; Da Costa, J. M.; Desportes, I.
1994-10-01
Whole cell parasitic protozoa have been entrapped within sol-gel porous silica matrices. Stationary phase promastigote cells of Leishmania donovani infantum are mixed with a silica sol before gelation occurs. They remain trapped within the growing oxide network and their cellular organization appears to be well preserved. Moreover protozoa retain their antigenic properties in the porous gel. They are still able to detect parasite specific antibodies in serum samples from infected patients via an enzyme linked immunosorbent assay (ELISA). Antigen- antibody associations occurring in the gel are optically detected via the reactions of a peroxidase conjugate with ortho-phenylenediamine leading to the formation of a yellow coloration. A clear-cut difference in optical density is measured between positive and negative sera. Such an entrapment of antigenic species into porous sol-gel matrices avoids the main problems due to non specific binding and could be advantageously used in diagnostic kits.
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.
The degeneracy of the genetic code and Hadamard matrices
Petoukhov, Sergey V
2008-01-01
The matrix form of the presentation of the genetic code is described as the cognitive form to analyze structures of the genetic code. A similar matrix form is utilized in the theory of signal processing. The Kronecker family of the genetic matrices is investigated, which is based on the genetic matrix [C A; U G], where C, A, U, G are the letters of the genetic alphabet. This matrix in the third Kronecker power is the (8*8)-matrix, which contains 64 triplets. Peculiarities of the degeneracy of the vertebrate mitochondria genetic code are reflected in the symmetrical black-and-white mosaic of this genetic (8*8)-matrix. This mosaic matrix is connected algorithmically with Hadamard matrices unexpectedly, which are famous in the theory of signal processing, quantum mechanics and quantum computers.
Construction of fermion mass matrices yielding two popular neutrino scenarios
Albright, Carl H.; Nandi, Satyanarayan
1995-07-01
A new procedure proposed recently enables one to start from the quark and lepton mass and mixing data at the low scale and construct mass matrices which exhibit a simple SO(10) structure at the supersymmetric-grand-unification scale. We elaborate here on the numerical details which lead us to an SO(10) model for the quark and lepton mass matrices that explains the known quark data at the low scale along with the observed depletions of solar and atmospheric neutrinos. We also apply the procedure to a second scenario incorporating the solar-neutrino depletion and a 7 eV τ neutrino for the cocktail model of mixed dark matter but find the SO(10) model deduced in this case does not exhibit as simple a structure as that observed for the first scenario.
Joint product numerical range and geometry of reduced density matrices
Chen, Jianxin; Guo, Cheng; Ji, Zhengfeng; Poon, Yiu-Tung; Yu, Nengkun; Zeng, Bei; Zhou, Jie
2016-01-01
The reduced density matrices of a many-body quantum system form a convex set, whose three-dimensional projection $\\Theta$ is convex in $\\mathbb{R}^3$. The boundary $\\partial\\Theta$ of $\\Theta$ may exhibit nontrivial geometry, in particular ruled surfaces. Two physical mechanisms are known for the origins of ruled surfaces: symmetry breaking and gapless. In this work, we study the emergence of ruled surfaces for systems with local Hamiltonians in infinite spatial dimension, where the reduced d...
Partitioning Rectangular and Structurally Nonsymmetric Sparse Matrices for Parallel Processing
Energy Technology Data Exchange (ETDEWEB)
B. Hendrickson; T.G. Kolda
1998-09-01
A common operation in scientific computing is the multiplication of a sparse, rectangular or structurally nonsymmetric matrix and a vector. In many applications the matrix- transpose-vector product is also required. This paper addresses the efficient parallelization of these operations. We show that the problem can be expressed in terms of partitioning bipartite graphs. We then introduce several algorithms for this partitioning problem and compare their performance on a set of test matrices.
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 $B+C$.
Algorithms for Finding Inverse of Two Patterned Matrices over Zp
Directory of Open Access Journals (Sweden)
Xiaoyu Jiang
2014-01-01
Full Text Available Circulant matrix families have become an important tool in network engineering. In this paper, two new patterned matrices over Zp which include row skew first-plus-last right circulant matrix and row first-plus-last left circulant matrix are presented. Their basic properties are discussed. Based on Newton-Hensel lifting and Chinese remaindering, two different algorithms are obtained. Moreover, the cost in terms of bit operations for each algorithm is given.
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, β2-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.
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.
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...
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
A norm inequality for pairs of commuting positive semidefinite matrices
Audenaert, Koenraad M. R.
2014-01-01
For $k=1,\\ldots,K$, let $A_k$ and $B_k$ be positive semidefinite matrices such that, for each $k$, $A_k$ commutes with $B_k$. We show that, for any unitarily invariant norm, \\[ |||\\sum_{k=1}^K A_kB_k||| \\le ||| (\\sum_{k=1}^K A_k)\\;(\\sum_{k=1}^K B_k)|||. \\
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.
Linear programming with positive semi-definite matrices
Directory of Open Access Journals (Sweden)
J. B. Lasserre
1996-01-01
Full Text Available We consider the general linear programming problem over the cone of positive semi-definite matrices. We first provide a simple sufficient condition for existence of optimal solutions and absence of a duality gap without requiring existence of a strictly feasible solution. We then simply characterize the analogues of the standard concepts of linear programming, i.e., extreme points, basis, reduced cost, degeneracy, pivoting step as well as a Simplex-like algorithm.
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
Interactions between Food Additive Silica Nanoparticles and Food Matrices.
Go, Mi-Ran; Bae, Song-Hwa; Kim, Hyeon-Jin; Yu, Jin; Choi, Soo-Jin
2017-01-01
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-grade NPs.
Vashaghian, Mahshid; Zandieh-Doulabi, Behrouz; Roovers, Jan-Paul; Smit, Theodoor Henri
2016-12-01
Electrospun matrices are proposed as an alternative for polypropylene meshes in reconstructive pelvic surgery. Here, we investigated the effect of fiber diameter on (1) the mechanical properties of electrospun poly (lactic-co-glycolic acid)-blended-poly(caprolactone) (PLGA/PCL) matrices; (2) cellular infiltration; and (3) the newly formed extracellular matrix (ECM) in vitro. We compared electrospun matrices with 1- and 8 μm fiber diameter and used nonporous PLGA/PCL films as controls. The 8-μm matrices were almost twice as stiff as the 1-μm matrices with 1.38 and 0.66 MPa, respectively. Matrices had the same ultimate tensile strength, but with 80% the 1-μm matrices were much more ductile than the 8-μm ones (18%). Cells infiltrated deeper into the matrices with larger pores, but cellular activity was comparable on both substrates. New ECM was deposited faster on the electrospun samples, but after 2 and 4 weeks the amount of collagen was comparable with that on nonporous films. The ECM deposited on the 1-μm matrices, and the nonporous film was about three times stiffer than the ECM found on the 8-μm matrices. Cell behavior in terms of myofibroblastic differentiation and remodeling was similar on the 1-μm matrices and nonporous films, in comparison to that on the 8-μm matrices. We conclude that electrospinning enhances the integration of host cells as compared with a nonporous film of the same material. The 1-μm matrices result in better mechanical behavior and qualitatively better matrix production than the 8-μm matrices, but with limited cellular infiltration. These data are useful for designing electrospun matrices for the pelvic floor.
Maximal-entropy random walk unifies centrality measures
Ochab, J. K.
2012-12-01
This paper compares a number of centrality measures and several (dis-)similarity matrices with which they can be defined. These matrices, which are used among others in community detection methods, represent quantities connected to enumeration of paths on a graph and to random walks. Relationships between some of these matrices are derived in the paper. These relationships are inherited by the centrality measures. They include measures based on the principal eigenvector of the adjacency matrix, path enumeration, as well as on the stationary state, stochastic matrix, or mean first-passage times of a random walk. As the random walk defining the centrality measure can be arbitrarily chosen, we pay particular attention to the maximal-entropy random walk, which serves as a very distinct alternative to the ordinary (diffusive) random walk used in network analysis. The various importance measures, defined both with the use of ordinary random walk and the maximal-entropy random walk, are compared numerically on a set of benchmark graphs with varying mixing parameter and are grouped with the use of the agglomerative clustering technique. It is shown that centrality measures defined with the two different random walks cluster into two separate groups. In particular, the group of centrality measures defined by the maximal-entropy random walk does not cluster with any other measures on change of graphs’ parameters, and members of this group produce mutually closer results than members of the group defined by the ordinary random walk.
Maximal-entropy random walk unifies centrality measures.
Ochab, J K
2012-12-01
This paper compares a number of centrality measures and several (dis-)similarity matrices with which they can be defined. These matrices, which are used among others in community detection methods, represent quantities connected to enumeration of paths on a graph and to random walks. Relationships between some of these matrices are derived in the paper. These relationships are inherited by the centrality measures. They include measures based on the principal eigenvector of the adjacency matrix, path enumeration, as well as on the stationary state, stochastic matrix, or mean first-passage times of a random walk. As the random walk defining the centrality measure can be arbitrarily chosen, we pay particular attention to the maximal-entropy random walk, which serves as a very distinct alternative to the ordinary (diffusive) random walk used in network analysis. The various importance measures, defined both with the use of ordinary random walk and the maximal-entropy random walk, are compared numerically on a set of benchmark graphs with varying mixing parameter and are grouped with the use of the agglomerative clustering technique. It is shown that centrality measures defined with the two different random walks cluster into two separate groups. In particular, the group of centrality measures defined by the maximal-entropy random walk does not cluster with any other measures on change of graphs' parameters, and members of this group produce mutually closer results than members of the group defined by the ordinary random walk.
Rate matrices for analyzing large families of protein sequences.
Devauchelle, C; Grossmann, A; Hénaut, A; Holschneider, M; Monnerot, M; Risler, J L; Torrésani, B
2001-01-01
We propose and study a new approach for the analysis of families of protein sequences. This method is related to the LogDet distances used in phylogenetic reconstructions; it can be viewed as an attempt to embed these distances into a multidimensional framework. The proposed method starts by associating a Markov matrix to each pairwise alignment deduced from a given multiple alignment. The central objects under consideration here are matrix-valued logarithms L of these Markov matrices, which exist under conditions that are compatible with fairly large divergence between the sequences. These logarithms allow us to compare data from a family of aligned proteins with simple models (in particular, continuous reversible Markov models) and to test the adequacy of such models. If one neglects fluctuations arising from the finite length of sequences, any continuous reversible Markov model with a single rate matrix Q over an arbitrary tree predicts that all the observed matrices L are multiples of Q. Our method exploits this fact, without relying on any tree estimation. We test this prediction on a family of proteins encoded by the mitochondrial genome of 26 multicellular animals, which include vertebrates, arthropods, echinoderms, molluscs, and nematodes. A principal component analysis of the observed matrices L shows that a single rate model can be used as a rough approximation to the data, but that systematic deviations from any such model are unmistakable and related to the evolutionary history of the species under consideration.
Investigation of Polycaprolactone Matrices for Intravaginal Delivery of Doxycycline.
Pathak, Meenakshi; Coombes, Allan G A; Turner, Mark S; Palmer, Cheryn; Wang, Dongjie; Steadman, Kathryn J
2015-12-01
Polycaprolactone (PCL) matrices loaded with doxycycline were produced by rapidly cooling suspensions of the drug powder in PCL solution in acetone. Drug loadings of 5%, 10%, and 15% (w/w) of the PCL content were achieved. Exposure of doxycycline powder to matrix processing conditions in the absence of PCL revealed an endothermic peak at 65°C with the main peak at 167°C, suggesting solvatomorph formation. Rapid "burst release" of 24%-32% was measured within 24 h when matrices were immersed in simulated vaginal fluid (SVF) at 37°C, because of the presence of drug at or close to the matrix surface, which is further confirmed by scanning electron microscopy. Gradual release of 66%-76% of the drug content occurred over the following 14 days. SVF containing doxycycline released from drug-loaded PCL matrices retained 81%-90% antimicrobial activity compared with the nonformulated drug. The concentrations of doxycycline predicted to be released into vaginal fluid from a PCL matrix in the form of an intravaginal ring would be sufficient to kill Neisseria gonorrhoea and many other pathogens. These results indicate that PCL may be a suitable polymer for controlled intravaginal delivery of doxycycline for the treatment of sexually transmitted infections. © 2015 Wiley Periodicals, Inc. and the American Pharmacists Association.
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.
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.
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.
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.
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...
Biomimetic matrices self-initiating the induction of bone formation.
Ripamonti, Ugo; Roden, Laura C; Ferretti, Carlo; Klar, Roland M
2011-09-01
The new strategy of tissue engineering, and regenerative medicine at large, is to construct biomimetic matrices to mimic nature's hierarchical structural assemblages and mechanisms of simplicity and elegance that are conserved throughout genera and species. There is a direct spatial and temporal relationship of morphologic and molecular events that emphasize the biomimetism of the remodeling cycles of the osteonic corticocancellous bone versus the "geometric induction of bone formation," that is, the induction of bone by "smart" concavities assembled in biomimetic matrices of macroporous calcium phosphate-based constructs. The basic multicellular unit of the corticocancellous bone excavates a trench across the bone surface, leaving in its wake a hemiosteon rather than an osteon, that is, a trench with cross-sectional geometric cues of concavities after cyclic episodes of osteoclastogenesis, eventually leading to osteogenesis. The concavities per se are geometric regulators of growth-inducing angiogenesis and osteogenesis as in the remodeling processes of the corticocancellous bone. The concavities act as a powerful geometric attractant for myoblastic/myoendothelial and/or endothelial/pericytic stem cells, which differentiate into bone-forming cells. The lacunae, pits, and concavities cut by osteoclastogenesis within the biomimetic matrices are the driving morphogenetic cues that induce bone formation in a continuum of sequential phases of resorption/dissolution and formation. To induce the cascade of bone differentiation, the soluble osteogenic molecular signals of the transforming growth factor β supergene family must be reconstituted with an insoluble signal or substratum that triggers the bone differentiation cascade. By carving a series of repetitive concavities into solid and/or macroporous biomimetic matrices of highly crystalline hydroxyapatite or biphasic hydroxyapatite/β-tricalcium phosphate, we were able to embed smart biologic functions within
Inner structure of vehicular ensembles and random matrix theory
Krbálek, Milan; Hobza, Tomáš
2016-05-01
We introduce a special class of random matrices (DUE) whose spectral statistics corresponds to statistics of microscopical quantities detected in vehicular flows. Comparing the level spacing distribution (for ordered eigenvalues in unfolded spectra of DUE matrices) with the time-clearance distribution extracted from various areas of the flux-density diagram (evaluated from original traffic data measured on Czech expressways with high occupancies) we demonstrate that the set of classical systems showing an universality associated with Random Matrix Ensembles can be extended by traffic systems.
Invertibility and Explicit Inverses of Circulant-Type Matrices with k-Fibonacci and k-Lucas Numbers
Directory of Open Access Journals (Sweden)
Zhaolin Jiang
2014-01-01
Full Text Available Circulant matrices have important applications in solving ordinary differential equations. In this paper, we consider circulant-type matrices with the k-Fibonacci and k-Lucas numbers. We discuss the invertibility of these circulant matrices and present the explicit determinant and inverse matrix by constructing the transformation matrices, which generalizes the results in Shen et al. (2011.
Experimental electron binding energies for thulium in different matrices
Energy Technology Data Exchange (ETDEWEB)
Inoyatov, A.Kh., E-mail: inoyatov@jinr.ru [Laboratory of Nuclear Problems, JINR, Dubna, Moscow Region (Russian Federation); Institute of Applied Physics, National University, Tashkent (Uzbekistan); Kovalík, A. [Laboratory of Nuclear Problems, JINR, Dubna, Moscow Region (Russian Federation); Nuclear Physics Institute of the ASCR, CZ-25068 Řež near Prague (Czech Republic); Filosofov, D.V. [Laboratory of Nuclear Problems, JINR, Dubna, Moscow Region (Russian Federation); Ryšavý, M. [Nuclear Physics Institute of the ASCR, CZ-25068 Řež near Prague (Czech Republic); Perevoshchikov, L.L.; Yushkevich, Yu.V. [Laboratory of Nuclear Problems, JINR, Dubna, Moscow Region (Russian Federation); Zbořil, M. [Institut für Kernphysik, Westfälische Wilhelms-Universität Münster, D-48149 Münster (Germany)
2015-07-15
Highlights: • The thulium L, M, N, O, and P subshell electron binding energies determined. • Five different matrices of the radioactive {sup 169}Yb atoms used in the investigation. • The greatest difference of 4.5 ± 0.1 eV in the average observed between the matrices. • The published N{sub 1}, N{sub 3}, and O{sub 2,3} values found to be higher by about 3 eV. • Natural widths of the thulium K, L, M, N, and O subshells also determined. - Abstract: The L{sub 1}, L{sub 2}, L{sub 3}, M{sub 1}, M{sub 2}, N{sub 1}, N{sub 3}, O{sub 1}, O{sub 2}, O{sub 3}, and P{sub 1} subshell electron binding energies (related to the Fermi level) in thulium generated by the electron capture decay of radioactive {sup 169}Yb atoms implanted at 30 keV into polycrystalline platinum and aluminum foils and deposited by vacuum evaporation on surfaces of polycrystalline platinum, carbon, and aluminum foils were determined by the internal conversion electron spectroscopy. The greatest differences in the electron binding energies (4.5 ± 0.1 eV in the average without the P{sub 1} shell and 7.0 ± 0.5 eV for the P{sub 1} shell alone) were found between the matrices of the evaporated ytterbium layer on the aluminum foil and the bulk of the high purity polycrystalline platinum. The thulium electron binding energies in the matrices of the evaporated ytterbium layers on both the platinum and carbon foils and in the aluminum bulk were observed to be the same within the experimental uncertainties. The N{sub 1}, N{sub 3}, and O{sub 2,3} electron binding energies most frequently presented in data compilations were found to be higher by about 3 eV. Natural widths of most of the K, L{sub 1}, L{sub 2}, L{sub 3}, M{sub 1}, M{sub 2}, M{sub 3}, N{sub 1}, N{sub 3}, and O{sub 1} subshells in Tm in the investigated matrices were also determined. No significant differences in the natural widths were found among the matrices. The results obtained demonstrate that the physicochemical surrounding of the
Energy Technology Data Exchange (ETDEWEB)
Zepon, Karine Modolon [CIMJECT, Departamento de Engenharia Mecânica, Universidade Federal de Santa Catarina, 88040-900 Florianópolis, SC (Brazil); TECFARMA, Universidade do Sul de Santa Catarina, 88704-900 Tubarão, SC (Brazil); Petronilho, Fabricia [FICEXP, Universidade do Sul de Santa Catarina, 88704-900 Tubarão, SC (Brazil); Soldi, Valdir [POLIMAT, Universidade Federal de Santa Catarina, 88040-900 Florianópolis, SC (Brazil); Salmoria, Gean Vitor [CIMJECT, Departamento de Engenharia Mecânica, Universidade Federal de Santa Catarina, 88040-900 Florianópolis, SC (Brazil); Kanis, Luiz Alberto, E-mail: luiz.kanis@unisul.br [TECFARMA, Universidade do Sul de Santa Catarina, 88704-900 Tubarão, SC (Brazil)
2014-11-01
The production and evaluation of cornstarch/cellulose acetate/silver sulfadiazine extrudate matrices are reported herein. The matrices were melt extruded under nine different conditions, altering the temperature and the screw speed values. The surface morphology of the matrices was examined by scanning electron microscopy. The micrographs revealed the presence of non-melted silver sulfadiazine microparticles in the matrices extruded at lower temperature and screw speed values. The thermal properties were evaluated and the results for both the biopolymer and the drug indicated no thermal degradation during the melt extrusion process. The differential scanning analysis of the extrudate matrices showed a shift to lower temperatures for the silver sulfadiazine melting point compared with the non-extruded drug. The starch/cellulose acetate matrices containing silver sulfadiazine demonstrated significant inhibition of the growth of Pseudomonas aeruginosa and Staphylococcus aureus. In vivo inflammatory response tests showed that the extrudate matrices, with or without silver sulfadiazine, did not trigger chronic inflammatory processes. - Highlights: • Melt extruded bio-based matrices containing silver sulfadiazine was produced. • The silver sulfadiazine is stable during melt-extrusion. • The extrudate matrices shown bacterial growth inhibition. • The matrices obtained have potential to development wound healing membranes.
Directory of Open Access Journals (Sweden)
Shiao-Wen Tsai
2014-01-01
Full Text Available In this study, we utilized a mandrel rotating collector consisting of two parallel, electrically conductive pieces of tape to fabricate aligned electrospun polycaprolactone/gelatin (PG and carbon nanotube/polycaprolactone/gelatin (PGC nanofibrous matrices. Furthermore, we examined the biological performance of the PGC nanofibrous and film matrices using an in vitro culture of RT4-D6P2T rat Schwann cells. Using cell adhesion tests, we found that carbon nanotube inhibited Schwann cell attachment on PGC nanofibrous and film matrices. However, the proliferation rates of Schwann cells were higher when they were immobilized on PGC nanofibrous matrices compared to PGC film matrices. Using western blot analysis, we found that NRG1 and P0 protein expression levels were higher for cells immobilized on PGC nanofibrous matrices compared to PG nanofibrous matrices. However, the carbon nanotube inhibited NRG1 and P0 protein expression in cells immobilized on PGC film matrices. Moreover, the NRG1 and P0 protein expression levels were higher for cells immobilized on PGC nanofibrous matrices compared to PGC film matrices. We found that the matrix topography and composition influenced Schwann cell behavior.
Reproducible quantitative proteotype data matrices for systems biology.
Röst, Hannes L; Malmström, Lars; Aebersold, Ruedi
2015-11-05
Historically, many mass spectrometry-based proteomic studies have aimed at compiling an inventory of protein compounds present in a biological sample, with the long-term objective of creating a proteome map of a species. However, to answer fundamental questions about the behavior of biological systems at the protein level, accurate and unbiased quantitative data are required in addition to a list of all protein components. Fueled by advances in mass spectrometry, the proteomics field has thus recently shifted focus toward the reproducible quantification of proteins across a large number of biological samples. This provides the foundation to move away from pure enumeration of identified proteins toward quantitative matrices of many proteins measured across multiple samples. It is argued here that data matrices consisting of highly reproducible, quantitative, and unbiased proteomic measurements across a high number of conditions, referred to here as quantitative proteotype maps, will become the fundamental currency in the field and provide the starting point for downstream biological analysis. Such proteotype data matrices, for example, are generated by the measurement of large patient cohorts, time series, or multiple experimental perturbations. They are expected to have a large effect on systems biology and personalized medicine approaches that investigate the dynamic behavior of biological systems across multiple perturbations, time points, and individuals. © 2015 Röst et al. This article is distributed by The American Society for Cell Biology under license from the author(s). Two months after publication it is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).
Edgington, Eugene
2007-01-01
Statistical Tests That Do Not Require Random Sampling Randomization Tests Numerical Examples Randomization Tests and Nonrandom Samples The Prevalence of Nonrandom Samples in Experiments The Irrelevance of Random Samples for the Typical Experiment Generalizing from Nonrandom Samples Intelligibility Respect for the Validity of Randomization Tests Versatility Practicality Precursors of Randomization Tests Other Applications of Permutation Tests Questions and Exercises Notes References Randomized Experiments Unique Benefits of Experiments Experimentation without Mani
Analytical stiffness matrices with Green-Lagrange strain measure
DEFF Research Database (Denmark)
Pedersen, Pauli
2005-01-01
a solution based on Green-Lagrange strain measure. The approach is especially useful in design optimization, because analytical sensitivity analysis then can be performed. The case of a three node triangular ring element for axisymmetric analysis involves small modifications and extension to four node......Separating the dependence on material and stress/strain state from the dependence on initial geometry, we obtain analytical secant and tangent stiffness matrices. For the case of a linear displacement triangle with uniform thickness and uniform constitutive behaviour closed-form results are listed...
Geometrical Inverse Preconditioning for Symmetric Positive Definite Matrices
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Jean-Paul Chehab
2016-07-01
Full Text Available We focus on inverse preconditioners based on minimizing F ( X = 1 − cos ( X A , I , where X A is the preconditioned matrix and A is symmetric and positive definite. We present and analyze gradient-type methods to minimize F ( X on a suitable compact set. For this, we use the geometrical properties of the non-polyhedral cone of symmetric and positive definite matrices, and also the special properties of F ( X on the feasible set. Preliminary and encouraging numerical results are also presented in which dense and sparse approximations are included.
On spectral distribution of high dimensional covariation matrices
DEFF Research Database (Denmark)
Heinrich, Claudio; Podolskij, Mark
In this paper we present the asymptotic theory for spectral distributions of high dimensional covariation matrices of Brownian diffusions. More specifically, we consider N-dimensional Itô integrals with time varying matrix-valued integrands. We observe n equidistant high frequency data points...... of the underlying Brownian diffusion and we assume that N/n -> c in (0,oo). We show that under a certain mixed spectral moment condition the spectral distribution of the empirical covariation matrix converges in distribution almost surely. Our proof relies on method of moments and applications of graph theory....
Applying weighted network measures to microarray distance matrices
Ahnert, S. E.; Garlaschelli, D.; Fink, T. M. A.; Caldarelli, G.
2008-06-01
In recent work we presented a new approach to the analysis of weighted networks, by providing a straightforward generalization of any network measure defined on unweighted networks. This approach is based on the translation of a weighted network into an ensemble of edges, and is particularly suited to the analysis of fully connected weighted networks. Here we apply our method to several such networks including distance matrices, and show that the clustering coefficient, constructed by using the ensemble approach, provides meaningful insights into the systems studied. In the particular case of two datasets from microarray experiments the clustering coefficient identifies a number of biologically significant genes, outperforming existing identification approaches.
Applying weighted network measures to microarray distance matrices
Energy Technology Data Exchange (ETDEWEB)
Ahnert, S E [Theory of Condensed Matter Group, Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE (United Kingdom); Garlaschelli, D [Dipartimento di Fisica, Universita di Siena, Via Roma 56, 53100 Siena (Italy); Fink, T M A [Institut Curie, CNRS UMR 144, 26 rue d' Ulm, 75248 Paris (France); Caldarelli, G [INFM-CNR Istituto dei Sistemi Complessi and Dipartimento di Fisica Universita di Roma ' La Sapienza' Piazzale Moro 2, 00185 Roma (Italy)
2008-06-06
In recent work we presented a new approach to the analysis of weighted networks, by providing a straightforward generalization of any network measure defined on unweighted networks. This approach is based on the translation of a weighted network into an ensemble of edges, and is particularly suited to the analysis of fully connected weighted networks. Here we apply our method to several such networks including distance matrices, and show that the clustering coefficient, constructed by using the ensemble approach, provides meaningful insights into the systems studied. In the particular case of two datasets from microarray experiments the clustering coefficient identifies a number of biologically significant genes, outperforming existing identification approaches.
Geometries and interpolations for symmetric positive definite matrices
DEFF Research Database (Denmark)
Feragen, Aasa; Fuster, Andrea
2017-01-01
In this survey we review classical and recently proposed Riemannian metrics and interpolation schemes on the space of symmetric positive definite (SPD) matrices. We perform simulations that illustrate the problem of tensor fattening not only in the usually avoided Frobenius metric, but also...... the visualization of scale and shape variation in tensorial data. With the paper, we will release a software package with Matlab scripts for computing the interpolations and statistics used for the experiments in the paper (Code is available at https://sites.google.com/site/aasaferagen/home/software)....
Thermal Expansion Behavior of Hot-Pressed Engineered Matrices
Raj, S. V.
2016-01-01
Advanced engineered matrix composites (EMCs) require that the coefficient of thermal expansion (CTE) of the engineered matrix (EM) matches those of the fiber reinforcements as closely as possible in order to reduce thermal compatibility strains during heating and cooling of the composites. The present paper proposes a general concept for designing suitable matrices for long fiber reinforced composites using a rule of mixtures (ROM) approach to minimize the global differences in the thermal expansion mismatches between the fibers and the engineered matrix. Proof-of-concept studies were conducted to demonstrate the validity of the concept.
Altland, Alexander; Fyodorov, Yan V; O'Connell, Neil; Cugliandolo, Leticia F
2017-01-01
Many of the distinctive and useful phenomena of soft matter come from its interaction with interfaces. Examples are the peeling of a strip of adhesive tape, the coating of a surface, the curling of a fiber via capillary forces, or the collapse of a porous sponge. These interfacial phenomena are distinct from the intrinsic behavior of a soft material like a gel or a microemulsion. Yet many forms of interfacial phenomena can be understood via common principles valid for many forms of soft matter. Our goal in organizing this school was to give students a grasp of these common principles and their many ramifications and possibilities. The Les Houches Summer School comprised over fifty 90-minute lectures over four weeks. Four four-lecture courses by Howard Stone, Michael Cates, David Nelson and L. Mahadevan served as an anchor for the program. A number of shorter courses and seminars rounded out the school. This volume collects the lecture notes of the school.
The Restricted Isometry Property for Time-Frequency Structured Random Matrices
2011-06-16
Madrid, Spain (2006) [10] Candès, E.J.: The restricted isometry property and its implications for compressed sensing. preprint (2008) [11] Candès...M. Fornasier (ed.) Theo- retical Foundations and Numerical Methods for Sparse Recovery, Radon Series Comp. Appl. Math., vol. 9, pp. 1–92. deGruyter
Brownian Motion in a Weyl Chamber, Non-Colliding Particles, and Random Matrices
Grabiner, David J.
1997-01-01
Let $n$ particles move in standard Brownian motion in one dimension, with the process terminating if two particles collide. This is a specific case of Brownian motion constrained to stay inside a Weyl chamber; the Weyl group for this chamber is $A_{n-1}$, the symmetric group. For any starting positions, we compute a determinant formula for the density function for the particles to be at specified positions at time $t$ without having collided by time $t$. We show that the probability that ther...
Fractional random walk lattice dynamics
Michelitsch, T. M.; Collet, B. A.; Riascos, A. P.; Nowakowski, A. F.; Nicolleau, F. C. G. A.
2017-02-01
We analyze time-discrete and time-continuous ‘fractional’ random walks on undirected regular networks with special focus on cubic periodic lattices in n = 1, 2, 3,.. dimensions. The fractional random walk dynamics is governed by a master equation involving fractional powers of Laplacian matrices {{L}\\fracα{2}}} where α =2 recovers the normal walk. First we demonstrate that the interval 0<α ≤slant 2 is admissible for the fractional random walk. We derive analytical expressions for the transition matrix of the fractional random walk and closely related the average return probabilities. We further obtain the fundamental matrix {{Z}(α )} , and the mean relaxation time (Kemeny constant) for the fractional random walk. The representation for the fundamental matrix {{Z}(α )} relates fractional random walks with normal random walks. We show that the matrix elements of the transition matrix of the fractional random walk exihibit for large cubic n-dimensional lattices a power law decay of an n-dimensional infinite space Riesz fractional derivative type indicating emergence of Lévy flights. As a further footprint of Lévy flights in the n-dimensional space, the transition matrix and return probabilities of the fractional random walk are dominated for large times t by slowly relaxing long-wave modes leading to a characteristic {{t}-\\frac{n{α}} -decay. It can be concluded that, due to long range moves of fractional random walk, a small world property is emerging increasing the efficiency to explore the lattice when instead of a normal random walk a fractional random walk is chosen.
A note on open-chain transfer matrices from q-deformed su(2 vertical stroke 2)S-matrices
Energy Technology Data Exchange (ETDEWEB)
Murgan, R. [Physics Department, Gustavus Adolphus College, St. Peter, MN (United States)
2009-09-15
In this note, we perform Sklyanin's construction of commuting open-chain/boundary transfer matrices to the q-deformed SU(2 vertical stroke 2) bulk S-matrix of Beisert and Koroteev and a corresponding boundary S-matrix. This also includes a corresponding commuting transfer matrix using the graded version of the q-deformed bulk S-matrix. Utilizing the crossing property for the bulk S-matrix, we argue that the transfer matrix for both graded and non-graded versions contains a crucial factor which is essential for commutativity. (Abstract Copyright [2009], Wiley Periodicals, Inc.)
Spectroscopic Studies on Graphenes Dispersed Within Polymeric Matrices
Ferreira, Filipe; Brito, Felipe; Chipara, Dorina; Ajayan, Pullickel; Francisco, Wesley; Chipara, Cristian; Simonetti, Evelyn; Cartwright, Charles; Cividanes, Luciana; Hinthorne, James; Thim, Gilmar; Vajtai, Robert; Chipara, Mircea; Instituto Tecnológico de Aeronáutica Collaboration; University of Texas Pan American Collaboration; Rice University Collaboration
Graphenes have been dispersed within various polymeric matrices (polyethylene, polyethylene oxide, polystyrene, and epoxy resins). Some have been used as purchased (pristine and functionalized graphene platelets from Cheap Tubes). Pristine and functionalized graphene oxides have been obtained in laboratory according to W. Hummers, R. Offeman, (''Preparation of Graphitic Oxide''. J Am Chem Soc 80, 6, 1339, 1958) and by original functionalization processes. All these samples were investigated by Raman spectroscopy using a Renishaw InVia spectrometer operating at 532 and 785 nm. Additional information has been obtained by Wide Angle X-Ray Scattering using a Bruker Discover 8 spectrometer. Raman spectra have been fitted by a convolution of modified Breit-Wigner-Fano line shapes and the main parameters (position, intensity, width, asymmetry factor) of each line are discussed. The research aims to a better identification of graphene related nanostructures isolated or dispersed within polymeric matrices by Raman spectroscopy. FAPESP (Grant 2013/20218-0) and CNPq (Grant 141197/2014 5) for financial support, LAS/INPE and LEFE/UNESP for collaboration.
Behavior of metal oxide nanoparticles in natural aqueous matrices
Keller, A. A.; Zhou, D.; Wang, H.
2009-12-01
The increasing use of nanomaterials in consumer products that are exposed to environmental media has led to a need to understand their fate and transport. In particular, metal oxide (MeO) nanoparticles, such as TiO2, ZnO and CeO2, are increasingly incorporated into a wide range of products, from sunscreens to paints and other coatings, and catalysts. With regard to their transport, it is important to determine how far these nanoparticles will travel in different ambient waters, such as rivers, lakes and seawater. There have been a number of studies that have addressed the aggregation of different nanoparticles in simpler aqueous solutions. However, it is important to understand the combined effect of pH, ionic strength, ionic composition, NOM and other characteristics of the aqueous media in which the nanoparticles will be dispersed, which may result in either aggregation and settling, or stabilization and transport. This also affects the bioavailability of the nanomaterials, and the phase (water column or sediments) in which the bulk of the particles are likely to reside. For this study we considered several natural aqueous matrices, including seawater, freshwater, groundwater, rainwater and treated wastewater, as well as two different water matrices used in micro- and mesocosm studies of nanoparticle toxicity. We determined that the two most important water quality characteristics controlling the rate of aggregation, relatively independent of particle composition, are [NOM] and ionic strength.
Response matrices of NE213 scintillation detectors for neutrons
Energy Technology Data Exchange (ETDEWEB)
Guldbakke, S.; Klein, H. [Physikalisch-Technische Bundesanstalt, Braunschweig (Germany); Meister, A.; Scheler, U.; Unholzer, S. [Technical Univ., Dresden (Germany); Pulpan, J.; Tichy, M. [Inst. of Radiation Dosimetry, Prague (Czech Republic)
1994-12-31
Four NE213 detectors of different size have been calibrated at the accelerator facility of the PTB. The response functions were experimentally determined for 33 neutron energies between 1 MeV and 16 MeV and compared with Monte Carlo simulations using the NRESP7 code. The light output functions for recoil protons were found to be significantly different for all detectors even if they were of the same size. The neutron fluence determined on the basis of the response functions calculated with the corresponding light output functions agreed to better than {+-}2% with reference values if energy independent adjustment factors between 0.98 and 1.03 were applied. The response matrices required for the unfolding of neutron induced pulse height spectra were therefore calculated with the NRESP7 code taking into account the adjustment factors. Similarly, the response matrices for photons were calculated with the EGS4 code, but without any adjustment. Finally, the DIFBAS code was applied for the unfolding of pure neutron- and photon-induced pulse height spectra. The resulting spectral fluences are in reasonable agreement with the results obtained by time-of-flight measurements and by spectrometry with a Ge detector.
Efficient modified Chebyshev differentiation matrices for fractional differential equations
Dabiri, Arman; Butcher, Eric A.
2017-09-01
This paper compares several fractional operational matrices for solving a system of linear fractional differential equations (FDEs) of commensurate or incommensurate order. For this purpose, three fractional collocation differentiation matrices (FCDMs) based on finite differences are first proposed and compared with Podlubny's matrix previously used in the literature, after which two new efficient FCDMs based on Chebyshev collocation are proposed. It is shown via an error analysis that the use of the well-known property of fractional differentiation of polynomial bases applied to these methods results in a limitation in the size of the obtained Chebyshev-based FCDMs. To compensate for this limitation, a new fast spectrally accurate FCDM for fractional differentiation which does not require the use of the gamma function is proposed. Then, the Schur-Pade and Schur decomposition methods are implemented to enhance and improve numerical stability. Therefore, this method overcomes the previous limitation regarding the size limitation. In several illustrative examples, the convergence and computation time of the proposed FCDMs are compared and their advantages and disadvantages are outlined.
Joint product numerical range and geometry of reduced density matrices
Chen, Jianxin; Guo, Cheng; Ji, Zhengfeng; Poon, Yiu-Tung; Yu, Nengkun; Zeng, Bei; Zhou, Jie
2017-02-01
The reduced density matrices of a many-body quantum system form a convex set, whose three-dimensional projection Θ is convex in R3. The boundary ∂Θ of Θ may exhibit nontrivial geometry, in particular ruled surfaces. Two physical mechanisms are known for the origins of ruled surfaces: symmetry breaking and gapless. In this work, we study the emergence of ruled surfaces for systems with local Hamiltonians in infinite spatial dimension, where the reduced density matrices are known to be separable as a consequence of the quantum de Finetti's theorem. This allows us to identify the reduced density matrix geometry with joint product numerical range Π of the Hamiltonian interaction terms. We focus on the case where the interaction terms have certain structures, such that a ruled surface emerges naturally when taking a convex hull of Π. We show that, a ruled surface on ∂Θ sitting in Π has a gapless origin, otherwise it has a symmetry breaking origin. As an example, we demonstrate that a famous ruled surface, known as the oloid, is a possible shape of Θ, with two boundary pieces of symmetry breaking origin separated by two gapless lines.
Raven's colored progressive matrices (CPM - basic metric characteristics and norms
Directory of Open Access Journals (Sweden)
Fajgelj Stanislav
2007-01-01
Full Text Available Principal measuring characteristics and norms of Raven’s colored matrices were determined on the sample of 2.334 children from Vojvodina at the age of 3.5 and 11. The basic metric characteristics were determined according to classical test theory (CTT and item response theory (IRT. By testing a dimensionality it was showed that the test had one main object of measuring. The norms were also evaluated in terms of their precision in statistical and psychometric sense. It was found that there was no statistically significant difference in solving the test requirements between boys and girls at any age, nor was there any significant interaction of gender and age. Reliability of the test at the age group of 6 - 11 was over 0.85, at the age of 5 it was 0.75, whereas at the youngest age it was only 0.59. The complete test was too easy at older ages due to the Flynn’s effect. It is owing to this reason that a conclusion can be drawn that there’s a big question mark over its application at the age of 11,and even 10. It is recommended that standard Raven’s matrices should be used at that age. .
Single-channel noise reduction using optimal rectangular filtering matrices.
Long, Tao; Chen, Jingdong; Benesty, Jacob; Zhang, Zhenxi
2013-02-01
This paper studies the problem of single-channel noise reduction in the time domain and presents a block-based approach where a vector of the desired speech signal is recovered by filtering a frame of the noisy signal with a rectangular filtering matrix. With this formulation, the noise reduction problem becomes one of estimating an optimal filtering matrix. To achieve such estimation, a method is introduced to decompose a frame of the clean speech signal into two orthogonal components: One correlated and the other uncorrelated with the current desired speech vector to be estimated. Different optimization cost functions are then formulated from which non-causal optimal filtering matrices are derived. The relationships among these optimal filtering matrices are discussed. In comparison with the classical sample-based technique that uses only forward prediction, the block-based method presented in this paper exploits both the forward and backward prediction as well as the temporal interpolation and, therefore, can improve the noise reduction performance by fully taking advantage of the speech property of self correlation. There is also a side advantage of this block-based method as compared to the sample-based technique, i.e., it is computationally more efficient and, as a result, more suitable for practical implementation.
Permuting sparse rectangular matrices into block-diagonal form
Energy Technology Data Exchange (ETDEWEB)
Aykanat, Cevdet; Pinar, Ali; Catalyurek, Umit V.
2002-12-09
This work investigates the problem of permuting a sparse rectangular matrix into block diagonal form. Block diagonal form of a matrix grants an inherent parallelism for the solution of the deriving problem, as recently investigated in the context of mathematical programming, LU factorization and QR factorization. We propose graph and hypergraph models to represent the nonzero structure of a matrix, which reduce the permutation problem to those of graph partitioning by vertex separator and hypergraph partitioning, respectively. Besides proposing the models to represent sparse matrices and investigating related combinatorial problems, we provide a detailed survey of relevant literature to bridge the gap between different societies, investigate existing techniques for partitioning and propose new ones, and finally present a thorough empirical study of these techniques. Our experiments on a wide range of matrices, using state-of-the-art graph and hypergraph partitioning tools MeTiS and PaT oH, revealed that the proposed methods yield very effective solutions both in terms of solution quality and run time.
Characterization of a New Heat Dissipation Matric Potential Sensor
Directory of Open Access Journals (Sweden)
Rolf Krebs
2013-01-01
Full Text Available Soil moisture sensors can help to reduce the amount of water needed for irrigation. In this paper we describe the PlantCare soil moisture sensor as a new type of heat dissipation sensor, its calibration and the correction for temperature changes. With the PlantCare sensor it is possible to measure the matric potential indirectly to monitor or control irrigation. This sensor is based on thermal properties of a synthetic felt. After a defined heating phase the cooling time to a threshold temperature is a function of the water content in the synthetic felt. The water content in this porous matrix is controlled by the matric potential in the surrounding soil. Calibration measurements have shown that the sensor is most sensitive to −400 hPa and allows lower sensitivity measurements to −800 hPa. The disturbing effect of the temperature change during the measurement on the cooling time can be corrected by a linear function and the differences among sensors are minimized by a two point calibration.
Simulations and spectra of water in CO matrices.
Escribano, Rafael; Artacho, Emilio; Kouchi, Akira; Hama, Tetusya; Kimura, Yuki; Hidaka, Hiroshi; Watanabe, Naoki
2017-03-08
Models for the inclusion of water molecules in carbon monoxide matrices are developed using density functional theory applied to amorphous solid systems. The models cover a large range of systems for smaller or larger CO matrices with different water content, consisting of either individual H2O molecules or small clusters linked by H-bonds. The vibrational spectra of the samples are predicted at the minimum of their potential energy surface. The spectra allow instances where the water molecules remain isolated or form aggregates to be discerned, and they also provide an indication of the strength of the H-bonding, when present. The calculations support recent experimental observations that linked IR bands at 3707 cm-1 and 3617 cm-1 to the presence of unbound water molecules in water-poor CO/H2O mixed ices. Assignment of some observed bands to water dimers or trimers is suggested as well. The residual static pressure in fixed-volume simulation cells is also calculated.
Functional Brain Network Classification With Compact Representation of SICE Matrices.
Zhang, Jianjia; Zhou, Luping; Wang, Lei; Li, Wanqing
2015-06-01
Recently, a sparse inverse covariance estimation (SICE) technique has been employed to model functional brain connectivity. The inverse covariance matrix (SICE matrix in short) estimated for each subject is used as a representation of brain connectivity to discriminate Alzheimers disease from normal controls. However, we observed that direct use of the SICE matrix does not necessarily give satisfying discrimination, due to its high dimensionality and the scarcity of training subjects. Looking into this problem, we argue that the intrinsic dimensionality of these SICE matrices shall be much lower, considering 1) an SICE matrix resides on a Riemannian manifold of symmetric positive definiteness matrices, and 2) human brains share common patterns of connectivity across subjects. Therefore, we propose to employ manifold-based similarity measures and kernel-based PCA to extract principal connectivity components as a compact representation of brain network. Moreover, to cater for the requirement of both discrimination and interpretation in neuroimage analysis, we develop a novel preimage estimation algorithm to make the obtained connectivity components anatomically interpretable. To verify the efficacy of our method and gain insights into SICE-based brain networks, we conduct extensive experimental study on synthetic data and real rs-fMRI data from the ADNI dataset. Our method outperforms the comparable methods and improves the classification accuracy significantly.
A Class of Non Invertible Matrices in GF (2) for Practical One Way Hash Algorithm
Berisha, Artan; Baxhaku, Behar; Alidema, Artan
2012-01-01
In this paper, we describe non invertible matrix in GF(2)which can be used as multiplication matrix in Hill Cipher technique for one way hash algorithm. The matrices proposed are permutation matrices with exactly one entry 1 in each row and each column and 0 elsewhere. Such matrices represent a permutation of m elements. Since the invention, Hill cipher algorithm was used for symmetric encryption, where the multiplication matrix is the key. The Hill cipher requires the inverse of the matrix t...
Efecto de pseudopolirrotaxanos como nanorrefuerzos en matrices poliméricas
Xu, Qunwei
2012-01-01
En este trabajo, nos centraremos en las matrices poliméricas, las cuales pueden ser de tres tipos: Termoestables, Termoplásticas y Elastoméricas. De ellas, particularmente nos centraremos sólo en el uso de las matrices termoestables (diglicidiléter de bisfenol A (DGEBA)) y las matrices termoplásticas (polimetilmetacrilato (PMMA)). Ingeniería Industrial
Improved Hidden Clique Detection by Optimal Linear Fusion of Multiple Adjacency Matrices
2015-11-30
Improved Hidden Clique Detection by Optimal Linear Fusion of Multiple Adjacency Matrices (Invited Paper) Himanshu Nayar∗, Rajmonda S. Caceres†, Kelly...where we are a given multiple Erdős- Renyi modeled adjacency matrices containing a common hidden or planted clique. The objective is to combine them...probability—we adopt a linear fusion model in which we analyze a convex combination of the adjacency matrices of the graphs. Within this context, we
Comparing Implementations of a Calculator for Exact Real Number Computation
Directory of Open Access Journals (Sweden)
José Raymundo Marcial-Romero
2012-01-01
Full Text Available Al ser uno de los primeros lenguajes de programación teóricos para el cómputo con números reales, Real PCF demostró ser impráctico debido a los constructores paralelos que necesita para el cálculo de funciones básicas. Posteriormente, se propuso LRT como una variante de Real PCF el cual evita el uso de constructores paralelos introduciendo un constructor no determinista dentro del lenguaje. En este artículo se presenta la implementación de una calculadora para el cómputo con números reales exactos basada en LRT y se compara su eficacia con una aplicación de números reales estándar en un lenguaje de programación imperativo. Finalmente, la implementación se compara con una implementación estándar de computación de números reales exactos, basada en la representación de dígitos con signo, que a su vez se basa sobre la computación de números reales exactos.
p-Absolutely summable sequences of fuzzy real numbers
Directory of Open Access Journals (Sweden)
Ayhan Esi
2013-03-01
Full Text Available In this paper the fuzzy sequence space is introduced and some algebraic properties such as solidness, symmetricalness, convergence free and sequence algebra are studied, and some inclusion relations for the space are provided.
Hagiwara, Tomomichi
2011-08-01
This article introduces what we call block checker matrices with some specific structures characterised by a set of integers, and then introduces the permutation matrices called block checker/diagonal (BCD) transformation matrices that relate block checker matrices with block diagonal matrices through similarity transformations. The study is motivated by the importance of the fast-lifting technique in control theory, especially in the study of sampled-data systems and time-delay systems. More precisely, it is partly motivated by the desire for alleviating the bother of describing the class of the matrices commuting with block diagonal matrices, and for such a purpose the permutation with BCD transformation matrices is helpful. The study further extends to investigating the various useful properties among BCD transformation matrices, as well as their interplay relations with various variants of fast-lifting, e.g. full-vector fast-lifting and subvector-wise fast-lifting, or one-stage fast-lifting and two-stage fast-lifting. The usefulness of the results in the context of the fast-lifting treatment is also suggested.
Kyrpychova, Liubov; Carr, Richard A; Martinek, Petr; Vanecek, Tomas; Perret, Raul; Chottová-Dvořáková, Magdalena; Zamecnik, Michal; Hadravsky, Ladislav; Michal, Michal; Kazakov, Dmitry V
2017-06-01
Basal cell carcinoma (BCC) with matrical differentiation is a fairly rare neoplasm, with about 30 cases documented mainly as isolated case reports. We studied a series of this neoplasm, including cases with an atypical matrical component, a hitherto unreported feature. Lesions coded as BCC with matrical differentiation were reviewed; 22 cases were included. Immunohistochemical studies were performed using antibodies against BerEp4, β-catenin, and epithelial membrane antigen (EMA). Molecular genetic studies using Ion AmpliSeq Cancer Hotspot Panel v2 by massively parallel sequencing on Ion Torrent PGM were performed in 2 cases with an atypical matrical component (1 was previously subjected to microdissection to sample the matrical and BCC areas separately). There were 13 male and 9 female patients, ranging in age from 41 to 89 years. Microscopically, all lesions manifested at least 2 components, a BCC area (follicular germinative differentiation) and areas with matrical differentiation. A BCC component dominated in 14 cases, whereas a matrical component dominated in 4 cases. Matrical differentiation was recognized as matrical/supramatrical cells (n=21), shadow cells (n=21), bright red trichohyaline granules (n=18), and blue-gray corneocytes (n=18). In 2 cases, matrical areas manifested cytologic atypia, and a third case exhibited an infiltrative growth pattern, with the tumor metastasizing to a lymph node. BerEP4 labeled the follicular germinative cells, whereas it was markedly reduced or negative in matrical areas. The reverse pattern was seen with β-catenin. EMA was negative in BCC areas but stained a proportion of matrical/supramatrical cells. Genetic studies revealed mutations of the following genes: CTNNB1, KIT, CDKN2A, TP53, SMAD4, ERBB4, and PTCH1, with some differences between the matrical and BCC components. It is concluded that matrical differentiation in BCC in most cases occurs as multiple foci. Rare neoplasms manifest atypia in the matrical areas
Pieper, J S; van der Kraan, P M; Hafmans, T; Kamp, J; Buma, P; van Susante, J L C; van den Berg, W B; Veerkamp, J H; van Kuppevelt, T H
2002-08-01
The limited intrinsic repair capacity of articular cartilage has stimulated continuing efforts to develop tissue engineered analogues. Matrices composed of type II collagen and chondroitin sulfate (CS), the major constituents of hyaline cartilage, may create an appropriate environment for the generation of cartilage-like tissue. In this study, we prepared, characterized, and evaluated type 11 collagen matrices with and without CS. Type II collagen matrices were prepared using purified, pepsin-treated, type II collagen. Techniques applied to prepare type I collagen matrices were found unsuitable for type II collagen. Crosslinking of collagen and covalent attachment of CS was performed using 1-ethyl-3-(3-dimethyl aminopropyl)carbodiimide. Porous matrices were prepared by freezing and lyophilization, and their physico-chemical characteristics (degree of crosslinking, denaturing temperature, collagenase-resistance, amount of CS incorporated) established. Matrices were evaluated for their capacity to sustain chondrocyte proliferation and differentiation in vitro. After 7 d of culture, chondrocytes were mainly located at the periphery of the matrices. In contrast to type I collagen, type II collagen supported the distribution of cells throughout the matrix. After 14 d of culture, matrices were surfaced with a cartilagenous-like layer, and occasionally clusters of chondrocytes were present inside the matrix. Chondrocytes proliferated and differentiated as indicated by biochemical analyses, ultrastructural observations, and reverse transcriptase PCR for collagen types I, II and X. No major differences were observed with respect to the presence or absence of CS in the matrices.
Data depth and rank-based tests for covariance and spectral density matrices
Chau, Joris
2017-06-26
In multivariate time series analysis, objects of primary interest to study cross-dependences in the time series are the autocovariance or spectral density matrices. Non-degenerate covariance and spectral density matrices are necessarily Hermitian and positive definite, and our primary goal is to develop new methods to analyze samples of such matrices. The main contribution of this paper is the generalization of the concept of statistical data depth for collections of covariance or spectral density matrices by exploiting the geometric properties of the space of Hermitian positive definite matrices as a Riemannian manifold. This allows one to naturally characterize most central or outlying matrices, but also provides a practical framework for rank-based hypothesis testing in the context of samples of covariance or spectral density matrices. First, the desired properties of a data depth function acting on the space of Hermitian positive definite matrices are presented. Second, we propose two computationally efficient pointwise and integrated data depth functions that satisfy each of these requirements. Several applications of the developed methodology are illustrated by the analysis of collections of spectral matrices in multivariate brain signal time series datasets.
A Conceptual Cost Benefit Analysis of Tailings Matrices Use in Construction Applications
Directory of Open Access Journals (Sweden)
Mahmood Ali A.
2016-01-01
Full Text Available As part of a comprehensive research program, new tailings matrices are formulated of combinations of tailings and binder materials. The research program encompasses experimental and numerical analysis of the tailings matrices to investigate the feasibility of using them as construction materials in cold climates. This paper discusses a conceptual cost benefit analysis for the use of these new materials. It is shown here that the financial benefits of using the proposed new tailings matrices in terms of environmental sustainability are much higher when compared to normal sand matrices.
Sericin-carboxymethyl cellulose porous matrices as cellular wound dressing material.
Nayak, Sunita; Kundu, S C
2014-06-01
In this study, porous three-dimensional (3D) hydrogel matrices are fabricated composed of silk cocoon protein sericin of non-mulberry silkworm Antheraea mylitta and carboxymethyl cellulose. The matrices are prepared via freeze-drying technique followed by dual cross-linking with glutaraldehyde and aluminum chloride. The microstructure of the hydrogel matrices is assessed using scanning electron microscopy and biophysical characterization are carried out using Fourier transform infrared spectroscopy and X-ray diffraction. The transforming growth factor β1 release from the cross-linked matrices as a growth factor is evaluated by immunosorbent assay. Live dead assay and 3-[4,5-dimethylthiazolyl-2]-2,5-diphenyl tetrazolium bromide assay show no cytotoxicity of blended matrices toward human keratinocytes. The matrices support the cell attachment and proliferation of human keratinocytes as observed through scanning electron microscope and confocal images. Gelatin zymography demonstrates the low levels of matrix metalloproteinase 2 (MMP-2) and insignificant amount of MMP-9 in the culture media of cell seeded matrices. Low inflammatory response of the matrices is indicated through tumor necrosis factor alpha release assay. The results indicate that the fabricated matrices constitute 3D cell-interactive environment for tissue engineering applications and its potential use as a future cellular biological wound dressing material. © 2013 Wiley Periodicals, Inc.
Laminin active peptide/agarose matrices as multifunctional biomaterials for tissue engineering.
Yamada, Yuji; Hozumi, Kentaro; Aso, Akihiro; Hotta, Atsushi; Toma, Kazunori; Katagiri, Fumihiko; Kikkawa, Yamato; Nomizu, Motoyoshi
2012-06-01
Cell adhesive peptides derived from extracellular matrix components are potential candidates to afford bio-adhesiveness to cell culture scaffolds for tissue engineering. Previously, we covalently conjugated bioactive laminin peptides to polysaccharides, such as chitosan and alginate, and demonstrated their advantages as biomaterials. Here, we prepared functional polysaccharide matrices by mixing laminin active peptides and agarose gel. Several laminin peptide/agarose matrices showed cell attachment activity. In particular, peptide AG73 (RKRLQVQLSIRT)/agarose matrices promoted strong cell attachment and the cell behavior depended on the stiffness of agarose matrices. Fibroblasts formed spheroid structures on the soft AG73/agarose matrices while the cells formed a monolayer with elongated morphologies on the stiff matrices. On the stiff AG73/agarose matrices, neuronal cells extended neuritic processes and endothelial cells formed capillary-like networks. In addition, salivary gland cells formed acini-like structures on the soft matrices. These results suggest that the peptide/agarose matrices are useful for both two- and three-dimensional cell culture systems as a multifunctional biomaterial for tissue engineering. Copyright Â© 2012 Elsevier Ltd. All rights reserved.
Random matrix theory for pseudo-Hermitian systems: Cyclic blocks
Indian Academy of Sciences (India)
tems, and, for Hamiltonians that break parity P and time-reversal invariance T. In an attempt to understand the ... Keywords. Random matrices; circulants; quantum chaos; PT symmetry; pseudo-. Hermiticity. ... local fluctuation properties of complex quantum systems have universal properties, independent of the details of the ...
Optimum allocation in multivariate stratified random sampling: Stochastic matrix optimisation
Diaz-Garcia, Jose A.; Ramos-Quiroga, Rogelio
2011-01-01
The allocation problem for multivariate stratified random sampling as a problem of stochastic matrix integer mathematical programming is considered. With these aims the asymptotic normality of sample covariance matrices for each strata is established. Some alternative approaches are suggested for its solution. An example is solved by applying the proposed techniques.
Extreme eigenvalues of sample covariance and correlation matrices
DEFF Research Database (Denmark)
Heiny, Johannes
of the problem at hand. We develop a theory for the point process of the normalized eigenvalues of the sample covariance matrix in the case where rows and columns of the data are linearly dependent. Based on the weak convergence of this point process we derive the limit laws of various functionals......This thesis is concerned with asymptotic properties of the eigenvalues of high-dimensional sample covariance and correlation matrices under an infinite fourth moment of the entries. In the first part, we study the joint distributional convergence of the largest eigenvalues of the sample covariance...... matrix of a p-dimensional heavy-tailed time series when p converges to infinity together with the sample size n. We generalize the growth rates of p existing in the literature. Assuming a regular variation condition with tail index
Extreme eigenvalues of sample covariance and correlation matrices
DEFF Research Database (Denmark)
Heiny, Johannes
2017-01-01
dimension of the problem at hand. We develop a theory for the point process of the normalized eigenvalues of the sample covariance matrix in the case where rows and columns of the data are linearly dependent. Based on the weak convergence of this point process we derive the limit laws of various functionals......This thesis is concerned with asymptotic properties of the eigenvalues of high-dimensional sample covariance and correlation matrices under an infinite fourth moment of the entries. In the first part, we study the joint distributional convergence of the largest eigenvalues of the sample covariance...... matrix of a $p$-dimensional heavy-tailed time series when $p$ converges to infinity together with the sample size $n$. We generalize the growth rates of $p$ existing in the literature. Assuming a regular variation condition with tail index $\\alpha
Physicochemical and numerical modeling of electrokinetics in inhomogenous matrices
DEFF Research Database (Denmark)
Paz-Garcia, Juan Manuel
, for example, that formation of gypsum is a limiting factor in the desalination of sulfate-contaminated bricks or stones, and that there is a connection between the presence of magnesium and the capacity of buffering the alkaline front produced in the cathodic reaction. 2.Using the chemical equilibrium model...... and the surface charge, but also the chemical equilibrium condition between the chemical species in the electrolyte. Apart from this new approach for the distribution of species under chemical equilibrium conditions, some conclusions were drawn from the simulations. For example, concentration profiles for the non...... into porous solid matrices of different kinds. These techniques are typically denoted as electrokinetic treatments. In these kind of electrochemically-induced transport processes, the driving force is related the concentration gradients and the unbalanced in ionic charge produced by the electrochemical...
Tissue fluorescence origins evaluation using excitation-emission matrices
Zhelyazkova, A.; Borisova, E.; Angelova, L.; Pavlova, E.; Keremedchiev, M.; Avramov, L.
2015-01-01
Autofluorescence has been proven to be a very sensitive, accurate, noninvasive method for detection of early pathological changes in tissues. This optical method has the potential to provide a real-time diagnosis of different benign, dysplastic and malignant tissue pathologies. We obtain tissue samples after surgical excision of preliminary clinically diagnosed tumours. Ethical approval for our investigations is received from Ethical Committee of University Hospital "Queen Jiovanna-ISUL" - Sofia, where the samples will be obtained as well. The investigations presented in this report are based on ex vivo measurements of excitation-emission matrices (EEM) for normal and neoplastic human tissue samples with various cutaneous malignant and dysplastic lesions, as well for gastrointestinal tract (GIT) normal mucosa, polyps and carcinoma. The origins of the endogenous fluorescence are found and the differences observed are discussed from the point of view of their diagnostic value and correlation with the morphological and biochemical changes occurred during the tumour development.
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.
Noncrossing Monochromatic Subtrees and Staircases in 0-1 Matrices
Directory of Open Access Journals (Sweden)
Siyuan Cai
2014-01-01
Full Text Available The following question is asked by the senior author (Gyárfás (2011. What is the order of the largest monochromatic noncrossing subtree (caterpillar that exists in every 2-coloring of the edges of a simple geometric Kn,n? We solve one particular problem asked by Gyárfás (2011: separate the Ramsey number of noncrossing trees from the Ramsey number of noncrossing double stars. We also reformulate the question as a Ramsey-type problem for 0-1 matrices and pose the following conjecture. Every n×n 0-1 matrix contains n−1 zeros or n−1 ones, forming a staircase: a sequence which goes right in rows and down in columns, possibly skipping elements, but not at turning points. We prove this conjecture in some special cases and put forward some related problems as well.
Use of Doehlert matrices for study of poliovirus-1 adsorption.
Quignon, F; Huyard, A; Schwartzbrod, L; Thomas, F
1997-10-01
Experiments designed according to Doehlert matrices were carried out to study poliovirus-1 adsorption to Na-montmorillonite in a complex aqueous environment. Salt concentration and valence, virus load, clay concentration, and organic matter concentration were included in the design as selected parameters for possible or known involvement in viral adsorption in environmental waters. Use of this experimental design not only allowed to detect and quantify direct influence of the tested parameters upon the viral response, but also to reveal the influence of interactions between these tested factors. Thus, beyond the reassessment of the higher efficiency of multivalent cations on virus adsorption, as opposed to monovalent ones, detection was enabled of a tannic acid/aluminium specific interaction that seemed to be responsible for the nonavailability of these elements for interaction with viruses. Such a statistical tool allows for a gain in experimental accuracy beyond technical improvements and is particularly suited for low-cost study of multifactorial phenomena.
Uranium Metal Reaction Behavior in Water, Sludge, and Grout Matrices
Energy Technology Data Exchange (ETDEWEB)
Delegard, Calvin H.; Schmidt, Andrew J.
2008-09-25
This report summarizes information and data on the reaction behavior of uranium metal in water, in water-saturated simulated and genuine K Basin sludge, and in grout matrices. This information and data are used to establish the technical basis for metallic uranium reaction behavior for the K Basin Sludge Treatment Project (STP). The specific objective of this report is to consolidate the various sources of information into a concise document to serve as a high-level reference and road map for customers, regulators, and interested parties outside the STP (e.g., external reviewers, other DOE sites) to clearly understand the current basis for the corrosion of uranium metal in water, sludge, and grout.
Uranium Metal Reaction Behavior in Water, Sludge, and Grout Matrices
Energy Technology Data Exchange (ETDEWEB)
Delegard, Calvin H.; Schmidt, Andrew J.
2009-05-27
This report summarizes information and data on the reaction behavior of uranium metal in water, in water-saturated simulated and genuine K Basin sludge, and in grout matrices. This information and data are used to establish the technical basis for metallic uranium reaction behavior for the K Basin Sludge Treatment Project (STP). The specific objective of this report is to consolidate the various sources of information into a concise document to serve as a high-level reference and road map for customers, regulators, and interested parties outside the STP (e.g., external reviewers, other DOE sites) to clearly understand the current basis for the corrosion of uranium metal in water, sludge, and grout.
Buckling of Fiber Reinforced Composite Plates with Nanofiber Reinforced Matrices
Chamis, Christos C.; Murthy, Pappu L. N.
2010-01-01
Anisotropic composite plates were evaluated with nanofiber reinforced matrices (NFRM). The nanofiber reinforcement volumes ratio in the matrix was 0.01. The plate dimensions were 20 by 10 by 1.0 in. (508 by 254 by 25.4 mm). Seven different loading condition cases were evaluated: three for uniaxial loading, three for pairs of combined loading, and one with three combined loadings. The anisotropy arose from the unidirectional plates having been at 30 from the structural axis. The anisotropy had a full 6 by 6 rigidities matrix which were satisfied and solved by a Galerkin buckling algorithm. The buckling results showed that the NFRM plates buckled at about twice those with conventional matrix.
Multigroup covariance matrices for fast-reactor studies
Energy Technology Data Exchange (ETDEWEB)
Smith, J.D. III; Broadhead, B.L.
1981-04-01
This report presents the multigroup covariance matrices based on the ENDF/B-V nuclear data evaluations. The materials and reactions have been chosen according to the specifications of ORNL-5517. Several cross section covariances, other than those specified by that report, are included due to the derived nature of the uncertainty files in ENDF/B-V. The materials represented are Ni, Cr, /sup 16/O, /sup 12/C, Fe, Na, /sup 235/U, /sup 238/U, /sup 239/Pu, /sup 240/Pu, /sup 241/Pu, and /sup 10/B (present due to its correlation to /sup 238/U). The data have been originally processed into a 52-group energy structure by PUFF-II and subsequently collapsed to smaller subgroup strutures. The results are illustrated in 52-group correlation matrix plots and tabulated into thirteen groups for convenience.
Harmonic R Matrices for Scattering Amplitudes and Spectral Regularization
Ferro, Livia; Łukowski, Tomasz; Meneghelli, Carlo; Plefka, Jan; Staudacher, Matthias
2013-03-01
Planar N=4 supersymmetric Yang-Mills theory appears to be integrable. While this allows one to find this theory’s exact spectrum, integrability has hitherto been of no direct use for scattering amplitudes. To remedy this, we deform all scattering amplitudes by a spectral parameter. The deformed tree-level four-point function turns out to be essentially the one-loop R matrix of the integrable N=4 spin chain satisfying the Yang-Baxter equation. Deformed on-shell three-point functions yield novel three-leg R matrices satisfying bootstrap equations. Finally, we supply initial evidence that the spectral parameter might find its use as a novel symmetry-respecting regulator replacing dimensional regularization. Its physical meaning is a local deformation of particle helicity, a fact which might be useful for a much larger class of nonintegrable four-dimensional field theories.
Electrospun Phospholipid Fibers as Micro-Encapsulation and Antioxidant Matrices
Directory of Open Access Journals (Sweden)
Elhamalsadat Shekarforoush
2017-10-01
Full Text Available 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 within phospholipid fibers. Release studies in aqueous media revealed that the phenolic bioactives were released mainly due to swelling of the phospholipid fiber matrix over time. The above studies confirm the efficacy of electrospun phospholipid microfibers as encapsulation and antioxidant systems.
Electrospun Phospholipid Fibers as Micro-Encapsulation and Antioxidant Matrices.
Shekarforoush, Elhamalsadat; Mendes, Ana C; Baj, Vanessa; Beeren, Sophie R; Chronakis, Ioannis S
2017-10-17
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 within phospholipid fibers. Release studies in aqueous media revealed that the phenolic bioactives were released mainly due to swelling of the phospholipid fiber matrix over time. The above studies confirm the efficacy of electrospun phospholipid microfibers as encapsulation and antioxidant systems.
Structural Damage Identification and Location Using Grammian Matrices
Directory of Open Access Journals (Sweden)
D.D. Bueno
2012-01-01
Full Text Available In this paper, an approach using observability and controllability grammian matrices is proposed to determine if structural damage has occurred together with an estimate of its location. The theory is outlined and simulations are carried out on a simple structure to demonstrate the method. Experimental tests were also carried out to demonstrate the validity of the approach using real signals. The dynamic properties of the structure are identified using the eigensystem realization algorithm (ERA and a reduced order state-space model of the system subsequently constructed. Either the observability or controllability grammians can then be used depending on the number of sensors available. It is shown that these are sensitive to both the degree and location of the damage and offer promise for structural health monitoring applications.
What Randomized Benchmarking Actually Measures
Proctor, Timothy; Rudinger, Kenneth; Young, Kevin; Sarovar, Mohan; Blume-Kohout, Robin
2017-09-01
Randomized benchmarking (RB) is widely used to measure an error rate of a set of quantum gates, by performing random circuits that would do nothing if the gates were perfect. In the limit of no finite-sampling error, the exponential decay rate of the observable survival probabilities, versus circuit length, yields a single error metric r . For Clifford gates with arbitrary small errors described by process matrices, r was believed to reliably correspond to the mean, over all Clifford gates, of the average gate infidelity between the imperfect gates and their ideal counterparts. We show that this quantity is not a well-defined property of a physical gate set. It depends on the representations used for the imperfect and ideal gates, and the variant typically computed in the literature can differ from r by orders of magnitude. We present new theories of the RB decay that are accurate for all small errors describable by process matrices, and show that the RB decay curve is a simple exponential for all such errors. These theories allow explicit computation of the error rate that RB measures (r ), but as far as we can tell it does not correspond to the infidelity of a physically allowed (completely positive) representation of the imperfect gates.
Comprehensive proteomic characterization of stem cell-derived extracellular matrices.
Ragelle, Héloïse; Naba, Alexandra; Larson, Benjamin L; Zhou, Fangheng; Prijić, Miralem; Whittaker, Charles A; Del Rosario, Amanda; Langer, Robert; Hynes, Richard O; Anderson, Daniel G
2017-06-01
In the stem-cell niche, the extracellular matrix (ECM) serves as a structural support that additionally provides stem cells with signals that contribute to the regulation of stem-cell function, via reciprocal interactions between cells and components of the ECM. Recently, cell-derived ECMs have emerged as in vitro cell culture substrates to better recapitulate the native stem-cell microenvironment outside the body. Significant changes in cell number, morphology and function have been observed when mesenchymal stem cells (MSC) were cultured on ECM substrates as compared to standard tissue-culture polystyrene (TCPS). As select ECM components are known to regulate specific stem-cell functions, a robust characterization of cell-derived ECM proteomic composition is critical to better comprehend the role of the ECM in directing cellular processes. Here, we characterized and compared the protein composition of ECM produced in vitro by bone marrow-derived MSC, adipose-derived MSC and neonatal fibroblasts from different donors, employing quantitative proteomic methods. Each cell-derived ECM displayed a specific and unique matrisome signature, yet they all shared a common set of proteins. We evaluated the biological response of cells cultured on the different matrices and compared them to cells on standard TCPS. The matrices lead to differential survival and gene-expression profiles among the cell types and as compared to TCPS, indicating that the cell-derived ECMs influence each cell type in a different manner. This general approach to understanding the protein composition of different tissue-specific and cell-derived ECM will inform the rational design of defined systems and biomaterials that recapitulate critical ECM signals for stem-cell culture and tissue engineering. Copyright © 2017 Elsevier Ltd. All rights reserved.
Glial cells assemble hyaluronan-based pericellular matrices in vitro.
Maleski, M; Hockfield, S
1997-07-01
The extracellular matrix (ECM) of the brain contains hyaluronan and proteoglycans, as does the ECM of cartilage. Aggrecan, the major proteoglycan of cartilage, forms large aggregates with hyaluronan, which then associate with the chondrocyte cell surface through an interaction with surface hyaluronan binding proteins. In culture, chondrocytes elaborate hyaluronan-proteoglycan aggregates, which form large hydrated pericellular matrices (PCMs) that can be visualized by a particle exclusion assay (Knudson and Toole: Dev Biol 112:308, 1985). It has recently been demonstrated that embryonic glial cells can also elaborate PCMs in culture (Deyst and Toole: Dev Brain Res 28:351, 1995). We demonstrate here that different classes of glial cells elaborate different types of endogenous PCMs in culture. Less differentiated glial cells, as evidenced by their immunoreactivity for nestin, elaborate larger endogenously produced PCMs than differentiated astrocytes, as defined by immunoreactivity for GFAP. This in vitro result may be a reflection of the larger volume of extracellular space present in the embryonic than in the mature brain. We show further that glial cells can incorporate cartilage aggrecan into their PCMs, and that both endogenous and aggrecan-supplemented glial PCMs are dependent on hyaluronan. In contrast, primary neurons from newborn (P0) and P1 rat cortex neither express endogenous matrices nor can assemble exogenous hyaluronan/aggrecan aggregates into PCMs. These results suggest that immature neurons may not have the ability to assemble hyaluronan-based PCMs, and they raise the possibility that neural proteoglycans associate with neuronal surfaces through a mechanism that may not directly involve hyaluronan.
Analogies between random matrix ensembles and the one-component plasma in two-dimensions
Directory of Open Access Journals (Sweden)
Peter J. Forrester
2016-03-01
Full Text Available The eigenvalue PDF for some well known classes of non-Hermitian random matrices — the complex Ginibre ensemble for example — can be interpreted as the Boltzmann factor for one-component plasma systems in two-dimensional domains. We address this theme in a systematic fashion, identifying the plasma system for the Ginibre ensemble of non-Hermitian Gaussian random matrices G, the spherical ensemble of the product of an inverse Ginibre matrix and a Ginibre matrix G1−1G2, and the ensemble formed by truncating unitary matrices, as well as for products of such matrices. We do this when each has either real, complex or real quaternion elements. One consequence of this analogy is that the leading form of the eigenvalue density follows as a corollary. Another is that the eigenvalue correlations must obey sum rules known to characterise the plasma system, and this leads us to an exhibit of an integral identity satisfied by the two-particle correlation for real quaternion matrices in the neighbourhood of the real axis. Further random matrix ensembles investigated from this viewpoint are self dual non-Hermitian matrices, in which a previous study has related to the one-component plasma system in a disk at inverse temperature β=4, and the ensemble formed by the single row and column of quaternion elements from a member of the circular symplectic ensemble.
Directory of Open Access Journals (Sweden)
Keith Stuart
2009-12-01
Full Text Available This article describes research undertaken in order to design a methodology for the reticular representation of knowledge of a specific discourse community. To achieve this goal, a representative corpus of the scientific production of the members of this discourse community (Universidad Politécnica de Valencia, UPV was created. The article presents the practical analysis (frequency, keyword, collocation and cluster analysis that was carried out in the initial phases of the study aimed at establishing the theoretical and practical background and framework for our matrix and network analysis of the scientific discourse of the UPV. In the methodology section, the processes that have allowed us to extract from the corpus the linguistic elements needed to develop co-occurrence matrices, as well as the computer tools used in the research, are described. From these co-occurrence matrices, semantic networks of subject and discipline knowledge were generated. Finally, based on the results obtained, we suggest that it may be viable to extract and to represent the intellectual capital of an academic institution using corpus linguistics methods in combination with the formulations of network theory.En este artículo describimos la investigación que se ha desarrollado en el diseño de una metodología para la representación reticular del conocimiento que se genera en el seno de una institución a partir de un corpus representativo de la producción científica de los integrantes de dicha comunidad discursiva, la Universidad Politécnica de Valencia.. Para ello, presentamos las acciones que se realizaron en las fases iniciales del estudio encaminadas a establecer el marco teórico y práctico en el que se inscribe nuestro análisis. En la sección de metodología se describen las herramientas informáticas utilizadas, así como los procesos que nos permitieron disponer de aquellos elementos presentes en el corpus, que nos llevarían al desarrollo de
A Random Matrix Approach to Credit Risk
Guhr, Thomas
2014-01-01
We estimate generic statistical properties of a structural credit risk model by considering an ensemble of correlation matrices. This ensemble is set up by Random Matrix Theory. We demonstrate analytically that the presence of correlations severely limits the effect of diversification in a credit portfolio if the correlations are not identically zero. The existence of correlations alters the tails of the loss distribution considerably, even if their average is zero. Under the assumption of randomly fluctuating correlations, a lower bound for the estimation of the loss distribution is provided. PMID:24853864
A random matrix approach to credit risk.
Directory of Open Access Journals (Sweden)
Michael C Münnix
Full Text Available We estimate generic statistical properties of a structural credit risk model by considering an ensemble of correlation matrices. This ensemble is set up by Random Matrix Theory. We demonstrate analytically that the presence of correlations severely limits the effect of diversification in a credit portfolio if the correlations are not identically zero. The existence of correlations alters the tails of the loss distribution considerably, even if their average is zero. Under the assumption of randomly fluctuating correlations, a lower bound for the estimation of the loss distribution is provided.
Directory of Open Access Journals (Sweden)
Zhaolin Jiang
2014-01-01
Full Text Available Circulant matrices play an important role in solving delay differential equations. In this paper, circulant type matrices including the circulant and left circulant and g-circulant matrices with any continuous Fibonacci and Lucas numbers are considered. Firstly, the invertibility of the circulant matrix is discussed and the explicit determinant and the inverse matrices by constructing the transformation matrices are presented. Furthermore, the invertibility of the left circulant and g-circulant matrices is also studied. We obtain the explicit determinants and the inverse matrices of the left circulant and g-circulant matrices by utilizing the relationship between left circulant, g-circulant matrices and circulant matrix, respectively.
An Algorithm for Synthesizing Mass and Stiffness Matrices from Experimental Vibration Modes
Ross, R. G., Jr.
1972-01-01
An algorithm is described for synthesizing the mass and stiffness matrices from experimentally derived modal data in a way that preserves the physical significance of the individual mass and stiffness elements. The mass and stiffness matrices are derived for a rollup solar array example, and are then used to define the modal response of a modified array.
Leeuwen, van S.P.J.; Kaerrman, A.; Zammit, A.; Bavel, van B.; Veen, van der I.; Kwadijk, C.J.A.F.; Boer, de J.; Lindstroem, G.
2005-01-01
This first worldwide interlaboratory study on the determination of perfluorinated compounds (PFCs) in environmental and human matrices was conducted in 2005. The main objective was to assess the betweenlaboratory reproducibility for various PFCs in a number of matrices: fish muscle tissue,
Kramer, K.J.M.; Dorten, W.S.; Groenewoud, H. van het; Haan, E. de; Kramer, G.N.; Monteiro, L.; Muntau, H.; Quevauviller, P.
1999-01-01
In order to control the quality of rare earth determinations in environmental matrices, the Standards, Measurements and Testing Programme (formerly Community Bureau of Reference, BCR) of the European Commission has started a project, the final aim of which is to certify four types of matrices (tuna
Numerically stable LDLT-factorization of F-type saddle point matrices
Niet, Arie C. de; Wubs, Fred W.
We present a new algorithm that constructs a fill-reducing ordering for a special class of saddle point matrices: the F-matrices. This class contains the matrix occurring after discretization of the Stokes equation on a C-grid. The commonly used approach is to construct a fill-reducing ordering for
Energy Technology Data Exchange (ETDEWEB)
Nardova, A.K.; Filippov, E.A. [All Research Institute of Chemical Technologies, Moscow (Russian Federation); Glagolenko, Y.B. [and others
1996-05-01
This report presents the results of investigations of plutonium immobilization from solutions on inorganic matrices with the purpose of producing a solid waste form. High-temperature sorption is described which entails the adsorption of radionuclides from solutions on porous, inorganic matrices, as for example silica gel. The solution is brought to a boil with additional thermal process (calcination) of the saturated granules.
The reflection of hierarchical cluster analysis of co-occurrence matrices in SPSS
Zhou, Q.; Leng, F.; Leydesdorff, L.
2015-01-01
Purpose: To discuss the problems arising from hierarchical cluster analysis of co-occurrence matrices in SPSS, and the corresponding solutions. Design/methodology/approach: We design different methods of using the SPSS hierarchical clustering module for co-occurrence matrices in order to compare
Numerical solutions of stochastic Lotka-Volterra equations via operational matrices
Directory of Open Access Journals (Sweden)
F. Hosseini Shekarabi
2016-03-01
Full Text Available In this paper, an efficient and convenient method for numerical solutions of stochastic Lotka-Volterra dynamical system is proposed. Here, we consider block pulse functions and their operational matrices of integration. Illustrative example is included to demonstrate the procedure and accuracy of the operational matrices based on block pulse functions.
Self-orthogonal codes from some bush-type Hadamard matrices ...
African Journals Online (AJOL)
By means of a construction method outlined by Harada and Tonchev, we determine some non-binary self-orthogonal codes obtained from the row span of orbit matrices of Bush-type Hadamard matrices that admit a xed-point-free and xed-block-free automorphism of prime order. We show that the code [20; 15; 4]5 obtained ...
Dissection of genomic correlation matrices of US Holsteins using multivariate factor analysis
Aim of the study was to compare correlation matrices between direct genomic predictions for 31 production, fitness and conformation traits both at genomic and chromosomal level in US Holstein bulls. Multivariate factor analysis was used to quantify basic features of correlation matrices. Factor extr...
The difference between 5 x 5 doubly nonnegative and completely positive matrices
Burer, Samuel; Anstreicher, Kurt M.; Duer, Mirjam
2009-01-01
The convex cone of n x n completely positive (CP) matrices and its dual cone of copositive matrices arise in several areas of applied mathematics, including optimization. Every CP matrix is doubly nonnegative (DNN), i.e., positive semidefinite and component-wise nonnegative, and it is known that,
The difference between 5 × 5 doubly nonnegative and completely positive matrices
Burer, Samuel; Anstreicher, Kurt M.; Dür, Mirjam
2009-01-01
The convex cone of n × n completely positive (CP) matrices and its dual cone of copositive matrices arise in several areas of applied mathematics, including optimization. Every CP matrix is doubly nonnegative (DNN), i.e., positive semidefinite and component-wise nonnegative, and it is known that,
Xia, Weiguo; Cao, Ming
In-depth understanding of the spectral properties of grounded Laplacian matrices is critical for the analysis of convergence speeds of dynamical processes over complex networks, such as opinion dynamics in social networks with stubborn agents. We focus on grounded Laplacian matrices for directed
Resistance to wear of four matrices with ball attachments for implant overdentures: a fatigue study.
Branchi, Roberto; Vangi, Dario; Virga, Antonio; Guertin, Genevieve; Fazi, Giovanni
2010-12-01
The study evaluated in vitro the retention force and the wear resistance over simulated function of four matrix components of ball attachments for implant-retained overdentures. Four types of matrices for ball attachments were evaluated in a fatigue study simulating 5500 cycles of insertion and removal. The matrices used were (1) a Teflon matrix supported by a metal housing, (2) a titanium matrix, (3) a gold alloy matrix, (4) an O-ring matrix using the red color ring for medium retention. Dimensional changes of the ball attachments were investigated with a profilometer. The Teflon matrices showed an increase of 27% in retention at 5500 cycles while the gold alloy matrices showed an increase of 50% in retention in the first 500 cycles and remained relatively stable up to 5500 cycles. On the other hand, titanium matrices and O-ring matrices exhibited progressive loss of retention ending with 68% and 75% of retention loss, respectively, at 5500 cycles. Dimensional analysis by profilometer revealed significant wear on the ball attachment only for titanium matrixes. Gold alloy and Teflon matrices showed the highest retention values without retention loss after 3 years of simulated function. Titanium and O-ring matrices presented a continuous loss of retention with the highest wear on the ball attachments when combined with the titanium matrix. © 2010 by The American College of Prosthodontists.
A Technique for Controlling Matric Suction on Filter Papers Used in ...
African Journals Online (AJOL)
Moist filter papers are widely usedfor seed gennination tests but their water confent and matric suction are not usually controlled. A technique for controlling filter paper matric suction is described and usedfor germination studies involving fresh and aged sorghum seed (Sorghummcolor (L) Moench). Filter papers wetted to ...
A Technique for Controlling Matric Suction on Filter Papers . GroWth ...
African Journals Online (AJOL)
'Abstract. Moist filter papers are widely usedfor seed gennination tests but their water confent and matric suction are not usually controlled. A technique for controlling filter paper matric suction is described and usedfor germination studies involving fresh and aged sorghum seed (Sorghummcolor (L) Moench). Filter papers ...
A Comparison between Element Salience versus Context as Item Difficulty Factors in Raven's Matrices
Perez-Salas, Claudia P.; Streiner, David L.; Roberts, Maxwell J.
2012-01-01
The nature of contextual facilitation effects for items derived from Raven's Progressive Matrices was investigated in two experiments. For these, the original matrices were modified, creating either abstract versions with high element salience, or versions which comprised realistic entities set in familiar contexts. In order to replicate and…
Fu, Xiaoling; Xu, Meng; Liu, Jie; Qi, Yanmei; Li, Shaohua; Wang, Hongjun
2014-02-01
Nanofibrous matrices hold great promise in skin wound repair partially due to their capability of recapturing the essential attributes of native extracellular matrix (ECM). With regard to limited studies on the effect of nanofibrous matrices on keratinocytes, the present study was aimed to understand how the topographical feature of nanofibrous matrices regulates keratinocyte motility by culturing keratinocytes on polycaprolactone (PCL)/collagen nanofibrous matrices (rough surface with fiber diameters of 331 ± 112 nm) or the matrices coated with a thin layer of collagen gel to form a secondary ultrafine fibrous network (smooth surface with ultrafine fiber diameters of 55 ± 26 nm). It was found that the PCL/collagen nanofibrous matrices alone did not stimulate cell migration, while collagen gel coating could significantly increase cell motility. Further studies demonstrated that the ultrafine fibrous network of collagen gel coating significantly activated integrin β1, Rac1 and Cdc42, facilitated the deposition of laminin-332 (formerly called laminin-5), and promoted the expression of active matrix metalloproteinases (MMPs) (i.e., MMP-2 and 9). Neutralization of integrin β1 activity abrogated the gel coating-induced keratinocyte migration. These findings provide important evidence on the role of topographical features of nanofibrous matrices in regulating the phenotypic alteration of keratinocytes and suggest the possible utility of collagen-containing nanofibrous matrices for skin regeneration especially in re-epithelialization. Copyright © 2013 Elsevier Ltd. All rights reserved.
Analyzing Matrices of Meta-Analytic Correlations: Current Practices and Recommendations
Sheng, Zitong; Kong, Wenmo; Cortina, Jose M.; Hou, Shuofei
2016-01-01
Researchers have become increasingly interested in conducting analyses on meta-analytic correlation matrices. Methodologists have provided guidance and recommended practices for the application of this technique. The purpose of this article is to review current practices regarding analyzing meta-analytic correlation matrices, to identify the gaps…
Use of job-exposure matrices to estimate occupational exposure to pesticides: A review.
Carles, Camille; Bouvier, Ghislaine; Lebailly, Pierre; Baldi, Isabelle
2017-03-01
The health effects of pesticides have been extensively studied in epidemiology, mainly in agricultural populations. However, pesticide exposure assessment remains a key methodological issue for epidemiological studies. Besides self-reported information, expert assessment or metrology, job-exposure matrices still appear to be an interesting tool. We reviewed all existing matrices assessing occupational exposure to pesticides in epidemiological studies and described the exposure parameters they included. We identified two types of matrices, (i) generic ones that are generally used in case-control studies and document broad categories of pesticides in a large range of jobs, and (ii) specific matrices, developed for use in agricultural cohorts, that generally provide exposure metrics at the active ingredient level. The various applications of these matrices in epidemiological studies have proven that they are valuable tools to assess pesticide exposure. Specific matrices are particularly promising for use in agricultural cohorts. However, results obtained with matrices have rarely been compared with those obtained with other tools. In addition, the external validity of the given estimates has not been adequately discussed. Yet, matrices would help in reducing misclassification and in quantifying cumulated exposures, to improve knowledge about the chronic health effects of pesticides.
Chen, Guoying; Smith, Emily; Qin, Feng; Liu, Linshu
2006-05-03
Analyses of chemical residues in animal tissue matrices require multistep sample preparation. To simplify this process, a methodology was developed that combines sorbent extraction and solid-matrix time-resolved luminescence (TRL); it was applied to tetracycline screening in milk. Reported here is an effort to extend its application to tissue matrices, illustrated by oxytetracycline (OTC) screening in catfish muscle. Extraction and enrichment are accomplished by immersing small C18 sorbent strips into tissue homogenates for 20 min, followed by a 3 min rinse in water and a 2 min dip in a reagent solution. After desiccation, TRL is measured directly on the sorbent surface. Tissue particulates no longer interfere via attenuation or scattering, rendering centrifugation and filtration unnecessary. The integrated TRL intensity shows a linear dependence on OTC concentration in the 0-8 microg/g range (R2 = 0.9992) with a 0.026 microg/g limit of detection. To screen OTC at 2 microg/g, the U.S. regulatory tolerance level, a threshold is established at x2-3sigma2, where x2 and sigma2 are the mean and standard deviation, respectively, of the TRL signals from 15 samples fortified at 2 microg/g. Among 45 blind samples randomly fortified at 0-4 microg/g, 41 were screened correctly and 4 negative samples were presumed positive. This method has the potential to improve throughput and save assay costs by eliminating acids, organic solvents, centrifugation, and filtration.
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.
Tapia, Liliana U; Lizana, Pablo A; Orellana, Yasna Z; Villagrán, Francisca S; Arias, Vanessa F; Almagià, Atilio F; Burrows, Raquel A; Ivanovic, Daniza M
2013-01-01
The aim of this study was to determine the relationship between somatotype and intellectual ability (IA) in 11-12 and 15-16 year-old students (n = 1,015) in the Chile's Metropolitan Region from a representative sample of 33 educational establishments chosen at random. The Heath-Carter somatotype and the IA assessed through the Raven Progressive Matrices Test were measured. The endomorph was observed in 59% of the students; 28% had a mesomorph and 13% ectomorph. The IA was distributed in: 11.2% Grade I, 26.8% Grade II, 41% Grade III, 17.6% Grade IV and 3.2% Grade V. A positive and significant correlation of IA with the endomorphic component (r = 0.074, p = 0.02) was found in the total sample and only in females (r = 0.109, p = 0.02); at the same time, a positive and significant correlation with the ectomorph component was also observed (r = 0.067, p < 0.05). This suggests that other variables would influence more strongly the IA for which further research is needed to quantitate this multifactorial problem. Copyright © AULA MEDICA EDICIONES 2013. Published by AULA MEDICA. All rights reserved.
Spectra of Adjacency Matrices in Networks of Extreme Introverts and Extroverts
Bassler, Kevin E.; Ezzatabadipour, Mohammadmehdi; Zia, R. K. P.
Many interesting properties were discovered in recent studies of preferred degree networks, suitable for describing social behavior of individuals who tend to prefer a certain number of contacts. In an extreme version (coined the XIE model), introverts always cut links while extroverts always add them. While the intra-group links are static, the cross-links are dynamic and lead to an ensemble of bipartite graphs, with extraordinary correlations between elements of the incidence matrix: nij In the steady state, this system can be regarded as one in thermal equilibrium with long-ranged interactions between the nij's, and displays an extreme Thouless effect. Here, we report simulation studies of a different perspective of networks, namely, the spectra associated with this ensemble of adjacency matrices {aij } . As a baseline, we first consider the spectra associated with a simple random (Erdős-Rényi) ensemble of bipartite graphs, where simulation results can be understood analytically. Work supported by the NSF through Grant DMR-1507371.
Newton`s iteration for inversion of Cauchy-like and other structured matrices
Energy Technology Data Exchange (ETDEWEB)
Pan, V.Y. [Lehman College, Bronx, NY (United States); Zheng, Ailong; Huang, Xiaohan; Dias, O. [CUNY, New York, NY (United States)
1996-12-31
We specify some initial assumptions that guarantee rapid refinement of a rough initial approximation to the inverse of a Cauchy-like matrix, by mean of our new modification of Newton`s iteration, where the input, output, and all the auxiliary matrices are represented with their short generators defined by the associated scaling operators. The computations are performed fast since they are confined to operations with short generators of the given and computed matrices. Because of the known correlations among various structured matrices, the algorithm is immediately extended to rapid refinement of rough initial approximations to the inverses of Vandermonde-like, Chebyshev-Vandermonde-like and Toeplitz-like matrices, where again, the computations are confined to operations with short generators of the involved matrices.
DEFF Research Database (Denmark)
Madsen, Claus G; Skov, Anders; Baldursdottir, Stefania
2015-01-01
PURPOSE: This study describes how protein release from polymer matrices correlate with simple measurements on the intrinsic viscosity of the polymer solutions used for casting the matrices and calculations of the solubility parameters of polymers and solvents used. METHOD: Matrices of poly......(dl-lactide-co-glycolide) (PLGA) were cast with bovine serum albumin (BSA) as a model drug using different solvents (acetone, dichloromethane, ethanol and water). The amount of released protein from the different matrices was correlated with the Hildebrand and Hansen solubility parameters of the solvents, and the intrinsic...... from PLGA matrices varied depending on the solvent used for casting. The maximum amount of released BSA decreased with higher intrinsic viscosity, and increased with solubility parameter difference between the solvent and polymer used. The solvent used also had an effect on the matrix microstructure...
Penile urethra replacement with autologous cell-seeded tubularized collagen matrices.
De Filippo, Roger E; Kornitzer, Benjamin S; Yoo, James J; Atala, Anthony
2015-03-01
Acellular collagen matrices have been used as an onlay material for urethral reconstruction. However, cell-seeded matrices have been recommended for tubularized urethral repairs. In this study we investigated whether long segmental penile urethral replacement using autologous cell-seeded tubularized collagen-based matrix is feasible. Autologous bladder epithelial and smooth muscle cells from nine male rabbits were grown and seeded onto preconfigured tubular matrices constructed from decellularized bladder matrices obtained from lamina propria. The entire anterior penile urethra was resected in 15 rabbits. Urethroplasties were performed with tubularized matrices seeded with cells in nine animals, and with matrices without cells in six. Serial urethrograms were performed at 1, 3 and 6 months. Retrieved urethral tissues were analysed using histo- and immunohistochemistry, western blot analyses and organ bath studies. The urethrograms showed that animals implanted with cell-seeded matrices maintained a wide urethral calibre without strictures. In contrast, the urethras with unseeded scaffolds collapsed and developed strictures. Histologically, a transitional cell layer surrounded by muscle was observed in the cell-seeded constructs. The epithelial and smooth muscle phenotypes were confirmed with AE1/AE3 and α-actin antibodies. Organ bath studies of the neourethras confirmed both physiological contractility and the presence of neurotransmitters. Tubularized collagen matrices seeded with autologous cells can be used successfully for long segmental penile urethra replacement, while implantation of tubularized collagen matrices without cells leads to poor tissue development and stricture formation. The cell-seeded collagen matrices are able to form new tissue, which is histologically similar to native urethra. Copyright © 2012 John Wiley & Sons, Ltd.
In vitro characterization of electrochemically compacted collagen matrices for corneal applications.
Kishore, Vipuil; Iyer, Ranjani; Frandsen, Athela; Nguyen, Thuy-Uyen
2016-10-06
Loss of vision due to corneal disease is a significant problem worldwide. Transplantation of donor corneas is a viable treatment option but limitations such as short supply and immune-related complications call for alternative options for the treatment of corneal disease. A tissue engineering-based approach using a collagen scaffold is a promising alternative to develop a bioengineered cornea that mimics the functionality of native cornea. In this study, an electrochemical compaction method was employed to synthesize highly dense and transparent collagen matrices. We hypothesized that chemical crosslinking of electrochemically compacted collagen (ECC) matrices will maintain transparency, improve stability, and enhance the mechanical properties of the matrices to the level of native cornea. Further, we hypothesized that keratocyte cell viability and proliferation will be maintained on crosslinked ECC matrices. The results indicated that uncrosslinked and 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide-N-hydroxysuccinimide (EDC-NHS) crosslinked ECC matrices were highly transparent with light transmission measurements comparable to native cornea. Stability tests showed that while the uncrosslinked ECC matrices degraded within 6 h when treated with collagenase, EDC-NHS or genipin crosslinking significantly improved the stability of ECC matrices (192 h for EDC-NHS and 256 h for genipin). Results from the mechanical tests showed that both EDC-NHS and genipin crosslinking significantly improved the strength and modulus of ECC matrices. Cell culture studies showed that keratocyte cell viability and proliferation are maintained on EDC-NHS crosslinked ECC matrices. Overall, results from this study suggest that ECC matrices have the potential to be developed as a functional biomaterial for corneal repair and regeneration.
3D Computational Simulation of Calcium Leaching in Cement Matrices
Directory of Open Access Journals (Sweden)
Gaitero, J. J.
2014-12-01
Full Text Available Calcium leaching is a degradation process consisting in progressive dissolution of the cement paste by migration of calcium atoms to the aggressive solution. It is therefore, a complex phenomenon involving several phases and dissolution and diffusion processes simultaneously. Along this work, a new computational scheme for the simulation of the degradation process in three dimensions was developed and tested. The toolkit was used to simulate accelerated calcium leaching by a 6M ammonium nitrate solution in cement matrices. The obtained outputs were the three dimensional representation of the matrix and the physicochemical properties of individual phases as a consequence of the degradation process. This not only makes it possible to study the evolution of such properties as a function of time but also as a function of the position within the matrix. The obtained results are in good agreement with experimental values of the elastic modulus in degraded and undegraded samples.El lixiviado de calcio es un proceso de degradación consistente en la disolución progresiva de la pasta de cemento por la migración de los átomos de calcio a la disolución agresiva. Se trata por tanto de un fenómeno complejo que involucra simultáneamente diferentes fases y procesos de disolución y difusión. En este trabajo se desarrolló y probó una nueva herramienta computacional para la simulación del proceso de degradación en tres dimensiones. Para ello se simuló el lixiviado de calcio acelerado provocado por una disolución de nitrato amónico 6M en matrices de cemento. Como resultado se obtuvieron la representación tridimensional de la matriz y las propiedades físico-químicas sus fases a lo largo del tiempo. Esto permitió estudiar la evolución de dichas propiedades a lo largo del proceso de degradación así como en función de su posición dentro de la matriz. Los resultados obtenidos coinciden con los valores experimentales del módulo elástico tanto
Random Tensor Theory: Extending Random Matrix Theory to Mixtures of Random Product States
Ambainis, Andris; Harrow, Aram W.; Hastings, Matthew B.
2012-02-01
We consider a problem in random matrix theory that is inspired by quantum information theory: determining the largest eigenvalue of a sum of p random product states in {(mathbb {C}^d)^{⊗ k}}, where k and p/ d k are fixed while d → ∞. When k = 1, the Marčenko-Pastur law determines (up to small corrections) not only the largest eigenvalue ({(1+sqrt{p/d^k})^2}) but the smallest eigenvalue {(min(0,1-sqrt{p/d^k})^2)} and the spectral density in between. We use the method of moments to show that for k > 1 the largest eigenvalue is still approximately {(1+sqrt{p/d^k})^2} and the spectral density approaches that of the Marčenko-Pastur law, generalizing the random matrix theory result to the random tensor case. Our bound on the largest eigenvalue has implications both for sampling from a particular heavy-tailed distribution and for a recently proposed quantum data-hiding and correlation-locking scheme due to Leung and Winter. Since the matrices we consider have neither independent entries nor unitary invariance, we need to develop new techniques for their analysis. The main contribution of this paper is to give three different methods for analyzing mixtures of random product states: a diagrammatic approach based on Gaussian integrals, a combinatorial method that looks at the cycle decompositions of permutations and a recursive method that uses a variant of the Schwinger-Dyson equations.
Stiffness Matrices and Anisotropy in the Trapezoidal Corrugated Composite Sheets
Directory of Open Access Journals (Sweden)
Mohammad Golzar
2013-10-01
Full Text Available In the some applications like as morphing technology, high strain and anisotropic behavior are essential design requirements. The corrugated composite sheets due to their special geometries have potential to high deflection under axial loading through longitudinal direction of corrugation. In this research, the strain and the anisotropic behavior of corrugated composite sheets are investigated by fabricating glass/epoxy samples with trapezoidal geometries. For evaluation of the mechanical behavior of the composites the samples were subjected to tension and flexural tests in the longitudinal and transverse directions of corrugation. In order to determine anisotropic behavior of the corrugated sheets, two approaches were introduced: (1 tensile anisotropic (E* and (2 flexural anisotropic (D*. The anisotropic behavior and ultimate deflections were investigated theoretically and experimentally. In this paper, mechanical behaviors based on theoretical and experimental analysis including the elastic constants and stiffness matrices of trapezoidal corrugated composite sheets were studied and the results were verified by finite element method. The results of the numerical and analytical solutions were compared with those of experimental tests. Finally, the load-displacement curves of tensile tests in longitudinal direction of corrugation, the ultimate deflection and anisotropy behavior of these exclusive composite sheets in the corrugated composite sheets were studied experimentally. The experimental results of the trapezoidal corrugated sheets showed that one of the most important parameters in the ultimate strain was amplitude of the corrugation elements. Generally, increasing the amplitude and element per length unit of trapezoidal corrugated specimen led to higher ultimate strain.
Spectral Regularization Algorithms for Learning Large Incomplete Matrices.
Mazumder, Rahul; Hastie, Trevor; Tibshirani, Robert
2010-03-01
We use convex relaxation techniques to provide a sequence of regularized low-rank solutions for large-scale matrix completion problems. Using the nuclear norm as a regularizer, we provide a simple and very efficient convex algorithm for minimizing the reconstruction error subject to a bound on the nuclear norm. Our algorithm Soft-Impute iteratively replaces the missing elements with those obtained from a soft-thresholded SVD. With warm starts this allows us to efficiently compute an entire regularization path of solutions on a grid of values of the regularization parameter. The computationally intensive part of our algorithm is in computing a low-rank SVD of a dense matrix. Exploiting the problem structure, we show that the task can be performed with a complexity linear in the matrix dimensions. Our semidefinite-programming algorithm is readily scalable to large matrices: for example it can obtain a rank-80 approximation of a 10(6) × 10(6) incomplete matrix with 10(5) observed entries in 2.5 hours, and can fit a rank 40 approximation to the full Netflix training set in 6.6 hours. Our methods show very good performance both in training and test error when compared to other competitive state-of-the art techniques.
Non aqueous dissolution of inert matrices for future nuclear fuels
Energy Technology Data Exchange (ETDEWEB)
Bourg, S.; Peron, F.; Lacquement, J
2004-07-01
The dissolution by non aqueous methods of two potential inert matrices of fuels for future reactors, TiN and SiC, was studied. The titanium nitride can be attacked in gas phase by chlorine gas above 400 deg C, to produce gaseous TiCl{sub 4} and N{sub 2}, with no solid or liquid residue. In molten LiCl-KCl melts at 550 deg C, the electrochemical oxidation of TiN produces TiCl], TiCl{sub 4} and N{sub 2} whereas liquid TiCl{sub 3}, remains in solution. The alpha silicon carbide can be attacked in gas phase by chlorine gas at 950 deg C. Gaseous SiCl{sub 4} and solid C are produced. A combination of Cl{sub 2} and O{sub 2} could lead to the formation of SiCl{sub 4} and CO, CO{sub 2}, with no solid or liquid residue. In molten KCl melts, at 950 deg C, the attack by dissolved Cl{sub 2} is very weak. With the used SiC, electrochemical studies were not possible because of a very low electrical conductivity of the material. Further studies are necessary to reduce the proportion of TiCl{sub 3} produced during the electro-dissolution in molten salt and to improve the oxidation of carbon during the attack of SiC. (authors)
Matrices: un modelo para las fotografías digitales
Directory of Open Access Journals (Sweden)
María Elena Domínguez Jiménez
2011-06-01
Full Text Available En este trabajo se resalta la relación que existe entre dos disciplinas, aparentemente muy distintas: la fotografía digital y las matemáticas. En efecto, las imágenes digitales -que todos manejamos hoy en día- se modelizan matemáticamente como matrices. Más aún, todas las manipulaciones sobre fotografías digitales se expresan mediante operaciones matriciales. En concreto, aquí se plantea un problema de compresión de imágenes digitales, basado en la DVS (descomposición en valores singulares que los alumnos aprenden en clase de Álgebra Lineal. De esta forma, los alumnos descubren por sí mismos algunas realidades importantes que los docentes queremos transmitirles: en primer lugar, que los conocimientos teóricos adquiridos en Álgebra Lineal tienen una aplicación directa a la tecnología que les rodea diariamente en este mundo digital; y en segundo lugar, cómo la modelización matemática es una poderosa herramienta para resolver problemas prácticos reales
REPRESENTACIONES DEL GRUPO SIMÉTRICO CON MATRICES ENTERAS
Directory of Open Access Journals (Sweden)
Fernando Novoa
2002-12-01
Full Text Available La representación de grupos de simetría es uno de los ternas en álgebra abstracta con más aplicaciones en la actualidad. El análisis espectral en diseño de experimentos, el diseño de redes de comunicación, la teoría de códigos, son algunos de los campos en donde esta teoría encuentra aplicación. A pesar de su utilidad, no siempre se encuentra a disposición del profesor y del estudiante una herramienta didáctica que le permita hacer ejemplos, cómputos y comprobaciones de los enunciados teóricos y se tiene que conformar con los ejemplos triviales que no le permiten ver realmente el grado de profundidad del concepto ni la complejidad del cálculo. El propósito de la siguiente nota es presentar un programa computacional para el sistema computacional CoCoA y en particular, ciertas rutinas que permiten calcular las representaciones irreducibles de los grupos de simetría en forma matricial, cuyas matrices tienen sus entradas enteras.
Spectral Regularization Algorithms for Learning Large Incomplete Matrices
Mazumder, Rahul; Hastie, Trevor; Tibshirani, Robert
2010-01-01
We use convex relaxation techniques to provide a sequence of regularized low-rank solutions for large-scale matrix completion problems. Using the nuclear norm as a regularizer, we provide a simple and very efficient convex algorithm for minimizing the reconstruction error subject to a bound on the nuclear norm. Our algorithm Soft-Impute iteratively replaces the missing elements with those obtained from a soft-thresholded SVD. With warm starts this allows us to efficiently compute an entire regularization path of solutions on a grid of values of the regularization parameter. The computationally intensive part of our algorithm is in computing a low-rank SVD of a dense matrix. Exploiting the problem structure, we show that the task can be performed with a complexity linear in the matrix dimensions. Our semidefinite-programming algorithm is readily scalable to large matrices: for example it can obtain a rank-80 approximation of a 106 × 106 incomplete matrix with 105 observed entries in 2.5 hours, and can fit a rank 40 approximation to the full Netflix training set in 6.6 hours. Our methods show very good performance both in training and test error when compared to other competitive state-of-the art techniques. PMID:21552465
Quantitative evaluation of single cell spread on collagen matrices.
De Vlieghere, E; Wagemans, G; De Backer, S; Drebert, Z; Tommelein, J; Rousseau, Q; Weyn, B; Van Troys, M; Bracke, M; De Wever, O
2016-11-15
Cells change their morphology as a response to environmental cues. The quantitative evaluation of single cell spread on extracellular matrices, such as type I collagen, is a key tool in cancer research. Inherent to the manual scoring of cellular spread is inter-observer but also intra-observer variation. To overcome these problems, we have developed the Morphology Analysis Software (MAS). MAS scores phase-contrast images of cells on native type I collagen gels and identifies whether a cell has a spread or round morphology using a combination of four unique parameters: the presence of a cellular extension, the cell area, the cell eccentricity and cell circularity. The MAS software scores are equivalent to the average score of five independent observers but MAS is faster, more objective and standardized. A functional screening assay using six cytokines identified TGFα as a stimulator of HCT8/E11 and SK-BR-3 single cell spreading on top of type I collagen gels. This change in morphology correlates with increased migration potential as evidenced by xCELLigence migration assays and are counteracted by EGFR signaling pathway inhibitors. This underscores the use of morphology classification on a population of unlabeled cells as read-out of an important cancer cell property and the potential for the MAS software in drug screening strategies. Copyright © 2016. Published by Elsevier Inc.
Chan, L W; Chow, K T; Heng, P W S
2006-02-01
This study reports the development of a method based on dynamic contact angle to investigate the wetting behavior of non-aqueous ethylcellulose (EC) gel matrices intended for topical drug delivery. Non-aqueous gel matrices were prepared from the three fine particle grades of EC and propylene glycol dicaprylate/dicaprate. Dynamic contact angle measurements of sessile drops of water and isopropylmyristate (IPM) on EC gel matrices were performed using a dynamic contact angle analyzer equipped with axisymmetric drop shape analysis of the sessile drop images. Gel density was determined by weighing known volumes of gel samples. The EC gel matrices were wetted by both water and IPM, with much higher wettability by the latter. Increased EC concentration and polymeric chain length decreased the extent and rate of wetting. Linear correlation was observed between wetting parameters and rheological as well as mechanical properties of EC gel matrices. The EC gel matrices exhibited both hydrophilic and lipophilic properties, with predominance of the latter. The extent and rate of wetting was governed by a balance of chemical and physical characteristics of the gel. EC gel matrices showed desirable wetting behavior in their function as a moisture-barrier, bioadhesive and vehicle for topical drug delivery.
Zepon, Karine Modolon; Petronilho, Fabricia; Soldi, Valdir; Salmoria, Gean Vitor; Kanis, Luiz Alberto
2014-11-01
The production and evaluation of cornstarch/cellulose acetate/silver sulfadiazine extrudate matrices are reported herein. The matrices were melt extruded under nine different conditions, altering the temperature and the screw speed values. The surface morphology of the matrices was examined by scanning electron microscopy. The micrographs revealed the presence of non-melted silver sulfadiazine microparticles in the matrices extruded at lower temperature and screw speed values. The thermal properties were evaluated and the results for both the biopolymer and the drug indicated no thermal degradation during the melt extrusion process. The differential scanning analysis of the extrudate matrices showed a shift to lower temperatures for the silver sulfadiazine melting point compared with the non-extruded drug. The starch/cellulose acetate matrices containing silver sulfadiazine demonstrated significant inhibition of the growth of Pseudomonas aeruginosa and Staphylococcus aureus. In vivo inflammatory response tests showed that the extrudate matrices, with or without silver sulfadiazine, did not trigger chronic inflammatory processes. Copyright © 2014. Published by Elsevier B.V.
Directory of Open Access Journals (Sweden)
Tingting Xu
2014-01-01
Full Text Available Circulant matrices may play a crucial role in solving various differential equations. In this paper, the techniques used herein are based on the inverse factorization of polynomial. We give the explicit determinants of the RFPrLrR circulant matrices and RLPrFrL circulant matrices involving Fibonacci, Lucas, Pell, and Pell-Lucas number, respectively.
Dosse, Mohammed Bennani; Berge, Jos M. F.
2008-01-01
The use of Candecomp to fit scalar products in the context of INDSCAL is based on the assumption that the symmetry of the data matrices involved causes the component matrices to be equal when Candecomp converges. Ten Berge and Kiers gave examples where this assumption is violated for Gramian data matrices. These examples are believed to be local…
On matrices with low-rank-plus-shift structure: Partial SVD and latent semantic indexing
Energy Technology Data Exchange (ETDEWEB)
Zha, H.; Zhang, Z.
1998-08-01
The authors present a detailed analysis of matrices satisfying the so-called low-rank-plus-shift property in connection with the computation of their partial singular value decomposition. The application they have in mind is Latent Semantic Indexing for information retrieval where the term-document matrices generated from a text corpus approximately satisfy this property. The analysis is motivated by developing more efficient methods for computing and updating partial SVD of large term-document matrices and gaining deeper understanding of the behavior of the methods in the presence of noise.
A complete survey of texture zeros in general and symmetric quark mass matrices
Directory of Open Access Journals (Sweden)
P.O. Ludl
2015-05-01
Full Text Available We perform a systematic analysis of all possible texture zeros in general and symmetric quark mass matrices. Using the values of masses and mixing parameters at the electroweak scale, we identify for both cases the maximally restrictive viable textures. Furthermore, we investigate the predictive power of these textures by applying a numerical predictivity measure recently defined by us. With this measure we find no predictive textures among the viable general quark mass matrices, while in the case of symmetric quark mass matrices most of the 15 maximally restrictive textures are predictive with respect to one or more light quark masses.
Norms and Spread of the Fibonacci and Lucas RSFMLR Circulant Matrices
Directory of Open Access Journals (Sweden)
Wenai Xu
2015-01-01
Full Text Available Circulant type matrices have played an important role in networks engineering. In this paper, firstly, some bounds for the norms and spread of Fibonacci row skew first-minus-last right (RSFMLR circulant matrices and Lucas row skew first-minus-last right (RSFMLR circulant matrices are given. Furthermore, the spectral norm of Hadamard product of a Fibonacci RSFMLR circulant matrix and a Lucas RSFMLR circulant matrix is obtained. Finally, the Frobenius norm of Kronecker product of a Fibonacci RSFMLR circulant matrix and a Lucas RSFMLR circulant matrix is presented.
Matrices and society matrix algebra and its applications in the social sciences
Bradley, Ian
2014-01-01
Matrices offer some of the most powerful techniques in modem mathematics. In the social sciences they provide fresh insights into an astonishing variety of topics. Dominance matrices can show how power struggles in offices or committees develop; Markov chains predict how fast news or gossip will spread in a village; permutation matrices illuminate kinship structures in tribal societies. All these invaluable techniques and many more are explained clearly and simply in this wide-ranging book. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to
Extremal Density Matrices for the Expectation Value of a Qudit Hamiltonian
Castaños, O.; Figueroa, A.; López, J.; López-Peña, R.
2017-05-01
An algebraic procedure to find extremal density matrices for the expectation value of a finite Hamiltonian matrix is established. The extremal density matrices for pure states provide a complete description of the system, that is, its corresponding energy spectrum and projectors. For density matrices representing mixed states, one gets the most probable eigenstates that yield extremal mean values of the energy. The procedure uses mainly the stationary solutions of the von Neumann equation of motion, the orbits of the Hamiltonian, and the positivity conditions of the density matrix. The method is illustrated for matrix Hamiltonians of dimensions d = 2 and d = 3.
Directory of Open Access Journals (Sweden)
Duc Manh Nguyen
2017-07-01
Full Text Available In this paper, new construction methods of entanglement-assisted quantum error correction code (EAQECC from circulant matrices are proposed. We first construct the matrices from two vectors of constraint size, and determine the isotropic subgroup. Then, we also propose a method for calculation of the entanglement subgroup based on standard forms of binary matrices to satisfy the constraint conditions of EAQECC. With isotropic and entanglement subgroups, we determine all the parameters and the minimum distance of the EAQECC. The proposed EAQECC with small lengths are presented to explain the practicality of this construction of EAQECC. Comparison with some earlier constructions of EAQECC shows that the proposed EAQECC is better.
Multiple Regression Analysis of Unconfined Compression Strength of Mine Tailings Matrices
Directory of Open Access Journals (Sweden)
Mahmood Ali A.
2017-01-01
Full Text Available As part of a novel approach of sustainable development of mine tailings, experimental and numerical analysis is carried out on newly formulated tailings matrices. Several physical characteristic tests are carried out including the unconfined compression strength test to ascertain the integrity of these matrices when subjected to loading. The current paper attempts a multiple regression analysis of the unconfined compressive strength test results of these matrices to investigate the most pertinent factors affecting their strength. Results of this analysis showed that the suggested equation is reasonably applicable to the range of binder combinations used.
SAR matrices: automated extraction of information-rich SAR tables from large compound data sets.
Wassermann, Anne Mai; Haebel, Peter; Weskamp, Nils; Bajorath, Jürgen
2012-07-23
We introduce the SAR matrix data structure that is designed to elucidate SAR patterns produced by groups of structurally related active compounds, which are extracted from large data sets. SAR matrices are systematically generated and sorted on the basis of SAR information content. Matrix generation is computationally efficient and enables processing of large compound sets. The matrix format is reminiscent of SAR tables, and SAR patterns revealed by different categories of matrices are easily interpretable. The structural organization underlying matrix formation is more flexible than standard R-group decomposition schemes. Hence, the resulting matrices capture SAR information in a comprehensive manner.
NUEVOS SISTEMAS SUPRAMOLECULARES: COMPUESTOS DE INCLUSION DE MATRICES BINARIAS DE UREA Y TIOUREA
MERCHAN VELEZ, JUAN EUGENIO
2002-01-01
Esta tesis constituye una incursión y contribución al conocimiento de la química supramolecular y de la química de las interacciones sutiles en el ámbito de compuestos polimoleculares derivados de las matrices binarias de urea y tiourea. Se sintetizaron y caracterizaron los compuestos de inclusión de las matrices aniónicas urea/cloruro, urea/bromuro, urea/yoduro, tiourea/cloruro, tiourea/bromuro, tiourea/yoduro incorporando como huésped el catión diquinuclidonio. Las matrices están f...
Aslan, Bahar; Guler, Selcan; Tevlek, Atakan; Aydin, Halil Murat
2017-10-12
Corneal tissue engineering efforts to obtain corneal tissue matrices through various types of materials for the replacement of damaged tissues. In this study, three different corneal constructs were prepared and evaluated in terms of morphological, optical, and biological characteristics. Type-I collagen was used to obtain collagen foam scaffolds through dehydrothermal crosslinking, while poly(l-lactic acid) (PLLA) was used to produce both random and aligned oriented electrospun corneal constructs. Bovine corneas were decellularized as third matrix. Software analyses showed that average pore size of collagen scaffolds was 88.207 ± 29.7 µm, while the average fiber diameter of aligned and random PLLA scaffolds were 0.69 ± 0.03 and 0.65 ± 0.03 μm, respectively. Degradation profiles revealed that collagen foam exhibits high degradation (20% mass loss) while electrospun PLLA scaffolds hold low degradation (9% mass loss) rates at day-28. Transmittance values of the obtained scaffolds were calculated as 92, 80, and 70% for collagen, PLLA, and decellularized cornea constructs, respectively. The evaluation of stromal keratocyte behavior on the constructs revealed that the cells exhibited their own morphology mostly on the aligned PLLA constructs, while they were mostly active on random PLLA electrospun corneal scaffolds. © 2017 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 2017. © 2017 Wiley Periodicals, Inc.
Molecular Modeling of Aerospace Polymer Matrices Including Carbon Nanotube-Enhanced Epoxy
Radue, Matthew S.
Carbon fiber (CF) composites are increasingly replacing metals used in major structural parts of aircraft, spacecraft, and automobiles. The current limitations of carbon fiber composites are addressed through computational material design by modeling the salient aerospace matrix materials. Molecular Dynamics (MD) models of epoxies with and without carbon nanotube (CNT) reinforcement and models of pure bismaleimides (BMIs) were developed to elucidate structure-property relationships for improved selection and tailoring of matrices. The influence of monomer functionality on the mechanical properties of epoxies is studied using the Reax Force Field (ReaxFF). From deformation simulations, the Young's modulus, yield point, and Poisson's ratio are calculated and analyzed. The results demonstrate an increase in stiffness and yield strength with increasing resin functionality. Comparison between the network structures of distinct epoxies is further advanced by the Monomeric Degree Index (MDI). Experimental validation demonstrates the MD results correctly predict the relationship in Young's moduli for all epoxies modeled. Therefore, the ReaxFF is confirmed to be a useful tool for studying the mechanical behavior of epoxies. While epoxies have been well-studied using MD, there has been no concerted effort to model cured BMI polymers due to the complexity of the network-forming reactions. A novel, adaptable crosslinking framework is developed for implementing 5 distinct cure reactions of Matrimid-5292 (a BMI resin) and investigating the network structure using MD simulations. The influence of different cure reactions and extent of curing are analyzed on the several thermo-mechanical properties such as mass density, glass transition temperature, coefficient of thermal expansion, elastic moduli, and thermal conductivity. The developed crosslinked models correctly predict experimentally observed trends for various properties. Finally, the epoxies modeled (di-, tri-, and tetra
Directory of Open Access Journals (Sweden)
Annie O Smith
Full Text Available We describe a novel 3D fibrin matrix model using recombinant hematopoietic stem cell cytokines under serum-free defined conditions which promotes the assembly of human endothelial cell (EC tubes with co-associated pericytes. Individual ECs and pericytes are randomly mixed together and EC tubes form that is accompanied by pericyte recruitment to the EC tube abluminal surface over a 3-5 day period. These morphogenic processes are stimulated by a combination of the hematopoietic stem cell cytokines, stem cell factor, interleukin-3, stromal derived factor-1α, and Flt-3 ligand which are added in conjunction with fibroblast growth factor (FGF-2 into the fibrin matrix. In contrast, this tube morphogenic response does not occur under serum-free defined conditions when VEGF and FGF-2 are added together in the fibrin matrices. We recently demonstrated that VEGF and FGF-2 are able to prime EC tube morphogenic responses (i.e. added overnight prior to the morphogenic assay to hematopoietic stem cell cytokines in collagen matrices and, interestingly, they also prime EC tube morphogenesis in 3D fibrin matrices. EC-pericyte interactions in 3D fibrin matrices leads to marked vascular basement membrane assembly as demonstrated using immunofluorescence and transmission electron microscopy. Furthermore, we show that hematopoietic stem cell cytokines and pericytes stimulate EC sprouting in fibrin matrices in a manner dependent on the α5β1 integrin. This novel co-culture system, under serum-free defined conditions, allows for a molecular analysis of EC tube assembly, pericyte recruitment and maturation events in a critical ECM environment (i.e. fibrin matrices that regulates angiogenic events in postnatal life.
Smith, Annie O.; Bowers, Stephanie L. K.; Stratman, Amber N.; Davis, George E.
2013-01-01
We describe a novel 3D fibrin matrix model using recombinant hematopoietic stem cell cytokines under serum-free defined conditions which promotes the assembly of human endothelial cell (EC) tubes with co-associated pericytes. Individual ECs and pericytes are randomly mixed together and EC tubes form that is accompanied by pericyte recruitment to the EC tube abluminal surface over a 3-5 day period. These morphogenic processes are stimulated by a combination of the hematopoietic stem cell cytokines, stem cell factor, interleukin-3, stromal derived factor-1α, and Flt-3 ligand which are added in conjunction with fibroblast growth factor (FGF)-2 into the fibrin matrix. In contrast, this tube morphogenic response does not occur under serum-free defined conditions when VEGF and FGF-2 are added together in the fibrin matrices. We recently demonstrated that VEGF and FGF-2 are able to prime EC tube morphogenic responses (i.e. added overnight prior to the morphogenic assay) to hematopoietic stem cell cytokines in collagen matrices and, interestingly, they also prime EC tube morphogenesis in 3D fibrin matrices. EC-pericyte interactions in 3D fibrin matrices leads to marked vascular basement membrane assembly as demonstrated using immunofluorescence and transmission electron microscopy. Furthermore, we show that hematopoietic stem cell cytokines and pericytes stimulate EC sprouting in fibrin matrices in a manner dependent on the α5β1 integrin. This novel co-culture system, under serum-free defined conditions, allows for a molecular analysis of EC tube assembly, pericyte recruitment and maturation events in a critical ECM environment (i.e. fibrin matrices) that regulates angiogenic events in postnatal life. PMID:24391990
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.
Chromium speciation in solid matrices and regulation: a review
Energy Technology Data Exchange (ETDEWEB)
Unceta, N. [University of the Basque Country, Department of Analytical Chemistry, Faculty of Pharmacy, Vitoria-Gasteiz (Spain); Seby, F. [Ultra Traces Analyses Aquitaine (UT2A), Helioparc Pau-Pyrenees, Pau (France); Malherbe, J.; Donard, O.F.X. [Universite de Pau et des Pays de l' Adour, Helioparc Pau-Pyrenees, Laboratoire de Chimie Analytique Bio-Inorganique et Environnement, IPREM, UMR CNRS 5254, Pau (France)
2010-06-15
In recent years, the extensive use of chromium in industrial processes has led to the promotion of several directives and recommendations by the European Union, that try to limit and regulate the presence of Cr(VI) in the environment and to protect industrial workers using chromium and end-users of manufactured products. As a consequence, new standard methods and analytical procedures have been published at the EU level for Cr(VI) determination in soil, sludge, sediment, and similar waste materials, workplace atmospheres, cement, packaging materials, industrially produced samples, and corrosion-protection layers on some components of vehicles and electrical and electronic equipment. The objective of this article is to summarize the different directives and recommendations and to critically review the currently existing standard methods and the methods published in the literature for chromium speciation in the above mentioned solid matrices, putting the emphasis on the different extraction procedures which have been developed for each matrix. Particular attention has been paid to Cr(III) and Cr(VI) inter-conversions that can occur during extraction and efforts to minimize these unwanted reactions. Although the use of NaOH-Na{sub 2}CO{sub 3} solutions with hot plate extraction seems to be the more widespread procedure, species transformation can still occur and several studies suggest that speciated isotope-dilution mass spectrometry (SIDMS) could be a suitable tool for correction of these interconversions. Besides, recent studies have proved the role of Cr(III) in chromium toxicology. As a consequence, the authors suggest an update of standard methods in the near future. (orig.)
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.
Trait level analysis of multitrait population projection matrices.
Coste, Christophe F D; Austerlitz, Frédéric; Pavard, Samuel
2017-08-01
In most matrix population projection models, individuals are characterized according to, usually, one or two traits such as age, stage, size or location. A broad theory of multitrait population projection matrices (MPPMs) incorporating larger number of traits was long held back by time and space computational complexity issues. As a consequence, no study has yet focused on the influence of the structure of traits describing a life-cycle on population dynamics and life-history evolution. We present here a novel vector-based MPPM building methodology that allows to computationally-efficiently model populations characterized by numerous traits with large distributions, and extend sensitivity analyses for these models. We then present a new method, the trait level analysis consisting in folding an MPPM on any of its traits to create a matrix with alternative trait structure (the number of traits and their characteristics) but similar asymptotic properties. Adding or removing one or several traits to/from the MPPM and analyzing the resulting changes in spectral properties, allows investigating the influence of the trait structure on the evolution of traits. We illustrate this by modeling a 3-trait (age, parity and fecundity) population designed to investigate the implications of parity-fertilitytrade-offs in a context of fecundity heterogeneity in humans. The trait level analysis, comparing models of the same population differing in trait structures, demonstrates that fertility selection gradients differ between cases with or without parity-fertility trade-offs. Moreover it shows that age-specific fertility has seemingly very different evolutionary significance depending on whether heterogeneity is accounted for. This is because trade-offs can vary strongly in strength and even direction depending on the trait structure used to model the population. Copyright © 2017 Elsevier Inc. All rights reserved.
A novel way to monitor urine concentration: fluorescent concentration matrices.
Dubayova, Katarina; Luckova, Iveta; Sabo, Jan; Karabinos, Anton
2015-01-01
The amount of water found in urine is important diagnostic information; nevertheless it is not yet directly determined. Indirectly, the water content in urine is expressed by its density (specific gravity). However, without the diuresis value it is not possible to determine whether the increase in density of urine is due to a decrease in water secretion or an increase in the concentration of secreted substances. This problem can be solved by the use of fluorescent concentration 3D-matrices which characterise urine concentration through the pφ (or -logφ) value of the first fluorescence centre. The urine fluorescent concentration 3D-matrix was created by the alignment of the synchronous spectra of the dilution series of urine starting from undiluted (pφ = 0) to 1000-fold diluted urine (pφ = 3). Using the fluorescence concentration 3D-matrix analysis of the urine samples from healthy individuals, a reference range was established for the value pφ, determining the normal, concentrated or diluted type of urine. The diagnostic potential of this approach was tested on urine samples from two patients with a chronic glomerulonephritis. The pφ value of the urine fluorescence concentration 3D-matrix analysis determines whether the urine sample falls within the normal, concentrated or diluted type of urine. This parameter can be directly utilised in sportsmen's hydration state monitoring, as well as in the diagnosis and treatment of serious diseases. An important advantage of this novel diagnostic approach is that a 12/24 h urine collection is not required, which predetermines it for use especially within paediatrics.
Comparison study of acellular dermal matrices in complicated hernia surgery.
Bochicchio, Grant V; De Castro, Gerard P; Bochicchio, Kelly M; Weeks, Jennifer; Rodriguez, Eduardo; Scalea, Thomas M
2013-10-01
Damage control surgery and management of the open abdomen has led to a significant improvement in survival in trauma and emergency surgical patients. However, subsequent abdominal reconstruction has become a significant challenge. The objective of this study was to compare 2 different acellular dermal matrices in regard to hernia recurrence and complications in patients who present with a large complicated ventral hernia as a result of trauma or emergency surgery. A prospective quasi-experimental time-interrupted series design was used to evaluate the incidence of hernia recurrence in trauma/emergency surgery patients who had a ventral hernia repair with a biologic matrix. From January 2005 to December 2007, 55 patients with a complicated ventral hernia were repaired with AlloDerm (Life Cell Corporation). Beginning in February 2008 to January 2010, 40 patients with the same criteria were repaired with FlexHD (Musculoskeletal Transplant Foundation) and followed prospectively over the following year. The primary outcome for this study was hernia recurrence (functional or real) at 1 year. Other outcomes variables included abdominal laxity, seroma formation, and wound or intra-abdominal infection. There was no significant difference in age, sex, and body mass index between the groups. In addition, there was no significant difference in the mean hernia size and size of the acellular dermis that was inserted. At 1 year postsurgery, all of the AlloDerm patients were diagnosed with recurrence requiring a second formal repair. Eleven patients (31%) whose hernias were repaired with FlexHD were diagnosed with a recurrence requiring a second formal repair. FlexHD appears to have reduced the recurrence and laxity rates while maintaining a similar complication profile compared with AlloDerm in trauma/emergency surgery patients with large complicated ventral hernias. Copyright © 2013 American College of Surgeons. Published by Elsevier Inc. All rights reserved.
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.
Pieper, J.S.; Kraan, P.M. van der; Hafmans, T.G.M.; Kamp, J.; Buma, P.; Susante, J.L.C. van; Berg, W.B. van den; Veerkamp, J.H.; Kuppevelt, A.H.M.S.M. van
2002-01-01
The limited intrinsic repair capacity of articular cartilage has stimulated continuing efforts to develop tissue engineered analogues. Matrices composed of type II collagen and chondroitin sulfate (CS), the major constituents of hyaline cartilage, may create an appropriate environment for the
Preparation and Evaluation of Gelatin-Based Disc Matrices for the ...
African Journals Online (AJOL)
linked with glutaraldehyde. The crosslinked hydrogel was cut into discs and dried under vacuum in a dessicator to form the disc-shaped matrices which were further evaluated for swelling, drug loading and in vitro drug dissolution properties.
National Research Council Canada - National Science Library
Hayes, Taylor R; Petrov, Alexander A; Sederberg, Per B
2011-01-01
...) that captures statistical regularities in temporally extended eye movement sequences. We demonstrate the effectiveness of the scanpath SR on eye movement data from participants solving items from Raven's Advanced Progressive Matrices Test...
MatGAT: an application that generates similarity/identity matrices using protein or DNA sequences
National Research Council Canada - National Science Library
Campanella, James J; Bitincka, Ledion; Smalley, John
2003-01-01
.... We have developed MatGAT (Matrix Global Alignment Tool), a simple, easy to use computer application that generates similarity/identity matrices for DNA or protein sequences without needing pre-alignment of the data...
The MATRICS Consensus Cognitive Battery (MCCB): Co-norming and standardization in China
Shi, Chuan; Kang, Lan; Yao, Shuqiao; Ma, Yibin; Li, Tao; Liang, Ying; Cheng, Zhang; Xu, Yifeng; Shi, Jianguo; Xu, Xiufeng; Zhang, Congpei; Franklin, Donald R.; Heaton, Robert K.; Jin, Hua; Yu, Xin
2015-01-01
MATRICS Consensus Cognitive Battery (MCCB), packaging 10 tests selected from more than 90 nominated tests, is a method developed by the Measurement and Treatment Research to Improve Cognition in Schizophrenia (MATRICS) group to evaluate the efficacy of treatments targeting cognitive impairments in schizophrenia. MCCB had been translated into a number of languages, but only the US and Spain had normative data reported. Inconsistency in translation and cultural differences make direct applicati...
Fate of Thallium(I) in Reverse Osmosis and Chlorinated Water Matrices
2014-02-01
THALLIUM(I) IN REVERSE OSMOSIS AND CHLORINATED WATER MATRICES ECBC-TR-1127 Approved for public release; distribution is unlimited...3. DATES COVERED (From - To) Apr 2010 - Dec 2011 4. TITLE AND SUBTITLE Fate of Thallium(I) in Reverse Osmosis and Chlorinated Water Matrices... osmosis (RO) and RO water with added chlorine (RO-Cl) was measured using inductively coupled plasma optical emission spectroscopy (ICP-OES) for a period of
Effect of HLB of additives on the properties and drug release from the glyceryl monooleate matrices.
Shah, Manish H; Paradkar, Anant
2007-08-01
Glyceryl monooleate (GMO) is an amphiphilic surfactant, which as such can solubilize hydrophilic, lipophilic and amphiphilic drug molecules in its different polarity regions. Addition of additives with different polarities in GMO leads to change in phase behavior and related properties of GMO. Effect of the additives with different hydrophilic lipophilic balance (HLB; 1.5, 3, 4, 5, 7, 10 and 11) in GMO matrices on its phase transformation, rheological properties, mechanical properties, wetting and release behavior was investigated. Polarizing light microscopy showed that the GMO matrices incorporated with lower HLB additive (1.5, 3, 4 and 5) form cubic phase at higher rate while lamellar phase was prominent for matrices with additive of HLB 7, 10 and 11. The diametrical crushing strength and viscosity was decreased with increased HLB of additive. Lower HLB additives enhanced contact angle as compared to plain matrices and high HLB additives induced change in solid-liquid interface from hydrophobic to hydrophilic leading to decline in contact angle. Percent swelling of matrices was increased linearly with increase in HLB of additives. Tensiometric method was used for determination of bioadhesive strength of hydrated matrices and it was observed that matrices with additives of HLB 10 presented highest bioadhesion due to higher rate of hydration and formation of lamellar phase. As the HLB of additives in matrix increased, release was shifted from anomalous (non-Fickian) diffusion and/or partially erosion-controlled release to Fickian diffusion. Initial lag was observed for drug released from matrices with additive of HLB 1.5, 3, 4 and 5. Thus incorporation of the additives of different HLB changed molecular packing, which significantly affected drug release pattern.
Petrů, Vít
2017-01-01
This thesis deals with replacement of performative scale of Wechsler Adult Intelligence Scale (3rd revision) through Raven's Standard Progressive Matrices and Advanced Progressive Matrices. In the theoretical part introduces the concepts of intelligence, approaches to its exploration and intelligence tests. The theoretical part is also devoted to the description of the used methods and presents an overview of the research on a similar theme as this work. In the empirical part of the thesis is...
Wise, Kristopher Eric (Inventor); Park, Cheol (Inventor); Kang, Jin Ho (Inventor); Siochi, Emilie J. (Inventor); Harrison, Joycelyn S. (Inventor)
2016-01-01
Stable dispersions of carbon nanotubes (CNTs) in polymeric matrices include CNTs dispersed in a host polymer or copolymer whose monomers have delocalized electron orbitals, so that a dispersion interaction results between the host polymer or copolymer and the CNTs dispersed therein. Nanocomposite products, which are presented in bulk, or when fabricated as a film, fiber, foam, coating, adhesive, paste, or molding, are prepared by standard means from the present stable dispersions of CNTs in polymeric matrices, employing dispersion interactions, as presented hereinabove.
Synthesis and characterization of CaO-loaded electrospun matrices for bone tissue engineering.
Münchow, Eliseu A; Pankajakshan, Divya; Albuquerque, Maria T P; Kamocki, Krzysztof; Piva, Evandro; Gregory, Richard L; Bottino, Marco C
2016-11-01
This study aims to synthesize and characterize biodegradable polymer-based matrices loaded with CaO nanoparticles for osteomyelitis treatment and bone tissue engineering. Poly(ε-caprolactone) (PCL) and PCL/gelatin (1:1, w/w) solutions containing CaO nanoparticles were electrospun into fibrous matrices. Scanning (SEM) and transmission (TEM) electron microscopy, Fourier transformed infrared (FTIR), energy dispersive X-ray spectroscopy (EDS), contact angle (CA), tensile testing, and antibacterial activity (agar diffusion assay) against Staphylococcus aureus were performed. Osteoprecursor cell (MC3T3-E1) response (i.e., viability and alkaline phosphatase expression/ALP) and infiltration into the matrices were evaluated. CaO nanoparticles were successfully incorporated into the fibers, with the median fiber diameter decreasing after CaO incorporation. The CA decreased with the addition of CaO, and the presence of gelatin made the matrix very hydrophilic (CA = 0°). Increasing CaO concentrations progressively reduced the mechanical properties (p ≤ 0.030). CaO-loaded matrices did not display consistent antibacterial activity. MC3T3-E1 cell viability demonstrated the highest levels for CaO-loaded matrices containing gelatin after 7 days in culture. An increased ALP expression was consistently seen for PCL/CaO matrices when compared to PCL and gelatin-containing counterparts. Despite inconsistent antibacterial activity, CaO nanoparticles can be effectively loaded into PCL or PCL/gelatin fibers without negatively affecting the overall performance of the matrices. More importantly, CaO incorporation enhanced cell viability as well as differentiation capacity, as demonstrated by an increased ALP expression. CaO-loaded electrospun matrices show potential for applications in bone tissue engineering.
Poppler, Louis; Cohen, Justin; Dolen, Utku Can; Schriefer, Andrew E.; Tenenbaum, Marissa M.; Deeken, Corey; Chole, Richard A.; Myckatyn, Terence M.
2015-01-01
Background Subclinical infections, manifest as biofilms, are considered an important cause of capsular contracture. Acellular dermal matrices (ADMs) are frequently used in revision surgery to prevent recurrent capsular contractures. Objective We sought to identify an association between capsular contracture and biofilm formation on breast prostheses, capsules, and ADMs in a tissue expander/implant (TE/I) exchange clinical paradigm. Methods Biopsies of the prosthesis, capsule, and ADM from patients (N = 26) undergoing TE/I exchange for permanent breast implant were evaluated for subclinical infection. Capsular contracture was quantified with Baker Grade and intramammary pressure. Biofilm formation was evaluated with specialized cultures, rtPCR, bacterial taxonomy, live:dead staining, and scanning electron microscopy (SEM). Collagen distribution, capsular histology, and ADM remodeling were quantified following fluorescent and light microscopy. Results Prosthetic devices were implanted from 91 to 1115 days. Intramammary pressure increased with Baker Grade. Of 26 patients evaluated, one patient had a positive culture and one patient demonstrated convincing evidence of biofilm morphology on SEM. Following PCR amplification 5 samples randomly selected for 16S rRNA gene sequencing demonstrated an abundance of suborder Micrococcineae, consistent with contamination. Conclusions Our data suggest that bacterial biofilms likely contribute to a proportion, but not all diagnosed capsular contractures. Biofilm formation does not appear to differ significantly between ADMs or capsules. While capsular contracture remains an incompletely understood but common problem in breast implant surgery, advances in imaging, diagnostic, and molecular techniques can now provide more sophisticated insights into the pathophysiology of capsular contracture. Level of Evidence PMID:26229126
On the application of correlation function matrices in OMA
DEFF Research Database (Denmark)
Brincker, Rune
2017-01-01
In this paper the theoretical solution for the correlation function matrix of the random response of a structural system is re-visited. It is shown that using the classical definition of the correlation functions, the row space is defined by the mode shapes of the system, whereas the column space...
Application of Random Matrix Theory to Complex Networks
Rai, Aparna; Jalan, Sarika
The present article provides an overview of recent developments in spectral analysis of complex networks under random matrix theory framework. Adjacency matrix of unweighted networks, reviewed here, differ drastically from a random matrix, as former have only binary entries. Remarkably, short range correlations in corresponding eigenvalues of such matrices exhibit Gaussian orthogonal statistics of RMT and thus bring them into the universality class. Spectral rigidity of spectra provides measure of randomness in underlying networks. We will consider several examples of model networks vastly studied in last two decades. To the end we would provide potential of RMT framework and obtained results to understand and predict behavior of complex systems with underlying network structure.
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.
Gelatin Nanofiber Matrices Derived from Schiff Base Derivative for Tissue Engineering Applications.
Jaiswal, Devina; James, Roshan; Shelke, Namdev B; Harmon, Matthew D; Brown, Justin L; Hussain, Fazle; Kumbar, Sangamesh G
2015-11-01
Electrospinning of water-soluble polymers and retaining their mechanical strength and bioactivity remain challenging. Volatile organic solvent soluble polymers and their derivatives are preferred for fabricating electrospun nanofibers. We report the synthesis and characterization of 2-nitrobenzyl-gelatin (N-Gelatin)--a novel gelatin Schiff base derivative--and the resulting electrospun nanofiber matrices. The 2-nitrobenzyl group is a photoactivatable-caged compound and can be cleaved from the gelatin nanofiber matrices following UV exposure. Such hydrophobic modification allowed the fabrication of gelatin and blend nanofibers with poly(caprolactone) (PCL) having significantly improved tensile properties. Neat gelatin and their PCL blend nanofiber matrices showed a modulus of 9.08 ± 1.5 MPa and 27.61 ± 4.3 MPa, respectively while the modified gelatin and their blends showed 15.63 ± 2.8 MPa and 24.47 ± 8.7 MPa, respectively. The characteristic infrared spectroscopy band for gelatin Schiff base derivative at 1560 cm(-1) disappeared following exposure to UV light indicating the regeneration of free NH2 group and gelatin. These nanofiber matrices supported cell attachment and proliferation with a well spread morphology as evidenced through cell proliferation assay and microscopic techniques. Modified gelatin fiber matrices showed a 73% enhanced cell attachment and proliferation rate compared to pure gelatin. This polymer modification methodology may offer a promising way to fabricate electrospun nanofiber matrices using a variety of proteins and peptides without loss of bioactivity and mechanical strength.
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.
Application of avidin-biotin technology to improve cell adhesion on nanofibrous matrices.
Pan, Jian-feng; Liu, Ning-hua; Shu, Lin-yuan; Sun, Hui
2015-05-16
Electrospinning is an easy and effective technique to produce submicron fibers possessing a range of attractive characteristics such as interconnected porous structures similar to natural ECM and good resilience to movement. Rapid and efficient cell attachment to nanofibrous matrices is a necessary prerequisite in tissue engineering. Thus, the aim of this study is to evaluate poly(ε-caprolactone-co-lactide)/Pluronic (PLCL/Pluronic) nanofibrous matrices with avidin-biotin technology for improving cell adhesion for the first time. PLCL/Pluronic nanofibers had relatively homogeneous fibers and interconnected porous structures. Pluronic significantly modified the hydrophilicity of nanofibrous matrices and PLCL/Pluronic nanofibrous matrices had better performance on maintaining cell proliferation. Avidin-biotin technology had no negative effect on the hydrophilic property, mechanical property and cell proliferation. Meanwhile, the attachment and spreading of adipose-derived stem cells (ADSCs) onto PLCL/Pluronic nanofibrous matrices with avidin-biotin technology was promoted obviously. PLCL/Pluronic nanofibrous matrices inheriting the excellent characteristics of both PLCL and Pluronic have the better cell adhesion ability through avidin-biotin technology, implying a promising application in skin care, tissue regeneration and other related area.
Helary, Christophe; Abed, Aicha; Mosser, Gervaise; Louedec, Liliane; Letourneur, Didier; Coradin, Thibaud; Giraud-Guille, Marie Madeleine; Meddahi-Pellé, Anne
2015-02-01
Cutaneous chronic wounds are characterized by an impaired wound healing which may lead to infection and amputation. When current treatments are not effective enough, the application of wound dressings is required. To date, no ideal biomaterial is available. In this study, highly dense collagen matrices have been evaluated as novel medicated wound dressings for the treatment of chronic wounds. For this purpose, the structure, mechanical properties, swelling ability and in vivo stability of matrices concentrated from 5 to 40 mg mL(-1) were tested. The matrix stiffness increased with the collagen concentration and was associated with the fibril density and thickness. Increased collagen concentration also enhanced the material resistance against accelerated digestion by collagenase. After subcutaneous implantation in rats, dense collagen matrices exhibited high stability without any degradation after 15 days. The absence of macrophages and neutrophils evidenced their biocompatibility. Subsequently, dense matrices at 40 mg mL(-1) were evaluated as drug delivery system for ampicillin release. More concentrated matrices exhibited the best swelling abilities and could absorb 20 times their dry weight in water, allowing for an efficient antibiotic loading from their dried form. They released efficient doses of antibiotics that inhibited the bacterial growth of Staphylococcus Aureus over 3 days. In parallel, they show no cytotoxicity towards human fibroblasts. These results show that dense collagen matrices are promising materials to develop medicated wound dressings for the treatment of chronic wounds.
Unique and concise system translation matrices for evaluating optical aberration variations.
Chen, Chaohsien
2017-08-01
New unique and concise translation matrices are derived for evaluating the aberration variations of conceptual and real lenses when the paraxial marginal and chief ray paths are arbitrarily changed. They are helpful in investigating the general behaviors of lenses and optimizing the balanced aberrations of lens components in prime and zoom lenses. These new matrices, with a dimension of 9×9 for monochromatic aberrations and a dimension of 4×4 for chromatic aberrations, are derived based on our earlier algorithms of which four cases with distinct translation factors and matrices are required according to the relationships of the original and new positions of the object and pupil; otherwise, division-by-zero errors or insufficient numerical accuracy will be encountered. As a comparison, the new matrices have several advantages. First, by introducing four meaningful equivalent optical invariants, multiplying the old matrices, and simplifying the new matrices, they have concise expressions to significantly reduce the calculation time. Second, they are unique and always accurate to apply for all kinds of object and pupil positions without suffering any mathematical problems, i.e., four separated algorithms are no longer necessary. Third, due to the unique property, the component contributions of original aberrations to new aberrations can be directly evaluated and analyzed.
The Role of Dermal Matrices in Treating Inflammatory and Diabetic Wounds.
Climov, Mihail; Bayer, Lauren R; Moscoso, Andrea V; Matsumine, Hajime; Orgill, Dennis P
2016-09-01
Dermal matrices are used to improve healing in both acute and chronic wounds including diabetic and lower extremity wounds, burns, trauma, and surgical reconstruction. The use of dermal matrices for the closure of inflammatory ulcerations is less frequent but growing. Currently available products include decellularized dermis and semisynthetic matrices. A review of the published literature was performed to identify reports that use acellular dermal matrices in diabetic and inflammatory wounds. Studies were evaluated for quality and outcomes, and a level of evidence was assigned according to the American Society of Plastic Surgeons' Rating Levels of Evidence. Case studies from the authors' experience are also presented. Seventeen primary studies evaluating the use of dermal matrices in diabetic ulcers were identified with 2 based on level I data. There are no prospective clinical trial reports of their use in atypical or inflammatory wounds, but there are several case studies. Treatment of diabetic and inflammatory wounds may include both medical and surgical modalities. The use of dermal matrices can be a useful adjunct, but their optimal use will require future clinical studies.
Soft matrices downregulate FAK activity to promote growth of tumor-repopulating cells.
Tan, Youhua; Wood, Adam Richard; Jia, Qiong; Zhou, Wenwen; Luo, Junyu; Yang, Fang; Chen, Junwei; Chen, Junjian; Sun, Jian; Seong, Jihye; Tajik, Arash; Singh, Rishi; Wang, Ning
2017-01-29
Tumor-repopulating cells (TRCs) are a tumorigenic sub-population of cancer cells that drives tumorigenesis. We have recently reported that soft fibrin matrices maintain TRC growth by promoting histone 3 lysine 9 (H3K9) demethylation and Sox2 expression and that Cdc42 expression influences H3K9 methylation. However, the underlying mechanisms of how soft matrices induce H3K9 demethylation remain elusive. Here we find that TRCs exhibit lower focal adhesion kinase (FAK) and H3K9 methylation levels in soft fibrin matrices than control melanoma cells on 2D rigid substrates. Silencing FAK in control melanoma cells decreases H3K9 methylation, whereas overexpressing FAK in tumor-repopulating cells enhances H3K9 methylation. Overexpressing Cdc42 or RhoA in the presence of FAK knockdown restores H3K9 methylation levels. Importantly, silencing FAK, Cdc42, or RhoA promotes Sox2 expression and proliferation of control melanoma cells in stiff fibrin matrices, whereas overexpressing each gene suppresses Sox2 expression and reduces growth of TRCs in soft but not in stiff fibrin matrices. Our findings suggest that low FAK mediated by soft fibrin matrices downregulates H3K9 methylation through reduction of Cdc42 and RhoA and promotes TRC growth. Copyright © 2016 Elsevier Inc. All rights reserved.
Younis, Assiel J; Lerer-Serfaty, Galit; Stav, Dana; Sabbah, Bethsabee; Shochat, Tzippy; Kessler-Icekson, Gania; Zahalka, Muayad A; Shachar-Goldenberg, Michal; Ben-Haroush, Avi; Fisch, Benjamin; Abir, Ronit
2017-02-01
The possibility of maturing human primordial follicles in vitro would assist fertility restoration without the danger of reseeding malignancies. Leukaemia inhibitory factor (LIF) and certain culture matrices may promote human follicular growth. The present study compared human primordial follicular growth on novel culture matrices, namely human recombinant vitronectin (hrVit), small intestine submucosa (SIS), alginate scaffolds and human recombinant virgin collagen bioengineered in tobacco plant lines (CollPlant). The frozen-thawed ovarian samples that were used had been obtained from girls or young women undergoing fertility preservation. In the first part of the study, 20 samples were cultured for 6 days on hrVit or SIS with basic culture medium alone or supplemented with one of two concentrations of LIF (10ngmL-1 and 100ngmL-1), with and without LIF-neutralising antibody. In the second part of the study, 15 samples were cultured for 6 days on alginate scaffolds or CollPlant matrices with basic culture medium. Follicular development was assessed by follicular counts and classification, Ki67 immunohistochemistry and 17β-oestradiol and anti-Müllerian hormone measurements in spent media samples. Primordial follicular growth was not enhanced by LIF. Despite some significant differences among the four matrices, none appeared to have a clear advantage, apart from significantly more Ki67-stained follicles on alginate and CollPlant matrices. Further studies of other culture matrices and medium supplements are needed to obtain an optimal system.