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
Garcia, R.D.M.
1984-01-01
A new technique for generating the isotropic and linearly anisotropic componets of elastic and discrete inelastic transfer matrices is proposed. The technique allows certain angular integrals to be expressed in terms of functions that can be computed by recursion relations or series expansions alternatively to the use of numerical quadratures. (Author) [pt
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
Matching with transfer matrices
Perez-Alvarez, R.; Velasco, V.R.; Garcia-Moliner, F.; Rodriguez-Coppola, H.
1987-10-01
An ABC configuration - which corresponds to various systems of physical interest, such as a barrier or a quantum well - is studied by combining a surface Green function matching analysis of the entire system with a description of the intermediate (B) region in terms of a transfer matrix in the sense of Mora et al. (1985). This hybrid approach proves very useful when it is very difficult to construct the corresponding Green function G B . An application is made to the calculation of quantised subband levels in a parabolic quantum well. Further possibilities of extension of this approach are pointed out. (author). 27 refs, 1 tab
Transfer matrices for multilayer structures
Baquero, R.
1988-08-01
We consider four of the transfer matrices defined to deal with multilayer structures. We deduce algorithms to calculate them numerically, in a simple and neat way. We illustrate their application to semi-infinite systems using SGFM formulae. These algorithms are of fast convergence and allow a calculation of bulk-, surface- and inner-layers band structure in good agreement with much more sophisticated calculations. Supermatrices, interfaces and multilayer structures can be calculated in this way with a small computational effort. (author). 10 refs
Computing with linear equations and matrices
Churchhouse, R.F.
1983-01-01
Systems of linear equations and matrices arise in many disciplines. The equations may accurately represent conditions satisfied by a system or, more likely, provide an approximation to a more complex system of non-linear or differential equations. The system may involve a few or many thousand unknowns and each individual equation may involve few or many of them. Over the past 50 years a vast literature on methods for solving systems of linear equations and the associated problems of finding the inverse or eigenvalues of a matrix has been produced. These lectures cover those methods which have been found to be most useful for dealing with such types of problem. References are given where appropriate and attention is drawn to the possibility of improved methods for use on vector and parallel processors. (orig.)
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.
Linear circuit theory matrices in computer applications
Vlach, Jiri
2014-01-01
Basic ConceptsNodal and Mesh AnalysisMatrix MethodsDependent SourcesNetwork TransformationsCapacitors and InductorsNetworks with Capacitors and InductorsFrequency DomainLaplace TransformationTime DomainNetwork FunctionsActive NetworksTwo-PortsTransformersModeling and Numerical MethodsSensitivitiesModified Nodal FormulationFourier Series and TransformationAppendix: Scaling of Linear Networks.
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...
Solution of generalized shifted linear systems with complex symmetric matrices
Sogabe, Tomohiro; Hoshi, Takeo; Zhang, Shao-Liang; Fujiwara, Takeo
2012-01-01
We develop the shifted COCG method [R. Takayama, T. Hoshi, T. Sogabe, S.-L. Zhang, T. Fujiwara, Linear algebraic calculation of Green’s function for large-scale electronic structure theory, Phys. Rev. B 73 (165108) (2006) 1–9] and the shifted WQMR method [T. Sogabe, T. Hoshi, S.-L. Zhang, T. Fujiwara, On a weighted quasi-residual minimization strategy of the QMR method for solving complex symmetric shifted linear systems, Electron. Trans. Numer. Anal. 31 (2008) 126–140] for solving generalized shifted linear systems with complex symmetric matrices that arise from the electronic structure theory. The complex symmetric Lanczos process with a suitable bilinear form plays an important role in the development of the methods. The numerical examples indicate that the methods are highly attractive when the inner linear systems can efficiently be solved.
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.
Linear algebra for dense matrices on a hypercube
Sears, M.P.
1990-01-01
A set of routines has been written for dense matrix operations optimized for the NCUBE/6400 parallel processor. This paper was motivated by a Sandia effort to parallelize certain electronic structure calculations. Routines are included for matrix transpose, multiply, Cholesky decomposition, triangular inversion, and Householder tridiagonalization. The library is written in C and is callable from Fortran. Matrices up to order 1600 can be handled on 128 processors. For each operation, the algorithm used is presented along with typical timings and estimates of performance. Performance for order 1600 on 128 processors varies from 42 MFLOPs (House-holder tridiagonalization, triangular inverse) up to 126 MFLOPs (matrix multiply). The authors also present performance results for communications and basic linear algebra operations (saxpy and dot products)
Diagonalization of replicated transfer matrices for disordered Ising spin systems
Nikoletopoulos, T; Coolen, A C C
2004-01-01
We present an alternative procedure for solving the eigenvalue problem of replicated transfer matrices describing disordered spin systems with (random) 1D nearest neighbour bonds and/or random fields, possibly in combination with (random) long range bonds. Our method is based on transforming the original eigenvalue problem for a 2 n x 2 n matrix (where n → 0) into an eigenvalue problem for integral operators. We first develop our formalism for the Ising chain with random bonds and fields, where we recover known results. We then apply our methods to models of spins which interact simultaneously via a one-dimensional ring and via more complex long-range connectivity structures, e.g., (1 + ∞)-dimensional neural networks and 'small-world' magnets. Numerical simulations confirm our predictions satisfactorily
Parallel family trees for transfer matrices in the Potts model
Navarro, Cristobal A.; Canfora, Fabrizio; Hitschfeld, Nancy; Navarro, Gonzalo
2015-02-01
The computational cost of transfer matrix methods for the Potts model is related to the question in how many ways can two layers of a lattice be connected? Answering the question leads to the generation of a combinatorial set of lattice configurations. This set defines the configuration space of the problem, and the smaller it is, the faster the transfer matrix can be computed. The configuration space of generic (q , v) transfer matrix methods for strips is in the order of the Catalan numbers, which grows asymptotically as O(4m) where m is the width of the strip. Other transfer matrix methods with a smaller configuration space indeed exist but they make assumptions on the temperature, number of spin states, or restrict the structure of the lattice. In this paper we propose a parallel algorithm that uses a sub-Catalan configuration space of O(3m) to build the generic (q , v) transfer matrix in a compressed form. The improvement is achieved by grouping the original set of Catalan configurations into a forest of family trees, in such a way that the solution to the problem is now computed by solving the root node of each family. As a result, the algorithm becomes exponentially faster than the Catalan approach while still highly parallel. The resulting matrix is stored in a compressed form using O(3m ×4m) of space, making numerical evaluation and decompression to be faster than evaluating the matrix in its O(4m ×4m) uncompressed form. Experimental results for different sizes of strip lattices show that the parallel family trees (PFT) strategy indeed runs exponentially faster than the Catalan Parallel Method (CPM), especially when dealing with dense transfer matrices. In terms of parallel performance, we report strong-scaling speedups of up to 5.7 × when running on an 8-core shared memory machine and 28 × for a 32-core cluster. The best balance of speedup and efficiency for the multi-core machine was achieved when using p = 4 processors, while for the cluster
SNR Estimation in Linear Systems with Gaussian Matrices
Suliman, Mohamed Abdalla Elhag; Alrashdi, Ayed; Ballal, Tarig; Al-Naffouri, Tareq Y.
2017-01-01
This letter proposes a highly accurate algorithm to estimate the signal-to-noise ratio (SNR) for a linear system from a single realization of the received signal. We assume that the linear system has a Gaussian matrix with one sided left correlation. The unknown entries of the signal and the noise are assumed to be independent and identically distributed with zero mean and can be drawn from any distribution. We use the ridge regression function of this linear model in company with tools and techniques adapted from random matrix theory to achieve, in closed form, accurate estimation of the SNR without prior statistical knowledge on the signal or the noise. Simulation results show that the proposed method is very accurate.
SNR Estimation in Linear Systems with Gaussian Matrices
Suliman, Mohamed Abdalla Elhag
2017-09-27
This letter proposes a highly accurate algorithm to estimate the signal-to-noise ratio (SNR) for a linear system from a single realization of the received signal. We assume that the linear system has a Gaussian matrix with one sided left correlation. The unknown entries of the signal and the noise are assumed to be independent and identically distributed with zero mean and can be drawn from any distribution. We use the ridge regression function of this linear model in company with tools and techniques adapted from random matrix theory to achieve, in closed form, accurate estimation of the SNR without prior statistical knowledge on the signal or the noise. Simulation results show that the proposed method is very accurate.
Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices
Freund, Roland
1989-01-01
We consider conjugate gradient type methods for the solution of large sparse linear system Ax equals b with complex symmetric coefficient matrices A equals A(T). Such linear systems arise in important applications, such as the numerical solution of the complex Helmholtz equation. Furthermore, most complex non-Hermitian linear systems which occur in practice are actually complex symmetric. We investigate conjugate gradient type iterations which are based on a variant of the nonsymmetric Lanczos algorithm for complex symmetric matrices. We propose a new approach with iterates defined by a quasi-minimal residual property. The resulting algorithm presents several advantages over the standard biconjugate gradient method. We also include some remarks on the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.
Comparison results on preconditioned SOR-type iterative method for Z-matrices linear systems
Wang, Xue-Zhong; Huang, Ting-Zhu; Fu, Ying-Ding
2007-09-01
In this paper, we present some comparison theorems on preconditioned iterative method for solving Z-matrices linear systems, Comparison results show that the rate of convergence of the Gauss-Seidel-type method is faster than the rate of convergence of the SOR-type iterative method.
Secret Message Decryption: Group Consulting Projects Using Matrices and Linear Programming
Gurski, Katharine F.
2009-01-01
We describe two short group projects for finite mathematics students that incorporate matrices and linear programming into fictional consulting requests presented as a letter to the students. The students are required to use mathematics to decrypt secret messages in one project involving matrix multiplication and inversion. The second project…
DOWNER (version 79-1): group collapse cross section and transfer matrices
Cullen, D.E.
1979-01-01
FORTRAN-callable subroutines are provided to allow a user to group-collapse cross sections and/or transfer matrices from any arbitrary initial group structure to any arbitrary final group structure. 3 figures
Surprisal analysis and probability matrices for rotational energy transfer
Levine, R.D.; Bernstein, R.B.; Kahana, P.; Procaccia, I.; Upchurch, E.T.
1976-01-01
The information-theoretic approach is applied to the analysis of state-to-state rotational energy transfer cross sections. The rotational surprisal is evaluated in the usual way, in terms of the deviance of the cross sections from their reference (''prior'') values. The surprisal is found to be an essentially linear function of the energy transferred. This behavior accounts for the experimentally observed exponential gap law for the hydrogen halide systems. The data base here analyzed (taken from the literature) is largely computational in origin: quantal calculations for the hydrogenic systems H 2 +H, He, Li + ; HD+He; D 2 +H and for the N 2 +Ar system; and classical trajectory results for H 2 +Li + ; D 2 +Li + and N 2 +Ar. The surprisal analysis not only serves to compact a large body of data but also aids in the interpretation of the results. A single surprisal parameter theta/subR/ suffices to account for the (relative) magnitude of all state-to-state inelastic cross sections at a given energy
A class of singular Ro-matrices and extensions to semidefinite linear complementarity problems
Sivakumar K.C.
2013-01-01
Full Text Available For ARnxn and qRn, the linear complementarity problem LCP(A, q is to determine if there is xRn such that x ≥ 0; y = Ax + q ≥ 0 and xT y = 0. Such an x is called a solution of LCP(A,q. A is called an Ro-matrix if LCP(A,0 has zero as the only solution. In this article, the class of R0-matrices is extended to include typically singular matrices, by requiring in addition that the solution x above belongs to a subspace of Rn. This idea is then extended to semidefinite linear complementarity problems, where a characterization is presented for the multplicative transformation.
Hamid Reza Bahrami
2007-01-01
Full Text Available The ergodic capacity of MIMO frequency-flat and -selective channels depends greatly on the eigenvalue distribution of spatial correlation matrices. Knowing the eigenstructure of correlation matrices at the transmitter is very important to enhance the capacity of the system. This fact becomes of great importance in MIMO wireless systems where because of the fast changing nature of the underlying channel, full channel knowledge is difficult to obtain at the transmitter. In this paper, we first investigate the effect of eigenvalues distribution of spatial correlation matrices on the capacity of frequency-flat and -selective channels. Next, we introduce a practical scheme known as linear precoding that can enhance the ergodic capacity of the channel by changing the eigenstructure of the channel by applying a linear transformation. We derive the structures of precoders using eigenvalue decomposition and linear algebra techniques in both cases and show their similarities from an algebraic point of view. Simulations show the ability of this technique to change the eigenstructure of the channel, and hence enhance the ergodic capacity considerably.
Groups, matrices, and vector spaces a group theoretic approach to linear algebra
Carrell, James B
2017-01-01
This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory ...
Transfer matrices and excitations with matrix product states
Zauner, V; Rams, M M; Verstraete, F; Draxler, D; Vanderstraeten, L; Degroote, M; Haegeman, J; Stojevic, V; Schuch, N
2015-01-01
We use the formalism of tensor network states to investigate the relation between static correlation functions in the ground state of local quantum many-body Hamiltonians and the dispersion relations of the corresponding low-energy excitations. In particular, we show that the matrix product state transfer matrix (MPS-TM)—a central object in the computation of static correlation functions—provides important information about the location and magnitude of the minima of the low-energy dispersion relation(s), and we present supporting numerical data for one-dimensional lattice and continuum models as well as two-dimensional lattice models on a cylinder. We elaborate on the peculiar structure of the MPS-TM’s eigenspectrum and give several arguments for the close relation between the structure of the low-energy spectrum of the system and the form of the static correlation functions. Finally, we discuss how the MPS-TM connects to the exact quantum transfer matrix of the model at zero temperature. We present a renormalization group argument for obtaining finite bond dimension approximations of the MPS, which allows one to reinterpret variational MPS techniques (such as the density matrix renormalization group) as an application of Wilson’s numerical renormalization group along the virtual (imaginary time) dimension of the system. (paper)
Misguich, J.H.
2004-04-01
As a first step toward a nonlinear renormalized description of turbulence phenomena in magnetized plasmas, the lowest order quasi-linear description is presented here from a unified point of view for collisionless as well as for collisional plasmas in a constant magnetic field. The quasi-linear approximation is applied to a general kinetic equation obtained previously from the Klimontovich exact equation, by means of a generalised Dupree-Weinstock method. The so-obtained quasi-linear description of electromagnetic turbulence in a magnetoplasma is applied to three separate physical cases: -) weak electrostatic turbulence, -) purely magnetic field fluctuations (the classical quasi-linear results are obtained for cosmic ray diffusion in the 'slab model' of magnetostatic turbulence in the solar wind), and -) collisional kinetic equations of magnetized plasmas. This mathematical technique has allowed us to derive basic kinetic equations for turbulent plasmas and collisional plasmas, respectively in the quasi-linear and Landau approximation. In presence of a magnetic field we have shown that the systematic use of rotation matrices describing the helical particle motion allows for a much more compact derivation than usually performed. Moreover, from the formal analogy between turbulent and collisional plasmas, the results derived here in detail for the turbulent plasmas, can be immediately translated to obtain explicit results for the Landau kinetic equation
Misguich, J.H
2004-04-01
As a first step toward a nonlinear renormalized description of turbulence phenomena in magnetized plasmas, the lowest order quasi-linear description is presented here from a unified point of view for collisionless as well as for collisional plasmas in a constant magnetic field. The quasi-linear approximation is applied to a general kinetic equation obtained previously from the Klimontovich exact equation, by means of a generalised Dupree-Weinstock method. The so-obtained quasi-linear description of electromagnetic turbulence in a magnetoplasma is applied to three separate physical cases: -) weak electrostatic turbulence, -) purely magnetic field fluctuations (the classical quasi-linear results are obtained for cosmic ray diffusion in the 'slab model' of magnetostatic turbulence in the solar wind), and -) collisional kinetic equations of magnetized plasmas. This mathematical technique has allowed us to derive basic kinetic equations for turbulent plasmas and collisional plasmas, respectively in the quasi-linear and Landau approximation. In presence of a magnetic field we have shown that the systematic use of rotation matrices describing the helical particle motion allows for a much more compact derivation than usually performed. Moreover, from the formal analogy between turbulent and collisional plasmas, the results derived here in detail for the turbulent plasmas, can be immediately translated to obtain explicit results for the Landau kinetic equation.
Butrymowicz Dariusz
2016-09-01
Full Text Available The theoretical basis for the indirect measurement approach of mean heat transfer coefficient for the packed bed based on the modified single blow technique was presented and discussed in the paper. The methodology of this measurement approach dedicated to the matrix of the rotating regenerative gas heater was discussed in detail. The testing stand consisted of a dedicated experimental tunnel with auxiliary equipment and a measurement system are presented. Selected experimental results are presented and discussed for selected types of matrices of regenerative air preheaters for the wide range of Reynolds number of gas. The agreement between the theoretically predicted and measured temperature profiles was demonstrated. The exemplary dimensionless relationships between Colburn heat transfer factor, Darcy flow resistance factor and Reynolds number were presented for the investigated matrices of the regenerative gas heater.
Properties of the transfer matrices of deflecting magnet systems for free electron laser
Takao, Masaru
1993-01-01
The oscillation of the free electron laser (FEL) requires the high current and low emittance electron beam. The beam transport system should be achromatic and isochronous to preserve the brightness and the emittance of the electron beam. In this paper we clarify the algebraic properties of the transfer matrices of the magnetic deflection system, which is a key component in the beam transport line. (author)
СREATION OF CORRELATION FUNCTIONS OF LINEAR CONTINUOUS SYSTEMS BASED ON THEIR FUNDAMENTAL MATRICES
N. A. Vunder
2015-11-01
Full Text Available The paper presents a method of creating correlation matrices and functions of the state vectors and outputs of the linear continuous systems functioning under the conditions of stochastic stationary, in a broad sense, effects. Fundamental matrices form the basis of the method. We have shown that for the linear continuous systems with single dimensional input and single dimensional output the correlation output function of such system can be found as the free movement of this system generated by its initial state. This state is constructed from the variance matrix of the state vector and the transposed output matrix. We have elucidated that when a continuous system belongs to a class of multi-dimensional input – multi-dimensional output systems, the following options are available for solving the problem of creation of the correlation function of a linear system. The first option is to partition the system into separate channels. Then the approach developed for systems with onedimensional input and one-dimensional output is applied to each of the separate channels. The second option is used to preserve the vector nature of the stochastic external influence. It consists in partition of output vector to scalar components by separating output matrix into separate rows with subsequent formation of the correlation function according to the scheme for single dimensional input and single dimensional output type systems. The third option is based on the scalarization of matrix correlation output function by applying the singular value decomposition to it. That gives the possibility to form scalar majorant and minorant of correlation output functions. We have established that a key component of a computational procedure of creating the correlation function of continuous linear system is a variance matrix of the system state vector. In the case of functioning under an exogenous stochastic effect like "white noise" the variance matrix is calculated by
Diagonal K-matrices and transfer matrix eigenspectra associated with the G(1)2 R-matrix
Yung, C.M.; Batchelor, M.T.
1995-01-01
We find all the diagonal K-matrices for the R-matrix associated with the minimal representation of the exceptional affine algebra G (1) 2 . The corresponding transfer matrices are diagonalized with a variation of the analytic Bethe ansatz. We find many similarities with the case of the Izergin-Korepin R-matrix associated with the affine algebra A (2) 2 . ((orig.))
Linear Maps on Upper Triangular Matrices Spaces Preserving Idempotent Tensor Products
Li Yang
2014-01-01
Full Text Available Suppose m, n≥2 are positive integers. Let n be the space of all n×n complex upper triangular matrices, and let ϕ be an injective linear map on m⊗n. Then ϕ(A⊗B is an idempotent matrix in m⊗n whenever A⊗B is an idempotent matrix in m⊗n if and only if there exists an invertible matrix P∈m⊗n such that ϕ(A⊗B=P(ξ1(A⊗ξ2(BP-1, ∀A∈m, B∈n, or when m=n, ϕ(A⊗B=P(ξ1(B⊗ξ2(AP-1, ∀A∈m, B∈m, where ξ1([aij]=[aij] or ξ1([aij]=[am-i+1, m-j+1] and ξ2([bij]=[bij] or ξ2([bij]=[bn-i+1, n-j+1].
Online monitoring of dispersion functions and transfer matrices at the SLC
Emma, P.; Fieguth, T.H.; Lohse, T.; Burchat, P.R.; Panvini, R.S.
1989-03-01
The symmetries of the chromatic correction sections in the SLC Final Focus System allow a high-resolution determination of the pulse-to-pulse energy fluctuations by exploiting the information from beam position monitors (BPMs) in regions of large dispersion. By correlating this signal with other BPMs, one can infer the dispersion function as well as spatial components of transfer matrices anywhere in the arcs and the Final Focus System without interrupting normal machine operation. We present results from data recorded during either periods of stable operation or periods when the linac energy was intentionally varied. 6 refs., 7 figs
A. Aminataei
2014-05-01
Full Text Available In this paper, a new and ecient approach is applied for numerical approximation of the linear dierential equations with variable coecients based on operational matrices with respect to Hermite polynomials. Explicit formulae which express the Hermite expansioncoecients for the moments of derivatives of any dierentiable function in terms of the original expansion coecients of the function itself are given in the matrix form. The mainimportance of this scheme is that using this approach reduces solving the linear dierentialequations to solve a system of linear algebraic equations, thus greatly simplifying the problem. In addition, two experiments are given to demonstrate the validity and applicability of the method
Linear motor with contactless energy transfer
2014-01-01
An integrated electromagnetic energy conversions device is provided that includes a synchronous or brushless linear (SoBL) motor, and a transformer, where the transformer is integrated electromagnetically and topologically with the SoBL motor, where an electromagnetic field orientation of the
High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices
Dunham, Benjamin Z.
This work presents a new automatic differentiation method, Nilpotent Matrix Differentiation (NMD), capable of propagating any order of mixed or univariate derivative through common linear algebra functions--most notably third-party sparse solvers and decomposition routines, in addition to basic matrix arithmetic operations and power series--without changing data-type or modifying code line by line; this allows differentiation across sequences of arbitrarily many such functions with minimal implementation effort. NMD works by enlarging the matrices and vectors passed to the routines, replacing each original scalar with a matrix block augmented by derivative data; these blocks are constructed with special sparsity structures, termed "stencils," each designed to be isomorphic to a particular multidimensional hypercomplex algebra. The algebras are in turn designed such that Taylor expansions of hypercomplex function evaluations are finite in length and thus exactly track derivatives without approximation error. Although this use of the method in the "forward mode" is unique in its own right, it is also possible to apply it to existing implementations of the (first-order) discrete adjoint method to find high-order derivatives with lowered cost complexity; for example, for a problem with N inputs and an adjoint solver whose cost is independent of N--i.e., O(1)--the N x N Hessian can be found in O(N) time, which is comparable to existing second-order adjoint methods that require far more problem-specific implementation effort. Higher derivatives are likewise less expensive--e.g., a N x N x N rank-three tensor can be found in O(N2). Alternatively, a Hessian-vector product can be found in O(1) time, which may open up many matrix-based simulations to a range of existing optimization or surrogate modeling approaches. As a final corollary in parallel to the NMD-adjoint hybrid method, the existing complex-step differentiation (CD) technique is also shown to be capable of
TRANSFER-FUNCTIONS OF A LINEARIZED MULTI-REGION REACTOR
Higgins, Thomas J.
1963-09-15
The development of the transfer functions for a linearized multi-region reactor is studied, and an illustration is made of application of the corresponding theory by a numerical illustrative example. (auth)
A differential calculus for random matrices with applications to (max,+)-linear stochastic systems
Heidergott, B.F.
2001-01-01
We introducet he concept of weak differentiabilityf or randomm atricesa nd therebyo btain closedform analytical expressions for derivatives of functions of random matrices. More specifically, we develop a calculus of weak differentiationf or randomm atricest hat resembles the standardc alculus of
Overall mass-transfer coefficients in non-linear chromatography
Mollerup, Jørgen; Hansen, Ernst
1998-01-01
In case of mass transfer where concentration differences in both phases must be taken into account, one may define an over-all mass-transfer coefficient basd on the apparent over-all concentration difference. If the equilibrium relationship is linear, i.e. in cases where a Henry´s law relationshi...
Towards linearization of atmospheric radiative transfer in spherical geometry
Walter, Holger H.; Landgraf, Jochen
2005-01-01
We present a general approach for the linearization of radiative transfer in a spherical planetary atmosphere. The approach is based on the forward-adjoint perturbation theory. In the first part we develop the theoretical background for a linearization of radiative transfer in spherical geometry. Using an operator formulation of radiative transfer allows one to derive the linearization principles in a universally valid notation. The application of the derived principles is demonstrated for a radiative transfer problem in simplified spherical geometry in the second part of this paper. Here, we calculate the derivatives of the radiance at the top of the atmosphere with respect to the absorption properties of a trace gas species in the case of a nadir-viewing satellite instrument
Bui Xuan Hai.
1990-05-01
For an arbitrary skew field T we study the lattice of subgroups of the special linear group Γ=SL(n,T) that contain the subgroup Δ-SD(n,T) of diagonal matrices with Dieudonne's determinant equal to 1. We show that the description of these subgroups is standard in the following sense: For any subgroup H,Δ≤H≤Γ there exists a unique unital net such that Γ(σ) ≤H≤N(σ), where Γ(σ) is the net subgroup that corresponds to the net σ and N(σ) is the normalizer of Γ(σ) in Γ. (author). 11 refs
Behavioral modeling of the dominant dynamics in input-output transfer of linear(ized) circuits
Beelen, T.G.J.; Maten, ter E.J.W.; Sihaloho, H.J.; Eijndhoven, van S.J.L.
2010-01-01
We present a powerful procedure for determining both the dominant dynamics of the inputoutput transfer and the corresponding most influential circuit parameters of a linear(ized) circuit. The procedure consists of several steps in which a specific (sub)problem is solved and its solution is used in
Linear circuit transfer functions an introduction to fast analytical techniques
Basso, Christophe P
2016-01-01
Linear Circuit Transfer Functions: An introduction to Fast Analytical Techniques teaches readers how to determine transfer functions of linear passive and active circuits by applying Fast Analytical Circuits Techniques. Building on their existing knowledge of classical loop/nodal analysis, the book improves and expands their skills to unveil transfer functions in a swift and efficient manner. Starting with simple examples, the author explains step-by-step how expressing circuits time constants in different configurations leads to writing transfer functions in a compact and insightful way. By learning how to organize numerators and denominators in the fastest possible way, readers will speed-up analysis and predict the frequency resp nse of simple to complex circuits. In some cases, they will be able to derive the final expression by inspection, without writing a line of algebra. Key features: * Emphasizes analysis through employing time constant-based methods discussed in other text books but not widely us...
Application of gamma ray spectrometry for evaluation of transfer factors in environmental matrices
Rao, D.D.
2008-01-01
Gamma Ray Spectrometry (GRS) is performed using a variety of radiation detectors, to identify and determine radioactivity concentration of gamma emitting radionuclides qualitatively, in a wide range of samples. The samples can be of a high inventory power plant origin, NORM category or low level environmental samples, around a power plant. The method is usually applied to non-destructive analysis of environmental samples. However, it can also be applied to destructive analysis i.e. following extraction/separation of the analyte from the sample, if there is a need to pre-concentrate the analyte. The accuracy and precision of the method, depends on the quality of calibration, correction methods employed, stability of the system components, computational algorithms used, analysis of sources of uncertainties etc. The transfer factors among the environmental matrices are simple ratios, but the methodologies used in generating the respective concentrations have to be appropriately documented, including the validity of measurements. Validation mechanisms can include the results of international inter-comparison exercises, the certificates of standards issued by quality-accredited international laboratories. A few parameters involved in the qualitative analysis of gamma spectrometry are discussed here
Basilevsky, M. V.; Odinokov, A. V.; Titov, S. V.; Mitina, E. A.
2013-12-01
The algorithm for a theoretical calculation of transfer reaction rates for light quantum particles (i.e., the electron and H-atom transfers) in non-polar solid matrices is formulated and justified. The mechanism postulated involves a local mode (an either intra- or inter-molecular one) serving as a mediator which accomplishes the energy exchange between the reacting high-frequency quantum mode and the phonon modes belonging to the environment. This approach uses as a background the Fermi golden rule beyond the usually applied spin-boson approximation. The dynamical treatment rests on the one-dimensional version of the standard quantum relaxation equation for the reduced density matrix, which describes the frequency fluctuation spectrum for the local mode under consideration. The temperature dependence of a reaction rate is controlled by the dimensionless parameter ξ0 = ℏω0/kBT where ω0 is the frequency of the local mode and T is the temperature. The realization of the computational scheme is different for the high/intermediate (ξ0 conduction in photosensitive organic materials is considered, based on the above techniques. The electron transfer (ET) in active centers of such systems proceeds via local intra- and intermolecular modes. The active modes, as a rule, operate beyond the kinetic regimes, which are usually postulated in the existing theories of the ET. Our alternative dynamic ET model for local modes immersed in the continuum harmonic medium is formulated for both classical and quantum regimes, and accounts explicitly for the mode/medium interaction. The kinetics of the energy exchange between the local ET subsystem and the surrounding environment essentially determine the total ET rate. The efficient computer code for rate computations is elaborated on. The computations are available for a wide range of system parameters, such as the temperature, external field, local mode frequency, and characteristics of mode/medium interaction. The relation of the
Bouclé, J.; Kassiba, A.; Makowska-Janusik, M.; Herlin-Boime, N.; Reynaud, C.; Desert, A.; Emery, J.; Bulou, A.; Sanetra, J.; Pud, A. A.; Kodjikian, S.
2006-11-01
An electro-optical activity has been recently reported for hybrid nanocomposite thin films where inorganic silicon carbide nanocrystals (ncSiC) are incorporated into polymer matrices. The role of the interface SiC polymer is suggested as the origin of the observed second order nonlinear optical susceptibility in the hybrid materials based on poly-(methylmethacrylate) (PMMA) or poly-( N -vinylcarbazole) matrices. In this work, we report an analysis of the electro-optical response of this hybrid system as a function of the ncSiC content and surface state in order to precise the interface effect in the observed phenomenon. Two specific ncSiC samples with similar morphology and different surface states are incorporated in the PMMA matrix. The effective Pockels parameters of the corresponding hybrid nanocomposites have been estimated up to 7.59±0.74pm/V ( 1wt.% of ncSiC in the matrix). The interfacial region ncSiC polymer is found to play the main role in the observed effect. Particularly, the electronic defects on the ncSiC nanocrystal surface modify the interfacial electrical interactions between the two components. The results are interpreted and discussed on the basis of the strong influence of these active centers in the interfacial region at the nanoscale, which are found to monitor the local hyperpolarizabilities and the macroscopic nonlinear optical susceptibilities. This approach allows us to complete the description and understanding of the electro-optical response in the hybrid SiC /polymer systems.
An improved error bound for linear complementarity problems for B-matrices
Lei Gao
2017-06-01
Full Text Available Abstract A new error bound for the linear complementarity problem when the matrix involved is a B-matrix is presented, which improves the corresponding result in (Li et al. in Electron. J. Linear Algebra 31(1:476-484, 2016. In addition some sufficient conditions such that the new bound is sharper than that in (García-Esnaola and Peña in Appl. Math. Lett. 22(7:1071-1075, 2009 are provided.
M. Merlin
2010-04-01
Full Text Available In questo studio sono stati caratterizzati giunti Friction Stir Welding e Linear Friction Welding su compositi a matrice in lega di alluminio e rinforzo particellare ceramico. Il processo FSW è stato applicato a due compositi ottenuti con processo fusorio, quindi estrusi e trattati termicamente T6: AA6061/20%vol.Al2O3p e AA7005/10%vol.Al2O3p. I giunti LFW sono stati invece realizzati su un composito con matrice in lega di alluminio e rinforzo particellare in carburo di silicio, ottenuto mediante metallurgia delle polveri, quindi forgiato e trattato termicamente T4: AA2124/25%vol.SiCp. Sono stati esaminati gli effetti della saldatura sullecaratteristiche microstrutturali dei giunti, avvalendosi di tecniche di microscopia ottica con analisi di immagine e di microscopia elettronica in scansione (SEM con microsonda a dispersione di energia (EDS. Sono state quindi condotte prove di resilienza con pendolo strumentato Charpy. Lo studio dei meccanismi di danneggiamento è stato effettuato mediante analisi al SEM delle superfici di frattura. Entrambi i processi di saldatura hanno portato a giunti sostanzialmente esenti da difetti. La microstruttura dei cordoni è risultata dipendente sia dalle caratteristiche microstrutturali iniziali dei compositi considerati, sia dalla tipologia di processo di saldatura. Nel caso dei compositi AA6061/20%Al2O3p e AA7005/10%Al2O3p saldati FSW si è osservato un sostanziale incremento di resilienza, rispetto al materiale base, in conseguenza dell’affinamento dei grani della matrice, della riduzione della dimensione media delle particelle di rinforzo e della loro spigolosità, indotte dal processo di saldatura. Il composito AA2124/25%SiCp saldato LFW ha presentato valori di resilienza confrontabili con quelli del materiale base, in conseguenza, soprattutto, dei limitati effetti della saldatura su dimensione e distribuzione delle particelle di rinforzo.
Mordik, S N
2002-01-01
The third-order transfer matrices are calculated for an electrostatic toroidal sector condenser using a rigorously conserved matrix method that implies the conservation of the beam phase volume at each step in the calculations. The transfer matrices (matrizants) obtained, include the fringing-field effect due to the stray fields. In the case of a rectangular distribution of the field components along the optical axis, the analytical expressions for all aberration coefficients, including the dispersion ones, are derived accurate to the third-order terms. In simulations of real fields with the stray field width other than zero, a smooth distribution of the field components is used for which similar aberration coefficients were calculated by means of the conserved numerical method . It has been found that for a smooth model, as the stray field width tends to zero, the aberration coefficients approach the corresponding aberration values in the rectangular model.
Mordik, S.N.; Ponomarev, A.G.
2002-01-01
The third-order transfer matrices are calculated for an electrostatic toroidal sector condenser using a rigorously conserved matrix method that implies the conservation of the beam phase volume at each step in the calculations. The transfer matrices (matrizants) obtained, include the fringing-field effect due to the stray fields. In the case of a rectangular distribution of the field components along the optical axis, the analytical expressions for all aberration coefficients, including the dispersion ones, are derived accurate to the third-order terms. In simulations of real fields with the stray field width other than zero, a smooth distribution of the field components is used for which similar aberration coefficients were calculated by means of the conserved numerical method . It has been found that for a smooth model, as the stray field width tends to zero, the aberration coefficients approach the corresponding aberration values in the rectangular model
New classical r-matrices from integrable non-linear sigma-models
Laartz, J.; Bordemann, M.; Forger, M.; Schaper, U.
1993-01-01
Non-linear sigma models on Riemannian symmetric spaces constitute the most general class of classical non-linear sigma models which are known to be integrable. Using the current algebra structure of these models their canonical structure is analyzed and it is shown that their non-ultralocal fundamental Poisson bracket relation is governed by a field dependent non antisymmetric r-matrix obeying a dynamical Yang Baxter equation. The fundamental Poisson bracket relations and the r-matrix are derived explicitly and a new kind of algebra is found that is supposed to replace the classical Yang Baxter algebra governing the canonical structure of ultralocal models. (Author) 9 refs
Adaptive Kronrod-Patterson integration of non-linear finite-element matrices
Janssen, Hans
2010-01-01
inappropriate discretization. In response, this article develops adaptive integration, based on nested Kronrod-Patterson-Gauss integration schemes: basically, the integration order is adapted to the locally observed grade of non-linearity. Adaptive integration is developed based on a standard infiltration...
Basilevsky, M. V.; Mitina, E. A.; Odinokov, A. V.; Titov, S. V.
2013-01-01
The algorithm for a theoretical calculation of transfer reaction rates for light quantum particles (i.e., the electron and H-atom transfers) in non-polar solid matrices is formulated and justified. The mechanism postulated involves a local mode (an either intra- or inter-molecular one) serving as a mediator which accomplishes the energy exchange between the reacting high-frequency quantum mode and the phonon modes belonging to the environment. This approach uses as a background the Fermi golden rule beyond the usually applied spin-boson approximation. The dynamical treatment rests on the one-dimensional version of the standard quantum relaxation equation for the reduced density matrix, which describes the frequency fluctuation spectrum for the local mode under consideration. The temperature dependence of a reaction rate is controlled by the dimensionless parameter ξ 0 =ℏω 0 /k B T where ω 0 is the frequency of the local mode and T is the temperature. The realization of the computational scheme is different for the high/intermediate (ξ 0 0 ≫ 1) temperature ranges. For the first (quasi-classical) kinetic regime, the Redfield approximation to the solution of the relaxation equation proved to be sufficient and efficient in practical applications. The study of the essentially quantum-mechanical low-temperature kinetic regime in its asymptotic limit requires the implementation of the exact relaxation equation. The coherent mechanism providing a non-vanishing reaction rate has been revealed when T→ 0. An accurate computational methodology for the cross-over kinetic regime needs a further elaboration. The original model of the hopping mechanism for electronic conduction in photosensitive organic materials is considered, based on the above techniques. The electron transfer (ET) in active centers of such systems proceeds via local intra- and intermolecular modes. The active modes, as a rule, operate beyond the kinetic regimes, which are usually postulated in the
Basilevsky, M. V.; Mitina, E. A. [Photochemistry Center, Russian Academy of Sciences, 7a, Novatorov ul., Moscow (Russian Federation); Odinokov, A. V. [Photochemistry Center, Russian Academy of Sciences, 7a, Novatorov ul., Moscow (Russian Federation); National Research Nuclear University “MEPhI,” 31, Kashirskoye shosse, Moscow (Russian Federation); Titov, S. V. [Karpov Institute of Physical Chemistry, 3-1/12, Building 6, Obuha pereulok, Moscow (Russian Federation)
2013-12-21
The algorithm for a theoretical calculation of transfer reaction rates for light quantum particles (i.e., the electron and H-atom transfers) in non-polar solid matrices is formulated and justified. The mechanism postulated involves a local mode (an either intra- or inter-molecular one) serving as a mediator which accomplishes the energy exchange between the reacting high-frequency quantum mode and the phonon modes belonging to the environment. This approach uses as a background the Fermi golden rule beyond the usually applied spin-boson approximation. The dynamical treatment rests on the one-dimensional version of the standard quantum relaxation equation for the reduced density matrix, which describes the frequency fluctuation spectrum for the local mode under consideration. The temperature dependence of a reaction rate is controlled by the dimensionless parameter ξ{sub 0}=ℏω{sub 0}/k{sub B}T where ω{sub 0} is the frequency of the local mode and T is the temperature. The realization of the computational scheme is different for the high/intermediate (ξ{sub 0} < 1 − 3) and for low (ξ{sub 0}≫ 1) temperature ranges. For the first (quasi-classical) kinetic regime, the Redfield approximation to the solution of the relaxation equation proved to be sufficient and efficient in practical applications. The study of the essentially quantum-mechanical low-temperature kinetic regime in its asymptotic limit requires the implementation of the exact relaxation equation. The coherent mechanism providing a non-vanishing reaction rate has been revealed when T→ 0. An accurate computational methodology for the cross-over kinetic regime needs a further elaboration. The original model of the hopping mechanism for electronic conduction in photosensitive organic materials is considered, based on the above techniques. The electron transfer (ET) in active centers of such systems proceeds via local intra- and intermolecular modes. The active modes, as a rule, operate beyond the
Basilevsky, M V; Odinokov, A V; Titov, S V; Mitina, E A
2013-12-21
The algorithm for a theoretical calculation of transfer reaction rates for light quantum particles (i.e., the electron and H-atom transfers) in non-polar solid matrices is formulated and justified. The mechanism postulated involves a local mode (an either intra- or inter-molecular one) serving as a mediator which accomplishes the energy exchange between the reacting high-frequency quantum mode and the phonon modes belonging to the environment. This approach uses as a background the Fermi golden rule beyond the usually applied spin-boson approximation. The dynamical treatment rests on the one-dimensional version of the standard quantum relaxation equation for the reduced density matrix, which describes the frequency fluctuation spectrum for the local mode under consideration. The temperature dependence of a reaction rate is controlled by the dimensionless parameter ξ0 = ℏω0/k(B)T where ω0 is the frequency of the local mode and T is the temperature. The realization of the computational scheme is different for the high/intermediate (ξ0 regime, the Redfield approximation to the solution of the relaxation equation proved to be sufficient and efficient in practical applications. The study of the essentially quantum-mechanical low-temperature kinetic regime in its asymptotic limit requires the implementation of the exact relaxation equation. The coherent mechanism providing a non-vanishing reaction rate has been revealed when T → 0. An accurate computational methodology for the cross-over kinetic regime needs a further elaboration. The original model of the hopping mechanism for electronic conduction in photosensitive organic materials is considered, based on the above techniques. The electron transfer (ET) in active centers of such systems proceeds via local intra- and intermolecular modes. The active modes, as a rule, operate beyond the kinetic regimes, which are usually postulated in the existing theories of the ET. Our alternative dynamic ET model for local
Two new modified Gauss-Seidel methods for linear system with M-matrices
Zheng, Bing; Miao, Shu-Xin
2009-12-01
In 2002, H. Kotakemori et al. proposed the modified Gauss-Seidel (MGS) method for solving the linear system with the preconditioner [H. Kotakemori, K. Harada, M. Morimoto, H. Niki, A comparison theorem for the iterative method with the preconditioner () J. Comput. Appl. Math. 145 (2002) 373-378]. Since this preconditioner is constructed by only the largest element on each row of the upper triangular part of the coefficient matrix, the preconditioning effect is not observed on the nth row. In the present paper, to deal with this drawback, we propose two new preconditioners. The convergence and comparison theorems of the modified Gauss-Seidel methods with these two preconditioners for solving the linear system are established. The convergence rates of the new proposed preconditioned methods are compared. In addition, numerical experiments are used to show the effectiveness of the new MGS methods.
2D and 3D Matrices to Study Linear Invadosome Formation and Activity.
Di Martino, Julie; Henriet, Elodie; Ezzoukhry, Zakaria; Mondal, Chandrani; Bravo-Cordero, Jose Javier; Moreau, Violaine; Saltel, Frederic
2017-06-02
Cell adhesion, migration, and invasion are involved in many physiological and pathological processes. For example, during metastasis formation, tumor cells have to cross anatomical barriers to invade and migrate through the surrounding tissue in order to reach blood or lymphatic vessels. This requires the interaction between cells and the extracellular matrix (ECM). At the cellular level, many cells, including the majority of cancer cells, are able to form invadosomes, which are F-actin-based structures capable of degrading ECM. Invadosomes are protrusive actin structures that recruit and activate matrix metalloproteinases (MMPs). The molecular composition, density, organization, and stiffness of the ECM are crucial in regulating invadosome formation and activation. In vitro, a gelatin assay is the standard assay used to observe and quantify invadosome degradation activity. However, gelatin, which is denatured collagen I, is not a physiological matrix element. A novel assay using type I collagen fibrils was developed and used to demonstrate that this physiological matrix is a potent inducer of invadosomes. Invadosomes that form along the collagen fibrils are known as linear invadosomes due to their linear organization on the fibers. Moreover, molecular analysis of linear invadosomes showed that the discoidin domain receptor 1 (DDR1) is the receptor involved in their formation. These data clearly demonstrate the importance of using a physiologically relevant matrix in order to understand the complex interactions between cells and the ECM.
Introduction into Hierarchical Matrices
Litvinenko, Alexander
2013-12-05
Hierarchical matrices allow us to reduce computational storage and cost from cubic to almost linear. This technique can be applied for solving PDEs, integral equations, matrix equations and approximation of large covariance and precision matrices.
Introduction into Hierarchical Matrices
Litvinenko, Alexander
2013-01-01
Hierarchical matrices allow us to reduce computational storage and cost from cubic to almost linear. This technique can be applied for solving PDEs, integral equations, matrix equations and approximation of large covariance and precision matrices.
Appel, H.
2007-05-01
In part I of this work we present a double-pole approximation (DPA) to the response equations of time-dependent density functional theory (TDDFT). The double-pole approximation provides an exact description of systems with two strongly coupled excitations which are isolated from the rest of the spectrum. In contrast to the traditional single-pole approximation of TDDFT the DPA also yields corrections to the Kohn-Sham oscillator strengths. We also demonstrate how to invert the double-pole solution which allows us to predict matrix elements of the exchange-correlation kernel f xc from experimental input. We attempt some first steps towards a time-dependent generalization of reduced density matrix functional theory (RDMFT). In part II we derive equations of motion for natural orbitals and occupation numbers. Using the equation of motion for the occupation numbers we show that an adiabatic extension of presently known ground-state functionals of static RDMFT always leads to occupation numbers which are constant in time. From the stationary conditions of the equations of motion for the N-body correlations (correlated parts of the N-body matrices) we derive a new class of ground-state functionals which can be used in static RDMFT. Applications are presented for a one-dimensional model system where the time-dependent many-body Schroedinger equation can be propagated numerically. We use optimal control theory to find optimized laser pulses for transitions in a model for atomic Helium. From the numerically exact correlated wavefunction we extract the exact time evolution of natural orbitals and occupation numbers for (i) laser-driven Helium and (ii) electron-ion scattering. Part III of this work considers time-dependent quantum transport within TDDFT. We present an algorithm for the calculation of extended eigenstates of single-particle Hamiltonians which is especially tailored to a finite-difference discretization of the Schroedinger equation. We consider the propagation
Appel, H.
2007-05-15
In part I of this work we present a double-pole approximation (DPA) to the response equations of time-dependent density functional theory (TDDFT). The double-pole approximation provides an exact description of systems with two strongly coupled excitations which are isolated from the rest of the spectrum. In contrast to the traditional single-pole approximation of TDDFT the DPA also yields corrections to the Kohn-Sham oscillator strengths. We also demonstrate how to invert the double-pole solution which allows us to predict matrix elements of the exchange-correlation kernel f{sub xc} from experimental input. We attempt some first steps towards a time-dependent generalization of reduced density matrix functional theory (RDMFT). In part II we derive equations of motion for natural orbitals and occupation numbers. Using the equation of motion for the occupation numbers we show that an adiabatic extension of presently known ground-state functionals of static RDMFT always leads to occupation numbers which are constant in time. From the stationary conditions of the equations of motion for the N-body correlations (correlated parts of the N-body matrices) we derive a new class of ground-state functionals which can be used in static RDMFT. Applications are presented for a one-dimensional model system where the time-dependent many-body Schroedinger equation can be propagated numerically. We use optimal control theory to find optimized laser pulses for transitions in a model for atomic Helium. From the numerically exact correlated wavefunction we extract the exact time evolution of natural orbitals and occupation numbers for (i) laser-driven Helium and (ii) electron-ion scattering. Part III of this work considers time-dependent quantum transport within TDDFT. We present an algorithm for the calculation of extended eigenstates of single-particle Hamiltonians which is especially tailored to a finite-difference discretization of the Schroedinger equation. We consider the
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.
Jessamine P Winer
2009-07-01
Full Text Available Most tissue cells grown in sparse cultures on linearly elastic substrates typically display a small, round phenotype on soft substrates and become increasingly spread as the modulus of the substrate increases until their spread area reaches a maximum value. As cell density increases, individual cells retain the same stiffness-dependent differences unless they are very close or in molecular contact. On nonlinear strain-stiffening fibrin gels, the same cell types become maximally spread even when the low strain elastic modulus would predict a round morphology, and cells are influenced by the presence of neighbors hundreds of microns away. Time lapse microscopy reveals that fibroblasts and human mesenchymal stem cells on fibrin deform the substrate by several microns up to five cell lengths away from their plasma membrane through a force limited mechanism. Atomic force microscopy and rheology confirm that these strains locally and globally stiffen the gel, depending on cell density, and this effect leads to long distance cell-cell communication and alignment. Thus cells are acutely responsive to the nonlinear elasticity of their substrates and can manipulate this rheological property to induce patterning.
Mixed-mode chromatographic matrices for the resolution of transfer ribonucleic acids
Bischoff, Rainer; Mclaughlin, L.W.
1984-01-01
Modification of approximately 65% of the amine groups of an aminopropylsilyl bonded-phase silica high-performance liquid chromatographic anion exchanger (APS-Hypersil) with organic acids containing n-alkyl moieties of different chain lengths, results in mixed mode chromatographic matrices of varying
On Parametrization of the Linear GL(4,C) and Unitary SU(4) Groups in Terms of Dirac Matrices
Red'Kov, Victor M.; Bogush, Andrei A.; Tokarevskaya, Natalia G.
2008-02-01
Parametrization of 4 × 4-matrices G of the complex linear group GL(4,C) in terms of four complex 4-vector parameters (k,m,n,l) is investigated. Additional restrictions separating some subgroups of GL(4,C) are given explicitly. In the given parametrization, the problem of inverting any 4 × 4 matrix G is solved. Expression for determinant of any matrix G is found: det G = F(k,m,n,l). Unitarity conditions G+ = G-1 have been formulated in the form of non-linear cubic algebraic equations including complex conjugation. Several simplest solutions of these unitarity equations have been found: three 2-parametric subgroups G1, G2, G3 - each of subgroups consists of two commuting Abelian unitary groups; 4-parametric unitary subgroup consis! ting of a product of a 3-parametric group isomorphic SU(2) and 1-parametric Abelian group. The Dirac basis of generators Λk, being of Gell-Mann type, substantially differs from the basis λi used in the literature on SU(4) group, formulas relating them are found - they permit to separate SU(3) subgroup in SU(4). Special way to list 15 Dirac generators of GL(4,C) can be used {Λk} = {μiÅνjÅ(μiVνj = KÅL ÅM )}, which permit to factorize SU(4) transformations according to S = eiaμ eibνeikKeilLeimM, where two first factors commute with each other and are isomorphic to SU(2) group, the three last ones are 3-parametric groups, each of them consisting of three Abelian commuting unitary subgroups. Besides, the structure of fifteen Dirac matrices Λk permits to separate twenty 3-parametric subgroups in SU(4) isomorphic to SU(2); those subgroups might be used as bigger elementary blocks in constructing of a general transformation SU(4). It is shown how one can specify the present approach for the pseudounitary group SU(2,2) and SU(3,1).
Selinski, Natalie E.; Rasmussen, Chris; Wawro, Megan; Zandieh, Michelle
2014-01-01
The central goals of most introductory linear algebra courses are to develop students' proficiency with matrix techniques, to promote their understanding of key concepts, and to increase their ability to make connections between concepts. In this article, we present an innovative method using adjacency matrices to analyze students' interpretation…
Filtering Non-Linear Transfer Functions on Surfaces.
Heitz, Eric; Nowrouzezahrai, Derek; Poulin, Pierre; Neyret, Fabrice
2014-07-01
Applying non-linear transfer functions and look-up tables to procedural functions (such as noise), surface attributes, or even surface geometry are common strategies used to enhance visual detail. Their simplicity and ability to mimic a wide range of realistic appearances have led to their adoption in many rendering problems. As with any textured or geometric detail, proper filtering is needed to reduce aliasing when viewed across a range of distances, but accurate and efficient transfer function filtering remains an open problem for several reasons: transfer functions are complex and non-linear, especially when mapped through procedural noise and/or geometry-dependent functions, and the effects of perspective and masking further complicate the filtering over a pixel's footprint. We accurately solve this problem by computing and sampling from specialized filtering distributions on the fly, yielding very fast performance. We investigate the case where the transfer function to filter is a color map applied to (macroscale) surface textures (like noise), as well as color maps applied according to (microscale) geometric details. We introduce a novel representation of a (potentially modulated) color map's distribution over pixel footprints using Gaussian statistics and, in the more complex case of high-resolution color mapped microsurface details, our filtering is view- and light-dependent, and capable of correctly handling masking and occlusion effects. Our approach can be generalized to filter other physical-based rendering quantities. We propose an application to shading with irradiance environment maps over large terrains. Our framework is also compatible with the case of transfer functions used to warp surface geometry, as long as the transformations can be represented with Gaussian statistics, leading to proper view- and light-dependent filtering results. Our results match ground truth and our solution is well suited to real-time applications, requires only a few
Linearized vector radiative transfer model MCC++ for a spherical atmosphere
Postylyakov, O.V.
2004-01-01
Application of radiative transfer models has shown that optical remote sensing requires extra characteristics of radiance field in addition to the radiance intensity itself. Simulation of spectral measurements, analysis of retrieval errors and development of retrieval algorithms are in need of derivatives of radiance with respect to atmospheric constituents under investigation. The presented vector spherical radiative transfer model MCC++ was linearized, which allows the calculation of derivatives of all elements of the Stokes vector with respect to the volume absorption coefficient simultaneously with radiance calculation. The model MCC++ employs Monte Carlo algorithm for radiative transfer simulation and takes into account aerosol and molecular scattering, gas and aerosol absorption, and Lambertian surface albedo. The model treats a spherically symmetrical atmosphere. Relation of the estimated derivatives with other forms of radiance derivatives: the weighting functions used in gas retrieval and the air mass factors used in the DOAS retrieval algorithms, is obtained. Validation of the model against other radiative models is overviewed. The computing time of the intensity for the MCC++ model is about that for radiative models treating sphericity of the atmosphere approximately and is significantly shorter than that for the full spherical models used in the comparisons. The simultaneous calculation of all derivatives (i.e. with respect to absorption in all model atmosphere layers) and the intensity is only 1.2-2 times longer than the calculation of the intensity only
Garcia, R.D.M.
1985-01-01
The generalization of a semi-analytical technique for the evaluation of angular integrals that appear in the generation of elastic and discrete inelastic tranfer matrices for transport codes is carried out. In contrast to the generalized series expansions which are found to be too complex and thus of little practical value, when compared to the Gaussian quadrature technique, the recursion relations developed in this work are superior to the quadrature scheme, for those cases where the round-off error propagation is not significant. (Author) [pt
Pérez-Álvarez, R.; Pernas-Salomón, R.; Velasco, V. R.
2015-01-01
The transfer matrix method is usually employed to study problems described by $N$ equations of matrix Sturm-Liouville (MSL) kind. In some cases a numerical degradation (the so called $\\Omega d$ problem) appears thus impairing the performance of the method. We present here a procedure that can overcome this problem in the case of multilayer systems having piecewise constant coefficients. This is performed by studying the relations between the associated transfer matrix and other transfer matri...
Manin matrices and Talalaev's formula
Chervov, A; Falqui, G
2008-01-01
In this paper we study properties of Lax and transfer matrices associated with quantum integrable systems. Our point of view stems from the fact that their elements satisfy special commutation properties, considered by Yu I Manin some 20 years ago at the beginning of quantum group theory. These are the commutation properties of matrix elements of linear homomorphisms between polynomial rings; more explicitly these read: (1) elements of the same column commute; (2) commutators of the cross terms are equal: [M ij , M kl ] [M kj , M il ] (e.g. [M 11 , M 22 ] = [M 21 , M 12 ]). The main aim of this paper is twofold: on the one hand we observe and prove that such matrices (which we call Manin matrices in short) behave almost as well as matrices with commutative elements. Namely, the theorems of linear algebra (e.g., a natural definition of the determinant, the Cayley-Hamilton theorem, the Newton identities and so on and so forth) have a straightforward counterpart in the case of Manin matrices. On the other hand, we remark that such matrices are somewhat ubiquitous in the theory of quantum integrability. For instance, Manin matrices (and their q-analogs) include matrices satisfying the Yang-Baxter relation 'RTT=TTR' and the so-called Cartier-Foata matrices. Also, they enter Talalaev's remarkable formulae: det(∂ z -L gaudin (z)), det(1-e -∂z T Yangian (z)) for the 'quantum spectral curve', and appear in the separation of variables problem and Capelli identities. We show that theorems of linear algebra, after being established for such matrices, have various applications to quantum integrable systems and Lie algebras, e.g. in the construction of new generators in Z(U crit (gl-hat n )) (and, in general, in the construction of quantum conservation laws), in the Knizhnik-Zamolodchikov equation, and in the problem of Wick ordering. We propose, in the appendix, a construction of quantum separated variables for the XXX-Heisenberg system
Guernec, Anthony; Robichaud-Rincon, Philippe; Saucier, Linda
2012-10-01
Bacteria on meat are subjected to specific living conditions that differ drastically from typical laboratory procedures in synthetic media. This study was undertaken to determine the behavior of bacteria when transferred from a rich-liquid medium to solid matrices, as is the case during microbial process validation. Escherichia coli cultured in Brain-Heart Infusion (BHI) broth to different growth phases were inoculated in ground beef (GB) and stored at 5°C for 12 days or spread onto BHI agar and cooked meat medium (CMM), and incubated at 37°C for several hours. We monitored cell densities and the expression of σ factors and genes under their control over time. The initial growth phase of the inoculum influenced growth resumption after transfer onto BHI agar and CMM. Whatever the solid matrix, bacteria adapted to their new environment and did not perceive stress immediately after inoculation. During this period, the σ(E) and σ(H) regulons were not activated and rpoD mRNA levels adjusted quickly. The rpoS and gadA mRNA levels did not increase after inoculation on solid surfaces and displayed normal growth-dependent modifications. After transfer onto GB, dnaK and groEL gene expression was affected more by the low temperature than by the composition of a meat environment. Copyright © 2012 Elsevier Ltd. All rights reserved.
Zhou, L; Lund, M S; Wang, Y; Su, G
2014-08-01
This study investigated genomic predictions across Nordic Holstein and Nordic Red using various genomic relationship matrices. Different sources of information, such as consistencies of linkage disequilibrium (LD) phase and marker effects, were used to construct the genomic relationship matrices (G-matrices) across these two breeds. Single-trait genomic best linear unbiased prediction (GBLUP) model and two-trait GBLUP model were used for single-breed and two-breed genomic predictions. The data included 5215 Nordic Holstein bulls and 4361 Nordic Red bulls, which was composed of three populations: Danish Red, Swedish Red and Finnish Ayrshire. The bulls were genotyped with 50 000 SNP chip. Using the two-breed predictions with a joint Nordic Holstein and Nordic Red reference population, accuracies increased slightly for all traits in Nordic Red, but only for some traits in Nordic Holstein. Among the three subpopulations of Nordic Red, accuracies increased more for Danish Red than for Swedish Red and Finnish Ayrshire. This is because closer genetic relationships exist between Danish Red and Nordic Holstein. Among Danish Red, individuals with higher genomic relationship coefficients with Nordic Holstein showed more increased accuracies in the two-breed predictions. Weighting the two-breed G-matrices by LD phase consistencies, marker effects or both did not further improve accuracies of the two-breed predictions. © 2014 Blackwell Verlag GmbH.
Effect of high linear energy transfer radiation on biological membranes
Choudhary, D.; Srivastava, M.; Kale, R.K.; Sarma, A.
1998-01-01
Cellular membranes are vital elements, and their integrity is extremely essential for the viability of the cells. We studied the effects of high linear energy transfer (LET) radiation on the membranes. Rabbit erythrocytes (1 x 10 7 cells/ml) and microsomes (0.6 mg protein/ml) prepared from liver of rats were irradiated with 7 Li ions of energy 6.42 MeV/u and 16 O ions of energy 4.25 MeV/u having maximum LET values of 354 keV/μm and 1130 keV/μm, respectively. 7 Li- and 16 O-induced microsomal lipid peroxidation was found to increase with fluence. The 16 O ions were more effective than 7 Li ions, which could be due to the denser energy distribution in the track and the yield of free radicals. These findings suggested that the biological membranes could be peroxidized on exposure to high-LET radiation. Inhibition of the lipid peroxidation was observed in the presence of a membrane-active drug, chlorpromazine (CPZ), which could be due to scavenging of free radicals (mainly HO. and ROO.), electron donation, and hydrogen transfer reactions. The 7 Li and 16 O ions also induced hemolysis in erythrocytes. The extent of hemolysis was found to be a function of time and fluence, and showed a characteristic sigmoidal pattern. The 16 O ions were more effective in the lower fluence range than 7 Li ions. These results were compared with lipid peroxidation and hemolysis induced by gamma-radiation. (orig.)
Heavy ion mutagenesis: linear energy transfer effects and genetic linkage
Kronenberg, A.; Gauny, S.; Criddle, K.; Vannais, D.; Ueno, A.; Kraemer, S.; Waldren, C. A.; Chatterjee, A. (Principal Investigator)
1995-01-01
We have characterized a series of 69 independent mutants at the endogenous hprt locus of human TK6 lymphoblasts and over 200 independent S1-deficient mutants of the human x hamster hybrid cell line AL arising spontaneously or following low-fluence exposures to densely ionizing Fe ions (600 MeV/amu, linear energy transfer = 190 keV/microns). We find that large deletions are common. The entire hprt gene (> 44 kb) was missing in 19/39 Fe-induced mutants, while only 2/30 spontaneous mutants lost the entire hprt coding sequence. When the gene of interest (S1 locus = M1C1 gene) is located on a nonessential human chromosome 11, multilocus deletions of several million base pairs are observed frequently. The S1 mutation frequency is more than 50-fold greater than the frequency of hprt mutants in the same cells. Taken together, these results suggest that low-fluence exposures to Fe ions are often cytotoxic due to their ability to create multilocus deletions that may often include the loss of essential genes. In addition, the tumorigenic potential of these HZE heavy ions may be due to the high potential for loss of tumor suppressor genes. The relative insensitivity of the hprt locus to mutation is likely due to tight linkage to a gene that is required for viability.
Proton Linear Energy Transfer measurement using Emulsion Cloud Chamber
Shin, Jae-ik [Proton Therapy Center, National Cancer Center (Korea, Republic of); Division of Heavy Ion Clinical Research, Korea Institute of Radiological & Medical Sciences (KIRAMS), Seoul (Korea, Republic of); Park, Seyjoon [Department of Radiation Oncology, Samsung Medical Center, Sungkyunkwan University, School of Medicine, Seoul (Korea, Republic of); Kim, Haksoo; Kim, Meyoung [Proton Therapy Center, National Cancer Center (Korea, Republic of); Jeong, Chiyoung [Department of Radiation Oncology, Asan Medical Center, University of Ulsan College of Medicine, Seoul (Korea, Republic of); Cho, Sungkoo [Department of Radiation Oncology, Samsung Medical Center, Sungkyunkwan University, School of Medicine, Seoul (Korea, Republic of); Lim, Young Kyung; Shin, Dongho [Proton Therapy Center, National Cancer Center (Korea, Republic of); Lee, Se Byeong, E-mail: sblee@ncc.re.kr [Proton Therapy Center, National Cancer Center (Korea, Republic of); Morishima, Kunihiro; Naganawa, Naotaka; Sato, Osamu [Department of Physics, Nagoya University, Nagoya (Japan); Kwak, Jungwon [Department of Radiation Oncology, Asan Medical Center, University of Ulsan College of Medicine, Seoul (Korea, Republic of); Kim, Sung Hyun [Center for Underground Physics, Institute for Basic Science (IBS), Daejeon (Korea, Republic of); Cho, Jung Sook [Department of refinement education, Dongseo University, Busan (Korea, Republic of); Ahn, Jung Keun [Department of Physics, Korea University, Seoul (Korea, Republic of); Kim, Ji Hyun; Yoon, Chun Sil [Gyeongsang National University, Jinju (Korea, Republic of); Incerti, Sebastien [CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan (France); Université Bordeaux 1, CENBG, UMR 5797, F-33170 Gradignan (France)
2015-04-15
This study proposes to determine the correlation between the Volume Pulse Height (VPH) measured by nuclear emulsion and Linear Energy Transfer (LET) calculated by Monte Carlo simulation based on Geant4. The nuclear emulsion was irradiated at the National Cancer Center (NCC) with a therapeutic proton beam and was installed at 5.2 m distance from the beam nozzle structure with various thicknesses of water-equivalent material (PMMA) blocks to position with specific positions along the Bragg curve. After the beam exposure and development of the emulsion films, the films were scanned by S-UTS developed in Nagoya University. The proton tracks in the scanned films were reconstructed using the ‘NETSCAN’ method. Through this procedure, the VPH can be derived from each reconstructed proton track at each position along the Bragg curve. The VPH value indicates the magnitude of energy loss in proton track. By comparison with the simulation results obtained using Geant4, we found the correlation between the LET calculated by Monte Carlo simulation and the VPH measured by the nuclear emulsion.
Internal high linear energy transfer (LET) targeted radiotherapy for cancer
Allen, Barry J
2006-01-01
High linear energy transfer (LET) radiation for internal targeted therapy has been a long time coming on to the medical therapy scene. While fundamental principles were established many decades ago, the clinical implementation has been slow. Localized neutron capture therapy, and more recently systemic targeted alpha therapy, are at the clinical trial stage. What are the attributes of these therapies that have led a band of scientists and clinicians to dedicate so much of their careers? High LET means high energy density, causing double strand breaks in DNA, and short-range radiation, sparing adjacent normal tissues. This targeted approach complements conventional radiotherapy and chemotherapy. Such therapies fail on several fronts. Foremost is the complete lack of progress for the control of primary GBM, the holy grail for cancer therapies. Next is the inability to regress metastatic cancer on a systemic basis. This has been the task of chemotherapy, but palliation is the major application. Finally, there is the inability to inhibit the development of lethal metastatic cancer after successful treatment of the primary cancer. This review charts, from an Australian perspective, the developing role of local and systemic high LET, internal radiation therapy. (review)
Proton Linear Energy Transfer measurement using Emulsion Cloud Chamber
Shin, Jae-ik; Park, Seyjoon; Kim, Haksoo; Kim, Meyoung; Jeong, Chiyoung; Cho, Sungkoo; Lim, Young Kyung; Shin, Dongho; Lee, Se Byeong; Morishima, Kunihiro; Naganawa, Naotaka; Sato, Osamu; Kwak, Jungwon; Kim, Sung Hyun; Cho, Jung Sook; Ahn, Jung Keun; Kim, Ji Hyun; Yoon, Chun Sil; Incerti, Sebastien
2015-01-01
This study proposes to determine the correlation between the Volume Pulse Height (VPH) measured by nuclear emulsion and Linear Energy Transfer (LET) calculated by Monte Carlo simulation based on Geant4. The nuclear emulsion was irradiated at the National Cancer Center (NCC) with a therapeutic proton beam and was installed at 5.2 m distance from the beam nozzle structure with various thicknesses of water-equivalent material (PMMA) blocks to position with specific positions along the Bragg curve. After the beam exposure and development of the emulsion films, the films were scanned by S-UTS developed in Nagoya University. The proton tracks in the scanned films were reconstructed using the ‘NETSCAN’ method. Through this procedure, the VPH can be derived from each reconstructed proton track at each position along the Bragg curve. The VPH value indicates the magnitude of energy loss in proton track. By comparison with the simulation results obtained using Geant4, we found the correlation between the LET calculated by Monte Carlo simulation and the VPH measured by the nuclear emulsion
Proton Linear Energy Transfer measurement using Emulsion Cloud Chamber
Shin, Jae-ik; Park, Seyjoon; Kim, Haksoo; Kim, Meyoung; Jeong, Chiyoung; Cho, Sungkoo; Lim, Young Kyung; Shin, Dongho; Lee, Se Byeong; Morishima, Kunihiro; Naganawa, Naotaka; Sato, Osamu; Kwak, Jungwon; Kim, Sung Hyun; Cho, Jung Sook; Ahn, Jung Keun; Kim, Ji Hyun; Yoon, Chun Sil; Incerti, Sebastien
2015-04-01
This study proposes to determine the correlation between the Volume Pulse Height (VPH) measured by nuclear emulsion and Linear Energy Transfer (LET) calculated by Monte Carlo simulation based on Geant4. The nuclear emulsion was irradiated at the National Cancer Center (NCC) with a therapeutic proton beam and was installed at 5.2 m distance from the beam nozzle structure with various thicknesses of water-equivalent material (PMMA) blocks to position with specific positions along the Bragg curve. After the beam exposure and development of the emulsion films, the films were scanned by S-UTS developed in Nagoya University. The proton tracks in the scanned films were reconstructed using the 'NETSCAN' method. Through this procedure, the VPH can be derived from each reconstructed proton track at each position along the Bragg curve. The VPH value indicates the magnitude of energy loss in proton track. By comparison with the simulation results obtained using Geant4, we found the correlation between the LET calculated by Monte Carlo simulation and the VPH measured by the nuclear emulsion.
Collier, G.; Gibson, G.
1968-01-01
FORTRAN 4 program /P1-GAS/ calculates the P-O and P-1 transfer matrices for neutron moderation in a monatomic gas. The equations used are based on the conditions that there is isotropic scattering in the center-of-mass coordinate system, the scattering cross section is constant, and the target nuclear velocities satisfy a Maxwellian distribution.
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.
Soysal, A.O.; Semlyen, A.
1994-01-01
A general methodology is presented for the state equation approximation of a multiple input-output linear system from transfer matrix data. A complex transformation matrix, obtained by eigen analysis at a fixed frequency, is used for diagonalization of the transfer matrix over the whole frequency range. A scalar estimation procedure is applied for identification of the modal transfer functions. The state equations in the original coordinates are obtained by inverse transformation. An iterative Gauss-Newton refinement process is used to reduce the overall error of the approximation. The developed methodology is applied to the phase domain modeling of untransposed transmission lines. The approach makes it possible to perform EMTP calculations directly in the phase domain. This results in conceptual simplification and savings in computation time since modal transformations are not needed in the sequences of the transient analysis. The presented procedure is compared with the conventional modal approach in terms of accuracy and computation time
Maciej Leśkiewicz
2016-03-01
Full Text Available Quality of two linear methods (PCA and LDA applied to reduce dimensionality of feature analysis is compared and efficiency of their algorithms in classification of the selected biological materials according to their excitation-emission fluorescence matrices is examined. It has been found that LDA method reduces the dimensions (or a number of significant variables more effectively than PCA method. A relatively good discrimination within the examined biological material has been obtained with the use of LDA algorithm.[b]Keywords[/b]: Feature Analysis, Fluorescence Spectroscopy, Biological Material Classification
Linear energy transfer incorporated intensity modulated proton therapy optimization
Cao, Wenhua; Khabazian, Azin; Yepes, Pablo P.; Lim, Gino; Poenisch, Falk; Grosshans, David R.; Mohan, Radhe
2018-01-01
The purpose of this study was to investigate the feasibility of incorporating linear energy transfer (LET) into the optimization of intensity modulated proton therapy (IMPT) plans. Because increased LET correlates with increased biological effectiveness of protons, high LETs in target volumes and low LETs in critical structures and normal tissues are preferred in an IMPT plan. However, if not explicitly incorporated into the optimization criteria, different IMPT plans may yield similar physical dose distributions but greatly different LET, specifically dose-averaged LET, distributions. Conventionally, the IMPT optimization criteria (or cost function) only includes dose-based objectives in which the relative biological effectiveness (RBE) is assumed to have a constant value of 1.1. In this study, we added LET-based objectives for maximizing LET in target volumes and minimizing LET in critical structures and normal tissues. Due to the fractional programming nature of the resulting model, we used a variable reformulation approach so that the optimization process is computationally equivalent to conventional IMPT optimization. In this study, five brain tumor patients who had been treated with proton therapy at our institution were selected. Two plans were created for each patient based on the proposed LET-incorporated optimization (LETOpt) and the conventional dose-based optimization (DoseOpt). The optimized plans were compared in terms of both dose (assuming a constant RBE of 1.1 as adopted in clinical practice) and LET. Both optimization approaches were able to generate comparable dose distributions. The LET-incorporated optimization achieved not only pronounced reduction of LET values in critical organs, such as brainstem and optic chiasm, but also increased LET in target volumes, compared to the conventional dose-based optimization. However, on occasion, there was a need to tradeoff the acceptability of dose and LET distributions. Our conclusion is that the
Spectrum of quantum transfer matrices via classical many-body systems
Gorsky, A. [ITEP,Bolshaya Cheremushkinskaya str. 25, 117218, Moscow (Russian Federation); MIPT,Inststitutskii per. 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Zabrodin, A. [ITEP,Bolshaya Cheremushkinskaya str. 25, 117218, Moscow (Russian Federation); MIPT,Inststitutskii per. 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Institute of Biochemical Physics,Kosygina str. 4, 119991, Moscow (Russian Federation); National Research University Higher School of Economics,Myasnitskaya str. 20, 101000, Moscow (Russian Federation); Zotov, A. [ITEP,Bolshaya Cheremushkinskaya str. 25, 117218, Moscow (Russian Federation); MIPT,Inststitutskii per. 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Steklov Mathematical Institute, RAS,Gubkina str. 8, 119991, Moscow (Russian Federation)
2014-01-15
In this paper we clarify the relationship between inhomogeneous quantum spin chains and classical integrable many-body systems. It provides an alternative (to the nested Bethe ansatz) method for computation of spectra of the spin chains. Namely, the spectrum of the quantum transfer matrix for the inhomogeneous gl{sub n}-invariant XXX spin chain on N sites with twisted boundary conditions can be found in terms of velocities of particles in the rational N-body Ruijsenaars-Schneider model. The possible values of the velocities are to be found from intersection points of two Lagrangian submanifolds in the phase space of the classical model. One of them is the Lagrangian hyperplane corresponding to fixed coordinates of all N particles and the other one is an N-dimensional Lagrangian submanifold obtained by fixing levels of N classical Hamiltonians in involution. The latter are determined by eigenvalues of the twist matrix. To support this picture, we give a direct proof that the eigenvalues of the Lax matrix for the classical Ruijsenaars-Schneider model, where velocities of particles are substituted by eigenvalues of the spin chain Hamiltonians, calculated through the Bethe equations, coincide with eigenvalues of the twist matrix, with certain multiplicities. We also prove a similar statement for the gl{sub n} Gaudin model with N marked points (on the quantum side) and the Calogero-Moser system with N particles (on the classical side). The realization of the results obtained in terms of branes and supersymmetric gauge theories is also discussed.
IAS Admin
harmonic analysis and complex analysis, in ... gebra describes not only the study of linear transforma- tions and .... special case of the Jordan canonical form of matrices. ..... Richard Bronson, Schaum's Outline Series Theory And Problems Of.
Spurr, R.; Natraj, V.; Lerot, C.; Van Roozendael, M.; Loyola, D.
2013-01-01
Principal Component Analysis (PCA) is a promising tool for enhancing radiative transfer (RT) performance. When applied to binned optical property data sets, PCA exploits redundancy in the optical data, and restricts the number of full multiple-scatter calculations to those optical states corresponding to the most important principal components, yet still maintaining high accuracy in the radiance approximations. We show that the entire PCA RT enhancement process is analytically differentiable with respect to any atmospheric or surface parameter, thus allowing for accurate and fast approximations of Jacobian matrices, in addition to radiances. This linearization greatly extends the power and scope of the PCA method to many remote sensing retrieval applications and sensitivity studies. In the first example, we examine accuracy for PCA-derived UV-backscatter radiance and Jacobian fields over a 290–340 nm window. In a second application, we show that performance for UV-based total ozone column retrieval is considerably improved without compromising the accuracy. -- Highlights: •Principal Component Analysis (PCA) of spectrally-binned atmospheric optical properties. •PCA-based accelerated radiative transfer with 2-stream model for fast multiple-scatter. •Atmospheric and surface property linearization of this PCA performance enhancement. •Accuracy of PCA enhancement for radiances and bulk-property Jacobians, 290–340 nm. •Application of PCA speed enhancement to UV backscatter total ozone retrievals
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
Sanghavi, Suniti; Davis, Anthony B.; Eldering, Annmarie
2014-01-01
In this paper, we build up on the scalar model smartMOM to arrive at a formalism for linearized vector radiative transfer based on the matrix operator method (vSmartMOM). Improvements have been made with respect to smartMOM in that a novel method of computing intensities for the exact viewing geometry (direct raytracing) without interpolation between quadrature points has been implemented. Also, the truncation method employed for dealing with highly peaked phase functions has been changed to a vector adaptation of Wiscombe's delta-m method. These changes enable speedier and more accurate radiative transfer computations by eliminating the need for a large number of quadrature points and coefficients for generalized spherical functions. We verify our forward model against the benchmarking results of Kokhanovsky et al. (2010) [22]. All non-zero Stokes vector elements are found to show agreement up to mostly the seventh significant digit for the Rayleigh atmosphere. Intensity computations for aerosol and cloud show an agreement of well below 0.03% and 0.05% at all viewing angles except around the solar zenith angle (60°), where most radiative models demonstrate larger variances due to the strongly forward-peaked phase function. We have for the first time linearized vector radiative transfer based on the matrix operator method with respect to aerosol optical and microphysical parameters. We demonstrate this linearization by computing Jacobian matrices for all Stokes vector elements for a multi-angular and multispectral measurement setup. We use these Jacobians to compare the aerosol information content of measurements using only the total intensity component against those using the idealized measurements of full Stokes vector [I,Q,U,V] as well as the more practical use of only [I,Q,U]. As expected, we find for the considered example that the accuracy of the retrieved parameters improves when the full Stokes vector is used. The information content for the full Stokes
Cross-beam energy transfer: On the accuracy of linear stationary models in the linear kinetic regime
Debayle, A.; Masson-Laborde, P.-E.; Ruyer, C.; Casanova, M.; Loiseau, P.
2018-05-01
We present an extensive numerical study by means of particle-in-cell simulations of the energy transfer that occurs during the crossing of two laser beams. In the linear regime, when ions are not trapped in the potential well induced by the laser interference pattern, a very good agreement is obtained with a simple linear stationary model, provided the laser intensity is sufficiently smooth. These comparisons include different plasma compositions to cover the strong and weak Landau damping regimes as well as the multispecies case. The correct evaluation of the linear Landau damping at the phase velocity imposed by the laser interference pattern is essential to estimate the energy transfer rate between the laser beams, once the stationary regime is reached. The transient evolution obtained in kinetic simulations is also analysed by means of a full analytical formula that includes 3D beam energy exchange coupled with the ion acoustic wave response. Specific attention is paid to the energy transfer when the laser presents small-scale inhomogeneities. In particular, the energy transfer is reduced when the laser inhomogeneities are comparable with the Landau damping characteristic length of the ion acoustic wave.
Randrup, J.
1979-07-01
This lecture discusses a theory for the transport of mass, charge, linear, and angular momentum and energy in damped nuclear collisions, as induced by multiple transfer of individual nucleons. 11 references.
Direct interaction between linear electron transfer chains and solute transport systems in bacteria
Elferink, Marieke G.L.; Hellingwerf, Klaas J.; Belkum, Marco J. van; Poolman, Bert; Konings, Wil N.
1984-01-01
In studies on alanine and lactose transport in Rhodopseudomonas sphaeroides we have demonstrated that the rate of solute uptake in this phototrophic bacterium is regulated by the rate of light-induced cyclic electron transfer. In the present paper the interaction between linear electron transfer
Nygaard, K
1967-12-15
The numerical deconvolution of spectra is equivalent to the solution of a (large) system of linear equations with a matrix which is not necessarily a square matrix. The demand that the square sum of the residual errors shall be minimum is not in general sufficient to ensure a unique or 'sound' solution. Therefore other demands which may include the demand for minimum square errors are introduced which lead to 'sound' and 'non-oscillatory' solutions irrespective of the shape of the original matrix and of the determinant of the matrix of the normal equations.
Non-linearity in radiocaesium soil to plant transfer: fact or fiction?
Beresford, N.A.; Scott, W.A.; Wright, S.M.
2004-01-01
The basis premise of many radiological assessments is the assumption that the transfer of many radionuclides from soil to herbage and hence animal derived food products is a positive linear relationship for a given set of ecological conditions. However, a number of authors have published results which they conclude demonstrate non-linear transfer of radiocaesium to plants and animals with transfer being highest when soil concentrations are lowest. Whilst we may expect non-linear transfer of radionuclides under homeostatic control or present in comparatively large chemical quantities there appears no credible hypothesis to support such an observation for radiocaesium. In this paper we review those articles which have reported non-linear radiocaesium transfer and also analyse novel data. Mechanisms for the observation as presented in the original works are critically assessed. For instance, some authors have speculated that radiocaesium root uptake is saturated. We suggest that this is unlikely as whilst saturation of root uptake of radiocaesium has been observed above 1.37 mg Cs + L -1 in growth solutions, concentrations of Cs + in soil solutions are typically -1 , and 1 MBq m -2 of 137 Cs will add only 0.3 mg Cs + m -2 . We discuss alternative hypotheses to explain the reported observations and suggest that sampling bias, countermeasure application and statistical chance all contribute to the reported non-linearity in radiocaesium transfer. (author)
Numerical solution of non-linear dual-phase-lag bioheat transfer equation within skin tissues.
Kumar, Dinesh; Kumar, P; Rai, K N
2017-11-01
This paper deals with numerical modeling and simulation of heat transfer in skin tissues using non-linear dual-phase-lag (DPL) bioheat transfer model under periodic heat flux boundary condition. The blood perfusion is assumed temperature-dependent which results in non-linear DPL bioheat transfer model in order to predict more accurate results. A numerical method of line which is based on finite difference and Runge-Kutta (4,5) schemes, is used to solve the present non-linear problem. Under specific case, the exact solution has been obtained and compared with the present numerical scheme, and we found that those are in good agreement. A comparison based on model selection criterion (AIC) has been made among non-linear DPL models when the variation of blood perfusion rate with temperature is of constant, linear and exponential type with the experimental data and it has been found that non-linear DPL model with exponential variation of blood perfusion rate is closest to the experimental data. In addition, it is found that due to absence of phase-lag phenomena in Pennes bioheat transfer model, it achieves steady state more quickly and always predict higher temperature than thermal and DPL non-linear models. The effect of coefficient of blood perfusion rate, dimensionless heating frequency and Kirchoff number on dimensionless temperature distribution has also been analyzed. The whole analysis is presented in dimensionless form. Copyright © 2017 Elsevier Inc. All rights reserved.
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 ...
Finite element procedures for coupled linear analysis of heat transfer, fluid and solid mechanics
Sutjahjo, Edhi; Chamis, Christos C.
1993-01-01
Coupled finite element formulations for fluid mechanics, heat transfer, and solid mechanics are derived from the conservation laws for energy, mass, and momentum. To model the physics of interactions among the participating disciplines, the linearized equations are coupled by combining domain and boundary coupling procedures. Iterative numerical solution strategy is presented to solve the equations, with the partitioning of temporal discretization implemented.
Sentis, R.
1984-07-01
The radiative transfer equations may be approximated by a non linear diffusion equation (called Rosseland equation) when the mean free paths of the photons are small with respect to the size of the medium. Some technical assomptions are made, namely about the initial conditions, to avoid any problem of initial layer terms
Ferwerda, H.A.; Hoenders, B.J.; Slump, C.H.
The fully relativistic quantum mechanical treatment of paraxial electron-optical image formation initiated in the previous paper (this issue) is worked out and leads to a rigorous foundation of the linear transfer theory. Moreover, the status of the relativistic scaling laws for mass and wavelength,
Heat Transfer Characteristics on the Squealer Tip of gas turbine blade in a linear cascade
Lee, Woo Jin; Lee, Dong Hyun; Kim, Kyung Min; Cho, Hyung Hee; Lee, Dong Ho; Kang, Shin Hyoung
2007-01-01
The present study investigates local heat/mass transfer characteristics on blade tip surfaces with squealer rim in a linear cascade. A cascade experiment setup consists of three airfoils. The airfoil has variable tip clearance(1, 2, 3% of axial chord length) and rim height(3, 6, 9% of axial chord length). Main flow Reynolds number based on axial chord is 1.5 x 10 5 . The axial chord length and turning angle is 237mm and 126 .deg. respectively. Naphthalene sublimation method is used to measure detailed mass transfer coefficient on the blade. The results show that as the tip clearance increases, high heat transfer region moves from upstream to downstream. Also, as the rim height increases, high heat transfer region tends to move toward the suction side
Jeffrey R. Schmidt
2012-08-01
Full Text Available Using the most elementary methods and considerations, the solution of the star-triangle condition (a2+b2-c2/2ab = ((a’^2+(b’^2-(c’^2/2a’b’ is shown to be a necessary condition for the extension of the operator coalgebra of the six-vertex model to a bialgebra. A portion of the bialgebra acts as a spectrum-generating algebra for the algebraic Bethe ansatz, with which higher-dimensional representations of the bialgebra can be constructed. The star-triangle relation is proved to be necessary for the commutativity of the transfer matrices T(a, b, c and T(a’, b’, c’.
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…
Schwentner, N.; Koch, E.E.
1976-01-01
Thin films of solid Ar and Ne doped with 1% Xe were excited with photons in the energy range from 10 eV to 20 eV in order to measure the energy distribution of the emitted electrons. Binding energies of th host and guest levels are deduced. When host excitons are excited, strong emission of electrons is observed indicating an efficient transfer of the host exciton energy to the Xe guest atoms. The energy of the free excitons is transferred, as can be deduced from the kinetic energy of the photoemitted electrons, rather than the energy of the bound (self-trapped) excitons which are observed in luminescence experiments. Furthermore, there is a striking difference between the Ar and the Ne matrix: In the Ne matrix a fast relaxation from the n = 2 to the n = 1 state was observed and only the energy of the n = 1 exciton is transferred even when higher excitons are excited, in contrast to Ar, where the transferred energy is higher for excitation of the n = 2 excitons than for n = 1. From these observations, time hierarchies for the competition between electronic energy transfer and relaxation are deduced. (orig.) [de
Magnetically Suspended Linear Pulse Motor for Semiconductor Wafer Transfer in Vacuum Chamber
Moriyama, Shin-Ichi; Hiraki, Naoji; Watanabe, Katsuhide; Kanemitsu, Yoichi
1996-01-01
This paper describes a magnetically suspended linear pulse motor for a semiconductor wafer transfer robot in a vacuum chamber. The motor can drive a wafer transfer arm horizontally without mechanical contact. In the construction of the magnetic suspension system, four pairs of linear magnetic bearings for the lift control are used for the guidance control as well. This approach allows us to make the whole motor compact in size and light in weight. The tested motor consists of a double-sided stator and a transfer arm with a width of 50 mm and a total length of 700 mm. The arm, like a ladder in shape, is designed as the floating element with a tooth width of 4 mm (a tooth pitch of 8 mm). The mover mass is limited to about 1.6 kg by adopting such an arm structure, and the ratio of thrust to mover mass reaches to 3.2 N/kg under a broad air gap (1 mm) between the stator teeth and the mover teeth. The performance testing was carried out with a transfer distance less than 450 mm and a transfer speed less than 560 mm/s. The attitude of the arm was well controlled by the linear magnetic bearings with a combined use, and consequently the repeatability on the positioning of the arm reached to about 2 micron. In addition, the positioning accuracy was improved up to about 30 micron through a compensation of the 128-step wave current which was used for the micro-step drive with a step increment of 62.5 micron.
Energy storage and transfer with homopolar machine for a linear theta-pinch hybrid reactor
Vogel, H.F.; Brennan, M.; Dase, W.G.; Tolk, K.M.; Weldon, W.F.
1976-01-01
The energy storage and transfer system for the compression coils of a linear theta-pinch hybrid reactor (LTPHR) are described. High efficiency and low cost are the principal requirements for the energy storage and transfer of 25MJ/m or 25GJ for a 1-km LTPHR. The circuit efficiency must be approximately 90%, and the cost for the circuit 5-6c/J. Scaling laws and simple relationships between circuit efficiency and cost-per-unit energy as a function of the half cycle time are presented. An important consideration concerns the pulse repetition rate of 2.25 pulses per second, 70x10 6 shots/yr, or 1.7x10 9 shots over the 25-yr plant life. Current interruption to initiate energy transfer is not feasible at this rate. Therefore, a simple ringing circuit with contactors to make and break at the periodically occurring zero-current instances, is considered
Transfer of optical signals around bends in two-dimensional linear photonic networks
Nikolopoulos, G M
2015-01-01
The ability to navigate light signals in two-dimensional networks of waveguide arrays is a prerequisite for the development of all-optical integrated circuits for information processing and networking. In this article, we present a theoretical analysis of bending losses in linear photonic lattices with engineered couplings, and discuss possible ways for their minimization. In contrast to previous work in the field, the lattices under consideration operate in the linear regime, in the sense that discrete solitons cannot exist. The present results suggest that the functionality of linear waveguide networks can be extended to operations that go beyond the recently demonstrated point-to-point transfer of signals, such as blocking, routing, logic functions, etc. (paper)
Athanasios D. Karageorgos
2009-01-01
Full Text Available In many applications, and generally speaking in many dynamical differential systems, the problem of transferring the initial state of the system to a desired state in (almost zero-time time is desirable but difficult to achieve. Theoretically, this can be achieved by using a linear combination of Dirac -function and its derivatives. Obviously, such an input is physically unrealizable. However, we can think of it approximately as a combination of small pulses of very high magnitude and infinitely small duration. In this paper, the approximation process of the distributional behaviour of higher-order linear descriptor (regular differential systems is presented. Thus, new analytical formulae based on linear algebra methods and generalized inverses theory are provided. Our approach is quite general and some significant conditions are derived. Finally, a numerical example is presented and discussed.
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...
Purice, A.; Schou, Jørgen; Dinescu, M.
2006-01-01
Emission of PEG (polyethylene glycol) molecules and ions from an ice target induced by laser irradiation in the infrared (IR) regime at 1064 nm was studied. Matrices of 1 wt% PEG flash-frozen solutions were used for polymer deposition with MAPLE (matrix assisted pulsed laser evaporation). Even...
A phenomenological biological dose model for proton therapy based on linear energy transfer spectra.
Rørvik, Eivind; Thörnqvist, Sara; Stokkevåg, Camilla H; Dahle, Tordis J; Fjaera, Lars Fredrik; Ytre-Hauge, Kristian S
2017-06-01
The relative biological effectiveness (RBE) of protons varies with the radiation quality, quantified by the linear energy transfer (LET). Most phenomenological models employ a linear dependency of the dose-averaged LET (LET d ) to calculate the biological dose. However, several experiments have indicated a possible non-linear trend. Our aim was to investigate if biological dose models including non-linear LET dependencies should be considered, by introducing a LET spectrum based dose model. The RBE-LET relationship was investigated by fitting of polynomials from 1st to 5th degree to a database of 85 data points from aerobic in vitro experiments. We included both unweighted and weighted regression, the latter taking into account experimental uncertainties. Statistical testing was performed to decide whether higher degree polynomials provided better fits to the data as compared to lower degrees. The newly developed models were compared to three published LET d based models for a simulated spread out Bragg peak (SOBP) scenario. The statistical analysis of the weighted regression analysis favored a non-linear RBE-LET relationship, with the quartic polynomial found to best represent the experimental data (P = 0.010). The results of the unweighted regression analysis were on the borderline of statistical significance for non-linear functions (P = 0.053), and with the current database a linear dependency could not be rejected. For the SOBP scenario, the weighted non-linear model estimated a similar mean RBE value (1.14) compared to the three established models (1.13-1.17). The unweighted model calculated a considerably higher RBE value (1.22). The analysis indicated that non-linear models could give a better representation of the RBE-LET relationship. However, this is not decisive, as inclusion of the experimental uncertainties in the regression analysis had a significant impact on the determination and ranking of the models. As differences between the models were
Intrinsic character of Stokes matrices
Gagnon, Jean-François; Rousseau, Christiane
2017-02-01
Two germs of linear analytic differential systems x k + 1Y‧ = A (x) Y with a non-resonant irregular singularity are analytically equivalent if and only if they have the same eigenvalues and equivalent collections of Stokes matrices. The Stokes matrices are the transition matrices between sectors on which the system is analytically equivalent to its formal normal form. Each sector contains exactly one separating ray for each pair of eigenvalues. A rotation in S allows supposing that R+ lies in the intersection of two sectors. Reordering of the coordinates of Y allows ordering the real parts of the eigenvalues, thus yielding triangular Stokes matrices. However, the choice of the rotation in x is not canonical. In this paper we establish how the collection of Stokes matrices depends on this rotation, and hence on a chosen order of the projection of the eigenvalues on a line through the origin.
Investigation of incomplete linear momentum transfer in heavy ion reactions at intermediate energies
Leray, S.
1986-07-01
At intermediate energies, heavy ion central collisions lead to the incomplete fusion of the incident nuclei while part of the initial linear momentum is carried away by fast light particles. Experiments were performed with 30 MeV per nucleon neon and 20, 35 and 44 MeV per nucleon argon projectiles bombarding heavy targets. Results obtained with 30 MeV per nucleon neon and 20 MeV per nucleon argon beams are in good agreement with an empirical law established with lighter projectiles. On the contrary, 35 and 44 MeV per nucleon argon projectiles do not follow the same law and fission fragments progressively disappear. A simple model explains the evolution of the amount of transferred linear momentum versus incident energy. The disappearance of the fusion products of the composite system observed with argon projectiles beyond 35 MeV per nucleon is explained by a limitation of the excitation energy per nucleon which can be deposited in a nucleus. The limit is evaluated from nucleon binding energy in nuclei and probability to emit clusters and is in good agreement with experimental data. Because of the coupling between intrinsic motion of nucleons and relative motion of nuclei, some nucleons have a kinetic energy high enough to be emitted: a theoretical model is proposed which rather well fits the data concerning fast nucleons but cannot explain the measured amounts of transferred linear momentum. This is attributed to the existence of other mechanisms [fr
Energy storage and transfer with homopolar machine for a linear theta-pinch hybrid reactor
Vogel, H.F.; Brennan, M.; Dase, W.G.; Tolk, K.M.; Weldon, W.F.
1975-12-01
This report describes the energy storage and transfer system for the compression coil system of a linear theta-pinch hybrid reactor (LTPHR). High efficiency and low cost are the principal requirements for the energy storage and transfer of 25 MJ/m or 25 GJ for a 1-km LTPHR. The circuit efficiency must be approximately 90 percent, and the cost for the circuit 5 to 6 cents/J. Scaling laws and simple relationships between circuit efficiency and cost per unit energy as a function of the half cycle time are presented. Capacitors and homopolor machines are considered as energy storage elements with both functioning basically as capacitors. The advantage of the homopolar machine in this application is its relatively low cost, whereas that of capacitors is better efficiency
Averaging operations on matrices
2014-07-03
Jul 3, 2014 ... Role of Positive Definite Matrices. • Diffusion Tensor Imaging: 3 × 3 pd matrices model water flow at each voxel of brain scan. • Elasticity: 6 × 6 pd matrices model stress tensors. • Machine Learning: n × n pd matrices occur as kernel matrices. Tanvi Jain. Averaging operations on matrices ...
Uncertainties in linear energy transfer spectra measured with track-etched detectors in space
Pachnerová Brabcová, Kateřina; Ambrožová, Iva; Kolísková, Zlata; Malušek, Alexandr
2013-01-01
Roč. 713, JUN 11 (2013), s. 5-10 ISSN 0168-9002 R&D Projects: GA ČR GA205/09/0171; GA AV ČR IAA100480902; GA AV ČR KJB100480901; GA ČR GD202/09/H086 Institutional research plan: CEZ:AV0Z10480505 Institutional support: RVO:61389005 Keywords : CR-39 * linear energy transfer * uncertainty model * space dosimetry Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 1.316, year: 2013
Further development of a track detector as the spectrometer of linear energy transfer
Spurny, F.; Bednar, J.; Vlcek, B.; Botollier-Depois, J.F.
1998-01-01
Track revealing in a track etch detector is a phenomenon related to the linear energy transfer (LET) of the particle registered. The measurements of track parameters permit to determine the LET corresponding to each revealed track, i.e. LET spectrum. We have recently developed a spectrometer of LET based on the chemically etched polyallyldiglycolcarbonate (PADC). In this contribution the results obtained with such spectrometer in some neutron fields are presented, analyzed and discussed. Several radionuclide neutron sources have been used, LET spectrometer has been also exposed in high energy neutron reference fields at CERN and JINR Dubna, and on board aircraft. (author)
Trombetti, T.
1990-01-01
The exact kernel method is presented for linear transport problems with azimuth-dependent angular fluxes. It is based on the evaluation of average scattering densities (ASD's) that fully describe the neutron (or particle) transfer between subsets of the unit sphere of directions by anisotropic scattering. Reciprocity and other ASD functional properties are proved and combined with the symmetry properties of suitable SN quadrature sets. This greatly reduces the number of independent ASD's to be computed and stored. An approach for performing ASD computations with reciprocity checks is presented. ASD expressions of the scattering source for typical 2D geometries are explicitly given. (author)
Linear energy transfer (LET) effects in the radiation-induced inactivation of papain
Bisby, R.H.; Cundall, R.B.; Sims, H.E.; Burns, W.G.
1977-01-01
The inactivation of dilute aqueous solutions of papain by radiations of varying linear energy transfer has been studied in N 2 , N 2 0 and O 2 -saturated solutions. The results obtained with low LET radiation are very similar to those previously reported by Lin et al (Radiation Res.;62:438(1975)). The additional data obtained at higher LET, when radical product yields are reduced and the yield of hydrogen peroxide is increased, show that the hydrogen atom is more important in the inactivation of papain than previously considered. (author)
Tai-Yin Chiu
Full Text Available The ability to engineer synthetic systems in the biochemical context is constantly being improved and has a profound societal impact. Linear system design is one of the most pervasive methods applied in control tasks, and its biochemical realization has been proposed by Oishi and Klavins and advanced further in recent years. However, several technical issues remain unsolved. Specifically, the design process is not fully automated from specification at the transfer function level, systems once designed often lack dynamic adaptivity to environmental changes, matching rate constants of reactions is not always possible, and implementation may be approximative and greatly deviate from the specifications. Building upon the work of Oishi and Klavins, this paper overcomes these issues by introducing a design flow that transforms a transfer-function specification of a linear system into a set of chemical reactions, whose input-output response precisely conforms to the specification. This system is implementable using the DNA strand displacement technique. The underlying configurability is embedded into primitive components and template modules, and thus the entire system is adaptive. Simulation of DNA strand displacement implementation confirmed the feasibility and superiority of the proposed synthesis flow.
Hirota, Yuki; Masunaga, Shin-Ichiro; Kondo, Natsuko; Kawabata, Shinji; Hirakawa, Hirokazu; Yajima, Hirohiko; Fujimori, Akira; Ono, Koji; Kuroiwa, Toshihiko; Miyatake, Shin-Ichi
2014-01-01
Ionizing radiation is applied as the standard treatment for glioblastoma multiforme (GBM). However, radiotherapy remains merely palliative, not curative, because of the existence of glioma stem cells (GSCs), which are regarded as highly radioresistant to low linear-energy-transfer (LET) photons. Here we analyzed whether or not high-LET particles can overcome the radioresistance of GSCs. Glioma stem-like cells (GSLCs) were induced from the GBM cell line A172 in stem cell culture medium. The phenotypes of GSLCs and wild-type cells were confirmed using stem cell markers. These cells were irradiated with (60)Co gamma rays or reactor neutron beams. Under neutron-beam irradiation, high-LET proton particles can be produced through elastic scattering or nitrogen capture reaction. Radiosensitivity was assessed by a colony-forming assay, and the DNA double-strand breaks (DSBs) were assessed by a histone gamma-H2AX focus detection assay. In stem cell culture medium, GSLCs could form neurosphere-like cells and express neural stem cell markers (Sox2 and Musashi) abundantly in comparison with their parental cells. GSLCs were significantly more radioresistant to gamma rays than their parental cells, but neutron beams overcame this resistance. There were significantly fewer gamma-H2AX foci in the A172 GSLCs 24 h after irradiation with gamma rays than in their parental cultured cells, while there was no apparent difference following neutron-beam irradiation. High-LET radiation can overcome the radioresistance of GSLCs by producing unrepairable DNA DSBs. High-LET radiation therapy might have the potential to overcome GBM's resistance to X-rays in a clinical setting.
Hirota, Yuki; Kawabata, Shinji; Kuroiwa, Toshihiko; Miyatake, Shin-ichi; Masunaga, Shin-ichiro; Kondo, Natsuko; Ono, Koji; Hirakawa, Hirokazu; Yajima, Hirohiko; Fujimori, Akira
2014-01-01
Ionizing radiation is applied as the standard treatment for glioblastoma multiforme (GBM). However, radiotherapy remains merely palliative, not curative, because of the existence of glioma stem cells (GSCs), which are regarded as highly radioresistant to low linear-energy-transfer (LET) photons. Here we analyzed whether or not high-LET particles can overcome the radioresistance of GSCs. Glioma stem-like cells (GSLCs) were induced from the GBM cell line A172 in stem cell culture medium. The phenotypes of GSLCs and wild-type cells were confirmed using stem cell markers. These cells were irradiated with 60 Co gamma rays or reactor neutron beams. Under neutron-beam irradiation, high-LET proton particles can be produced through elastic scattering or nitrogen capture reaction. Radiosensitivity was assessed by a colony-forming assay, and the DNA double-strand breaks (DSBs) were assessed by a histone gamma-H2AX focus detection assay. In stem cell culture medium, GSLCs could form neurosphere-like cells and express neural stem cell markers (Sox2 and Musashi) abundantly in comparison with their parental cells. GSLCs were significantly more radioresistant to gamma rays than their parental cells, but neutron beams overcame this resistance. There were significantly fewer gamma-H2AX foci in the A172 GSLCs 24 h after irradiation with gamma rays than in their parental cultured cells, while there was no apparent difference following neutron-beam irradiation. High-LET radiation can overcome the radioresistance of GSLCs by producing unrepairable DNA DSBs. High-LET radiation therapy might have the potential to overcome GBM's resistance to X-rays in a clinical setting. (author)
Wang, Bing; Ninomiya, Yasuharu; Tanaka, Kaoru; Maruyama, Kouichi; Varès, Guillaume; Eguchi-Kasai, Kiyomi; Nenoi, Mitsuru
2012-12-01
Adaptive response (AR) of low linear energy transfer (LET) irradiations for protection against teratogenesis induced by high LET irradiations is not well documented. In this study, induction of AR by X-rays against teratogenesis induced by accelerated heavy ions was examined in fetal mice. Irradiations of pregnant C57BL/6J mice were performed by delivering a priming low dose from X-rays at 0.05 or 0.30 Gy on gestation day 11 followed one day later by a challenge high dose from either X-rays or accelerated heavy ions. Monoenergetic beams of carbon, neon, silicon, and iron with the LET values of about 15, 30, 55, and 200 keV/μm, respectively, were examined. Significant suppression of teratogenic effects (fetal death, malformation of live fetuses, or low body weight) was used as the endpoint for judgment of a successful AR induction. Existence of AR induced by low-LET X-rays against teratogenic effect induced by high-LET accelerated heavy ions was demonstrated. The priming low dose of X-rays significantly reduced the occurrence of prenatal fetal death, malformation, and/or low body weight induced by the challenge high dose from either X-rays or accelerated heavy ions of carbon, neon or silicon but not iron particles. Successful AR induction appears to be a radiation quality event, depending on the LET value and/or the particle species of the challenge irradiations. These findings would provide a new insight into the study on radiation-induced AR in utero. © 2012 Wiley Periodicals, Inc.
Tokaya, Janot P; Raaijmakers, Alexander J E; Luijten, Peter R; van den Berg, Cornelis A T
2018-04-24
We introduce the transfer matrix (TM) that makes MR-based wireless determination of transfer functions (TFs) possible. TFs are implant specific measures for RF-safety assessment of linear implants. The TF relates an incident tangential electric field on an implant to a scattered electric field at its tip that generally governs local heating. The TM extends this concept and relates an incident tangential electric field to a current distribution in the implant therewith characterizing the RF response along the entire implant. The TM is exploited to measure TFs with MRI without hardware alterations. A model of rightward and leftward propagating attenuated waves undergoing multiple reflections is used to derive an analytical expression for the TM. This allows parameterization of the TM of generic implants, e.g., (partially) insulated single wires, in a homogeneous medium in a few unknowns that simultaneously describe the TF. These unknowns can be determined with MRI making it possible to measure the TM and, therefore, also the TF. The TM is able to predict an induced current due to an incident electric field and can be accurately parameterized with a limited number of unknowns. Using this description the TF is determined accurately (with a Pearson correlation coefficient R ≥ 0.9 between measurements and simulations) from MRI acquisitions. The TM enables measuring of TFs with MRI of the tested generic implant models. The MR-based method does not need hardware alterations and is wireless hence making TF determination in more realistic scenarios conceivable. © 2018 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.
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...
Berberian, Sterling K
2014-01-01
Introductory treatment covers basic theory of vector spaces and linear maps - dimension, determinants, eigenvalues, and eigenvectors - plus more advanced topics such as the study of canonical forms for matrices. 1992 edition.
Huo, Pengfei; Miller, Thomas F. III; Coker, David F.
2013-01-01
A partial linearized path integral approach is used to calculate the condensed phase electron transfer (ET) rate by directly evaluating the flux-flux/flux-side quantum time correlation functions. We demonstrate for a simple ET model that this approach can reliably capture the transition between non-adiabatic and adiabatic regimes as the electronic coupling is varied, while other commonly used semi-classical methods are less accurate over the broad range of electronic couplings considered. Further, we show that the approach reliably recovers the Marcus turnover as a function of thermodynamic driving force, giving highly accurate rates over four orders of magnitude from the normal to the inverted regimes. We also demonstrate that the approach yields accurate rate estimates over five orders of magnitude of inverse temperature. Finally, the approach outlined here accurately captures the electronic coherence in the flux-flux correlation function that is responsible for the decreased rate in the inverted regime
Raisee, M.; Hejazi, S.H.
2007-01-01
This paper presents comparisons between heat transfer predictions and measurements for developing turbulent flow through straight rectangular channels with sudden contractions at the mid-channel section. The present numerical results were obtained using a two-dimensional finite-volume code which solves the governing equations in a vertical plane located at the lateral mid-point of the channel. The pressure field is obtained with the well-known SIMPLE algorithm. The hybrid scheme was employed for the discretization of convection in all transport equations. For modeling of the turbulence, a zonal low-Reynolds number k-ε model and the linear and non-linear low-Reynolds number k-ε models with the 'Yap' and 'NYP' length-scale correction terms have been employed. The main objective of present study is to examine the ability of the above turbulence models in the prediction of convective heat transfer in channels with sudden contraction at a mid-channel section. The results of this study show that a sudden contraction creates a relatively small recirculation bubble immediately downstream of the channel contraction. This separation bubble influences the distribution of local heat transfer coefficient and increases the heat transfer levels by a factor of three. Computational results indicate that all the turbulence models employed produce similar flow fields. The zonal k-ε model produces the wrong Nusselt number distribution by underpredicting heat transfer levels in the recirculation bubble and overpredicting them in the developing region. The linear low-Re k-ε model, on the other hand, returns the correct Nusselt number distribution in the recirculation region, although it somewhat overpredicts heat transfer levels in the developing region downstream of the separation bubble. The replacement of the 'Yap' term with the 'NYP' term in the linear low-Re k-ε model results in a more accurate local Nusselt number distribution. Moreover, the application of the non-linear k
Multidimensional radiative transfer with multilevel atoms. II. The non-linear multigrid method.
Fabiani Bendicho, P.; Trujillo Bueno, J.; Auer, L.
1997-08-01
A new iterative method for solving non-LTE multilevel radiative transfer (RT) problems in 1D, 2D or 3D geometries is presented. The scheme obtains the self-consistent solution of the kinetic and RT equations at the cost of only a few (iteration (Brandt, 1977, Math. Comp. 31, 333; Hackbush, 1985, Multi-Grid Methods and Applications, springer-Verlag, Berlin), an efficient multilevel RT scheme based on Gauss-Seidel iterations (cf. Trujillo Bueno & Fabiani Bendicho, 1995ApJ...455..646T), and accurate short-characteristics formal solution techniques. By combining a valid stopping criterion with a nested-grid strategy a converged solution with the desired true error is automatically guaranteed. Contrary to the current operator splitting methods the very high convergence speed of the new RT method does not deteriorate when the grid spatial resolution is increased. With this non-linear multigrid method non-LTE problems discretized on N grid points are solved in O(N) operations. The nested multigrid RT method presented here is, thus, particularly attractive in complicated multilevel transfer problems where small grid-sizes are required. The properties of the method are analyzed both analytically and with illustrative multilevel calculations for Ca II in 1D and 2D schematic model atmospheres.
A statistical theory of cell killing by radiation of varying linear energy transfer
Hawkins, R.B.
1994-01-01
A theory is presented that provides an explanation for the observed features of the survival of cultured cells after exposure to densely ionizing high-linear energy transfer (LET) radiation. It starts from a phenomenological postulate based on the linear-quadratic form of cell survival observed for low-LET radiation and uses principles of statistics and fluctuation theory to demonstrate that the effect of varying LET on cell survival can be attributed to random variation of dose to small volumes contained within the nucleus. A simple relation is presented for surviving fraction of cells after exposure to radiation of varying LET that depends on the α and β parameters for the same cells in the limit of low-LET radiation. This relation implies that the value of β is independent of LET. Agreement of the theory with selected observations of cell survival from the literature is demonstrated. A relation is presented that gives relative biological effectiveness (RBE) as a function of the α and β parameters for low-LET radiation. Measurements from microdosimetry are used to estimate the size of the subnuclear volume to which the fluctuation pertains. 11 refs., 4 figs., 2 tabs
Said-Houari, Belkacem
2017-01-01
This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing t...
Liu, Yan; Cai, Wensheng; Shao, Xueguang
2016-12-01
Calibration transfer is essential for practical applications of near infrared (NIR) spectroscopy because the measurements of the spectra may be performed on different instruments and the difference between the instruments must be corrected. For most of calibration transfer methods, standard samples are necessary to construct the transfer model using the spectra of the samples measured on two instruments, named as master and slave instrument, respectively. In this work, a method named as linear model correction (LMC) is proposed for calibration transfer without standard samples. The method is based on the fact that, for the samples with similar physical and chemical properties, the spectra measured on different instruments are linearly correlated. The fact makes the coefficients of the linear models constructed by the spectra measured on different instruments are similar in profile. Therefore, by using the constrained optimization method, the coefficients of the master model can be transferred into that of the slave model with a few spectra measured on slave instrument. Two NIR datasets of corn and plant leaf samples measured with different instruments are used to test the performance of the method. The results show that, for both the datasets, the spectra can be correctly predicted using the transferred partial least squares (PLS) models. Because standard samples are not necessary in the method, it may be more useful in practical uses.
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
Low and high linear energy transfer radiation sensitization of HCC cells by metformin
Kim, Eun Ho; Jung, Won-Gyun; Kim, Mi-Sook; Cho, Chul-Koo; Jeong, Youn Kyoung; Jeong, Jae-Hoon
2014-01-01
The purpose of this study was to investigate the efficacy of metformin as a radiosensitizer for use in combination therapy for human hepatocellular carcinoma (HCC). Three human HCC cell lines (Huh7, HepG2, Hep3B) and a normal human hepatocyte cell line were treated with metformin alone or with radiation followed by metformin. In vitro tests were evaluated by clonogenic survival assay, FACS analysis, western blotting, immunofluorescence and comet assay. Metformin significantly enhanced radiation efficacy under high and low Linear Energy Transfer (LET) radiation conditions in vitro. In combination with radiation, metformin abrogated G2/M arrest and increased the cell population in the sub-G1 phase and the ROS level, ultimately increasing HCC cellular apoptosis. Metformin inhibits the repair of DNA damage caused by radiation. The radiosensitizing effects of metformin are much higher in neutron (high LET)-irradiated cell lines than in γ (low LET)-irradiated cell lines. Metformin only had a moderate effect in normal hepatocytes. Metformin enhances the radiosensitivity of HCC, suggesting it may have clinical utility in combination cancer treatment with high-LET radiation. (author)
von Götz, N; Richter, O
1999-03-01
The degradation behaviour of bentazone in 14 different soils was examined at constant temperature and moisture conditions. Two soils were examined at different temperatures. On the basis of these data the influence of soil properties and temperature on degradation was assessed and modelled. Pedo-transfer functions (PTF) in combination with a linear and a non-linear model were found suitable to describe the bentazone degradation in the laboratory as related to soil properties. The linear PTF can be combined with a rate related to the temperature to account for both soil property and temperature influence at the same time.
Immanant Conversion on Symmetric Matrices
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.
Rong, Bao; Rui, Xiaoting; Lu, Kun; Tao, Ling; Wang, Guoping; Ni, Xiaojun
2018-05-01
In this paper, an efficient method of dynamics modeling and vibration control design of a linear hybrid multibody system (MS) is studied based on the transfer matrix method. The natural vibration characteristics of a linear hybrid MS are solved by using low-order transfer equations. Then, by constructing the brand-new body dynamics equation, augmented operator and augmented eigenvector, the orthogonality of augmented eigenvector of a linear hybrid MS is satisfied, and its state space model expressed in each independent model space is obtained easily. According to this dynamics model, a robust independent modal space-fuzzy controller is designed for vibration control of a general MS, and the genetic optimization of some critical control parameters of fuzzy tuners is also presented. Two illustrative examples are performed, which results show that this method is computationally efficient and with perfect control performance.
Hunter, Nezahat; Muirhead, Colin R
2009-01-01
Information on Japanese A-bomb survivors exposed to gamma radiation has been used to estimate cancer risks for the whole range of photon (x-rays) and electron energies which are commonly encountered by radiation workers in the work place or by patients and workers in diagnostic radiology. However, there is some uncertainty regarding the radiation effectiveness of various low-linear energy transfer (low-LET) radiations (x-rays, gamma radiation and electrons). In this paper we review information on the effectiveness of low-LET radiations on the basis of epidemiological and in vitro radiobiological studies. Data from various experimental studies for chromosome aberrations and cell transformation in human lymphocytes and from epidemiological studies of the Japanese A-bomb survivors, patients medically exposed to radiation for diagnostic and therapeutic procedures, and occupational exposures of nuclear workers are considered. On the basis of in vitro cellular radiobiology, there is considerable evidence that the relative biological effectiveness (RBE) of high-energy low-LET radiation (gamma radiation, electrons) is less than that of low-energy low-LET radiation (x-rays, betas). This is a factor of about 3 to 4 for 29 kVp x-rays (e.g. as in diagnostic radiation exposures of the female breast) and for tritium beta-rays (encountered in parts of the nuclear industry) relative to Co-60 gamma radiation and 2-5 MeV gamma-rays (as received by the Japanese A-bomb survivors). In epidemiological studies, although for thyroid and breast cancer there appears to be a small tendency for the excess relative risks to decrease as the radiation energy increases for low-LET radiations, it is not statistically feasible to draw any conclusion regarding an underlying dependence of cancer risk on LET for the nominally low-LET radiations. (review)
A simple model of heavy ion-induced linear momentum transfer
Skulski, W.; Blocki, J.
1990-01-01
This paper reports on linear momentum transfer (LMT) from the projectile to the heavy reaction residue which is among the observables, fair account of which is expected from any model of nuclear collisions. Almost thirty years ago it was shown that heavy ions bombarding highly fissionable targets like uranium give rise to double-peaked LMT distributions. (For such targets almost every projectile-target interaction leads to fission, enabling one to use the binary fission fragment correlation technique to obtain LMT distribution for the whole reaction cross section). Since the pioneering work comprehensive systematics of the LMT spectra were published for many HI projectiles, A p = 12-86, almost invariably double-peaked in the bombarding energy range E/A p = 10-40 MeV/nucleon. It was shown in the 16 O+ 238 U experiment at E/A p =20 MeV/nucleon, that the lower LMT peak is in the prompt coincidence with the projectile-like fragment detected at 15 degrees (LAB), an evidence of the peripheral collisions. LMT - neutron multiplicity coincidence study has shown, that the lower LMT peak has also low associated neutron multiplicity n > (and hence low excitation energy E * ), whereas the higher LMT peak has high coincident n > - an evidence of high E * . Low and high E * are plausible signatures of the peripheral and central collisions, respectively. The original interpretation of the double-peaked LMT distributions associates the low LMT peak with the incomplete fusion reaction, in which part of the projectile is emitted forward with the beam velocity. The double-peaked structure would thus reflect the probability of the different projectile divisions into the emitted and captured parts
Giantsoudi, Drosoula, E-mail: dgiantsoudi@partners.org [Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts (United States); Grassberger, Clemens; Craft, David; Niemierko, Andrzej; Trofimov, Alexei; Paganetti, Harald [Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts (United States)
2013-09-01
Purpose: To investigate the feasibility and potential clinical benefit of linear energy transfer (LET) guided plan optimization in intensity modulated proton therapy (IMPT). Methods and Materials: A multicriteria optimization (MCO) module was used to generate a series of Pareto-optimal IMPT base plans (BPs), corresponding to defined objectives, for 5 patients with head-and-neck cancer and 2 with pancreatic cancer. A Monte Carlo platform was used to calculate dose and LET distributions for each BP. A custom-designed MCO navigation module allowed the user to interpolate between BPs to produce deliverable Pareto-optimal solutions. Differences among the BPs were evaluated for each patient, based on dose–volume and LET–volume histograms and 3-dimensional distributions. An LET-based relative biological effectiveness (RBE) model was used to evaluate the potential clinical benefit when navigating the space of Pareto-optimal BPs. Results: The mean LET values for the target varied up to 30% among the BPs for the head-and-neck patients and up to 14% for the pancreatic cancer patients. Variations were more prominent in organs at risk (OARs), where mean LET values differed by a factor of up to 2 among the BPs for the same patient. An inverse relation between dose and LET distributions for the OARs was typically observed. Accounting for LET-dependent variable RBE values, a potential improvement on RBE-weighted dose of up to 40%, averaged over several structures under study, was noticed during MCO navigation. Conclusions: We present a novel strategy for optimizing proton therapy to maximize dose-averaged LET in tumor targets while simultaneously minimizing dose-averaged LET in normal tissue structures. MCO BPs show substantial LET variations, leading to potentially significant differences in RBE-weighted doses. Pareto-surface navigation, using both dose and LET distributions for guidance, provides the means for evaluating a large variety of deliverable plans and aids in
Primary processes in radiation chemistry. LET (Linear Energy Transfer) effect in water radiolysis
Trupin-Wasselin, V.
2000-01-01
The effect of ionizing radiations on aqueous solutions leads to water ionization and then to the formation of radical species and molecular products (e - aq , H . , OH . , H 2 O 2 , H 2 ). It has been shown that the stopping power, characterized by the LET value (Linear Energy Transfer) becomes different when the nature of the ionizing radiations is different. Few data are nowadays available for high LET radiations such as protons and high energy heavy ions. These particles have been used to better understand the primary processes in radiation chemistry. The yield of a chemical dosimeter (the Fricke dosimeter) and those of the hydrogen peroxide have been determined for different LET. The effect of the dose rate on the Fricke dosimeter yield and on the H 2 O 2 yield has been studied too. When the dose rate increases, an increase of the molecular products yield is observed. At very high dose rate, this yield decreases on account of the attack of the molecular products by radicals. The H 2 O 2 yield in alkaline medium decreases when the pH reaches 12. This decrease can be explained by a slowing down of the H 2 O 2 formation velocity in alkaline medium. Superoxide radical has also been studied in this work. A new detection method: the time-resolved chemiluminescence has been perfected for this radical. This technique is more sensitive than the absorption spectroscopy. Experiments with heavy ions have allowed to determine the O 2 .- yield directly in the irradiation cell. The experimental results have been compared with those obtained with a Monte Carlo simulation code. (O.M.)
Reoptimization of Intensity Modulated Proton Therapy Plans Based on Linear Energy Transfer
Unkelbach, Jan, E-mail: junkelbach@mgh.harvard.edu [Department of Radiation Oncology, Massachusetts General Hospital, Boston, Massachusetts (United States); Botas, Pablo [Department of Radiation Oncology, Massachusetts General Hospital, Boston, Massachusetts (United States); Faculty of Physics, Ruprecht-Karls-Universität Heidelberg, Heidelberg (Germany); Giantsoudi, Drosoula; Gorissen, Bram L.; Paganetti, Harald [Department of Radiation Oncology, Massachusetts General Hospital, Boston, Massachusetts (United States)
2016-12-01
Purpose: We describe a treatment plan optimization method for intensity modulated proton therapy (IMPT) that avoids high values of linear energy transfer (LET) in critical structures located within or near the target volume while limiting degradation of the best possible physical dose distribution. Methods and Materials: To allow fast optimization based on dose and LET, a GPU-based Monte Carlo code was extended to provide dose-averaged LET in addition to dose for all pencil beams. After optimizing an initial IMPT plan based on physical dose, a prioritized optimization scheme is used to modify the LET distribution while constraining the physical dose objectives to values close to the initial plan. The LET optimization step is performed based on objective functions evaluated for the product of LET and physical dose (LET×D). To first approximation, LET×D represents a measure of the additional biological dose that is caused by high LET. Results: The method is effective for treatments where serial critical structures with maximum dose constraints are located within or near the target. We report on 5 patients with intracranial tumors (high-grade meningiomas, base-of-skull chordomas, ependymomas) in whom the target volume overlaps with the brainstem and optic structures. In all cases, high LET×D in critical structures could be avoided while minimally compromising physical dose planning objectives. Conclusion: LET-based reoptimization of IMPT plans represents a pragmatic approach to bridge the gap between purely physical dose-based and relative biological effectiveness (RBE)-based planning. The method makes IMPT treatments safer by mitigating a potentially increased risk of side effects resulting from elevated RBE of proton beams near the end of range.
Giantsoudi, Drosoula; Grassberger, Clemens; Craft, David; Niemierko, Andrzej; Trofimov, Alexei; Paganetti, Harald
2013-01-01
Purpose: To investigate the feasibility and potential clinical benefit of linear energy transfer (LET) guided plan optimization in intensity modulated proton therapy (IMPT). Methods and Materials: A multicriteria optimization (MCO) module was used to generate a series of Pareto-optimal IMPT base plans (BPs), corresponding to defined objectives, for 5 patients with head-and-neck cancer and 2 with pancreatic cancer. A Monte Carlo platform was used to calculate dose and LET distributions for each BP. A custom-designed MCO navigation module allowed the user to interpolate between BPs to produce deliverable Pareto-optimal solutions. Differences among the BPs were evaluated for each patient, based on dose–volume and LET–volume histograms and 3-dimensional distributions. An LET-based relative biological effectiveness (RBE) model was used to evaluate the potential clinical benefit when navigating the space of Pareto-optimal BPs. Results: The mean LET values for the target varied up to 30% among the BPs for the head-and-neck patients and up to 14% for the pancreatic cancer patients. Variations were more prominent in organs at risk (OARs), where mean LET values differed by a factor of up to 2 among the BPs for the same patient. An inverse relation between dose and LET distributions for the OARs was typically observed. Accounting for LET-dependent variable RBE values, a potential improvement on RBE-weighted dose of up to 40%, averaged over several structures under study, was noticed during MCO navigation. Conclusions: We present a novel strategy for optimizing proton therapy to maximize dose-averaged LET in tumor targets while simultaneously minimizing dose-averaged LET in normal tissue structures. MCO BPs show substantial LET variations, leading to potentially significant differences in RBE-weighted doses. Pareto-surface navigation, using both dose and LET distributions for guidance, provides the means for evaluating a large variety of deliverable plans and aids in
Comparison between Linear and Nonlinear Regression in a Laboratory Heat Transfer Experiment
Gonçalves, Carine Messias; Schwaab, Marcio; Pinto, José Carlos
2013-01-01
In order to interpret laboratory experimental data, undergraduate students are used to perform linear regression through linearized versions of nonlinear models. However, the use of linearized models can lead to statistically biased parameter estimates. Even so, it is not an easy task to introduce nonlinear regression and show for the students…
Pearson, Jeremy [Department of Chemical Engineering and Materials Science - University of California Irvine, 916 Engineering Tower, Irvine, CA, 92697 (United States); Miller, George [Department of Chemistry- University of California Irvine, 2046D PS II, Irvine, CA, 92697 (United States); Nilsson, Mikael [Department of Chemical Engineering and Materials Science - University of California Irvine, 916 Engineering Tower, Irvine, CA, 92697 (United States)
2013-07-01
Treatment of used nuclear fuel through solvent extraction separation processes is hindered by radiolytic damage from radioactive isotopes present in used fuel. The nature of the damage caused by the radiation may depend on the radiation type, whether it be low linear energy transfer (LET) such as gamma radiation or high LET such as alpha radiation. Used nuclear fuel contains beta/gamma emitting isotopes but also a significant amount of transuranics which are generally alpha emitters. Studying the respective effects on matter of both of these types of radiation will allow for accurate prediction and modeling of process performance losses with respect to dose. Current studies show that alpha radiation has milder effects than that of gamma. This is important to know because it will mean that solvent extraction solutions exposed to alpha radiation may last longer than expected and need less repair and replacement. These models are important for creating robust, predictable, and economical processes that have strong potential for mainstream adoption on the commercial level. The effects of gamma radiation on solvent extraction ligands have been more extensively studied than the effects of alpha radiation. This is due to the inherent difficulty in producing a sufficient and confluent dose of alpha particles within a sample without leaving the sample contaminated with long lived radioactive isotopes. Helium ion beam and radioactive isotope sources have been studied in the literature. We have developed a method for studying the effects of high LET radiation in situ via {sup 10}B activation and the high LET particles that result from the {sup 10}B(n,a){sup 7}Li reaction which follows. Our model for dose involves solving a partial differential equation representing absorption by 10B of an isentropic field of neutrons penetrating a sample. This method has been applied to organic solutions of TBP and CMPO, two ligands common in TRU solvent extraction treatment processes. Rates
Rodriguez, P. Blanco; Tome, F. Vera; Fernandez, M. Perez; Lozano, J.C.
2006-01-01
The linearity assumption of the validation of soil-to-plant transfer factors of natural uranium and 226 Ra was tested using Helianthus annuus L. (sunflower) grown in a hydroponic medium. Transfer of natural uranium and 226 Ra was tested in both the aerial fraction of plants and in the overall seedlings (roots and shoots). The results show that the linearity assumption can be considered valid in the hydroponic growth of sunflowers for the radionuclides studied. The ability of sunflowers to translocate uranium and 226 Ra was also investigated, as well as the feasibility of using sunflower plants to remove uranium and radium from contaminated water, and by extension, their potential for phytoextraction. In this sense, the removal percentages obtained for natural uranium and 226 Ra were 24% and 42%, respectively. Practically all the uranium is accumulated in the roots. However, 86% of the 226 Ra activity concentration in roots was translocated to the aerial part
Rodriguez, P. Blanco [Departamento de Fisica, Facultad de Ciencias, Universidad de Extremadura, 06071 Badajoz (Spain); Tome, F. Vera [Departamento de Fisica, Facultad de Ciencias, Universidad de Extremadura, 06071 Badajoz (Spain)]. E-mail: fvt@unex.es; Fernandez, M. Perez [Area de Ecologia, Departamento de Fisica, Facultad de Ciencias, Universidad de Extremadura, 06071 Badajoz (Spain); Lozano, J.C. [Laboratorio de Radiactividad Ambiental, Facultad de Ciencias, Universidad de Salamanca, 37008 Salamanca (Spain)
2006-05-15
The linearity assumption of the validation of soil-to-plant transfer factors of natural uranium and {sup 226}Ra was tested using Helianthus annuus L. (sunflower) grown in a hydroponic medium. Transfer of natural uranium and {sup 226}Ra was tested in both the aerial fraction of plants and in the overall seedlings (roots and shoots). The results show that the linearity assumption can be considered valid in the hydroponic growth of sunflowers for the radionuclides studied. The ability of sunflowers to translocate uranium and {sup 226}Ra was also investigated, as well as the feasibility of using sunflower plants to remove uranium and radium from contaminated water, and by extension, their potential for phytoextraction. In this sense, the removal percentages obtained for natural uranium and {sup 226}Ra were 24% and 42%, respectively. Practically all the uranium is accumulated in the roots. However, 86% of the {sup 226}Ra activity concentration in roots was translocated to the aerial part.
Shokouhmand, H.; Kahrobaian, A.; Tabandeh, N.; Jalilvand, A.
2002-01-01
Micro heat pipes are widely used for the thermal control of spacecraft and their electronic components. In this paper the influence of linear accelerations in micro grooves has been studied. A mathematical model for predicating the minimum meniscus radius and the maximum heat transport in triangular groove under the influence of linear acceleration is presented and method for determining the theoretical minimum meniscus radius is developed. It is shown that both, the direction and the magnitude of the acceleration have a great effect upon heat transfer capability of micro heat pipes. The analysis presented here provides a mechanism where by the groove geometry can be optimized with respect to the length of the heat pipe and direction and magnitude of linear acceleration
Discrete canonical transforms that are Hadamard matrices
Healy, John J; Wolf, Kurt Bernardo
2011-01-01
The group Sp(2,R) of symplectic linear canonical transformations has an integral kernel which has quadratic and linear phases, and which is realized by the geometric paraxial optical model. The discrete counterpart of this model is a finite Hamiltonian system that acts on N-point signals through N x N matrices whose elements also have a constant absolute value, although they do not form a representation of that group. Those matrices that are also unitary are Hadamard matrices. We investigate the manifolds of these N x N matrices under the Sp(2,R) equivalence imposed by the model, and find them to be on two-sided cosets. By means of an algorithm we determine representatives that lead to collections of mutually unbiased bases.
Li, Guangqi; Govind, Niranjan; Ratner, Mark A; Cramer, Christopher J; Gagliardi, Laura
2015-12-17
The mechanism of charge transfer has been observed to change from tunneling to hopping with increasing numbers of DNA base pairs in polynucleotides and with the length of molecular wires. The aim of this paper is to investigate this transition by examining the population dynamics using a tight-binding Hamiltonian with model parameters to describe a linear donor-bridge-acceptor (D-B-A) system. The model includes a primary vibration and an electron-vibration coupling at each site. A further coupling of the primary vibration with a secondary phonon bath allows the system to dissipate energy to the environment and reach a steady state. We apply the quantum master equation (QME) approach, based on second-order perturbation theory in a quantum dissipative system, to examine the dynamical processes involved in charge-transfer and follow the population transfer rate at the acceptor, ka, to shed light on the transition from tunneling to hopping. With a small tunneling parameter, V, the on-site population tends to localize and form polarons, and the hopping mechanism dominates the transfer process. With increasing V, the population tends to be delocalized and the tunneling mechanism dominates. The competition between incoherent hopping and coherent tunneling governs the mechanism of charge transfer. By varying V and the total number of sites, we also examine the onset of the transition from tunneling to hopping with increasing length.
Non-linear heat transfer computer code by finite element method
Nagato, Kotaro; Takikawa, Noboru
1977-01-01
The computer code THETA-2D for the calculation of temperature distribution by the two-dimensional finite element method was made for the analysis of heat transfer in a high temperature structure. Numerical experiment was performed for the numerical integration of the differential equation of heat conduction. The Runge-Kutta method of the numerical experiment produced an unstable solution. A stable solution was obtained by the β method with the β value of 0.35. In high temperature structures, the radiative heat transfer can not be neglected. To introduce a term of the radiative heat transfer, a functional neglecting the radiative heat transfer was derived at first. Then, the radiative term was added after the discretion by variation method. Five model calculations were carried out by the computer code. Calculation of steady heat conduction was performed. When estimated initial temperature is 1,000 degree C, reasonable heat blance was obtained. In case of steady-unsteady temperature calculation, the time integral by THETA-2D turned out to be under-estimation for enthalpy change. With a one-dimensional model, the temperature distribution in a structure, in which heat conductivity is dependent on temperature, was calculated. Calculation with a model which has a void inside was performed. Finally, model calculation for a complex system was carried out. (Kato, T.)
The implications of non-linearity for excitation transfer in DNA
Baverstock, K.F.; Cundall, R.B.
1990-01-01
Non-linear effects which arise from the coupling of anharmonic interactions can completely change excitation transport through molecular chains. The consequences of this for an understanding of the effect of ionising radiation on DNA are discussed. We consider that these effects should be taken into account in the interpretation of experimental data. (author)
E. D. Resende
2007-09-01
Full Text Available The freezing process is considered as a propagation problem and mathematically classified as an "initial value problem." The mathematical formulation involves a complex situation of heat transfer with simultaneous changes of phase and abrupt variation in thermal properties. The objective of the present work is to solve the non-linear heat transfer equation for food freezing processes using orthogonal collocation on finite elements. This technique has not yet been applied to freezing processes and represents an alternative numerical approach in this area. The results obtained confirmed the good capability of the numerical method, which allows the simulation of the freezing process in approximately one minute of computer time, qualifying its application in a mathematical optimising procedure. The influence of the latent heat released during the crystallisation phenomena was identified by the significant increase in heat load in the early stages of the freezing process.
Linear energy transfer effects on time profiles of scintillation of Ce-doped LiCaAlF6 crystals
Yanagida, Takayuki; Koshimizu, Masanori; Kurashima, Satoshi; Iwamatsu, Kazuhiro; Kimura, Atsushi; Taguchi, Mitsumasa; Fujimoto, Yutaka; Asai, Keisuke
2015-01-01
We measured temporal profiles of the scintillation of Ce-doped LiCaAlF 6 scintillator crystals at different linear energy transfers (LETs). Based on the comparison of high-LET temporal profiles with those at low LET, a fast component was observed only at low LET. The disappearance of the fast component at high LET is tentatively ascribed to the quenching of excited states at crystal defects owing to the interaction between excited states via the Auger process. In addition, the rise and the initial decay behavior were dependent on the LET. This LET-dependent behavior is explained by an acceleration process and a deceleration process in energy transfer at high LET. The LET-dependent temporal profiles provide the basis for a discrimination technique of gamma-ray and neutron detection events using these scintillators based on the nuclear reaction, 6 Li(n,α)t.
Naganthran, Kohilavani; Nazar, Roslinda; Pop, Ioan
2018-05-01
This study investigated the influence of the non-linearly stretching/shrinking sheet on the boundary layer flow and heat transfer. A proper similarity transformation simplified the system of partial differential equations into a system of ordinary differential equations. This system of similarity equations is then solved numerically by using the bvp4c function in the MATLAB software. The generated numerical results presented graphically and discussed in the relevance of the governing parameters. Dual solutions found as the sheet stretched and shrunk in the horizontal direction. Stability analysis showed that the first solution is physically realizable whereas the second solution is not practicable.
Ponomarev, A. L.; Brenner, D.; Hlatky, L. R.; Sachs, R. K.
2000-01-01
DNA double-strand breaks (DSBs) produced by densely ionizing radiation are not located randomly in the genome: recent data indicate DSB clustering along chromosomes. Stochastic DSB clustering at large scales, from > 100 Mbp down to simulations and analytic equations. A random-walk, coarse-grained polymer model for chromatin is combined with a simple track structure model in Monte Carlo software called DNAbreak and is applied to data on alpha-particle irradiation of V-79 cells. The chromatin model neglects molecular details but systematically incorporates an increase in average spatial separation between two DNA loci as the number of base-pairs between the loci increases. Fragment-size distributions obtained using DNAbreak match data on large fragments about as well as distributions previously obtained with a less mechanistic approach. Dose-response relations, linear at small doses of high linear energy transfer (LET) radiation, are obtained. They are found to be non-linear when the dose becomes so large that there is a significant probability of overlapping or close juxtaposition, along one chromosome, for different DSB clusters from different tracks. The non-linearity is more evident for large fragments than for small. The DNAbreak results furnish an example of the RLC (randomly located clusters) analytic formalism, which generalizes the broken-stick fragment-size distribution of the random-breakage model that is often applied to low-LET data.
High-fidelity state transfer over an unmodulated linear XY spin chain
Bishop, C. Allen; Ou Yongcheng; Byrd, Mark S.; Wang Zhaoming
2010-01-01
We provide a class of initial encodings that can be sent with a high fidelity over an unmodulated, linear, XY spin chain. As an example, an average fidelity of 96% can be obtained using an 11-spin encoding to transmit a state over a chain containing 10 000 spins. An analysis of the magnetic-field dependence is given, and conditions for field optimization are provided.
Legland, J-B; Tournat, V; Dazel, O; Novak, A; Gusev, V
2012-06-01
Experimental results are reported on second harmonic generation and self-action in a noncohesive granular medium supporting wave energy propagation both in the solid frame and in the saturating fluid. The acoustic transfer function of the probed granular slab can be separated into two main frequency regions: a low frequency region where the wave propagation is controlled by the solid skeleton elastic properties, and a higher frequency region where the behavior is dominantly due to the air saturating the beads. Experimental results agree well with a recently developed nonlinear Biot wave model applied to granular media. The linear transfer function, second harmonic generation, and self-action effect are studied as a function of bead diameter, compaction step, excitation amplitude, and frequency. This parametric study allows one to isolate different propagation regimes involving a range of described and interpreted linear and nonlinear processes that are encountered in granular media experiments. In particular, a theoretical interpretation is proposed for the observed strong self-action effect.
Robinson, Tyler D.; Crisp, David
2018-05-01
Solar and thermal radiation are critical aspects of planetary climate, with gradients in radiative energy fluxes driving heating and cooling. Climate models require that radiative transfer tools be versatile, computationally efficient, and accurate. Here, we describe a technique that uses an accurate full-physics radiative transfer model to generate a set of atmospheric radiative quantities which can be used to linearly adapt radiative flux profiles to changes in the atmospheric and surface state-the Linearized Flux Evolution (LiFE) approach. These radiative quantities describe how each model layer in a plane-parallel atmosphere reflects and transmits light, as well as how the layer generates diffuse radiation by thermal emission and by scattering light from the direct solar beam. By computing derivatives of these layer radiative properties with respect to dynamic elements of the atmospheric state, we can then efficiently adapt the flux profiles computed by the full-physics model to new atmospheric states. We validate the LiFE approach, and then apply this approach to Mars, Earth, and Venus, demonstrating the information contained in the layer radiative properties and their derivatives, as well as how the LiFE approach can be used to determine the thermal structure of radiative and radiative-convective equilibrium states in one-dimensional atmospheric models.
Jie Wang
2017-03-01
Full Text Available Deep convolutional neural networks (CNNs have been widely used to obtain high-level representation in various computer vision tasks. However, in the field of remote sensing, there are not sufficient images to train a useful deep CNN. Instead, we tend to transfer successful pre-trained deep CNNs to remote sensing tasks. In the transferring process, generalization power of features in pre-trained deep CNNs plays the key role. In this paper, we propose two promising architectures to extract general features from pre-trained deep CNNs for remote scene classification. These two architectures suggest two directions for improvement. First, before the pre-trained deep CNNs, we design a linear PCA network (LPCANet to synthesize spatial information of remote sensing images in each spectral channel. This design shortens the spatial “distance” of target and source datasets for pre-trained deep CNNs. Second, we introduce quaternion algebra to LPCANet, which further shortens the spectral “distance” between remote sensing images and images used to pre-train deep CNNs. With five well-known pre-trained deep CNNs, experimental results on three independent remote sensing datasets demonstrate that our proposed framework obtains state-of-the-art results without fine-tuning and feature fusing. This paper also provides baseline for transferring fresh pretrained deep CNNs to other remote sensing tasks.
Sparse Matrices in Frame Theory
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...
Generation of discrete inelastic and elastic transfer matrix
Garcia, R.D.M.; Santina, M.D.
1985-01-01
A technique developed for the calculation of the isotropic and linearly anisotropic components components of elastic and discrete inelastic transfer matrices is presented in this work. The implementation of the technique is discussed in detail and numerical results obtained for some examples are compared with results reported in the literature or generated with the use of several processing codes. (author) [pt
Kunwar Aditya
2016-11-01
Full Text Available The extended describing function (EDF is a well-known method for modelling resonant converters due to its high accuracy. However, it requires complex mathematical formulation effort. This paper presents a simplified non-linear mathematical model of series-series (SS compensated inductive power transfer (IPT system, considering zero-voltage switching in the inverter. This simplified mathematical model permits the user to derive the small-signal model using the EDF method, with less computational effort, while maintaining the accuracy of an actual physical model. The derived model has been verified using a frequency sweep method in PLECS. The small-signal model has been used to design the voltage loop controller for a SS compensated IPT system. The designed controller was implemented on a 3.6 kW experimental setup, to test its robustness.
Tuovinen, Tiina S.; Roivainen, Paeivi, E-mail: paivi.roivainen@uef.fi; Makkonen, Sari; Kolehmainen, Mikko; Holopainen, Toini; Juutilainen, Jukka
2011-12-01
Element-specific concentration ratios (CRs) assuming that plant uptake of elements is linear are commonly used in radioecological modelling to describe the soil-to-plant transfer of elements. The goal of this study was to investigate the validity of the linearity assumption in boreal forest plants, for which only limited relevant data are available. The soil-to-plant transfer of three essential (Mo, Ni, Zn) and two non-essential (Pb, U) elements relevant to the safety of radioactive waste disposal was studied. Three understory species (blueberry, narrow buckler fern and May lily) and two tree species (Norway spruce and rowan) were included. Examining CRs as a function of soil concentration showed that CR was not constant but decreased with increasing soil concentrations for all elements and plant species. A non-linear equation fitted fairly well with the empirical data; the R{sup 2}-values for this equation were constantly higher than those for the linear fit. The difference between the two fits was most evident at low soil concentrations where the use of constant CRs underestimated transfer from soil to plants. Site-specific factors affected the transfer of Mo and Ni. The results suggested that systematic variation with soil concentrations explains a part of the large variation of empirically determined CRs, and the accuracy of modelling the soil-to-plant transfer might be improved by using non-linear methods. Non-linearity of soil-to-plant transfer has been previously reported for a few different species, elements and environments. The present study systematically tested the linearity assumption for five elements (both essential and non-essential) and in five boreal forest species representing different growth traits and phylogenies. The data supported non-linearity in all cases.
Yun, Sung Hwan
2004-02-01
Radiative transfer is a complex phenomenon in which radiation field interacts with material. This thermal radiative transfer phenomenon is composed of two equations which are the balance equation of photons and the material energy balance equation. The two equations involve non-linearity due to the temperature and that makes the radiative transfer equation more difficult to solve. During the last several years, there have been many efforts to solve the non-linear radiative transfer problems by Monte Carlo method. Among them, it is known that Semi-Analog Monte Carlo (SMC) method developed by Ahrens and Larsen is accurate regard-less of the time step size in low temperature region. But their works are limited to one-dimensional, low temperature problems. In this thesis, we suggest some method to remove their limitations in the SMC method and apply to the more realistic problems. An initially cold problem was solved over entire temperature region by using piecewise linear interpolation of the heat capacity, while heat capacity is still fitted as a cubic curve within the lowest temperature region. If we assume the heat capacity to be linear in each temperature region, the non-linearity still remains in the radiative transfer equations. We then introduce the first-order Taylor expansion to linearize the non-linear radiative transfer equations. During the linearization procedure, absorption-reemission phenomena may be described by a conventional reemission time sampling scheme which is similar to the repetitive sampling scheme in particle transport Monte Carlo method. But this scheme causes significant stochastic errors, which necessitates many histories. Thus, we present a new reemission time sampling scheme which reduces stochastic errors by storing the information of absorption times. The results of the comparison of the two schemes show that the new scheme has less stochastic errors. Therefore, the improved SMC method is able to solve more realistic problems with
Tuovinen, Tiina S.; Roivainen, Päivi; Makkonen, Sari; Kolehmainen, Mikko; Holopainen, Toini; Juutilainen, Jukka
2011-01-01
Element-specific concentration ratios (CRs) assuming that plant uptake of elements is linear are commonly used in radioecological modelling to describe the soil-to-plant transfer of elements. The goal of this study was to investigate the validity of the linearity assumption in boreal forest plants, for which only limited relevant data are available. The soil-to-plant transfer of three essential (Mo, Ni, Zn) and two non-essential (Pb, U) elements relevant to the safety of radioactive waste disposal was studied. Three understory species (blueberry, narrow buckler fern and May lily) and two tree species (Norway spruce and rowan) were included. Examining CRs as a function of soil concentration showed that CR was not constant but decreased with increasing soil concentrations for all elements and plant species. A non-linear equation fitted fairly well with the empirical data; the R 2 -values for this equation were constantly higher than those for the linear fit. The difference between the two fits was most evident at low soil concentrations where the use of constant CRs underestimated transfer from soil to plants. Site-specific factors affected the transfer of Mo and Ni. The results suggested that systematic variation with soil concentrations explains a part of the large variation of empirically determined CRs, and the accuracy of modelling the soil-to-plant transfer might be improved by using non-linear methods. Non-linearity of soil-to-plant transfer has been previously reported for a few different species, elements and environments. The present study systematically tested the linearity assumption for five elements (both essential and non-essential) and in five boreal forest species representing different growth traits and phylogenies. The data supported non-linearity in all cases.
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander; Genton, Marc G.; Sun, Ying
2015-01-01
We approximate large non-structured Matérn covariance matrices of size n×n in the H-matrix format with a log-linear computational cost and storage O(kn log n), where rank k ≪ n is a small integer. Applications are: spatial statistics, machine learning and image analysis, kriging and optimal design.
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.
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…
Pavanello, Michele [Department of Chemistry, Rutgers University, Newark, New Jersey 07102-1811 (United States); Van Voorhis, Troy [Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307 (United States); Visscher, Lucas [Amsterdam Center for Multiscale Modeling, VU University, De Boelelaan 1083, 1081 HV Amsterdam (Netherlands); Neugebauer, Johannes [Theoretische Organische Chemie, Organisch-Chemisches Institut der Westfaelischen Wilhelms-Universitaet Muenster, Corrensstrasse 40, 48149 Muenster (Germany)
2013-02-07
Quantum-mechanical methods that are both computationally fast and accurate are not yet available for electronic excitations having charge transfer character. In this work, we present a significant step forward towards this goal for those charge transfer excitations that take place between non-covalently bound molecules. In particular, we present a method that scales linearly with the number of non-covalently bound molecules in the system and is based on a two-pronged approach: The molecular electronic structure of broken-symmetry charge-localized states is obtained with the frozen density embedding formulation of subsystem density-functional theory; subsequently, in a post-SCF calculation, the full-electron Hamiltonian and overlap matrix elements among the charge-localized states are evaluated with an algorithm which takes full advantage of the subsystem DFT density partitioning technique. The method is benchmarked against coupled-cluster calculations and achieves chemical accuracy for the systems considered for intermolecular separations ranging from hydrogen-bond distances to tens of Angstroms. Numerical examples are provided for molecular clusters comprised of up to 56 non-covalently bound molecules.
Homero Ferracini Gumerato
2007-09-01
Full Text Available Foi estudada a transferência de calor transiente na agitação linear e intermitente (ALI de embalagens metálicas contendo simulantes de alimentos, objetivando-se sua aplicação em processos de pasteurização ou esterilização e conseqüentes tratamentos térmicos mais eficientes, homogêneos e com produto de melhor qualidade. Foram utilizados quatro meios fluidos simulantes de alimentos de diferentes viscosidades e massas específicas: três óleos e água. Foram combinados efeitos de cinco tratamentos, sendo: meio simulante (4 níveis, espaço livre (3 níveis, freqüência de agitação (4 níveis, amplitude de agitação (2 níveis e posição das latas (4 níveis. Os ensaios de aquecimento e resfriamento foram feitos em tanque com água à temperatura de 98 °C e 17-20 °C, respectivamente. Com os dados de penetração de calor em cada experimento, foram calculados os parâmetros de penetração de calor fh, jh, fc e jc. Os resultados foram modelados utilizando-se grupos de números adimensionais e expressos em termos de Nusselt, Prandtl, Reynolds e funções trigonométricas (com medidas de amplitude e freqüência de agitação, espaço livre e dimensões da embalagem. Foram estabelecidas as duas Equações gerais para as fases de aquecimento e resfriamento: Nu = ReA 0,199.Pr 0,288.sen(xa/AM0,406.cos(xf/FA1,039.cos((xf/FA.(EL/H.p4,556 Aquecimento Nu = 0,1295.ReA0,047.Pr 0,193.sen(xa/AM0,114.cos(xf/FA0,641.cos((xf/FA.(EL/H.p2,476 Resfriamento O processo de ALI pode ser aplicado em pasteurizadores ou autoclaves estáticas horizontais e verticais, com modificações simples. Concluiu-se que a ALI aumenta significativamente a taxa de transferência de calor, tanto no aquecimento como no resfriamento.The transient heat transfer during the intermittent and linear shaking of tin plate cans containing simulating food was studied in order to apply this technology in the pasteurization and sterilization processes, achieving
Gervais, Florence
2001-01-01
Soils rehabilitation using supercritical CO_2 seems an interesting alternative way to existing techniques. No effluents are generated during the supercritical fluid extraction, which is the main advantage of this process. In order to be extracted by this techniques, metals or radionuclides have to be complexed by suitable chelating agents. Beta-diketones and dithiocarbamates (fluorinated or not) have been chosen. The first part of this work deals with chemical equilibria mechanisms study in an aqueous phase. Experiments show a very weak cobalt complexation kinetics with acetylacetone. Moreover, this complex exhibit a hydrophilic behaviour. On the other hand, cobalt and dithiocarbamate instantaneously from a chelate which is very hydrophobic. Mass transfer between extracting and aqueous phases (hexane and SC CO_2) are also investigated. Supercritical CO_2 seems to have a greater affinity towards fluorinated beta-diketones than hexane. This tendency is confirmed by in situ commercial chelates (fluorinates or not) solubility measurements using X-ray absorption spectroscopy. However, cobalt-beta-diketonates are hydrophilic because of their partial hydration. This kind of chelating agents is not suitable to cobalt supercritical fluid extraction from an aqueous phase. Inversely, distribution coefficients of hydrophobic dithiocarbamates are higher than beta-diketonates, whatever the extracting solvent is. Metals extraction from an aqueous matrix seems possible with these chelating agents. (author) [fr
Chao Yu Chiu
2001-01-01
The LHC injection transfer lines TI 2 and TI 8 will transport intense high-energy beams over considerable distances. In their regular part a FODO lattice is used with 4 bending magnets per half-cell and a half-cell length of 30.3 m, similar to that of the SPS. The relatively tight apertures in these lines require precise trajectory control. Following an earlier study a baseline correction scheme was chosen where two out of every four consecutive quadrupoles are complemented with correctors and beam position monitors ("2-in-4"). With the ordering of the equipment approaching, a further in-depth investigation has been made using a newly developed analytic method. This method evaluates, based on the design specifications, the global performance of an orbit correction system in terms of observability, correctability, correction range and response singularity. In addition, orbit and error envelopes are obtained over the full beam line in an efficient and rigorous manner, providing insights not easily accessible wi...
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.
Chemiluminescence in cryogenic matrices
Lotnik, S. V.; Kazakov, Valeri P.
1989-04-01
The literature data on chemiluminescence (CL) in cryogenic matrices have been classified and correlated for the first time. The role of studies on phosphorescence and CL at low temperatures in the development of cryochemistry is shown. The features of low-temperature CL in matrices of nitrogen and inert gases (fine structure of spectra, matrix effects) and the data on the mobility and reactivity of atoms and radicals at very low temperatures are examined. The trends in the development of studies on CL in cryogenic matrices, such as the search for systems involving polyatomic molecules and extending the forms of CL reactions, are followed. The reactions of active nitrogen with hydrocarbons that are accompanied by light emission and CL in the oxidation of carbenes at T >= 77 K are examined. The bibliography includes 112 references.
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
Advanced incomplete factorization algorithms for Stiltijes matrices
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.
Bataille, F.; Younis, B.A.; Bellettre, J.; Lallemand, A.
2003-01-01
The paper reports on the prediction of the effects of blowing on the evolution of the thermal and velocity fields in a flat-plate turbulent boundary layer developing over a porous surface. Closure of the time-averaged equations governing the transport of momentum and thermal energy is achieved using a complete Reynolds-stress transport model for the turbulent stresses and a non-linear, algebraic and explicit model for the turbulent heat fluxes. The latter model accounts explicitly for the dependence of the turbulent heat fluxes on the gradients of mean velocity. Results are reported for the case of a heated boundary layer which is first developed into equilibrium over a smooth impervious wall before encountering a porous section through which cooler fluid is continuously injected. Comparisons are made with LDA measurements for an injection rate of 1%. The reduction of the wall shear stress with increase in injection rate is obtained in the calculations, and the computed rates of heat transfer between the hot flow and the wall are found to agree well with the published data
Awad, E M
1999-01-01
In this work, we have studied the effect of the radiation damage caused by the incident particles on the activation energy of etching for CR-39 samples. The damage produced by the incident particle is expressed in terms of the linear energy transfer (LET). CR-39 samples from American Acrylic were irradiated to three different LET particles. These are N (LET sub 2 sub 0 sub 0 = 20 KeV/mu m) as a light particle, Fe (LET sub 2 sub 0 sub 0 = 110 KeV/mu m) as a medium particle and fission fragments (ff) from a sup 2 sup 5 sup 2 Cf source as heavy particles. In general the bulk etch rate was calculated using the weight difference method and the track etch rate was determined using the track geometry at various temperatures (50-90 deg. C) and concentrations (4-9 N) of the NaOH etchant. The average activation energy E sub b related to the bulk etch rate v sub b was calculated from 1n v sub b vs. 1/T. The average activation energy E sub t related to the track etch rate v sub t was estimated from 1n v sub t vs. 1/T. It...
Verhaegen, F.; Seuntjens, J.
1994-01-01
For irradiation of thin samples of biological material with low-energy X rays, conversion of measured air kerma, free in air to average absorbed dose to the sample is necessary. In the present paper, conversion factors from measured air kerma to average absorbed dose in thin blood samples are given for four low-energy X-ray qualities (14-50 kVp). These factors were obtained by Monte Carlo simulation of a practical sample holder. Data for different thicknesses of the blood and backing layer are presented. The conversion factors are found to depend strongly on the thicknesses of the blood layer and backing layer. In radiobiological work, knowledge of linear energy transfer (LET) values for the radiation quality used is often required. Track-averaged LET values for low-energy X rays are presented in this work. It is concluded that the thickness of the sample does not influence the LET value appreciably, indicating that for all radiobiological purposes this value can be regarded as a constant throughout the sample. Furthermore, the large difference between the LET value for a 50 kV spectrum found in this work and the value given in ICRU Report 16 is pointed out. 16 refs., 7 figs., 1 tab
Fager, Marcus; Toma-Dasu, Iuliana; Kirk, Maura; Dolney, Derek; Diffenderfer, Eric S.; Vapiwala, Neha; Carabe, Alejandro
2015-01-01
Purpose: The purpose of this study was to propose a proton treatment planning method that trades physical dose (D) for dose-averaged linear energy transfer (LET d ) while keeping the radiobiologically weighted dose (D RBE ) to the target the same. Methods and Materials: The target is painted with LET d by using 2, 4, and 7 fields aimed at the proximal segment of the target (split target planning [STP]). As the LET d within the target increases with increasing number of fields, D decreases to maintain the D RBE the same as the conventional treatment planning method by using beams treating the full target (full target planning [FTP]). Results: The LET d increased 61% for 2-field STP (2STP) compared to FTP, 72% for 4STP, and 82% for 7STP inside the target. This increase in LET d led to a decrease of D with 5.3 ± 0.6 Gy for 2STP, 4.4 ± 0.7 Gy for 4STP, and 5.3 ± 1.1 Gy for 7STP, keeping the DRBE at 90% of the volume (DRBE, 90) constant to FTP. Conclusions: LET d painting offers a method to reduce prescribed dose at no cost to the biological effectiveness of the treatment
Fager, Marcus, E-mail: Marcus.Fager@UPHS.UPenn.edu [Department of Radiation Oncology, School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania (United States); Medical Radiation Physics, Stockholm University, Stockholm (Sweden); Toma-Dasu, Iuliana [Medical Radiation Physics, Stockholm University and Karolinska Institutet, Stockholm (Sweden); Kirk, Maura; Dolney, Derek; Diffenderfer, Eric S.; Vapiwala, Neha [Department of Radiation Oncology, School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania (United States); Carabe, Alejandro, E-mail: Alejandro.Carabe-Fernandez@UPHS.UPenn.edu [Department of Radiation Oncology, School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania (United States)
2015-04-01
Purpose: The purpose of this study was to propose a proton treatment planning method that trades physical dose (D) for dose-averaged linear energy transfer (LET{sub d}) while keeping the radiobiologically weighted dose (D{sub RBE}) to the target the same. Methods and Materials: The target is painted with LET{sub d} by using 2, 4, and 7 fields aimed at the proximal segment of the target (split target planning [STP]). As the LET{sub d} within the target increases with increasing number of fields, D decreases to maintain the D{sub RBE} the same as the conventional treatment planning method by using beams treating the full target (full target planning [FTP]). Results: The LET{sub d} increased 61% for 2-field STP (2STP) compared to FTP, 72% for 4STP, and 82% for 7STP inside the target. This increase in LET{sub d} led to a decrease of D with 5.3 ± 0.6 Gy for 2STP, 4.4 ± 0.7 Gy for 4STP, and 5.3 ± 1.1 Gy for 7STP, keeping the DRBE at 90% of the volume (DRBE, 90) constant to FTP. Conclusions: LET{sub d} painting offers a method to reduce prescribed dose at no cost to the biological effectiveness of the treatment.
2014-04-01
materials, the affinity ligand would need identification , as well as chemistries that graft the affinity ligand onto the surface of magnetic...ACTIVE CAPTURE MATRICES FOR THE DETECTION/ IDENTIFICATION OF PHARMACEUTICALS...6 As shown in Figure 2.3-1a, the spectra exhibit similar baselines and the spectral peaks lineup . Under these circumstances, the spectral
Mehnati, P.; Keshtkar, A.; Mesbahi, A.; Sasaki, H.
2006-01-01
The fatal effect of ionizing radiation on cells depends on Linear Energy Transfer level. The distribution of ionizing radiation is sparse and homogeneous for low Linear Energy Transfer radiations such as X or y, but it is dense and concentrated for high Linear Energy Transfer radiation such as heavy-ions radiation. Materials and Methods: Chinese hamster ovary cells (CHO-K1) were exposed to 4 Gy Fe-ion 2000 keV/μm. The Cr-39 is a special and sensitive plastic used to verify exact position of heavy-ions traversal. Terminal deoxynucleotidyl transferase is an enzyme labeled with [3 H ] d ATP for detection of cellular DNA damage by autoradiography assay. Results: The track of heavy ions traversals presented by pit size was almost similar for all different doses of radiation. No pits to show the track of traversal were found in 20% of the cell nuclei of the irradiation. Apparently these fractions of cells wave not hit by heavy ions. Conclusion: This study indicated the possible usefulness of both the Cr-39 plastics and DNA labeling with Terminal deoxynucleotidyl transferase method for evaluating the biological effect of heavy-ions in comparison with low Linear Energy Transfer ionizing radiation
Wahlgren, Bjarne; Aarkrog, Vibe
Bogen er den første samlede indføring i transfer på dansk. Transfer kan anvendes som praksis-filosofikum. Den giver en systematisk indsigt til den studerende, der spørger: Hvordan kan teoretisk viden bruges til at reflektere over handlinger i situationer, der passer til min fremtidige arbejdsplads?...
Nevy Triditha Putri
2016-12-01
Full Text Available Intraoral periapical radiograph examination is the additional examination which is the most widely used in Dentistry. This radiograph examination using an x-ray ionizing radiation with low LET (Linear Energy Transfer, and may affect submandibular salivary gland. Ionizing radiation exposure can cause damage by inducing a series of changes at the molecular and cellular level. This study aimed to prove the effects of x-ray ionizing radiation with low LET towards the catalase activity of Rattus norvegicus strain Wistar’s submandibular gland. The subjects were 28 male Wistar rats and divided into 4 groups (n=7. Three groups were exposed 4, 8 and 14 times to radiation with 0.002 µSv for each exposure. The catalase activity of each rat was examined by a spectrophotometer. Data were analyzed using one-way ANOVA followed by Bonferroni test. The results showed the average of catalase activity on Wistar rat’s submandibular gland, respectively for: 0.150±0.0895 (KK, 0.1405±0.0607 (K1, 0.1228±0.0290 (K2, 0.1227±0.0556 (K3. Data showed significant differences of catalase activity between test groups, but showed not significant differences of catalase activity between each groups of Rattus norvegicus strain Wistar’s submandibular gland. In this study concluded decreased catalase activity of Rattus norvegicus strain Wistar’s submandibular gland resulting from x-rays ionizing radiation by 4 times, 8 times and 14 times exposures.
The In Vitro Response of Tissue Stem Cells to Irradiation With Different Linear Energy Transfers
Nagle, Peter W.; Hosper, Nynke A. [Department of Cell Biology, University of Groningen, University Medical Center Groningen, Groningen (Netherlands); Department of Radiation Oncology, University of Groningen, University Medical Center Groningen, Groningen (Netherlands); Ploeg, Emily M. [Department of Cell Biology, University of Groningen, University Medical Center Groningen, Groningen (Netherlands); Goethem, Marc-Jan van [Department of Radiation Oncology, University of Groningen, University Medical Center Groningen, Groningen (Netherlands); KVI-Center for Advanced Radiation Research, University of Groningen, Groningen (Netherlands); Brandenburg, Sytze [KVI-Center for Advanced Radiation Research, University of Groningen, Groningen (Netherlands); Langendijk, Johannes A. [Department of Radiation Oncology, University of Groningen, University Medical Center Groningen, Groningen (Netherlands); Chiu, Roland K. [Department of Cell Biology, University of Groningen, University Medical Center Groningen, Groningen (Netherlands); Department of Radiation Oncology, University of Groningen, University Medical Center Groningen, Groningen (Netherlands); Coppes, Robert P., E-mail: r.p.coppes@umcg.nl [Department of Cell Biology, University of Groningen, University Medical Center Groningen, Groningen (Netherlands); Department of Radiation Oncology, University of Groningen, University Medical Center Groningen, Groningen (Netherlands)
2016-05-01
Purpose: A reduction in the dose, irradiated volume, and sensitivity of, in particular, normal tissue stem cells is needed to advance radiation therapy. This could be obtained with the use of particles for radiation therapy. However, the radiation response of normal tissue stem cells is still an enigma. Therefore, in the present study, we developed a model to investigate the in vitro response of stem cells to particle irradiation. Methods and Materials: We used the immortalized human salivary gland (HSG) cell line resembling salivary gland (SG) cells to translate the radiation response in 2-dimensional (2D) to 3-dimensional (3D) conditions. This response was subsequently translated to the response of SG stem cells (SGSCs). Dispersed single cells were irradiated with photons or carbon ions at different linear energy transfers (LETs; 48.76 ± 2.16, 149.9 ± 10.8, and 189 ± 15 keV/μm). Subsequently, 2D or 3D clonogenicity was determined by counting the colonies or secondary stem cell-derived spheres in Matrigel. γH2AX immunostaining was used to assess DNA double strand break repair. Results: The 2D response of HSG cells showed a similar increase in dose response to increasing higher LET irradiation as other cell lines. The 3D response of HSG cells to increasing LET irradiation was reduced compared with the 2D response. Finally, the response of mouse SGSCs to photons was similar to the 3D response of HSG cells. The response to higher LET irradiation was reduced in the stem cells. Conclusions: Mouse SGSC radiosensitivity seems reduced at higher LET radiation compared with transformed HSG cells. The developed model to assess the radiation response of SGSCs offers novel possibilities to study the radiation response of normal tissue in vitro.
The In Vitro Response of Tissue Stem Cells to Irradiation With Different Linear Energy Transfers
Nagle, Peter W.; Hosper, Nynke A.; Ploeg, Emily M.; Goethem, Marc-Jan van; Brandenburg, Sytze; Langendijk, Johannes A.; Chiu, Roland K.; Coppes, Robert P.
2016-01-01
Purpose: A reduction in the dose, irradiated volume, and sensitivity of, in particular, normal tissue stem cells is needed to advance radiation therapy. This could be obtained with the use of particles for radiation therapy. However, the radiation response of normal tissue stem cells is still an enigma. Therefore, in the present study, we developed a model to investigate the in vitro response of stem cells to particle irradiation. Methods and Materials: We used the immortalized human salivary gland (HSG) cell line resembling salivary gland (SG) cells to translate the radiation response in 2-dimensional (2D) to 3-dimensional (3D) conditions. This response was subsequently translated to the response of SG stem cells (SGSCs). Dispersed single cells were irradiated with photons or carbon ions at different linear energy transfers (LETs; 48.76 ± 2.16, 149.9 ± 10.8, and 189 ± 15 keV/μm). Subsequently, 2D or 3D clonogenicity was determined by counting the colonies or secondary stem cell-derived spheres in Matrigel. γH2AX immunostaining was used to assess DNA double strand break repair. Results: The 2D response of HSG cells showed a similar increase in dose response to increasing higher LET irradiation as other cell lines. The 3D response of HSG cells to increasing LET irradiation was reduced compared with the 2D response. Finally, the response of mouse SGSCs to photons was similar to the 3D response of HSG cells. The response to higher LET irradiation was reduced in the stem cells. Conclusions: Mouse SGSC radiosensitivity seems reduced at higher LET radiation compared with transformed HSG cells. The developed model to assess the radiation response of SGSCs offers novel possibilities to study the radiation response of normal tissue in vitro.
Marsolat, F; De Marzi, L; Mazal, A; Pouzoulet, F
2016-01-01
In proton therapy, the relative biological effectiveness (RBE) depends on various types of parameters such as linear energy transfer (LET). An analytical model for LET calculation exists (Wilkens’ model), but secondary particles are not included in this model. In the present study, we propose a correction factor, L sec , for Wilkens’ model in order to take into account the LET contributions of certain secondary particles. This study includes secondary protons and deuterons, since the effects of these two types of particles can be described by the same RBE-LET relationship. L sec was evaluated by Monte Carlo (MC) simulations using the GATE/GEANT4 platform and was defined by the ratio of the LET d distributions of all protons and deuterons and only primary protons. This method was applied to the innovative Pencil Beam Scanning (PBS) delivery systems and L sec was evaluated along the beam axis. This correction factor indicates the high contribution of secondary particles in the entrance region, with L sec values higher than 1.6 for a 220 MeV clinical pencil beam. MC simulations showed the impact of pencil beam parameters, such as mean initial energy, spot size, and depth in water, on L sec . The variation of L sec with these different parameters was integrated in a polynomial function of the L sec factor in order to obtain a model universally applicable to all PBS delivery systems. The validity of this correction factor applied to Wilkens’ model was verified along the beam axis of various pencil beams in comparison with MC simulations. A good agreement was obtained between the corrected analytical model and the MC calculations, with mean-LET deviations along the beam axis less than 0.05 keV μm −1 . These results demonstrate the efficacy of our new correction of the existing LET model in order to take into account secondary protons and deuterons along the pencil beam axis. (paper)
Kotaro Ishii
Full Text Available A heavy-ion beam has been recognized as an effective mutagen for plant breeding and applied to the many kinds of crops including rice. In contrast with X-ray or γ-ray, the heavy-ion beam is characterized by a high linear energy transfer (LET. LET is an important factor affecting several aspects of the irradiation effect, e.g. cell survival and mutation frequency, making the heavy-ion beam an effective mutagen. To study the mechanisms behind LET-dependent effects, expression profiling was performed after heavy-ion beam irradiation of imbibed rice seeds. Array-based experiments at three time points (0.5, 1, 2 h after the irradiation revealed that the number of up- or down-regulated genes was highest 2 h after irradiation. Array-based experiments with four different LETs at 2 h after irradiation identified LET-independent regulated genes that were up/down-regulated regardless of the value of LET; LET-dependent regulated genes, whose expression level increased with the rise of LET value, were also identified. Gene ontology (GO analysis of LET-independent up-regulated genes showed that some GO terms were commonly enriched, both 2 hours and 3 weeks after irradiation. GO terms enriched in LET-dependent regulated genes implied that some factor regulates genes that have kinase activity or DNA-binding activity in cooperation with the ATM gene. Of the LET-dependent up-regulated genes, OsPARP3 and OsPCNA were identified, which are involved in DNA repair pathways. This indicates that the Ku-independent alternative non-homologous end-joining pathway may contribute to repairing complex DNA legions induced by high-LET irradiation. These findings may clarify various LET-dependent responses in rice.
Ishii, Kotaro; Kazama, Yusuke; Morita, Ryouhei; Hirano, Tomonari; Ikeda, Tokihiro; Usuda, Sachiko; Hayashi, Yoriko; Ohbu, Sumie; Motoyama, Ritsuko; Nagamura, Yoshiaki; Abe, Tomoko
2016-01-01
A heavy-ion beam has been recognized as an effective mutagen for plant breeding and applied to the many kinds of crops including rice. In contrast with X-ray or γ-ray, the heavy-ion beam is characterized by a high linear energy transfer (LET). LET is an important factor affecting several aspects of the irradiation effect, e.g. cell survival and mutation frequency, making the heavy-ion beam an effective mutagen. To study the mechanisms behind LET-dependent effects, expression profiling was performed after heavy-ion beam irradiation of imbibed rice seeds. Array-based experiments at three time points (0.5, 1, 2 h after the irradiation) revealed that the number of up- or down-regulated genes was highest 2 h after irradiation. Array-based experiments with four different LETs at 2 h after irradiation identified LET-independent regulated genes that were up/down-regulated regardless of the value of LET; LET-dependent regulated genes, whose expression level increased with the rise of LET value, were also identified. Gene ontology (GO) analysis of LET-independent up-regulated genes showed that some GO terms were commonly enriched, both 2 hours and 3 weeks after irradiation. GO terms enriched in LET-dependent regulated genes implied that some factor regulates genes that have kinase activity or DNA-binding activity in cooperation with the ATM gene. Of the LET-dependent up-regulated genes, OsPARP3 and OsPCNA were identified, which are involved in DNA repair pathways. This indicates that the Ku-independent alternative non-homologous end-joining pathway may contribute to repairing complex DNA legions induced by high-LET irradiation. These findings may clarify various LET-dependent responses in rice.
Amir-Moez, A R; Sneddon, I N
1962-01-01
Elements of Linear Space is a detailed treatment of the elements of linear spaces, including real spaces with no more than three dimensions and complex n-dimensional spaces. The geometry of conic sections and quadric surfaces is considered, along with algebraic structures, especially vector spaces and transformations. Problems drawn from various branches of geometry are given.Comprised of 12 chapters, this volume begins with an introduction to real Euclidean space, followed by a discussion on linear transformations and matrices. The addition and multiplication of transformations and matrices a
Hierarchical quark mass matrices
Rasin, A.
1998-02-01
I define a set of conditions that the most general hierarchical Yukawa mass matrices have to satisfy so that the leading rotations in the diagonalization matrix are a pair of (2,3) and (1,2) rotations. In addition to Fritzsch structures, examples of such hierarchical structures include also matrices with (1,3) elements of the same order or even much larger than the (1,2) elements. Such matrices can be obtained in the framework of a flavor theory. To leading order, the values of the angle in the (2,3) plane (s 23 ) and the angle in the (1,2) plane (s 12 ) do not depend on the order in which they are taken when diagonalizing. We find that any of the Cabbibo-Kobayashi-Maskawa matrix parametrizations that consist of at least one (1,2) and one (2,3) rotation may be suitable. In the particular case when the s 13 diagonalization angles are sufficiently small compared to the product s 12 s 23 , two special CKM parametrizations emerge: the R 12 R 23 R 12 parametrization follows with s 23 taken before the s 12 rotation, and vice versa for the R 23 R 12 R 23 parametrization. (author)
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-01-07
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(n log n). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and optimal design
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-01-05
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(nlogn). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and op- timal design.
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander; Genton, Marc G.; Sun, Ying; Tempone, Raul
2015-01-01
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(n log n). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and optimal design
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander; Genton, Marc G.; Sun, Ying; Tempone, Raul
2015-01-01
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(nlogn). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and op- timal design.
Sethi, Roshan V.; Giantsoudi, Drosoula; Raiford, Michael; Malhi, Imran; Niemierko, Andrzej; Rapalino, Otto; Caruso, Paul; Yock, Torunn I.; Tarbell, Nancy J.; Paganetti, Harald; MacDonald, Shannon M.
2014-01-01
Purpose: The pattern of failure in medulloblastoma patients treated with proton radiation therapy is unknown. For this increasingly used modality, it is important to ensure that outcomes are comparable to those in modern photon series. It has been suggested this pattern may differ from photons because of variations in linear energy transfer (LET) and relative biological effectiveness (RBE). In addition, the use of matching fields for delivery of craniospinal irradiation (CSI) may influence patterns of relapse. Here we report the patterns of failure after the use of protons, compare it to that in the available photon literature, and determine the LET and RBE values in areas of recurrence. Methods and Materials: Retrospective review of patients with medulloblastoma treated with proton radiation therapy at Massachusetts General Hospital (MGH) between 2002 and 2011. We documented the locations of first relapse. Discrete failures were contoured on the original planning computed tomography scan. Monte Carlo calculation methods were used to estimate the proton LET distribution. Models were used to estimate RBE values based on the LET distributions. Results: A total of 109 patients were followed for a median of 38.8 months (range, 1.4-119.2 months). Of the patients, 16 experienced relapse. Relapse involved the supratentorial compartment (n=8), spinal compartment (n=11), and posterior fossa (n=5). Eleven failures were isolated to a single compartment; 6 failures in the spine, 4 failures in the supratentorium, and 1 failure in the posterior fossa. The remaining patients had multiple sites of disease. One isolated spinal failure occurred at the spinal junction of 2 fields. None of the 70 patients treated with an involved-field-only boost failed in the posterior fossa outside of the tumor bed. We found no correlation between Monte Carlo-calculated LET distribution and regions of recurrence. Conclusions: The most common site of failure in patients treated with protons for
Hohensee, Charles
2014-01-01
The transfer of learning has been the subject of much scientific inquiry in the social sciences. However, mathematics education research has given little attention to a subclass called backward transfer, which is when learning about new concepts influences learners' ways of reasoning about previously encountered concepts. This study examined when…
Model-independent analysis with BPM correlation matrices
Irwin, J.; Wang, C.X.; Yan, Y.T.; Bane, K.; Cai, Y.; Decker, F.; Minty, M.; Stupakov, G.; Zimmermann, F.
1998-06-01
The authors discuss techniques for Model-Independent Analysis (MIA) of a beamline using correlation matrices of physical variables and Singular Value Decomposition (SVD) of a beamline BPM matrix. The beamline matrix is formed from BPM readings for a large number of pulses. The method has been applied to the Linear Accelerator of the SLAC Linear Collider (SLC)
Murthy, P.V.S.N.
2011-12-26
Thermo-diffusion effect on free convection heat and mass transfer from a vertical surface embedded in a liquid saturated thermally stratified non - Darcy porous medium has been analyzed using a local non-similar procedure. The wall temperature and concentration are constant and the medium is linearly stratified in the vertical direction with respect to the thermal conditions. The fluid flow, temperature and concentration fields are affected by the complex interactions among the diffusion ratio Le, buoyancy ratio N, thermo-diffusion parameter Sr and stratification parameter ?. Non-linear interactions of all these parameters on the convective transport has been analyzed and variation of heat and mass transfer coefficients with thermo-diffusion parameter in the thermally stratified non-Darcy porous media is presented through computer generated plots.
Murthy, P.V.S.N.; El-Amin, Mohamed
2011-01-01
Thermo-diffusion effect on free convection heat and mass transfer from a vertical surface embedded in a liquid saturated thermally stratified non - Darcy porous medium has been analyzed using a local non-similar procedure. The wall temperature and concentration are constant and the medium is linearly stratified in the vertical direction with respect to the thermal conditions. The fluid flow, temperature and concentration fields are affected by the complex interactions among the diffusion ratio Le, buoyancy ratio N, thermo-diffusion parameter Sr and stratification parameter ?. Non-linear interactions of all these parameters on the convective transport has been analyzed and variation of heat and mass transfer coefficients with thermo-diffusion parameter in the thermally stratified non-Darcy porous media is presented through computer generated plots.
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
Intermittency and random matrices
Sokoloff, Dmitry; Illarionov, E. A.
2015-08-01
A spectacular phenomenon of intermittency, i.e. a progressive growth of higher statistical moments of a physical field excited by an instability in a random medium, attracted the attention of Zeldovich in the last years of his life. At that time, the mathematical aspects underlying the physical description of this phenomenon were still under development and relations between various findings in the field remained obscure. Contemporary results from the theory of the product of independent random matrices (the Furstenberg theory) allowed the elaboration of the phenomenon of intermittency in a systematic way. We consider applications of the Furstenberg theory to some problems in cosmology and dynamo theory.
Dimension from covariance matrices.
Carroll, T L; Byers, J M
2017-02-01
We describe a method to estimate embedding dimension from a time series. This method includes an estimate of the probability that the dimension estimate is valid. Such validity estimates are not common in algorithms for calculating the properties of dynamical systems. The algorithm described here compares the eigenvalues of covariance matrices created from an embedded signal to the eigenvalues for a covariance matrix of a Gaussian random process with the same dimension and number of points. A statistical test gives the probability that the eigenvalues for the embedded signal did not come from the Gaussian random process.
This paper reports on further studies on long range energy transfer between curcumine as donor and another thiazine dye, thionine, which is closely related to methylene blue as energy harvester (Figure 1). Since thionine is known to have a higher quantum yield of singlet oxygen sensitization than methylene blue [8], it is ...
Blyth, T S
2002-01-01
Basic Linear Algebra is a text for first year students leading from concrete examples to abstract theorems, via tutorial-type exercises. More exercises (of the kind a student may expect in examination papers) are grouped at the end of each section. The book covers the most important basics of any first course on linear algebra, explaining the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations and complex numbers. Linear equations are treated via Hermite normal forms which provides a successful and concrete explanation of the notion of linear independence. Another important highlight is the connection between linear mappings and matrices leading to the change of basis theorem which opens the door to the notion of similarity. This new and revised edition features additional exercises and coverage of Cramer's rule (omitted from the first edition). However, it is the new, extra chapter on computer assistance that will be of particular interest to readers:...
Murphy, G.V.; Bailey, J.M.
1990-01-01
This paper uses the linear quadratic Gaussian with loop transfer recovery (LQG/LTR) control system design method to obtain a level control system for a low-pressure feedwater heater train. The control system performance and stability robustness are evaluated for a given set of system design specifications. The tools for analysis are the return ratio, return difference, and inverse return difference singular-valve plots for a loop break at the plant output. 3 refs., 7 figs., 2 tabs
Galin, J.; Ingold, G.; Jahnke, U.; Hilscher, D.; Lehmann, M.; Rossner, H.; Schwinn, E.
1988-01-01
The 20 Ne+U reactions are investigated at 290 MeV bombarding energy. The linear momentum transfer and excitation energy are deduced eventwise from the respective measurements of the folding angle between correlated fission fragments and the neutron multiplicity. A simple incomplete fusion picture is shown to essentially account for the data. The sensitivity of the two measurements in order to infer the violence of a collision is discussed in details. (orig.)
Krop, D.C.J.; Lomonova, E.A.; Jansen, J.W.; Paulides, J.J.H.
2009-01-01
Linear motors find their utilization in an increasing number of industrial applications. Permanent magnet linear synchronous motors (PMLSMs) are favorable in many applications due to their servo characteristics, robustness, and high force density. The major disadvantage of moving coil type PMLSMs is
Jin, Peitong
2000-11-01
Local mass/heat transfer measurements from the turbine blade near-tip and the tip surfaces are performed using the naphthalene sublimation technique. The experiments are conducted in a linear cascade consisting of five high-pressure blades with a central test-blade configuration. The incoming flow conditions are close to those of the gas turbine engine environment (boundary layer displacement thickness is about 0.01 of chord) with an exit Reynolds number of 6.2 x 105. The effects of tip clearance level (0.86%--6.90% of chord), mainstream Reynolds number and turbulence intensity (0.2 and 12.0%) are investigated. Two methods of flow visualization---oil and lampblack, laser light sheet smoke wire---as well as static pressure measurement on the blade surface are used to study the tip leakage flow and vortex in the cascade. In addition, numerical modeling of the flow and heat transfer processes in the linear cascade with different tip clearances is conducted using commercial software incorporating advanced turbulence models. The present study confirms many important results on the tip leakage flow and vortex from the literature, contributes to the current understanding in the effects of tip leakage flow and vortex on local heat transfer from the blade near-tip and the tip surfaces, and provides detailed local and average heat/mass transfer data applicable to turbine blade tip cooling design.
Teaching Fourier optics through ray matrices
Moreno, I; Sanchez-Lopez, M M; Ferreira, C; Davis, J A; Mateos, F
2005-01-01
In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this derivation to fractional Fourier transform optical systems, and derive the order of the transform from the ray matrix. Some examples are provided to stress this point of view, both with classical and with graded index lenses. This formulation cannot replace the complete explanation of Fourier optics provided by the wave theory, but it is a complementary tool useful to simplify many aspects of Fourier optics and to relate them to geometrical optics
An introduction to linear algebra
Mirsky, L
2003-01-01
Rigorous, self-contained coverage of determinants, vectors, matrices and linear equations, quadratic forms, more. Elementary, easily readable account with numerous examples and problems at the end of each chapter.
An algorithmic characterization of P-matricity
Ben Gharbia , Ibtihel; Gilbert , Jean Charles
2013-01-01
International audience; It is shown that a matrix M is a P-matrix if and only if, whatever is the vector q, the Newton-min algorithm does not cycle between two points when it is used to solve the linear complementarity problem 0 ≤ x ⊥ (Mx+q) ≥ 0.; Nous montrons dans cet article qu'une matrice M est une P-matrice si, et seulement si, quel que soit le vecteur q, l'algorithme de Newton-min ne fait pas de cycle de deux points lorsqu'il est utilisé pour résoudre le problème de compl\\émentarité lin...
Complex Wedge-Shaped Matrices: A Generalization of Jacobi Matrices
Hnětynková, Iveta; Plešinger, M.
2015-01-01
Roč. 487, 15 December (2015), s. 203-219 ISSN 0024-3795 R&D Projects: GA ČR GA13-06684S Keywords : eigenvalues * eigenvector * wedge-shaped matrices * generalized Jacobi matrices * band (or block) Krylov subspace methods Subject RIV: BA - General Mathematics Impact factor: 0.965, year: 2015
Generalisations of Fisher Matrices
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.
Fukuma, Masafumi; Sugishita, Sotaro; Umeda, Naoya [Department of Physics, Kyoto University,Kitashirakawa Oiwake-cho, Kyoto 606-8502 (Japan)
2015-07-17
We propose a class of models which generate three-dimensional random volumes, where each configuration consists of triangles glued together along multiple hinges. The models have matrices as the dynamical variables and are characterized by semisimple associative algebras A. Although most of the diagrams represent configurations which are not manifolds, we show that the set of possible diagrams can be drastically reduced such that only (and all of the) three-dimensional manifolds with tetrahedral decompositions appear, by introducing a color structure and taking an appropriate large N limit. We examine the analytic properties when A is a matrix ring or a group ring, and show that the models with matrix ring have a novel strong-weak duality which interchanges the roles of triangles and hinges. We also give a brief comment on the relationship of our models with the colored tensor models.
VanderLaan Circulant Type Matrices
Hongyan Pan
2015-01-01
Full Text Available Circulant matrices have become a satisfactory tools in control methods for modern complex systems. In the paper, VanderLaan circulant type matrices are presented, which include VanderLaan circulant, left circulant, and g-circulant matrices. The nonsingularity of these special matrices is discussed by the surprising properties of VanderLaan numbers. The exact determinants of VanderLaan circulant type matrices are given by structuring transformation matrices, determinants of well-known tridiagonal matrices, and tridiagonal-like matrices. The explicit inverse matrices of these special matrices are obtained by structuring transformation matrices, inverses of known tridiagonal matrices, and quasi-tridiagonal matrices. Three kinds of norms and lower bound for the spread of VanderLaan circulant and left circulant matrix are given separately. And we gain the spectral norm of VanderLaan g-circulant matrix.
Diagonalization of the mass matrices
Rhee, S.S.
1984-01-01
It is possible to make 20 types of 3x3 mass matrices which are hermitian. We have obtained unitary matrices which could diagonalize each mass matrix. Since the three elements of mass matrix can be expressed in terms of the three eigenvalues, msub(i), we can also express the unitary matrix in terms of msub(i). (Author)
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…
Positive projections of symmetric matrices and Jordan algebras
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....
Pettofrezzo, Anthony J
1978-01-01
Elementary, concrete approach: fundamentals of matrix algebra, linear transformation of the plane, application of properties of eigenvalues and eigenvectors to study of conics. Includes proofs of most theorems. Answers to odd-numbered exercises.
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.
Linearization of the interaction principle: Analytic Jacobians in the 'Radiant' model
Spurr, R.J.D.; Christi, M.J.
2007-01-01
In this paper we present a new linearization of the Radiant radiative transfer model. Radiant uses discrete ordinates for solving the radiative transfer equation in a multiply-scattering anisotropic medium with solar and thermal sources, but employs the adding method (interaction principle) for the stacking of reflection and transmission matrices in a multilayer atmosphere. For the linearization, we show that the entire radiation field is analytically differentiable with respect to any surface or atmospheric parameter for which we require Jacobians (derivatives of the radiance field). Derivatives of the discrete ordinate solutions are based on existing methods developed for the LIDORT radiative transfer models. Linearization of the interaction principle is completely new and constitutes the major theme of the paper. We discuss the application of the Radiant model and its linearization in the Level 2 algorithm for the retrieval of columns of carbon dioxide as the main target of the Orbiting Carbon Observatory (OCO) mission
Linear energy transfer effects on time profiles of scintillation of Ce-doped LiCaAlF{sub 6} crystals
Yanagida, Takayuki [Graduate School of Materials Science, Nara Institute of Science and Technology, 8916-5 Takayama-Cho, Ikoma, Nara 630-0192 (Japan); Koshimizu, Masanori [Department of Applied Chemistry, Graduate School of Engineering, Tohoku University, 6-6-07 Aoba, Aramaki, Aoba-ku, Sendai 980-8579 (Japan); Kurashima, Satoshi [Takasaki Advanced Radiation Research Institute, Japan Atomic Energy Agency, 1233 Watanuki, Takasaki, Gunma 370-1292 (Japan); Iwamatsu, Kazuhiro [Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656 (Japan); Kimura, Atsushi; Taguchi, Mitsumasa [Quantum Beam Science Directorate, Japan Atomic Energy Agency, 1233 Watanuki, Takasaki, Gunma 370-1292 (Japan); Fujimoto, Yutaka; Asai, Keisuke [Department of Applied Chemistry, Graduate School of Engineering, Tohoku University, 6-6-07 Aoba, Aramaki, Aoba-ku, Sendai 980-8579 (Japan)
2015-12-15
We measured temporal profiles of the scintillation of Ce-doped LiCaAlF{sub 6} scintillator crystals at different linear energy transfers (LETs). Based on the comparison of high-LET temporal profiles with those at low LET, a fast component was observed only at low LET. The disappearance of the fast component at high LET is tentatively ascribed to the quenching of excited states at crystal defects owing to the interaction between excited states via the Auger process. In addition, the rise and the initial decay behavior were dependent on the LET. This LET-dependent behavior is explained by an acceleration process and a deceleration process in energy transfer at high LET. The LET-dependent temporal profiles provide the basis for a discrimination technique of gamma-ray and neutron detection events using these scintillators based on the nuclear reaction, {sup 6}Li(n,α)t.
2D gravity and random matrices
Zinn-Justin, J.
1990-01-01
Recent progress in 2D gravity coupled to d ≤ 1 matter, based on a representation of discrete gravity in terms of random matrices, is reported. The matrix problem can be solved in many cases by the introduction of suitable orthogonal polynomials. Alternatively in the continuum limit the orthogonal polynomial method can be shown to be equivalent to the construction of representation of the canonical commutation relations in terms of differential operators. In the case of pure gravity or discrete Ising-like matter the sum over topologies is reduced to the solution of non-linear differential equations. The d = 1 problem can be solved by semiclassical methods
Helama, S.; Holopainen, J.; Eronen, M. [Department of Geology, University of Helsinki, (Finland); Makarenko, N.G. [Russian Academy of Sciences, St. Petersburg (Russian Federation). Pulkovo Astronomical Observatory; Karimova, L.M.; Kruglun, O.A. [Institute of Mathematics, Almaty (Kazakhstan); Timonen, M. [Finnish Forest Research Institute, Rovaniemi Research Unit (Finland); Merilaeinen, J. [SAIMA Unit of the Savonlinna Department of Teacher Education, University of Joensuu (Finland)
2009-07-01
Tree-rings tell of past climates. To do so, tree-ring chronologies comprising numerous climate-sensitive living-tree and subfossil time-series need to be 'transferred' into palaeoclimate estimates using transfer functions. The purpose of this study is to compare different types of transfer functions, especially linear and nonlinear algorithms. Accordingly, multiple linear regression (MLR), linear scaling (LSC) and artificial neural networks (ANN, nonlinear algorithm) were compared. Transfer functions were built using a regional tree-ring chronology and instrumental temperature observations from Lapland (northern Finland and Sweden). In addition, conventional MLR was compared with a hybrid model whereby climate was reconstructed separately for short- and long-period timescales prior to combining the bands of timescales into a single hybrid model. The fidelity of the different reconstructions was validated against instrumental climate data. The reconstructions by MLR and ANN showed reliable reconstruction capabilities over the instrumental period (AD 1802-1998). LCS failed to reach reasonable verification statistics and did not qualify as a reliable reconstruction: this was due mainly to exaggeration of the low-frequency climatic variance. Over this instrumental period, the reconstructed low-frequency amplitudes of climate variability were rather similar by MLR and ANN. Notably greater differences between the models were found over the actual reconstruction period (AD 802-1801). A marked temperature decline, as reconstructed by MLR, from the Medieval Warm Period (AD 931-1180) to the Little Ice Age (AD 1601-1850), was evident in all the models. This decline was approx. 0.5 C as reconstructed by MLR. Different ANN based palaeotemperatures showed simultaneous cooling of 0.2 to 0.5 C, depending on algorithm. The hybrid MLR did not seem to provide further benefit above conventional MLR in our sample. The robustness of the conventional MLR over the calibration
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.
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
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.
Meera, M. R.; Joselin Beaula, T.; Rayar, S. L.; Bena Jothy, V.
2017-09-01
NLO materials are gaining importance in technologies such as optical communication, optical computing and dynamic image processing. Many NLO crystals grown by mixing amino acids with various organic and inorganic acids have been reported in the literature. Hence, glycine mixed semi-organic material will be of special interest as a fundamental building block to develop many complex crystals with improved NLO properties. A semi organic Single crystal of Triglycine Phosphate (TGP) which was grown and spectral analysis have been using FTIR and Raman spectral analysis. Natural Bond Orbital Analysis and the atomic natural charges are also predicted. HOMO LUMO energy gap value suggests the possibility of charge transfer within the molecule.
(b) The numerical range of a bounded linear op- erator T on a complex Hilbert space 1i, which is defined by .... Let us see how this 'algebra-geometry' nexus goes. The correspondence. =Z. (4) sets up an identification ..... We wish to discuss elementary proofs of the following three well-known results: (A) A square complex ...
Thrall, Robert M
2011-01-01
This volume is suitable as a primary or supplementary text for college-level courses in linear algebra. It possesses the distinct advantage of approaching the subject simultaneously at two levels, the concrete and the axiomatic. Students thus receive the benefits of axiom-based mathematical reasoning as well as a grasp of concrete formulations. 1957 edition.
First page Back Continue Last page Overview Graphics. Heat transfer. Heat conduction in solid slab. Convective heat transfer. Non-linear temperature. variation due to flow. HEAT FLUX AT SURFACE. conduction/diffusion.
Diego Alfredo Núñez-Altamirano
2016-07-01
Full Text Available This article deals with the kinematics and dynamics of a novel leg based on the Peaucellier–Lipkin mechanism, which is better known as the straight path tracer. The basic Peaucellier–Lipkin linkage with 1 degree of freedom was transformed into a more skillful mechanism, through the addition of 4 more degrees of freedom. The resulting 5-degree-of-freedom leg enables the walking machine to move along paths that are straight lines and/or concave or convex curves. Three degrees of freedom transform the leg in relation to a reachable center of rotation that the machine walks around. Once the leg is transformed, the remaining 2 degrees of freedom position the foot at a desirable Cartesian point during the transfer or support phase. We analyzed the direct and inverse kinematics developed for the leg when the foot describes a straight line and found some interesting relationships among the motion parameters. The dynamic model equations of motion for the leg were derived from the Lagrangian dynamic formulation to calculate the required torques during a particular transfer phase.
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...
Quantum matrices in two dimensions
Ewen, H.; Ogievetsky, O.; Wess, J.
1991-01-01
Quantum matrices in two-dimensions, admitting left and right quantum spaces, are classified: they fall into two families, the 2-parametric family GL p,q (2) and a 1-parametric family GL α J (2). Phenomena previously found for GL p,q (2) hold in this general situation: (a) powers of quantum matrices are again quantum and (b) entries of the logarithm of a two-dimensional quantum matrix form a Lie algebra. (orig.)
Blanco Rodriguez, P.; Vera Tome, F. [Natural Radioactivity Group. Universidad de Extremadura, 06071 Badajoz (Spain); Lozano, J.C. [Laboratorio de Radiactividad Ambiental. Universidad de Salamanca, 37008 Salamanca (Spain)
2014-07-01
Transfer from soil to plant is an important input of radionuclides into the food chain. Also, the mobility of radionuclides in soils is enhanced through their passage into the plant compartment. Thus, the soil-to-plant transfer of radionuclides raises the potential human dose. In radiological risk assessment models, this process is usually considered to be an equilibrium process such that the activity concentration in plants is linearly related to the soil concentration through a constant transfer factor (TF). However, the large variability present by measured TF values leads to major uncertainties in the assessment of risks. One possible way to reduce this variability in TF values is to parametrize their determination. This paper presents correlations of TF with the major element concentrations in soils. The findings confirm the major influence of the chemical environment of a soil on the assimilation process. The variability of TF might be greatly reduced if only the labile fraction were considered. Experiments performed with plants (Helianthus annuus L.) growing in a hydroponic medium appear to confirm this suggestion, showing a linear correlation between the plant and the soil solution activity concentrations. Extracting the labile fraction of a real soil is no trivial task, however. A possible operationally definable method is to consider the water-soluble together with the exchangeable fractions of the soil. Studies performed in granitic soils showed that the labile concentration of uranium and radium strongly depended on the soil's textural characteristics. In this sense, a parametrization is proposed of the labile uranium and radium concentration as a function of the soil's granulometric parameters. (authors)
A definition of column reduced proper rational matrices
Ruiz-León, J. J.; Castellanos, A.; Ramos-Velasco, Luis Enrique
2002-01-01
Roč. 75, č. 3 (2002), s. 195-203 ISSN 0020-7179 R&D Projects: GA AV ČR KSK1019101 Institutional research plan: CEZ:AV0Z1075907 Keywords : linear systems * columm reduced polynomial matrices * decoupling Subject RIV: BC - Control Systems Theory Impact factor: 0.861, year: 2002
Verbeken, Mathieu; Wynendaele, Evelien; Mauchauffee, Elodie
2015-01-01
Enkephalins are active in regulation of nociception in the body and are key in development of new synthetic peptide analogs that target centrally located opioid receptors. In this study, we investigated the in vivo blood–brain barrier (BBB) penetration behavior and antinociceptive activity of two...... cyclic enkephalin analogs with a thiourea (CycS) or a N-methyl-guanidine bridge (CycNMe), and their linear counterparts (LinS and LinNMe) in mice, as well as their in vitro metabolic stability. 125I-LinS had the highest blood–brain clearance (K1 = 3.46 μL/g min), followed by 125I-LinNMe, 125I...
On reflectionless equi-transmitting matrices
Pavel Kurasov
2014-01-01
Full Text Available Reflectionless equi-transmitting unitary matrices are studied in connection to matching conditions in quantum graphs. All possible such matrices of size 6 are described explicitly. It is shown that such matrices form 30 six-parameter families intersected along 12 five-parameter families closely connected to conference matrices.
Spectra of sparse random matrices
Kuehn, Reimer
2008-01-01
We compute the spectral density for ensembles of sparse symmetric random matrices using replica. Our formulation of the replica-symmetric ansatz shares the symmetries of that suggested in a seminal paper by Rodgers and Bray (symmetry with respect to permutation of replica and rotation symmetry in the space of replica), but uses a different representation in terms of superpositions of Gaussians. It gives rise to a pair of integral equations which can be solved by a stochastic population-dynamics algorithm. Remarkably our representation allows us to identify pure-point contributions to the spectral density related to the existence of normalizable eigenstates. Our approach is not restricted to matrices defined on graphs with Poissonian degree distribution. Matrices defined on regular random graphs or on scale-free graphs, are easily handled. We also look at matrices with row constraints such as discrete graph Laplacians. Our approach naturally allows us to unfold the total density of states into contributions coming from vertices of different local coordinations and an example of such an unfolding is presented. Our results are well corroborated by numerical diagonalization studies of large finite random matrices
Endo, A.; Sato, T.
2013-01-01
Absorbed doses, linear energy transfers (LETs) and quality factors of secondary charged particles in organs and tissues, generated via the interactions of the spontaneous fission neutrons from. 252 Cf and. 244 Pu within the human body, were studied using the Particle and Heavy Ion Transport Code System (PHITS) coupled with the ICRP Reference Phantom. Both the absorbed doses and the quality factors in target organs generally decrease with increasing distance from the source organ. The analysis of LET distributions of secondary charged particles led to the identification of the relationship between LET spectra and target-source organ locations. A comparison between human body-averaged mean quality factors and fluence-averaged radiation weighting factors showed that the current numerical conventions for the radiation weighting factors of neutrons, updated in ICRP103, and the quality factors for internal exposure are valid. (authors)
Shweta Mishra
2016-12-01
Full Text Available In this paper magnetoconvective heat and mass transfer characteristics of a two-dimensional steady flow of a nanofluid over a non-linear stretching sheet in the presence of thermal radiation, Ohmic heating and viscous dissipation have been investigated numerically. The model used for the nanofluid incorporates the effects of the Brownian motion and the presence of nanoparticles in the base fluid. The governing equations are transformed into a system of nonlinear ordinary differential equations by using similarity transformation. The numerical solutions are obtained by using fifth order Runge–Kutta–Fehlberg method with shooting technique. The non-dimensional parameters on velocity, temperature and concentration profiles and also on local Nusselt number and Sherwood number are discussed. The results indicate that the local skin friction coefficient decreases as the value of the magnetic parameter increases whereas the Nusselt number and Sherwood number increase as the values of the Brownian motion parameter and magnetic parameter increase.
M Taki
2017-05-01
Full Text Available Introduction Controlling greenhouse microclimate not only influences the growth of plants, but also is critical in the spread of diseases inside the greenhouse. The microclimate parameters were inside air, greenhouse roof and soil temperature, relative humidity and solar radiation intensity. Predicting the microclimate conditions inside a greenhouse and enabling the use of automatic control systems are the two main objectives of greenhouse climate model. The microclimate inside a greenhouse can be predicted by conducting experiments or by using simulation. Static and dynamic models are used for this purpose as a function of the metrological conditions and the parameters of the greenhouse components. Some works were done in past to 2015 year to simulation and predict the inside variables in different greenhouse structures. Usually simulation has a lot of problems to predict the inside climate of greenhouse and the error of simulation is higher in literature. The main objective of this paper is comparison between heat transfer and regression models to evaluate them to predict inside air and roof temperature in a semi-solar greenhouse in Tabriz University. Materials and Methods In this study, a semi-solar greenhouse was designed and constructed at the North-West of Iran in Azerbaijan Province (geographical location of 38°10′ N and 46°18′ E with elevation of 1364 m above the sea level. In this research, shape and orientation of the greenhouse, selected between some greenhouses common shapes and according to receive maximum solar radiation whole the year. Also internal thermal screen and cement north wall was used to store and prevent of heat lost during the cold period of year. So we called this structure, ‘semi-solar’ greenhouse. It was covered with glass (4 mm thickness. It occupies a surface of approximately 15.36 m2 and 26.4 m3. The orientation of this greenhouse was East–West and perpendicular to the direction of the wind prevailing
Free probability and random matrices
Mingo, James A
2017-01-01
This volume opens the world of free probability to a wide variety of readers. From its roots in the theory of operator algebras, free probability has intertwined with non-crossing partitions, random matrices, applications in wireless communications, representation theory of large groups, quantum groups, the invariant subspace problem, large deviations, subfactors, and beyond. This book puts a special emphasis on the relation of free probability to random matrices, but also touches upon the operator algebraic, combinatorial, and analytic aspects of the theory. The book serves as a combination textbook/research monograph, with self-contained chapters, exercises scattered throughout the text, and coverage of important ongoing progress of the theory. It will appeal to graduate students and all mathematicians interested in random matrices and free probability from the point of view of operator algebras, combinatorics, analytic functions, or applications in engineering and statistical physics.
Chequered surfaces and complex matrices
Morris, T.R.; Southampton Univ.
1991-01-01
We investigate a large-N matrix model involving general complex matrices. It can be reinterpreted as a model of two hermitian matrices with specific couplings, and as a model of positive definite hermitian matrices. Large-N perturbation theory generates dynamical triangulations in which the triangles can be chequered (i.e. coloured so that neighbours are opposite colours). On a sphere there is a simple relation between such triangulations and those generated by the single hermitian matrix model. For the torus (and a quartic potential) we solve the counting problem for the number of triangulations that cannot be quechered. The critical physics of chequered triangulations is the same as that of the hermitian matrix model. We show this explicitly by solving non-perturbatively pure two-dimensional ''chequered'' gravity. The interpretative framework given here applies to a number of other generalisations of the hermitian matrix model. (orig.)
Transfer-matrix approach for modulated structures with defects
Kostyrko, T.
2000-01-01
We consider scattering of electrons by defects in a periodically modulated, quasi-one-dimensional structure, within a tight-binding model. Combining a transfer matrix method and a Green function method we derive a formula for a Landauer conductance and show its equivalence to the result of Kubo linear response theory. We obtain explicitly unperturbed lattice Green functions from their equations of motion, using the transfer matrices. We apply the presented formalism in computations of the conductance of several multiband modulated structures with defects: (a) carbon nanotubes (b) two-dimensional (2D) superlattice (c) modulated leads with 1D wire in the tunneling regime. (c) 2000 The American Physical Society
Loop diagrams without γ matrices
McKeon, D.G.C.; Rebhan, A.
1993-01-01
By using a quantum-mechanical path integral to compute matrix elements of the form left-angle x|exp(-iHt)|y right-angle, radiative corrections in quantum-field theory can be evaluated without encountering loop-momentum integrals. In this paper we demonstrate how Dirac γ matrices that occur in the proper-time ''Hamiltonian'' H lead to the introduction of a quantum-mechanical path integral corresponding to a superparticle analogous to one proposed recently by Fradkin and Gitman. Direct evaluation of this path integral circumvents many of the usual algebraic manipulations of γ matrices in the computation of quantum-field-theoretical Green's functions involving fermions
Two-mode Gaussian density matrices and squeezing of photons
Tucci, R.R.
1992-01-01
In this paper, the authors generalize to 2-mode states the 1-mode state results obtained in a previous paper. The authors study 2-mode Gaussian density matrices. The authors find a linear transformation which maps the two annihilation operators, one for each mode, into two new annihilation operators that are uncorrelated and unsqueezed. This allows the authors to express the density matrix as a product of two 1-mode density matrices. The authors find general conditions under which 2-mode Gaussian density matrices become pure states. Possible pure states include the 2-mode squeezed pure states commonly mentioned in the literature, plus other pure states never mentioned before. The authors discuss the entropy and thermodynamic laws (Second Law, Fundamental Equation, and Gibbs-Duhem Equation) for the 2-mode states being considered
A Workshop on Algebraic Design Theory and Hadamard Matrices
2015-01-01
This volume develops the depth and breadth of the mathematics underlying the construction and analysis of Hadamard matrices and their use in the construction of combinatorial designs. At the same time, it pursues current research in their numerous applications in security and cryptography, quantum information, and communications. Bridges among diverse mathematical threads and extensive applications make this an invaluable source for understanding both the current state of the art and future directions. The existence of Hadamard matrices remains one of the most challenging open questions in combinatorics. Substantial progress on their existence has resulted from advances in algebraic design theory using deep connections with linear algebra, abstract algebra, finite geometry, number theory, and combinatorics. Hadamard matrices arise in a very diverse set of applications. Starting with applications in experimental design theory and the theory of error-correcting codes, they have found unexpected and important ap...
Critical statistics for non-Hermitian matrices
Garcia-Garcia, A.M.; Verbaarschot, J.J.M.; Nishigaki, S.M.
2002-01-01
We introduce a generalized ensemble of non-Hermitian matrices interpolating between the Gaussian Unitary Ensemble, the Ginibre ensemble, and the Poisson ensemble. The joint eigenvalue distribution of this model is obtained by means of an extension of the Itzykson-Zuber formula to general complex matrices. Its correlation functions are studied both in the case of weak non-Hermiticity and in the case of strong non-Hermiticity. In the weak non-Hermiticity limit we show that the spectral correlations in the bulk of the spectrum display critical statistics: the asymptotic linear behavior of the number variance is already approached for energy differences of the order of the eigenvalue spacing. To lowest order, its slope does not depend on the degree of non-Hermiticity. Close the edge, the spectral correlations are similar to the Hermitian case. In the strong non-Hermiticity limit the crossover behavior from the Ginibre ensemble to the Poisson ensemble first appears close to the surface of the spectrum. Our model may be relevant for the description of the spectral correlations of an open disordered system close to an Anderson transition
Hypersymmetric functions and Pochhammers of 2×2 nonautonomous matrices
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.
On families of anticommuting matrices
Hrubeš, Pavel
2016-01-01
Roč. 493, March 15 (2016), s. 494-507 ISSN 0024-3795 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : anticommuting matrices * sum-of-squares formulas Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2016 http://www.sciencedirect.com/science/article/pii/S0024379515007296
On families of anticommuting matrices
Hrubeš, Pavel
2016-01-01
Roč. 493, March 15 (2016), s. 494-507 ISSN 0024-3795 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : anticommuting matrices * sum -of-squares formulas Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2016 http://www.sciencedirect.com/science/article/pii/S0024379515007296
Mendi, P.; Moner-colonques, R.; Sempere-Monerris, J. J.
2012-07-01
This paper provides a quantitative view of the international market for technology, in which most of the transfers happen within multinational firms by means of royalty based contracts. We develop a competition model where one of the firms, partially owned by a multinational firm that holds a process innovation, has been transferred the technology. When the affiliated firm is the most efficient one in the market, a higher share implies the rival of the affiliated firm paying positive and greater royalties in more cases and so the multinational can control the intensity of competition. (Author)
Cespedes Quiros, Yehudi; Pereira Barrantes, Edgar
2010-01-01
Patients with oncological pathology have attended daily in sessions for several weeks in the linear accelerator radiation therapy. Persons subject to this intervention have moved to the Hospital Mexico of the social security of Costa Rica, place that centralizes this treatment. The Caja Costarricense de Seguro Social (CCSS) has considered two options depending on the place of origin of users: bear the costs of commuting from the area of habitual residence, or place them temporarily in a shelter provided by the institution; the CCSS has chosen the first alternative. This research has consisted of a cost-minimization analysis between these two alternatives. The study population are patients with oncological pathology attending sessions of radiotherapy with linear accelerator at the Hospital Mexico in the first half of 2009 using ambulances of Cruz Roja Costarricense. The size of the study population is 107 persons, the total number of transferred recorded in the Fondo Rotatorio de Operaciones of Hospital Mexico is 998. Patients came from five regions and twenty areas of health according to the geographical division of the CCSS. The variables included have been: cost per day by way of transfer, which involves the distance to the radiotherapy center of Hospital Mexico and the cost of the rate at Cruz Roja ambulance per Km (326.86 colons, according to the agreement CCSS-Cruz Roja in June 2009) estimated daily cost of lodging in a shelter, and the reason daily cost of relocation / daily cost of shelter. The cost of shelter includes food and were used data from the company International Medical Suppliers S. A. as a basis for estimating the daily cost, the price fixed by the company was 65 dollars a day, and the conversion into colons exchange rate as established by the Banco Central de Costa Rica; dated April 30, 2010, the amount has been 33.542.60 colons. The reason for each area of health was given by the ratio of the average daily cost in colons by way of ambulance of
Delaunay, F.
1990-01-01
In this experiment performed at GANIL, the use of the gaseous multidetectors DELF and XYZT allows the detection of the heavy fragments (Z ≥ 5) whose velocity is larger than 3 cm/ns when the emission angle is lower than 30 0 and whose velocity is larger than 0.5 cm/ns when the emission angle is greater than 30 0 . For the reactions Kr + Au and Kr + Th at 43 MeV/u, we have observed with a still significative occurrence, events where 6 fragments are produced and we have studied the events where at least 3 heavy fragments were detected. In order to separate the peripheral collisions from the central ones, a collective variable measuring the dispersion of the relative velocity between each couple of fragment is used for events where 3 or 4 heavy fragments are recorded. Afterwards, a selection method is presented for the peripheral events in order to deal only with almost complete events. The atomical number of the fragment whose velocity is nearly equal to the beam velocity, is used to estimate the impact parameter. We find that for a given impact parameter, some different mechanisms are present. A method of measurement of the angular momentum is elaborated from the angular distribution of the fission fragments. A study of incomplete linear momentum transfer leads to a transfer rate of about 40%. The angular momentum of the target like fragment just before fission is also small. The results of the abrasion-ablation model and of the two-step model are quite close to the experimental results [fr
Bras, D
1967-09-27
This study presents five methods used to realize a transfer function on analog computer - method of operational amplifiers - method of successive integrations - method of the auxiliary variable - method of the Horner decomposition - method of the direct analog transposition. The method that seems to us the most interesting, this one of Horner, is exposed with some complements. The last method presents the study of a linear network (mechanical, electronic) by direct analog transposition, without having to calculate its transfer function. Several aspects are studied the economy or the material type, the simpleness of implementing the adaptation of coefficients to the computer, the introduction of initial conditions of input and output functions. Every method presented is discussed in function of these problems. The precision of the result is not studied here, but we can indicate that the methods treated here, do not include approximations other than these ones of the computer elements. [French] Cette etude presente cinq methodes utilisees pour realiser une fonction de transfert quelconque sur calculateur analogique - methode des Amplificateurs operationnels - methode des integrations successives - methode de la variable auxiliaire - methode de la decomposition de Horner - methode de la transposition analogique directe. La methode qui nous semble la plus interessante, celle de Horner, est exposee avec quelques complements. La derniere methode presente l'etude d'un reseau lineaire (mecanique, electronique...) par transposition analogique directe, sans avoir a calculer sa fonction de transfert. Plusieurs aspects sont etudies l'economie ou le type de materiel, la simplicite de mise en oeuvre l'adaptation des coefficients au calculateur, l'introduction des conditions initiales des fonctions d'entree et de sortie. Chaque methode presentee est discutee en fonction de ces problemes. La precision du resultat n'est pas etudiee ici, mais on peut indiquer toutefois que les
The modified Gauss diagonalization of polynomial matrices
Saeed, K.
1982-10-01
The Gauss algorithm for diagonalization of constant matrices is modified for application to polynomial matrices. Due to this modification the diagonal elements become pure polynomials rather than rational functions. (author)
Double stochastic matrices in quantum mechanics
Louck, J.D.
1997-01-01
The general set of doubly stochastic matrices of order n corresponding to ordinary nonrelativistic quantum mechanical transition probability matrices is given. Lande's discussion of the nonquantal origin of such matrices is noted. Several concrete examples are presented for elementary and composite angular momentum systems with the focus on the unitary symmetry associated with such systems in the spirit of the recent work of Bohr and Ulfbeck. Birkhoff's theorem on doubly stochastic matrices of order n is reformulated in a geometrical language suitable for application to the subset of quantum mechanical doubly stochastic matrices. Specifically, it is shown that the set of points on the unit sphere in cartesian n'-space is subjective with the set of doubly stochastic matrices of order n. The question is raised, but not answered, as to what is the subset of points of this unit sphere that correspond to the quantum mechanical transition probability matrices, and what is the symmetry group of this subset of matrices
Virial expansion for almost diagonal random matrices
Yevtushenko, Oleg; Kravtsov, Vladimir E.
2003-08-01
Energy level statistics of Hermitian random matrices hat H with Gaussian independent random entries Higeqj is studied for a generic ensemble of almost diagonal random matrices with langle|Hii|2rangle ~ 1 and langle|Hi\
Phenomenological mass matrices with a democratic warp
Kleppe, A.
2018-01-01
Taking into account all available data on the mass sector, we obtain unitary rotation matrices that diagonalize the quark matrices by using a specific parametrization of the Cabibbo-Kobayashi-Maskawa mixing matrix. In this way, we find mass matrices for the up- and down-quark sectors of a specific, symmetric form, with traces of a democratic texture.
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.
Bombardelli, Diego
2016-01-01
In these notes we review the S-matrix theory in (1+1)-dimensional integrable models, focusing mainly on the relativistic case. Once the main definitions and physical properties are introduced, we discuss the factorization of scattering processes due to integrability. We then focus on the analytic properties of the two-particle scattering amplitude and illustrate the derivation of the S-matrices for all the possible bound states using the so-called bootstrap principle. General algebraic structures underlying the S-matrix theory and its relation with the form factors axioms are briefly mentioned. Finally, we discuss the S-matrices of sine-Gordon and SU (2), SU (3) chiral Gross–Neveu models. (topical review)
Synthesised standards in natural matrices
Olsen, D.G.
1980-01-01
The problem of securing the most reliable standards for the accurate analysis of radionuclides is discussed in the paper and in the comment on the paper. It is contended in the paper that the best standards can be created by quantitative addition of accurately known spiking solutions into carefully selected natural matrices. On the other hand it is argued that many natural materials can be successfully standardized for numerous trace constituents. Both points of view are supported with examples. (U.K.)
Contributions to Large Covariance and Inverse Covariance Matrices Estimation
Kang, Xiaoning
2016-01-01
Estimation of covariance matrix and its inverse is of great importance in multivariate statistics with broad applications such as dimension reduction, portfolio optimization, linear discriminant analysis and gene expression analysis. However, accurate estimation of covariance or inverse covariance matrices is challenging due to the positive definiteness constraint and large number of parameters, especially in the high-dimensional cases. In this thesis, I develop several approaches for estimat...
A Robust Incomplete Factorization Preconditioner for Positive Definite Matrices
Benzi, M.; Tůma, Miroslav
2003-01-01
Roč. 10, - (2003), s. 385-400 ISSN 1070-5325 R&D Projects: GA AV ČR IAA2030801; GA AV ČR IAA1030103 Institutional research plan: AV0Z1030915 Keywords : sparse linear systems * positive definite matrices * preconditioned conjugate gradient s * incomplete factorization * A-orthogonalization * SAINV Subject RIV: BA - General Mathematics Impact factor: 1.042, year: 2003
Blyth, T S
2002-01-01
Most of the introductory courses on linear algebra develop the basic theory of finite dimensional vector spaces, and in so doing relate the notion of a linear mapping to that of a matrix. Generally speaking, such courses culminate in the diagonalisation of certain matrices and the application of this process to various situations. Such is the case, for example, in our previous SUMS volume Basic Linear Algebra. The present text is a continuation of that volume, and has the objective of introducing the reader to more advanced properties of vector spaces and linear mappings, and consequently of matrices. For readers who are not familiar with the contents of Basic Linear Algebra we provide an introductory chapter that consists of a compact summary of the prerequisites for the present volume. In order to consolidate the student's understanding we have included a large num ber of illustrative and worked examples, as well as many exercises that are strategi cally placed throughout the text. Solutions to the ex...
PRIMITIVE MATRICES AND GENERATORS OF PSEUDO RANDOM SEQUENCES OF GALOIS
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.
Dirac matrices for Chern-Simons gravity
Izaurieta, Fernando; Ramirez, Ricardo; Rodriguez, Eduardo [Departamento de Matematica y Fisica Aplicadas, Universidad Catolica de la Santisima Concepcion, Alonso de Ribera 2850, 4090541 Concepcion (Chile)
2012-10-06
A genuine gauge theory for the Poincare, de Sitter or anti-de Sitter algebras can be constructed in (2n- 1)-dimensional spacetime by means of the Chern-Simons form, yielding a gravitational theory that differs from General Relativity but shares many of its properties, such as second order field equations for the metric. The particular form of the Lagrangian is determined by a rank n, symmetric tensor invariant under the relevant algebra. In practice, the calculation of this invariant tensor can be reduced to the computation of the trace of the symmetrized product of n Dirac Gamma matrices {Gamma}{sub ab} in 2n-dimensional spacetime. While straightforward in principle, this calculation can become extremely cumbersome in practice. For large enough n, existing computer algebra packages take an inordinate long time to produce the answer or plainly fail having used up all available memory. In this talk we show that the general formula for the trace of the symmetrized product of 2n Gamma matrices {Gamma}{sub ab} can be written as a certain sum over the integer partitions s of n, with every term being multiplied by a numerical cofficient {alpha}{sub s}. We then give a general algorithm that computes the {alpha}-coefficients as the solution of a linear system of equations generated by evaluating the general formula for different sets of tensors B{sup ab} with random numerical entries. A recurrence relation between different coefficients is shown to hold and is used in a second, 'minimal' algorithm to greatly speed up the computations. Runtime of the minimal algorithm stays below 1 min on a typical desktop computer for up to n = 25, which easily covers all foreseeable applications of the trace formula.
Classical r-matrices for the generalised Chern–Simons formulation of 3d gravity
Osei, Prince K.; Schroers, Bernd J.
2018-04-01
We study the conditions for classical r-matrices to be compatible with the generalised Chern–Simons action for 3d gravity. Compatibility means solving the classical Yang–Baxter equations with a prescribed symmetric part for each of the real Lie algebras and bilinear pairings arising in the generalised Chern–Simons action. We give a new construction of r-matrices via a generalised complexification and derive a non-linear set of matrix equations determining the most general compatible r-matrix. We exhibit new families of solutions and show that they contain some known r-matrices for special parameter values.
sariano ferni
2017-07-01
Full Text Available Background: Background: Intraoral radiography use some lower LET (Linear Energy Transfer and could penetrate submandibular salivary gland. Radiography have negative impact which is decrease catalase enzyme of human body. Brown algae (Sargassum sp. has a flavonoid antioxidant, polysaccharides as Fucoidan and alginat (Na-alginat can be used for immunomodulator, antioxidative and activation modulation of immune. Purpose: To knowing effectiveness of brown algae (Sargassum sp. on activity catalase enzyme submandibular salivary gland Rattus Novergicus strain Wistar with irradiation low LET. Material and Methods: 28 samples of Rattus Novergicus strain Wistar, weight 200gr, age 2-3months, gender male, sample divide into 4 groups, K1 (control with brown algae dosage 0,018mg/kgbw K2 (use brown algae and irradiation 4 times, K3 (use brown algae and irradiation 8 times, K4 (use brown algae and irradiation 14 times. Brown algae been given 7days before apply irradiotion on day 8, then did euthanasia and took submandibular salivary gland. After that did measurement activity of catalase enzyme and counted by spectrophotometer with 240 λ. Result: Data were analyze by Shapiro-wilk, One Way ANOVA and Bonferroni. The activity of catalase enzyme have increased; 0,2586 ± 0,1050 (K1, 0,2595 ± 0,0630 (K2, 0,3252 ± 0,1663 (K3, 0,3668 ± 0,0852 (K4 but theres no significant differences activity of catalase enzyme between one group to other group. Conclusion: Brown algae dosage 0,018mg/kgbw can’t increase activity of catalase enzyme on Rattus Novergicus strain Wistar.
Greinert, R; Harder, D
1997-06-01
Experimental data for the induction of dicentric chromosomes in phytohemagglutinin (PHA)-stimulated human T lymphocytes by 241Am alpha-particles obtained by Schmid et al. have been analyzed in the light of biophysical theory. As usual in experiments with alpha-particles, the relative variance of the intercellular distribution of the number of aberrations per cell exceeds unity, and the multiplicity of the aberrations per particle traversal through the cell is understood as the basic effect causing this overdispersion. However, the clearly expressed dose dependence of the relative variance differs from the dose-independent relative variance predicted by the multiplicity effect alone. Since such dose dependence is often observed in experiments with alpha-particles, protons, and high-energy neutrons, the interpretation of the overdispersion needs to be supplemented. In a new, more general statistical model, the distribution function of the number of aberrations is interpreted as resulting from the convolution of a Poisson distribution for the spontaneous aberrations with the overdispersed distributions for the aberrations caused by intratrack or intertrack lesion interaction, and the fluctuation of the cross-sectional area of the cellular chromatin must also be considered. Using a suitable mathematical formulation of the resulting dose-dependent over-dispersion, the mean number lambda 1 of the aberrations produced by a single particle traversal through the cell nucleus and the mean number lambda 2 of the aberrations per pairwise approach between two alpha-particle tracks could be estimated. Coefficient alpha of the dose-proportional yield component, when compared between 241Am alpha-particle irradiation and 137Cs gamma-ray exposure, is found to increase approximately in proportion to dose-mean restricted linear energy transfer, which indicates an underlying pairwise molecular lesion interaction on the nanometer scale.
Ståhl, Sara; Fung, Eva; Adams, Christopher; Lengqvist, Johan; Mörk, Birgitta; Stenerlöw, Bo; Lewensohn, Rolf; Lehtiö, Janne; Zubarev, Roman; Viktorsson, Kristina
2009-05-01
During the past decade, we have witnessed an explosive increase in generation of large proteomics data sets, not least in cancer research. There is a growing need to extract and correctly interpret information from such data sets to generate biologically relevant hypotheses. A pathway search engine (PSE) has recently been developed as a novel tool intended to meet these requirements. Ionizing radiation (IR) is an anticancer treatment modality that triggers multiple signal transduction networks. In this work, we show that high linear energy transfer (LET) IR induces apoptosis in a non-small cell lung cancer cell line, U-1810, whereas low LET IR does not. PSE was applied to study changes in pathway status between high and low LET IR to find pathway candidates of importance for high LET-induced apoptosis. Such pathways are potential clinical targets, and they were further validated in vitro. We used an unsupervised shotgun proteomics approach where high resolution mass spectrometry coupled to nanoflow liquid chromatography determined the identity and relative abundance of expressed proteins. Based on the proteomics data, PSE suggested the JNK pathway (p = 6.10(-6)) as a key event in response to high LET IR. In addition, the Fas pathway was found to be activated (p = 3.10(-5)) and the p38 pathway was found to be deactivated (p = 0.001) compared with untreated cells. Antibody-based analyses confirmed that high LET IR caused an increase in phosphorylation of JNK. Moreover pharmacological inhibition of JNK blocked high LET-induced apoptotic signaling. In contrast, neither an activation of p38 nor a role for p38 in high LET IR-induced apoptotic signaling was found. We conclude that, in contrast to conventional low LET IR, high LET IR can trigger activation of the JNK pathway, which in turn is critical for induction of apoptosis in these cells. Thus PSE predictions were largely confirmed, and PSE was proven to be a useful hypothesis-generating tool.
Nusrat, H; Pang, G; Ahmad, S; Keller, B; Sarfehnia, A
2015-01-01
Purpose: This research seeks to develop a portable, clinically-suitable linear energy transfer (LET) detector. In radiotherapy, absorbed dose is commonly used to measure the amount of delivered radiation, though, it is not a good indicator of actual biological damage. LET is the energy absorbed per unit length by a medium along charged particle’s pathway; studies have shown that LET correlates well with relative biological effectiveness (RBE). Methods: According to Birks’ law, light output of plastic scintillators is stopping-power dependent. This dependency can be varied through doping by various high-Z elements. By measuring light output signals of differently doped plastic scintillators (represented by column vector S, where each row corresponds to different scintillator material), the fluence of charged particles of a given LET (represented by column vector Φ, where each row corresponds to different LET bins) can be unfolded by S=R*Φ where R is system response matrix (each row represents a different scintillator, each column corresponds to different electron LET). Monte Carlo (MC) GEANT4.10.1 was used to evaluate ideal detector response of BC408 scintillating material doped with various concentrations of several high Z dopants. Measurements were performed to validate MC. Results: Signal for 1%-lead doped BC408 and the non-doped scintillator was measured experimentally by guiding light emitted by the scintillator (via in-house made taper, fiber system) to a PMT and then an electrometer. Simulations of 1%Pb-doped scintillator to non-doped scintillator revealed 9.3% reduction in light output for 6 MeV electrons which compared well (within uncertainty) with measurements showing 10% reduction (6MeV electrons). Conclusion: Measurements were used to validate MC simulation of light output from doped scintillators. The doping of scintillators is a viable technique to induce LET dependence. Our goal is to use this effect to resolve the LET spectrum of an incident
Kwon Joong Yong
2016-05-01
Full Text Available Radiolabeled antibodies (mAbs provide efficient tools for cancer therapy. The combination of low energy β−-emissions (500 keVmax; 130 keVave along with a γ-emission for imaging makes 177Lu (T1/2 = 6.7 day a suitable radionuclide for radioimmunotherapy (RIT of tumor burdens possibly too large to treat with α-particle radiation. RIT with 177Lu-trastuzumab has proven to be effective for treatment of disseminated HER2 positive peritoneal disease in a pre-clinical model. To elucidate mechanisms originating from this RIT therapy at the molecular level, tumor bearing mice (LS-174T intraperitoneal xenografts were treated with 177Lu-trastuzumab comparatively to animals treated with a non-specific control, 177Lu-HuIgG, and then to prior published results obtained using 212Pb-trastuzumab, an α-particle RIT agent. 177Lu-trastuzumab induced cell death via DNA double strand breaks (DSB, caspase-3 apoptosis, and interfered with DNA-PK expression, which is associated with the repair of DNA non-homologous end joining damage. This contrasts to prior results, wherein 212Pb-trastuzumab was found to down-regulate RAD51, which is involved with homologous recombination DNA damage repair. 177Lu-trastuzumab therapy was associated with significant chromosomal disruption and up-regulation of genes in the apoptotic process. These results suggest an inhibition of the repair mechanism specific to the type of radiation damage being inflicted by either high or low linear energy transfer radiation. Understanding the mechanisms of action of β−- and α-particle RIT comparatively through an in vivo tumor environment offers real information suitable to enhance combination therapy regimens involving α- and β−-particle RIT for the management of intraperitoneal disease.
Pirlepesov, F.; Shin, J.; Moskvin, V. P.; Gray, J.; Hua, C.; Gajjar, A.; Krasin, M. J.; Merchant, T. E.; Farr, J. B. [St. Jude Children’s Research Hospital, Memphis, TN (United States); Li, Z. [University of Florida Proton Therapy Institute, Jacksonville, FL (United States)
2015-06-15
Purpose: Dose weighted Linear Energy Transfer (LETd) analysis of critical structures may be useful in understanding the side effects of the proton therapy. The objective is to analyze the differences between LETd and dose distributions in brain tumor patients receiving double scattering proton therapy, to quantify LETd variation in critical organs, and to identify beam arrangements contributing to high LETd in critical organs. Methods: Monte Carlo simulations of 9 pediatric brain tumor patients were performed. The treatment plans were reconstructed with the TOPAS Monte Carlo code to calculate LETd and dose. The beam data were reconstructed proximal to the aperture of the double scattering nozzle. The dose and LETd to target and critical organs including brain stem, optic chiasm, lens, optic nerve, pituitary gland, and hypothalamus were computed for each beam. Results: Greater variability in LETd compared to dose was observed in the brainstem for patients with a variety of tumor types including 5 patients with tumors located in the posterior fossa. Approximately 20%–44% brainstem volume received LETd of 5kev/µm or greater from beams within gantry angles 180°±30° for 5 patients treated with a 3 beam arrangement. Critical organs received higher LETd when located in the vicinity of the beam distal edge. Conclusion: This study presents a novel strategy in the evaluation of the proton treatment impact on critical organs. While the dose to critical organs is confined below the required limits, the LETd may have significant variation. Critical organs in the vicinity of beam distal edge receive higher LETd and depended on beam arrangement, e.g. in posterior fossa tumor treatment, brainstem receive higher LETd from posterior-anterior beams. This study shows importance of the LETd analysis of the radiation impact on the critical organs in proton therapy and may be used to explain clinical imaging observations after therapy.
Alsanea, F; Therriault-Proulx, F; Sawakuchi, G; Beddar, S [UT MD Anderson Cancer Center, Houston, TX (United States)
2016-06-15
Purpose: The light generated in organic scintillators depends on both the radiation dose and the linear energy transfer (LET). The LET dependence leads to an under-response of the detector in the Bragg peak of proton beams. This phenomenon, called ionization quenching, must be corrected to obtain accurate dose measurements of proton beams. This work exploits the ionization quenching phenomenon to provide a method of measuring LET and auto correcting quenching. Methods: We exposed simultaneously four different organic scintillators (BCF-12, PMMA, PVT, and LSD; 1mm in diameter) and a plane parallel ionization chamber in passively scattered proton beams to doses between 32 and 43 cGy and fluence averaged LET values from 0.47 to 1.26 keV/µm. The LET values for each irradiation condition were determined using a validated Monte Carlo model of the beam line. We determined the quenching parameter in the Birk’s equation for scintillation in BCF-12 for dose measurements. One set of irradiation conditions was used to correlate the scintillation response ratio to the LET values and plot a scintillation response ratio versus LET calibration curve. Irradiation conditions independent from the calibration ones were used to validate this method. Comparisons to the expected values were made on both the basis of dose and LET. Results: Among all the scintillators investigated, the ratio of PMMA to BCF-12 provided the best correlation to LET values and was used as the LET calibration curve. The expected LET values in the validation set were within 2%±6%, which resulted in dose accuracy of 1.5%±5.8% for the range of LET values investigated in this work. Conclusion: We have demonstrated the feasibility of using the ratio between the light output of two organic scintillators to simultaneously measure LET and dose of therapeutic proton beams. Further studies are needed to verify the response in higher LET values.
Eckl, P.
1981-01-01
This study was initiated to investigate, whether there are any radiation-induced changes in DNA-content and if these changes can be repaired. Seeds of Vicia faba L. were grown in glass culture vessels. After 10 to 20 days the seedings were irradiated using a 1 C1 60 Co gammasource (90mrad/h and 33 rad/h) and a 5 mCi 252 Cf neutronsource (90 mrad/h). Both, neutron and gamma irradiation cause a reduction in nuclear DNA-content even after low doses (1 to 10 rad). The extent of depression is only depending on linear energy transfer. Parallel to the induced minimum in DNA-content, but shifted to higher doses, also the mitotic activity reaches a minimum. Whereas neutron irradiation results in a total stop after doses of 8 rad, gamma-irradiation only induces a depression of 80 %. Whith higher doses the mitotic activity increases again. The neutron-induced changes in DNA-content seem to be restored within 90 minutes after irradiation. No continuous increase could be found after low gamma-doses. Gamma-irradiation with higher dose rates ( 60 Co, 33 rad/h) causes a general decrease over the dose-range studied (100 to 1600 rad). Following doses of 100 rad the mitotic activity increases significantly. With higher doses the decrease is exponential. A dose-dependent mitotic delay could also be observed. As described by many authors, unscheduled DNA-synthesis (UDS) could not be detected in nuclei of Vicia faba. This indicates that an other system, perhaps acting in situ - at the damaged place - is responsible for the repair of radiation-induced thymine-damages. (Author)
Drepper, F; Mathis, P
1997-02-11
The photosynthetic reaction center (RC) and its secondary electron donor the water-soluble cytochrome (cyt) c2 from the purple bacterium Rhodobacter sphaeroides have been used in cross-linked and non-cross-linked complexes, oriented in compressed gels or partially dried multilayers, to study the respective orientation of the primary donor P (BChl dimer) and of cyt c2. Three methods were used: (i) Polarized optical absorption spectra at 295 and 10 K were measured and the linear dichroism of the two individual transitions (Qx, Qy), which are nearly degenerate within the alpha-band of reduced cyt c2, was determined. Attribution of the polarization directions to the molecular axes within the heme plane yielded the average cyt orientation in the complexes. (ii) Time-resolved flash absorption measurements using polarized light allowed determination of the orientation of cyt c2 in complexes which differ in their kinetics of electron transfer. (iii) EPR spectroscopy of ferricyt c2 in cross-linked RC-cyt c2 complexes was used to determine the angle between the heme and the membrane plane. The results suggest the following structural properties for the docking of cyt c2 to the RC: (i) In cross-linked complexes, the two cytochromes displaying half-lives of 0.7 and 60 micros for electron transfer to P+ are similarly oriented (difference plane is parallel to the symmetry axis of the RC (0 degrees +/- 10 degrees). Moreover, the Qy transition, which is assumed to be polarized within the ring III-ring I direction of the heme plane, makes an angle of 56 degrees +/- 1 degree with the symmetry axis. (iii) The dichroism spectrum for the fast phase (0.7 micros) for the non-cross-linked cyt c2-RC complex suggests an orientation similar to that of cross-linked cyt c2, but the heme plane is tilted about 20 degrees closer to the membrane. An alternative model is that two or more bound states of cyt c2 with heme plane tilt angles between 0 degrees and 30 degrees allow the fast electron
The Inverse of Banded Matrices
2013-01-01
indexed entries all zeros. In this paper, generalizing a method of Mallik (1999) [5], we give the LU factorization and the inverse of the matrix Br,n (if it...r ≤ i ≤ r, 1 ≤ j ≤ r, with the remaining un-indexed entries all zeros. In this paper generalizing a method of Mallik (1999) [5...matrices and applications to piecewise cubic approximation, J. Comput. Appl. Math. 8 (4) (1982) 285–288. [5] R.K. Mallik , The inverse of a lower
Fusion algebra and fusing matrices
Gao Yihong; Li Miao; Yu Ming.
1989-09-01
We show that the Wilson line operators in topological field theories form a fusion algebra. In general, the fusion algebra is a relation among the fusing (F) matrices. In the case of the SU(2) WZW model, some special F matrix elements are found in this way, and the remaining F matrix elements are then determined up to a sign. In addition, the S(j) modular transformation of the one point blocks on the torus is worked out. Our results are found to agree with those obtained from the quantum group method. (author). 24 refs
Orthogonal polynomials and random matrices
Deift, Percy
2000-01-01
This volume expands on a set of lectures held at the Courant Institute on Riemann-Hilbert problems, orthogonal polynomials, and random matrix theory. The goal of the course was to prove universality for a variety of statistical quantities arising in the theory of random matrix models. The central question was the following: Why do very general ensembles of random n {\\times} n matrices exhibit universal behavior as n {\\rightarrow} {\\infty}? The main ingredient in the proof is the steepest descent method for oscillatory Riemann-Hilbert problems.
Yohannes S.M. Simamora
2014-09-01
Full Text Available A simple approach of active surge control of compression systems is presented. Specifically, nonlinear components of the pressure ratio and rotating speed states of the Moore-Greitzer model are transferred into the input vectors. Subsequently, the compressor characteristic is linearized into two modes, which describe the stable region and the unstable region respectively. As a result, the system’s state and input matrices both appear linear, to which linear realization and analysis are applicable. A linear quadratic regulator plus integrator is then chosen as closed-loop controller. By simulation it was shown that the modified model and characteristics can describe surge behavior, while the closed-loop controller can stabilize the system in the unstable operating region. The last-mentioned was achieved when massflow was 5.38 per cent less than the surge point.
Analytical study of dynamic aperture for storage ring by using successive linearization method
Yang Jiancheng; Xia Jiawen; Wu Junxia; Xia Guoxing; Liu Wei; Yin Xuejun
2004-01-01
The determination of dynamic aperture is a critical issue in circular accelerator. In this paper, authors solved the equation of motion including non-linear forces by using successive linearization method and got a criterion for the determining of the dynamic aperture of the machine. Applying this criterion, a storage ring with FODO lattice has been studied. The results are agree well with the tracking results in a large range of linear turn (Q). The purpose is to improve our understanding of the mechanisms driving the particle motion in the presence of non-linear forces and got another mechanism driving instability of particle in storage ring-parametric resonance caused by 'fluctuating transfer matrices' at small amplification
Applicability of non-invasively collected matrices for human biomonitoring
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.
Consolidity analysis for fully fuzzy functions, matrices, probability and statistics
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.
Threshold partitioning of sparse matrices and applications to Markov chains
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.
Hypercyclic Abelian Semigroups of Matrices on Cn
Ayadi, Adlene; Marzougui, Habib
2010-07-01
We give a complete characterization of existence of dense orbit for any abelian semigroup of matrices on C n . For finitely generated semigroups, this characterization is explicit and is used to determine the minimal number of matrices in normal form over C which forms a hypercyclic abelian semigroup on C n . In particular, we show that no abelian semigroup generated by n matrices on C n can be hypercyclic. (author)
Wound care matrices for chronic leg ulcers: role in therapy
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
Yves Le Grand on matrices in optics with application to vision: Translation and critical analysis
William Frith Harris
2013-12-01
Full Text Available An appendix to Le Grand’s 1945 book, Optique Physiologique: Tome Premier: La Dioptrique de l’Œil et Sa Correction, briefly dealt with the application of matrices in optics. However the appendix was omitted from the well-known English translation, Physiological Optics, which appeared in 1980. Consequently the material is all but forgotten. This is unfortunate in view of the importance of the dioptric power matrix and the ray transference which entered the optometric literature many years later. Motivated by the perception that there has not been enough care in optometry to attribute concepts appropriately this paper attempts a careful analysis of Le Grand’s thinking as reflected in his appendix. A translation into English is provided in the appendix to this paper. The paper opens with a summary of the basics of Gaussian and linear optics sufficient for the interpretation of Le Grand’s appendix which follows. The paper looks more particularly at what Le Grand says in relation to the transference and the dioptric power matrix though many other issues are also touched on including the conditions under which distant objects will map to clear images on the retina and, more particularly, to clear images that are undistorted. Detailed annotations of Le Grand’s translated appendix are provided. (S Afr Optom 2013 72(4 145-166
Ståhl, Sara; Fung, Eva; Adams, Christopher; Lengqvist, Johan; Mörk, Birgitta; Stenerlöw, Bo; Lewensohn, Rolf; Lehtiö, Janne; Zubarev, Roman; Viktorsson, Kristina
2009-01-01
During the past decade, we have witnessed an explosive increase in generation of large proteomics data sets, not least in cancer research. There is a growing need to extract and correctly interpret information from such data sets to generate biologically relevant hypotheses. A pathway search engine (PSE) has recently been developed as a novel tool intended to meet these requirements. Ionizing radiation (IR) is an anticancer treatment modality that triggers multiple signal transduction networks. In this work, we show that high linear energy transfer (LET) IR induces apoptosis in a non-small cell lung cancer cell line, U-1810, whereas low LET IR does not. PSE was applied to study changes in pathway status between high and low LET IR to find pathway candidates of importance for high LET-induced apoptosis. Such pathways are potential clinical targets, and they were further validated in vitro. We used an unsupervised shotgun proteomics approach where high resolution mass spectrometry coupled to nanoflow liquid chromatography determined the identity and relative abundance of expressed proteins. Based on the proteomics data, PSE suggested the JNK pathway (p = 6·10−6) as a key event in response to high LET IR. In addition, the Fas pathway was found to be activated (p = 3·10−5) and the p38 pathway was found to be deactivated (p = 0.001) compared with untreated cells. Antibody-based analyses confirmed that high LET IR caused an increase in phosphorylation of JNK. Moreover pharmacological inhibition of JNK blocked high LET-induced apoptotic signaling. In contrast, neither an activation of p38 nor a role for p38 in high LET IR-induced apoptotic signaling was found. We conclude that, in contrast to conventional low LET IR, high LET IR can trigger activation of the JNK pathway, which in turn is critical for induction of apoptosis in these cells. Thus PSE predictions were largely confirmed, and PSE was proven to be a useful hypothesis-generating tool. PMID:19168796
Bracalente, Candelaria; Ibañez, Irene L.; Molinari, Beatriz; Palmieri, Mónica; Kreiner, Andrés; Valda, Alejandro
2013-01-01
Purpose: To evaluate the cell response to DNA double-strand breaks induced by low and high linear energy transfer (LET) radiations when the catalytic subunit of DNA-dependent protein kinase (DNA-PKcs), an essential protein of the nonhomologous end-joining repair pathway, lacks kinase activity. Methods and Materials: CHO10B2, a Chinese hamster ovary cell line, and its derived radiosensitive mutant cell line, irs-20, lacking DNA-PKcs activity, were evaluated after 0 to 3 Gy of γ-rays, plateau and Bragg peak protons, and lithium beams by clonogenic assay, and as a measurement of double-strand breaks, phosphorylated H2AX (γH2AX) foci number and size were quantified by immunocytofluorescence. Results: Irs-20 exhibited greater radiosensitivity and a higher amount of γH2AX foci than CHO10B2 at 6 hours after irradiation for all types of radiations. Remarkably, CHO10B2 and irs-20 maintained their difference in radiosensitivity after high-LET radiation. Six hours after low-LET radiations, irs-20 did not reach basal levels of γH2AX at high doses, whereas CHO10B2 recovered basal levels for all doses. After high-LET radiation, only CHO10B2 exhibited a reduction in γH2AX foci, but it never reached basal levels. Persistent foci in irs-20 confirmed a repair deficiency. Interestingly, after 30 minutes of high-LET radiation both cell lines exhibited large foci (size >0.9 μm 2 ) related to the damage nature, whereas at 6 hours irs-20 showed a higher amount of large foci than CHO10B2, with a 7-fold increase at 3 Gy, that could also be associated to radiosensitivity. Conclusions: We demonstrated, for the first time, an association between deficient DNA-PKcs activity and not only high levels of H2AX phosphorylation but also persistence and size increase of γH2AX foci after high-LET irradiation
Bracalente, Candelaria; Ibañez, Irene L. [Departamento de Micro y Nanotecnología, Comisión Nacional de Energía Atómica, San Martín, Buenos Aires (Argentina); Consejo Nacional de Investigaciones Científicas y Técnicas, Buenos Aires (Argentina); Molinari, Beatriz [Departamento de Radiobiología, Comisión Nacional de Energía Atómica, San Martín, Buenos Aires (Argentina); Consejo Nacional de Investigaciones Científicas y Técnicas, Buenos Aires (Argentina); Palmieri, Mónica [Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires (Argentina); Kreiner, Andrés [Consejo Nacional de Investigaciones Científicas y Técnicas, Buenos Aires (Argentina); Gerencia de Investigación y Aplicaciones, Comisión Nacional de Energía Atómica, San Martín, Buenos Aires (Argentina); Escuela de Ciencia y Tecnología, Universidad Nacional de San Martín, San Martín, Buenos Aires (Argentina); Valda, Alejandro [Escuela de Ciencia y Tecnología, Universidad Nacional de San Martín, San Martín, Buenos Aires (Argentina); and others
2013-11-15
Purpose: To evaluate the cell response to DNA double-strand breaks induced by low and high linear energy transfer (LET) radiations when the catalytic subunit of DNA-dependent protein kinase (DNA-PKcs), an essential protein of the nonhomologous end-joining repair pathway, lacks kinase activity. Methods and Materials: CHO10B2, a Chinese hamster ovary cell line, and its derived radiosensitive mutant cell line, irs-20, lacking DNA-PKcs activity, were evaluated after 0 to 3 Gy of γ-rays, plateau and Bragg peak protons, and lithium beams by clonogenic assay, and as a measurement of double-strand breaks, phosphorylated H2AX (γH2AX) foci number and size were quantified by immunocytofluorescence. Results: Irs-20 exhibited greater radiosensitivity and a higher amount of γH2AX foci than CHO10B2 at 6 hours after irradiation for all types of radiations. Remarkably, CHO10B2 and irs-20 maintained their difference in radiosensitivity after high-LET radiation. Six hours after low-LET radiations, irs-20 did not reach basal levels of γH2AX at high doses, whereas CHO10B2 recovered basal levels for all doses. After high-LET radiation, only CHO10B2 exhibited a reduction in γH2AX foci, but it never reached basal levels. Persistent foci in irs-20 confirmed a repair deficiency. Interestingly, after 30 minutes of high-LET radiation both cell lines exhibited large foci (size >0.9 μm{sup 2}) related to the damage nature, whereas at 6 hours irs-20 showed a higher amount of large foci than CHO10B2, with a 7-fold increase at 3 Gy, that could also be associated to radiosensitivity. Conclusions: We demonstrated, for the first time, an association between deficient DNA-PKcs activity and not only high levels of H2AX phosphorylation but also persistence and size increase of γH2AX foci after high-LET irradiation.
Žakula Jelena
2016-01-01
Full Text Available Background & objectives: The main goal when treating malignancies with radiation is to deprive tumour cells of their reproductive potential. One approach is to induce tumour cell apoptosis. This study was conducted to evaluate the ability of carbon ions ( [12] C to induce apoptosis and cell cycle arrest in human HTB140 melanoma cells. Methods: In this in vitro study, human melanoma HTB140 cells were irradiated with the 62 MeV/n carbon ( [12] C ion beam, having two different linear energy transfer (LET values: 197 and 382 keV/μm. The dose range was 2 to 16 Gy. Cell viability was estimated by the sulforhodamine B assay seven days after irradiation. The cell cycle and apoptosis were evaluated 48 h after irradiation using flow cytometry. At the same time point, protein and gene expression of apoptotic regulators were estimated using the Western blot and q-PCR methods, respectively. Results: Cell viability experiments indicated strong anti-tumour effects of [12] C ions. The analysis of cell cycle showed that [12] C ions blocked HTB140 cells in G2 phase and induced the dose dependent increase of apoptosis. The maximum value of 21.8 per cent was attained after irradiation with LET of 197 keV/μm at the dose level of 16 Gy. Pro-apoptotic effects of [12] C ions were confirmed by changes of key apoptotic molecules: the p53, Bax, Bcl-2, poly ADP ribose polymerase (PARP as well as nuclear factor kappa B (NFκB. At the level of protein expression, the results indicated significant increases of p53, NFκB and Bax/Bcl-2 ratio and PARP cleavage. The Bax/Bcl-2 mRNA ratio was also increased, while no change was detected in the level of NFκB mRNA. Interpretation & conclusions: The present results indicated that anti-tumour effects of [12] C ions in human melanoma HTB140 cells were accomplished through induction of the mitochondrial apoptotic pathway as well as G2 arrest.
Pathological rate matrices: from primates to pathogens
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
LIBS analysis of artificial calcified tissues matrices.
Kasem, M A; Gonzalez, J J; Russo, R E; Harith, M A
2013-04-15
In most laser-based analytical methods, the reproducibility of quantitative measurements strongly depends on maintaining uniform and stable experimental conditions. For LIBS analysis this means that for accurate estimation of elemental concentration, using the calibration curves obtained from reference samples, the plasma parameters have to be kept as constant as possible. In addition, calcified tissues such as bone are normally less "tough" in their texture than many samples, especially metals. Thus, the ablation process could change the sample morphological features rapidly, and result in poor reproducibility statistics. In the present work, three artificial reference sample sets have been fabricated. These samples represent three different calcium based matrices, CaCO3 matrix, bone ash matrix and Ca hydroxyapatite matrix. A comparative study of UV (266 nm) and IR (1064 nm) LIBS for these three sets of samples has been performed under similar experimental conditions for the two systems (laser energy, spot size, repetition rate, irradiance, etc.) to examine the wavelength effect. The analytical results demonstrated that UV-LIBS has improved reproducibility, precision, stable plasma conditions, better linear fitting, and the reduction of matrix effects. Bone ash could be used as a suitable standard reference material for calcified tissue calibration using LIBS with a 266 nm excitation wavelength. Copyright © 2013 Elsevier B.V. All rights reserved.
A new version of transfer matrix method for multibody systems
Rui, Xiaoting, E-mail: ruixt@163.net [Nanjing University of Science and Technology, Institute of Launch Dynamics (China); Bestle, Dieter, E-mail: bestle@b-tu.de [Brandenburg University of Technology, Engineering Mechanics and Vehicle Dynamics (Germany); Zhang, Jianshu, E-mail: zhangdracpa@sina.com; Zhou, Qinbo, E-mail: zqb912-new@163.com [Nanjing University of Science and Technology, Institute of Launch Dynamics (China)
2016-10-15
In order to avoid the global dynamics equations and increase the computational efficiency for multibody system dynamics (MSD), the transfer matrix method of multibody system (MSTMM) has been developed and applied very widely in research and engineering in recent 20 years. It differs from ordinary methods in multibody system dynamics with respect to the feature that there is no need for a global dynamics equation, and it uses low-order matrices for high computational efficiency. For linear systems, MSTMM is exact even if continuous elements like beams are involved. The discrete time MSTMM, however, has to use local linearization. In order to release the method from such approximations, a new version of MSTMM is presented in this paper where translational and angular accelerations, on the one hand, and internal forces and moments, on the other hand, are used as state variables. Already linear relationships among these quantities are utilized, which results in new element transfer matrices and algorithms making the study of multibody systems as simple as the study of single bodies. The proposed approach also allows combining MSTMM with any general numerical integration procedure. Some numerical examples of MSD are given to demonstrate the proposed method.
Quantum Hilbert matrices and orthogonal polynomials
Andersen, Jørgen Ellegaard; Berg, Christian
2009-01-01
Using the notion of quantum integers associated with a complex number q≠0 , we define the quantum Hilbert matrix and various extensions. They are Hankel matrices corresponding to certain little q -Jacobi polynomials when |q|<1 , and for the special value they are closely related to Hankel matrice...
The construction of factorized S-matrices
Chudnovsky, D.V.
1981-01-01
We study the relationships between factorized S-matrices given as representations of the Zamolodchikov algebra and exactly solvable models constructed using the Baxter method. Several new examples of symmetric and non-symmetric factorized S-matrices are proposed. (orig.)
Skew-adjacency matrices of graphs
Cavers, M.; Cioaba, S.M.; Fallat, S.; Gregory, D.A.; Haemers, W.H.; Kirkland, S.J.; McDonald, J.J.; Tsatsomeros, M.
2012-01-01
The spectra of the skew-adjacency matrices of a graph are considered as a possible way to distinguish adjacency cospectral graphs. This leads to the following topics: graphs whose skew-adjacency matrices are all cospectral; relations between the matchings polynomial of a graph and the characteristic
On Investigating GMRES Convergence using Unitary Matrices
Duintjer Tebbens, Jurjen; Meurant, G.; Sadok, H.; Strakoš, Z.
2014-01-01
Roč. 450, 1 June (2014), s. 83-107 ISSN 0024-3795 Grant - others:GA AV ČR(CZ) M100301201; GA MŠk(CZ) LL1202 Institutional support: RVO:67985807 Keywords : GMRES convergence * unitary matrices * unitary spectra * normal matrices * Krylov residual subspace * Schur parameters Subject RIV: BA - General Mathematics Impact factor: 0.939, year: 2014
Exact Inverse Matrices of Fermat and Mersenne Circulant Matrix
Yanpeng Zheng
2015-01-01
Full Text Available The well known circulant matrices are applied to solve networked systems. In this paper, circulant and left circulant matrices with the Fermat and Mersenne numbers are considered. The nonsingularity of these special matrices is discussed. Meanwhile, the exact determinants and inverse matrices of these special matrices are presented.
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.
Liu, Chengyuan; Zhu, Yanan; Zhou, Zhongyue; Yang, Jiuzhong; Qi, Fei; Pan, Yang
2015-09-03
A novel ultrasonic nebulization extraction/low-pressure photoionization (UNE-LPPI) system has been designed and employed for the rapid mass spectrometric analysis of chemicals in matrices. An ultrasonic nebulizer was used to extract the chemicals in solid sample and nebulize the solvent in the nebulization cell. Aerosols formed by ultrasonic were evaporated by passing through a transferring tube, and desolvated chemicals were ionized by the emitted light (10.6 eV) from a Krypton discharge lamp at low pressure (∼68 Pa). First, a series of semi/non-volatile compounds with different polarities, such as polycyclic aromatic hydrocarbons (PAHs), amino acids, dipeptides, drugs, nucleic acids, alkaloids, and steroids were used to test the system. Then, the quantification capability of UNE-LPPI was checked with: 1) pure chemicals, such as 9,10-phenanthrenequinone and 1,4-naphthoquinone dissolved in solvent; 2) soil powder spiked with different amounts of phenanthrene and pyrene. For pure chemicals, the correlation coefficient (R(2)) for the standard curve of 9,10-phenanthrenequinone in the range of 3 ng-20 μg mL(-1) was 0.9922, and the measured limits of detection (LOD) was 1 ng ml(-1). In the case of soil powder, linear relationships for phenanthrene and pyrene from 10 to 400 ng mg(-1) were obtained with correlation coefficients of 0.9889 and 0.9893, respectively. At last, the feasibility of UNE-LPPI for the detection of chemicals in real matrices such as tablets and biological tissues (tea, Citrus aurantium peel and sage (Salvia officinalis) leaf) were successfully demonstrated. Copyright © 2015 Elsevier B.V. All rights reserved.
Puneet Rana
2017-09-01
Practice implications: The present problem has numerous applications in engineering and petroleum industries such as glass blowing, annealing and thinning of copper wires. The study of radiation heat transfer plays an important role in the industrial applications at high temperature.
Iglesias, Marco; Sawlan, Zaid A; Scavino, Marco; Tempone, Raul; Wood, Christopher
2017-01-01
In this work, we present the ensemble-marginalized Kalman filter (EnMKF), a sequential algorithm analogous to our previously proposed approach [1,2], for estimating the state and parameters of linear parabolic partial differential equations
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.
Likelihood Approximation With Parallel Hierarchical Matrices For Large Spatial Datasets
Litvinenko, Alexander; Sun, Ying; Genton, Marc G.; Keyes, David E.
2017-01-01
The main goal of this article is to introduce the parallel hierarchical matrix library HLIBpro to the statistical community. We describe the HLIBCov package, which is an extension of the HLIBpro library for approximating large covariance matrices and maximizing likelihood functions. We show that an approximate Cholesky factorization of a dense matrix of size $2M\\times 2M$ can be computed on a modern multi-core desktop in few minutes. Further, HLIBCov is used for estimating the unknown parameters such as the covariance length, variance and smoothness parameter of a Matérn covariance function by maximizing the joint Gaussian log-likelihood function. The computational bottleneck here is expensive linear algebra arithmetics due to large and dense covariance matrices. Therefore covariance matrices are approximated in the hierarchical ($\\H$-) matrix format with computational cost $\\mathcal{O}(k^2n \\log^2 n/p)$ and storage $\\mathcal{O}(kn \\log n)$, where the rank $k$ is a small integer (typically $k<25$), $p$ the number of cores and $n$ the number of locations on a fairly general mesh. We demonstrate a synthetic example, where the true values of known parameters are known. For reproducibility we provide the C++ code, the documentation, and the synthetic data.
Fundamental Matrix for a Class of Point Delay Linear Systems
Sen, M. de la; Alastruey, C. F.
1998-01-01
It is difficult to establish explicit analytic forms for fundamental matrices of delayed linear systems. In this paper, an explicit form of exponential type is given for such a matrix in the case of punctual delays. The existence of real and complex fundamental matrices, for the case of real parameterizations of the differential system, is studied and discussed. Some additional commutativity properties involving the matrices parameters and the fundamental matrices as well as explicit expressions for the solution of the delayed differential system are also given. (Author)
Analytical stiffness matrices with Green-Lagrange strain measure
Pedersen, Pauli
2005-01-01
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...... 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...
Community Detection for Correlation Matrices
Mel MacMahon
2015-04-01
Full Text Available A challenging problem in the study of complex systems is that of resolving, without prior information, the emergent, mesoscopic organization determined by groups of units whose dynamical activity is more strongly correlated internally than with the rest of the system. The existing techniques to filter correlations are not explicitly oriented towards identifying such modules and can suffer from an unavoidable information loss. A promising alternative is that of employing community detection techniques developed in network theory. Unfortunately, this approach has focused predominantly on replacing network data with correlation matrices, a procedure that we show to be intrinsically biased because of its inconsistency with the null hypotheses underlying the existing algorithms. Here, we introduce, via a consistent redefinition of null models based on random matrix theory, the appropriate correlation-based counterparts of the most popular community detection techniques. Our methods can filter out both unit-specific noise and system-wide dependencies, and the resulting communities are internally correlated and mutually anticorrelated. We also implement multiresolution and multifrequency approaches revealing hierarchically nested subcommunities with “hard” cores and “soft” peripheries. We apply our techniques to several financial time series and identify mesoscopic groups of stocks which are irreducible to a standard, sectorial taxonomy; detect “soft stocks” that alternate between communities; and discuss implications for portfolio optimization and risk management.
Community Detection for Correlation Matrices
MacMahon, Mel; Garlaschelli, Diego
2015-04-01
A challenging problem in the study of complex systems is that of resolving, without prior information, the emergent, mesoscopic organization determined by groups of units whose dynamical activity is more strongly correlated internally than with the rest of the system. The existing techniques to filter correlations are not explicitly oriented towards identifying such modules and can suffer from an unavoidable information loss. A promising alternative is that of employing community detection techniques developed in network theory. Unfortunately, this approach has focused predominantly on replacing network data with correlation matrices, a procedure that we show to be intrinsically biased because of its inconsistency with the null hypotheses underlying the existing algorithms. Here, we introduce, via a consistent redefinition of null models based on random matrix theory, the appropriate correlation-based counterparts of the most popular community detection techniques. Our methods can filter out both unit-specific noise and system-wide dependencies, and the resulting communities are internally correlated and mutually anticorrelated. We also implement multiresolution and multifrequency approaches revealing hierarchically nested subcommunities with "hard" cores and "soft" peripheries. We apply our techniques to several financial time series and identify mesoscopic groups of stocks which are irreducible to a standard, sectorial taxonomy; detect "soft stocks" that alternate between communities; and discuss implications for portfolio optimization and risk management.
Sports drug testing using complementary matrices: Advantages and limitations.
Thevis, Mario; Geyer, Hans; Tretzel, Laura; Schänzer, Wilhelm
2016-10-25
Today, routine doping controls largely rely on testing whole blood, serum, and urine samples. These matrices allow comprehensively covering inorganic as well as low and high molecular mass organic analytes relevant to doping controls and are collecting and transferring from sampling sites to accredited anti-doping laboratories under standardized conditions. Various aspects including time and cost-effectiveness as well as intrusiveness and invasiveness of the sampling procedure but also analyte stability and breadth of the contained information have been motivation to consider and assess values potentially provided and added to modern sports drug testing programs by alternative matrices. Such alternatives could be dried blood spots (DBS), dried plasma spots (DPS), oral fluid (OF), exhaled breath (EB), and hair. In this review, recent developments and test methods concerning these alternative matrices and expected or proven contributions as well as limitations of these specimens in the context of the international anti-doping fight are presented and discussed, guided by current regulations for prohibited substances and methods of doping as established by the World Anti-Doping Agency (WADA). Focusing on literature published between 2011 and 2015, examples for doping control analytical assays concerning non-approved substances, anabolic agents, peptide hormones/growth factors/related substances and mimetics, β 2 -agonists, hormone and metabolic modulators, diuretics and masking agents, stimulants, narcotics, cannabinoids, glucocorticoids, and beta-blockers were selected to outline the advantages and limitations of the aforementioned alternative matrices as compared to conventional doping control samples (i.e. urine and blood/serum). Copyright © 2016 Elsevier B.V. All rights reserved.
Specht, Judith F.; Richter, Marten
2015-03-01
In this manuscript, we study the impact of the two Coulomb induced resonance energy transfer processes, Förster and Dexter coupling, on the spectral signatures obtained by double quantum coherence spectroscopy. We show that the specific coupling characteristics allow us to identify the underlying excitation transfer mechanism by means of specific signatures in coherent spectroscopy. Therefore, we control the microscopic calculated coupling strength of spin preserving and spin flipping Förster transfer processes by varying the mutual orientation of the two quantum emitters. The calculated spectra reveal the optical selection rules altered by Förster and Dexter coupling between two semiconductor quantum dots. We show that Dexter coupling between bright and dark two-exciton states occurs.
Advanced linear algebra for engineers with Matlab
Dianat, Sohail A
2009-01-01
Matrices, Matrix Algebra, and Elementary Matrix OperationsBasic Concepts and NotationMatrix AlgebraElementary Row OperationsSolution of System of Linear EquationsMatrix PartitionsBlock MultiplicationInner, Outer, and Kronecker ProductsDeterminants, Matrix Inversion and Solutions to Systems of Linear EquationsDeterminant of a MatrixMatrix InversionSolution of Simultaneous Linear EquationsApplications: Circuit AnalysisHomogeneous Coordinates SystemRank, Nu
The Antitriangular Factorization of Saddle Point Matrices
Pestana, J.
2014-01-01
Mastronardi and Van Dooren [SIAM J. Matrix Anal. Appl., 34 (2013), pp. 173-196] recently introduced the block antitriangular ("Batman") decomposition for symmetric indefinite matrices. Here we show the simplification of this factorization for saddle point matrices and demonstrate how it represents the common nullspace method. We show that rank-1 updates to the saddle point matrix can be easily incorporated into the factorization and give bounds on the eigenvalues of matrices important in saddle point theory. We show the relation of this factorization to constraint preconditioning and how it transforms but preserves the structure of block diagonal and block triangular preconditioners. © 2014 Society for Industrial and Applied Mathematics.
Polynomial sequences generated by infinite Hessenberg matrices
Verde-Star Luis
2017-01-01
Full Text Available We show that an infinite lower Hessenberg matrix generates polynomial sequences that correspond to the rows of infinite lower triangular invertible matrices. Orthogonal polynomial sequences are obtained when the Hessenberg matrix is tridiagonal. We study properties of the polynomial sequences and their corresponding matrices which are related to recurrence relations, companion matrices, matrix similarity, construction algorithms, and generating functions. When the Hessenberg matrix is also Toeplitz the polynomial sequences turn out to be of interpolatory type and we obtain additional results. For example, we show that every nonderogative finite square matrix is similar to a unique Toeplitz-Hessenberg matrix.
Emran Tohidi
2013-01-01
Full Text Available The idea of approximation by monomials together with the collocation technique over a uniform mesh for solving state-space analysis and optimal control problems (OCPs has been proposed in this paper. After imposing the Pontryagins maximum principle to the main OCPs, the problems reduce to a linear or nonlinear boundary value problem. In the linear case we propose a monomial collocation matrix approach, while in the nonlinear case, the general collocation method has been applied. We also show the efficiency of the operational matrices of differentiation with respect to the operational matrices of integration in our numerical examples. These matrices of integration are related to the Bessel, Walsh, Triangular, Laguerre, and Hermite functions.
R. Caballero-Águila
2014-01-01
Full Text Available The optimal least-squares linear estimation problem is addressed for a class of discrete-time multisensor linear stochastic systems subject to randomly delayed measurements with different delay rates. For each sensor, a different binary sequence is used to model the delay process. The measured outputs are perturbed by both random parameter matrices and one-step autocorrelated and cross correlated noises. Using an innovation approach, computationally simple recursive algorithms are obtained for the prediction, filtering, and smoothing problems, without requiring full knowledge of the state-space model generating the signal process, but only the information provided by the delay probabilities and the mean and covariance functions of the processes (signal, random parameter matrices, and noises involved in the observation model. The accuracy of the estimators is measured by their error covariance matrices, which allow us to analyze the estimator performance in a numerical simulation example that illustrates the feasibility of the proposed algorithms.
Measuring emittances and sigma matrices
Rees, J.; Rivkin, L.
1984-03-01
The method used for measuring emittance at the SLAC Linac and the linear collider damping ring is described. The basis of the method is derived using one two-by-two matrix to specify the state of the input beam (sigma matrix) and another to describe the lens-drift transport system (R-matrix)
Environmental assessment of waste matrices contaminated with arsenic.
Sanchez, F; Garrabrants, A C; Vandecasteele, C; Moszkowicz, P; Kosson, D S
2003-01-31
The use of equilibrium-based and mass transfer-based leaching tests has been proposed to provide an integrated assessment of leaching processes from solid wastes. The objectives of the research presented here are to (i) validate this assessment approach for contaminated soils and cement-based matrices, (ii) evaluate the use of diffusion and coupled dissolution-diffusion models for estimating constituent release, and (iii) evaluate model parameterization using results from batch equilibrium leaching tests and physical characterization. The test matrices consisted of (i) a soil contaminated with arsenic from a pesticide production facility, (ii) the same soil subsequently treated by a Portland cement stabilization/solidification (S/S) process, and (iii) a synthetic cement-based matrix spiked with arsenic(III) oxide. Results indicated that a good assessment of contaminant release from contaminated soils and cement-based S/S treated wastes can be obtained by the integrated use of equilibrium-based and mass transfer-based leaching tests in conjunction with the appropriate release model. During the time scale of laboratory testing, the release of arsenic from the contaminated soil matrix was governed by diffusion and the solubility of arsenic in the pore solution while the release of arsenic from the cement-based matrices was mainly controlled by solubilization at the interface between the matrix and the bulk leaching solution. In addition, results indicated that (i) estimation of the activity coefficient within the matrix pore water is necessary for accurate prediction of constituent release rates and (ii) inaccurate representation of the factors controlling release during laboratory testing can result in significant errors in release estimates.
Synchronous correlation matrices and Connes’ embedding conjecture
Dykema, Kenneth J., E-mail: kdykema@math.tamu.edu [Department of Mathematics, Texas A& M University, College Station, Texas 77843-3368 (United States); Paulsen, Vern, E-mail: vern@math.uh.edu [Department of Mathematics, University of Houston, Houston, Texas 77204 (United States)
2016-01-15
In the work of Paulsen et al. [J. Funct. Anal. (in press); preprint arXiv:1407.6918], the concept of synchronous quantum correlation matrices was introduced and these were shown to correspond to traces on certain C*-algebras. In particular, synchronous correlation matrices arose in their study of various versions of quantum chromatic numbers of graphs and other quantum versions of graph theoretic parameters. In this paper, we develop these ideas further, focusing on the relations between synchronous correlation matrices and microstates. We prove that Connes’ embedding conjecture is equivalent to the equality of two families of synchronous quantum correlation matrices. We prove that if Connes’ embedding conjecture has a positive answer, then the tracial rank and projective rank are equal for every graph. We then apply these results to more general non-local games.
ESTIMATION OF FUNCTIONALS OF SPARSE COVARIANCE MATRICES.
Fan, Jianqing; Rigollet, Philippe; Wang, Weichen
High-dimensional statistical tests often ignore correlations to gain simplicity and stability leading to null distributions that depend on functionals of correlation matrices such as their Frobenius norm and other ℓ r norms. Motivated by the computation of critical values of such tests, we investigate the difficulty of estimation the functionals of sparse correlation matrices. Specifically, we show that simple plug-in procedures based on thresholded estimators of correlation matrices are sparsity-adaptive and minimax optimal over a large class of correlation matrices. Akin to previous results on functional estimation, the minimax rates exhibit an elbow phenomenon. Our results are further illustrated in simulated data as well as an empirical study of data arising in financial econometrics.
The Antitriangular Factorization of Saddle Point Matrices
Pestana, J.; Wathen, A. J.
2014-01-01
Mastronardi and Van Dooren [SIAM J. Matrix Anal. Appl., 34 (2013), pp. 173-196] recently introduced the block antitriangular ("Batman") decomposition for symmetric indefinite matrices. Here we show the simplification of this factorization for saddle
Considerations in designing and using superconductors with high resistivity matrices
Bartlett, R.J.; Carlson, R.V.; Laquer, H.L.; Migliori, A.
1976-01-01
Superconductors are often designed with matrices of much higher residual resistivities than copper for reasons of manufacturing (multifilamentary Nb 3 Sn in CuSn bronze) or loss reduction (mixed matrix NbTi with Cu and CuNi). The high resistivity matrix may complicate or degrade contact resistances at the joints, generate excess heat, reduce the stability of the conductor, and interfere with the observation of flux flow resistivities in the 10 -12 Ω-cm region. The minimization of these effects is discussed, presenting both simple and more refined models for the current transfer length, and it is shown how variations in transfer length (with current), particularly under significant self field conditions, can mimic flux flow resistivity
Flux Jacobian Matrices For Equilibrium Real Gases
Vinokur, Marcel
1990-01-01
Improved formulation includes generalized Roe average and extension to three dimensions. Flux Jacobian matrices derived for use in numerical solutions of conservation-law differential equations of inviscid flows of ideal gases extended to real gases. Real-gas formulation of these matrices retains simplifying assumptions of thermodynamic and chemical equilibrium, but adds effects of vibrational excitation, dissociation, and ionization of gas molecules via general equation of state.
Supercritical fluid extraction behaviour of polymer matrices
Sujatha, K.; Kumar, R.; Sivaraman, N.; Srinivasan, T.G.; Vasudeva Rao, P.R.
2007-01-01
Organic compounds present in polymeric matrices such as neoprene, surgical gloves and PVC were co-extracted during the removal of uranium using supercritical fluid extraction (SFE) technique. Hence SFE studies of these matrices were carried out to establish the extracted species using HPLC, IR and mass spectrometry techniques. The initial study indicated that uranium present in the extract could be purified from the co-extracted organic species. (author)
Shilov, Georgi E
1977-01-01
Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.
Finding column depedencies in sparse matrices over $ F_ 2 $ by block Wiedemann
O. Penninga
1998-01-01
textabstractLarge systems of linear equations over $mathbb{F_2$ with sparse coefficient matrices have to be solved as a part of integer factorization with sieve-based methods such as in the Number Field Sieve algorithm. In this report, we first discuss the Wiedemann algorithm to solve these systems
Implicit-shifted Symmetric QR Singular Value Decomposition of 3x3 Matrices
2016-04-01
Graph 33, 4, 138:1– 138:11. TREFETHEN, L. N., AND BAU III, D. 1997. Numerical linear algebra , vol. 50. Siam. XU, H., SIN, F., ZHU, Y., AND BARBIČ, J...matrices with minimal branching and elementary floating point operations. Tech. rep., University of Wisconsin- Madison. SAITO, S., ZHOU, Z.-Y., AND
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
MERSENNE AND HADAMARD MATRICES CALCULATION BY SCARPIS METHOD
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
Bayesian Nonparametric Clustering for Positive Definite Matrices.
Cherian, Anoop; Morellas, Vassilios; Papanikolopoulos, Nikolaos
2016-05-01
Symmetric Positive Definite (SPD) matrices emerge as data descriptors in several applications of computer vision such as object tracking, texture recognition, and diffusion tensor imaging. Clustering these data matrices forms an integral part of these applications, for which soft-clustering algorithms (K-Means, expectation maximization, etc.) are generally used. As is well-known, these algorithms need the number of clusters to be specified, which is difficult when the dataset scales. To address this issue, we resort to the classical nonparametric Bayesian framework by modeling the data as a mixture model using the Dirichlet process (DP) prior. Since these matrices do not conform to the Euclidean geometry, rather belongs to a curved Riemannian manifold,existing DP models cannot be directly applied. Thus, in this paper, we propose a novel DP mixture model framework for SPD matrices. Using the log-determinant divergence as the underlying dissimilarity measure to compare these matrices, and further using the connection between this measure and the Wishart distribution, we derive a novel DPM model based on the Wishart-Inverse-Wishart conjugate pair. We apply this model to several applications in computer vision. Our experiments demonstrate that our model is scalable to the dataset size and at the same time achieves superior accuracy compared to several state-of-the-art parametric and nonparametric clustering algorithms.
High performance linear algebra algorithms: An introduction
Gustavson, F.G.; Wasniewski, Jerzy
2006-01-01
his Mini-Symposium consisted of two back to back sessions, each consisting of five presentations, held on the afternoon of Monday, June 21, 2004. A major theme of both sessions was novel data structures for the matrices of dense linear algebra, DLA. Talks one to four of session one all centered...
A Linear Algebra Measure of Cluster Quality.
Mather, Laura A.
2000-01-01
Discussion of models for information retrieval focuses on an application of linear algebra to text clustering, namely, a metric for measuring cluster quality based on the theory that cluster quality is proportional to the number of terms that are disjoint across the clusters. Explains term-document matrices and clustering algorithms. (Author/LRW)
Generalised Assignment Matrix Methodology in Linear Programming
Jerome, Lawrence
2012-01-01
Discrete Mathematics instructors and students have long been struggling with various labelling and scanning algorithms for solving many important problems. This paper shows how to solve a wide variety of Discrete Mathematics and OR problems using assignment matrices and linear programming, specifically using Excel Solvers although the same…
Random matrices and random difference equations
Uppuluri, V.R.R.
1975-01-01
Mathematical models leading to products of random matrices and random difference equations are discussed. A one-compartment model with random behavior is introduced, and it is shown how the average concentration in the discrete time model converges to the exponential function. This is of relevance to understanding how radioactivity gets trapped in bone structure in blood--bone systems. The ideas are then generalized to two-compartment models and mammillary systems, where products of random matrices appear in a natural way. The appearance of products of random matrices in applications in demography and control theory is considered. Then random sequences motivated from the following problems are studied: constant pulsing and random decay models, random pulsing and constant decay models, and random pulsing and random decay models
Quantum Entanglement and Reduced Density Matrices
Purwanto, Agus; Sukamto, Heru; Yuwana, Lila
2018-05-01
We investigate entanglement and separability criteria of multipartite (n-partite) state by examining ranks of its reduced density matrices. Firstly, we construct the general formula to determine the criterion. A rank of origin density matrix always equals one, meanwhile ranks of reduced matrices have various ranks. Next, separability and entanglement criterion of multipartite is determined by calculating ranks of reduced density matrices. In this article we diversify multipartite state criteria into completely entangled state, completely separable state, and compound state, i.e. sub-entangled state and sub-entangledseparable state. Furthermore, we also shorten the calculation proposed by the previous research to determine separability of multipartite state and expand the methods to be able to differ multipartite state based on criteria above.
Forecasting Covariance Matrices: A Mixed Frequency Approach
Halbleib, Roxana; Voev, Valeri
This paper proposes a new method for forecasting covariance matrices of financial returns. The model mixes volatility forecasts from a dynamic model of daily realized volatilities estimated with high-frequency data with correlation forecasts based on daily data. This new approach allows for flexi......This paper proposes a new method for forecasting covariance matrices of financial returns. The model mixes volatility forecasts from a dynamic model of daily realized volatilities estimated with high-frequency data with correlation forecasts based on daily data. This new approach allows...... for flexible dependence patterns for volatilities and correlations, and can be applied to covariance matrices of large dimensions. The separate modeling of volatility and correlation forecasts considerably reduces the estimation and measurement error implied by the joint estimation and modeling of covariance...
Iglesias, Marco
2017-11-26
In this work, we present the ensemble-marginalized Kalman filter (EnMKF), a sequential algorithm analogous to our previously proposed approach [1,2], for estimating the state and parameters of linear parabolic partial differential equations in initial-boundary value problems when the boundary data are noisy. We apply EnMKF to infer the thermal properties of building walls and to estimate the corresponding heat flux from real and synthetic data. Compared with a modified Ensemble Kalman Filter (EnKF) that is not marginalized, EnMKF reduces the bias error, avoids the collapse of the ensemble without needing to add inflation, and converges to the mean field posterior using $50\\\\%$ or less of the ensemble size required by EnKF. According to our results, the marginalization technique in EnMKF is key to performance improvement with smaller ensembles at any fixed time.
Wishart and anti-Wishart random matrices
Janik, Romuald A; Nowak, Maciej A
2003-01-01
We provide a compact exact representation for the distribution of the matrix elements of the Wishart-type random matrices A † A, for any finite number of rows and columns of A, without any large N approximations. In particular, we treat the case when the Wishart-type random matrix contains redundant, non-random information, which is a new result. This representation is of interest for a procedure for reconstructing the redundant information hidden in Wishart matrices, with potential applications to numerous models based on biological, social and artificial intelligence networks
Topological expansion of the chain of matrices
Eynard, B.; Ferrer, A. Prats
2009-01-01
We solve the loop equations to all orders in 1/N 2 , for the Chain of Matrices matrix model (with possibly an external field coupled to the last matrix of the chain). We show that the topological expansion of the free energy, is, like for the 1 and 2-matrix model, given by the symplectic invariants of [19]. As a consequence, we find the double scaling limit explicitly, and we discuss modular properties, large N asymptotics. We also briefly discuss the limit of an infinite chain of matrices (matrix quantum mechanics).
Partitioning sparse rectangular matrices for parallel processing
Kolda, T.G.
1998-05-01
The authors are interested in partitioning sparse rectangular matrices for parallel processing. The partitioning problem has been well-studied in the square symmetric case, but the rectangular problem has received very little attention. They will formalize the rectangular matrix partitioning problem and discuss several methods for solving it. They will extend the spectral partitioning method for symmetric matrices to the rectangular case and compare this method to three new methods -- the alternating partitioning method and two hybrid methods. The hybrid methods will be shown to be best.
NEW SPECTRAL STATISTICS FOR ENSEMBLES OF 2 × 2 REAL SYMMETRIC RANDOM MATRICES
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.
Zhang, Xuping; Sørensen, Rasmus; RahbekIversen, Mathias
2018-01-01
, and then is linearized based on the acceleration-based state vector. The transfer matrices for each type of components/elements are developed, and used to establish the system equations of a flexible robot manipulator by concatenating the state vector from the base to the end-effector. With this strategy, the size...... manipulators, and only involves calculating and transferring component/element dynamic equations that have small size. The numerical simulations and experimental testing of flexible-link manipulators are conducted to validate the proposed methodologies....
Characterization of a New Heat Dissipation Matric Potential Sensor
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.
Suwono.
1978-01-01
A linear gate providing a variable gate duration from 0,40μsec to 4μsec was developed. The electronic circuity consists of a linear circuit and an enable circuit. The input signal can be either unipolar or bipolar. If the input signal is bipolar, the negative portion will be filtered. The operation of the linear gate is controlled by the application of a positive enable pulse. (author)
Vretenar, M
2014-01-01
The main features of radio-frequency linear accelerators are introduced, reviewing the different types of accelerating structures and presenting the main characteristics aspects of linac beam dynamics
Theoretical origin of quark mass matrices
Mohapatra, R.N.
1987-01-01
This paper presents the theoretical origin of specific quark mass matrices in the grand unified theories. The author discusses the first natural derivation of the Stech-type mass matrix in unified gauge theories. A solution to the strong CP-problem is provided
Malware Analysis Using Visualized Image Matrices
KyoungSoo Han
2014-01-01
Full Text Available This paper proposes a novel malware visual analysis method that contains not only a visualization method to convert binary files into images, but also a similarity calculation method between these images. The proposed method generates RGB-colored pixels on image matrices using the opcode sequences extracted from malware samples and calculates the similarities for the image matrices. Particularly, our proposed methods are available for packed malware samples by applying them to the execution traces extracted through dynamic analysis. When the images are generated, we can reduce the overheads by extracting the opcode sequences only from the blocks that include the instructions related to staple behaviors such as functions and application programming interface (API calls. In addition, we propose a technique that generates a representative image for each malware family in order to reduce the number of comparisons for the classification of unknown samples and the colored pixel information in the image matrices is used to calculate the similarities between the images. Our experimental results show that the image matrices of malware can effectively be used to classify malware families both statically and dynamically with accuracy of 0.9896 and 0.9732, respectively.
Moment matrices, border bases and radical computation
B. Mourrain; J.B. Lasserre; M. Laurent (Monique); P. Rostalski; P. Trebuchet (Philippe)
2013-01-01
htmlabstractIn this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming it complex (resp. real) variety is nte. The aim is to combine approaches for solving a system of polynomial equations with dual methods which involve moment matrices and
Moment matrices, border bases and radical computation
Lasserre, J.B.; Laurent, M.; Mourrain, B.; Rostalski, P.; Trébuchet, P.
2013-01-01
In this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming its complex (resp. real) variety is finite. The aim is to combine approaches for solving a system of polynomial equations with dual methods which involve moment matrices and semi-definite
Moment matrices, border bases and radical computation
B. Mourrain; J.B. Lasserre; M. Laurent (Monique); P. Rostalski; P. Trebuchet (Philippe)
2011-01-01
htmlabstractIn this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming it complex (resp. real) variety is nte. The aim is to combine approaches for solving a system of polynomial equations with dual methods which involve moment matrices and
Malware analysis using visualized image matrices.
Han, KyoungSoo; Kang, BooJoong; Im, Eul Gyu
2014-01-01
This paper proposes a novel malware visual analysis method that contains not only a visualization method to convert binary files into images, but also a similarity calculation method between these images. The proposed method generates RGB-colored pixels on image matrices using the opcode sequences extracted from malware samples and calculates the similarities for the image matrices. Particularly, our proposed methods are available for packed malware samples by applying them to the execution traces extracted through dynamic analysis. When the images are generated, we can reduce the overheads by extracting the opcode sequences only from the blocks that include the instructions related to staple behaviors such as functions and application programming interface (API) calls. In addition, we propose a technique that generates a representative image for each malware family in order to reduce the number of comparisons for the classification of unknown samples and the colored pixel information in the image matrices is used to calculate the similarities between the images. Our experimental results show that the image matrices of malware can effectively be used to classify malware families both statically and dynamically with accuracy of 0.9896 and 0.9732, respectively.
Generation speed in Raven's Progressive Matrices Test
Verguts, T.; Boeck, P. De; Maris, E.G.G.
1999-01-01
In this paper, we investigate the role of response fluency on a well-known intelligence test, Raven's (1962) Advanced Progressive Matrices (APM) test. Critical in solving this test is finding rules that govern the items. Response fluency is conceptualized as generation speed or the speed at which a
Inversion of General Cyclic Heptadiagonal Matrices
A. A. Karawia
2013-01-01
Full Text Available We describe a reliable symbolic computational algorithm for inverting general cyclic heptadiagonal matrices by using parallel computing along with recursion. The computational cost of it is operations. The algorithm is implementable to the Computer Algebra System (CAS such as MAPLE, MATLAB, and MATHEMATICA. Two examples are presented for the sake of illustration.
Calibration of Ge gamma-ray spectrometers for complex sample geometries and matrices
Semkow, T.M., E-mail: thomas.semkow@health.ny.gov [Wadsworth Center, New York State Department of Health, Empire State Plaza, Albany, NY 12201 (United States); Department of Environmental Health Sciences, School of Public Health, University at Albany, State University of New York, Rensselaer, NY 12144 (United States); Bradt, C.J.; Beach, S.E.; Haines, D.K.; Khan, A.J.; Bari, A.; Torres, M.A.; Marrantino, J.C.; Syed, U.-F. [Wadsworth Center, New York State Department of Health, Empire State Plaza, Albany, NY 12201 (United States); Kitto, M.E. [Wadsworth Center, New York State Department of Health, Empire State Plaza, Albany, NY 12201 (United States); Department of Environmental Health Sciences, School of Public Health, University at Albany, State University of New York, Rensselaer, NY 12144 (United States); Hoffman, T.J. [Wadsworth Center, New York State Department of Health, Empire State Plaza, Albany, NY 12201 (United States); Curtis, P. [Kiltel Systems, Inc., Clyde Hill, WA 98004 (United States)
2015-11-01
A comprehensive study of the efficiency calibration and calibration verification of Ge gamma-ray spectrometers was performed using semi-empirical, computational Monte-Carlo (MC), and transfer methods. The aim of this study was to evaluate the accuracy of the quantification of gamma-emitting radionuclides in complex matrices normally encountered in environmental and food samples. A wide range of gamma energies from 59.5 to 1836.0 keV and geometries from a 10-mL jar to 1.4-L Marinelli beaker were studied on four Ge spectrometers with the relative efficiencies between 102% and 140%. Density and coincidence summing corrections were applied. Innovative techniques were developed for the preparation of artificial complex matrices from materials such as acidified water, polystyrene, ethanol, sugar, and sand, resulting in the densities ranging from 0.3655 to 2.164 g cm{sup −3}. They were spiked with gamma activity traceable to international standards and used for calibration verifications. A quantitative method of tuning MC calculations to experiment was developed based on a multidimensional chi-square paraboloid. - Highlights: • Preparation and spiking of traceable complex matrices in extended geometries. • Calibration of Ge gamma spectrometers for complex matrices. • Verification of gamma calibrations. • Comparison of semi-empirical, computational Monte Carlo, and transfer methods of Ge calibration. • Tuning of Monte Carlo calculations using a multidimensional paraboloid.
Calibration of Ge gamma-ray spectrometers for complex sample geometries and matrices
Semkow, T.M.; Bradt, C.J.; Beach, S.E.; Haines, D.K.; Khan, A.J.; Bari, A.; Torres, M.A.; Marrantino, J.C.; Syed, U.-F.; Kitto, M.E.; Hoffman, T.J.; Curtis, P.
2015-01-01
A comprehensive study of the efficiency calibration and calibration verification of Ge gamma-ray spectrometers was performed using semi-empirical, computational Monte-Carlo (MC), and transfer methods. The aim of this study was to evaluate the accuracy of the quantification of gamma-emitting radionuclides in complex matrices normally encountered in environmental and food samples. A wide range of gamma energies from 59.5 to 1836.0 keV and geometries from a 10-mL jar to 1.4-L Marinelli beaker were studied on four Ge spectrometers with the relative efficiencies between 102% and 140%. Density and coincidence summing corrections were applied. Innovative techniques were developed for the preparation of artificial complex matrices from materials such as acidified water, polystyrene, ethanol, sugar, and sand, resulting in the densities ranging from 0.3655 to 2.164 g cm −3 . They were spiked with gamma activity traceable to international standards and used for calibration verifications. A quantitative method of tuning MC calculations to experiment was developed based on a multidimensional chi-square paraboloid. - Highlights: • Preparation and spiking of traceable complex matrices in extended geometries. • Calibration of Ge gamma spectrometers for complex matrices. • Verification of gamma calibrations. • Comparison of semi-empirical, computational Monte Carlo, and transfer methods of Ge calibration. • Tuning of Monte Carlo calculations using a multidimensional paraboloid
Linearization Method and Linear Complexity
Tanaka, Hidema
We focus on the relationship between the linearization method and linear complexity and show that the linearization method is another effective technique for calculating linear complexity. We analyze its effectiveness by comparing with the logic circuit method. We compare the relevant conditions and necessary computational cost with those of the Berlekamp-Massey algorithm and the Games-Chan algorithm. The significant property of a linearization method is that it needs no output sequence from a pseudo-random number generator (PRNG) because it calculates linear complexity using the algebraic expression of its algorithm. When a PRNG has n [bit] stages (registers or internal states), the necessary computational cost is smaller than O(2n). On the other hand, the Berlekamp-Massey algorithm needs O(N2) where N(≅2n) denotes period. Since existing methods calculate using the output sequence, an initial value of PRNG influences a resultant value of linear complexity. Therefore, a linear complexity is generally given as an estimate value. On the other hand, a linearization method calculates from an algorithm of PRNG, it can determine the lower bound of linear complexity.
Mathematical methods linear algebra normed spaces distributions integration
Korevaar, Jacob
1968-01-01
Mathematical Methods, Volume I: Linear Algebra, Normed Spaces, Distributions, Integration focuses on advanced mathematical tools used in applications and the basic concepts of algebra, normed spaces, integration, and distributions.The publication first offers information on algebraic theory of vector spaces and introduction to functional analysis. Discussions focus on linear transformations and functionals, rectangular matrices, systems of linear equations, eigenvalue problems, use of eigenvectors and generalized eigenvectors in the representation of linear operators, metric and normed vector
Cheng, Heming; Huang, Xieqing; Fan, Jiang; Wang, Honggang
1999-10-01
The calculation of a temperature field has a great influence upon the analysis of thermal stresses and stains during quenching. In this paper, a 42CrMo steel cylinder was used an example for investigation. From the TTT diagram of the 42CrMo steel, the CCT diagram was simulated by mathematical transformation, and the volume fraction of phase constituents was calculated. The thermal physical properties were treated as functions of temperature and the volume fraction of phase constituents. The rational approximation was applied to the finite element method. The temperature field with phase transformation and non-linear surface heat-transfer coefficients was calculated using this technique, which can effectively avoid oscillationin the numerical solution for a small time step. The experimental results of the temperature field calculation coincide with the numerical solutions.
Spurny, F.; Vlcek, B.; Bamblevskij, V.P.; Timoshenko, G.N.
1999-01-01
A spectrometer of the linear energy transfer (LET) on the base of CR-39 detector was used to establish the spectra of LET in the beam of protons with the primary energy of 1 GeV. It was found out that the LET spectra of secondary charged particles between 100 and 7000 MeV cm 2 g -1 do not depend on the radiator. The average quality factors for the LET region mentioned were obtained about 11.6 with ICRP 26 quality factors and about 14.0 with ICRP 60 quality factors. The spectra obtained permitted to calculate the contributions of these secondary charged particles to the dosimetric quantities. It was observed that these contributions were about 7.0% for the total absorbed dose of protons and close 90% in the case of the equivalent doses. It is more than it was found out for few hundred MeV protons
P. S. Timashev
2016-01-01
Full Text Available Aim. Controlled treatment of the physico-chemical and mechanical properties of a three-dimensional crosslinked matrix based on reactive chitosan. Materials and methods. The three-dimensional matrices were obtained using photosensitive composition based on allyl chitosan (5 wt%, poly(ethylene glycol diacrylate (8 wt% and the photoinitiator Irgacure 2959 (1 wt% by laser stereolithography setting. The kinetic swelling curves were constructed for structures in the base and salt forms of chitosan using gravimetric method and the contact angles were measured using droplet spreading. The supercritical fl uid setting (40 °C, 12 MPa was used to process matrices during 1.5 hours. Using nanohardness Piuma Nanoindenter we calculated values of Young’s modulus. The study of cytotoxicity was performed by direct contact with the culture of the NIH 3T3 mouse fi broblast cell line. Results. Architectonics of matrices fully repeats the program model. Matrices are uniform throughout and retain their shape after being transferred to the base form. Matrices compressed by 5% after treatment in supercritical carbon dioxide (scCO2 . The elastic modulus of matrices after scCO2 treatment is 4 times higher than the original matrix. The kinetic swelling curves have similar form. In this case the maximum degree of swelling for matrices in base form is 2–2.5 times greater than that of matrices in salt form. There was a surface hydrophobization after the material was transferred to the base form: the contact angle is 94°, and for the salt form it is 66°. The basic form absorbs liquid approximately 1.6 times faster. The fi lm thickness was increased in the area of contact with the liquid droplets after absorption by 133 and 87% for the base and the salt forms, respectively. Treatment of samples in scCO2 reduces their cytotoxicity from 2 degree of reaction (initial samples down to 1 degree of reaction. Conclusion. The use of supercritical carbon dioxide for scaffolds
Moualeu, Leolein Patrick Gouemeni
heat transfer approach is the method used to obtain knowledge of the state of the boundary layer on the surface of the blade. Pressure and temperature distributions are acquired for Reynolds numbers of 50,000, 66,000, 228,000, and 568,000 at an exit Mach number of 0.72, and Reynolds numbers of 228,000, and 568,000 at an exit Mach number of 0.35. These experimental flow conditions are conducted at different flow inlet angles of 40°, 34.2°, 28°, 18°, 8°, -2.6°, -12°, and -17°, and at two free-stream turbulence levels. Results of the analyses performed show that as the incidence angle decreases, a region of laminar separation bubble forms on the pressure surface and grows toward the trailing-edge. It is also noted that the position of the leading-edge moves as the incidence angle varies. A transitional flow is observed on both the pressure and suction surfaces, mainly at the two highest incidence angles, for the high turbulence case. This investigation also reveals that the Stanton number increases as the mainstream turbulence increases, and that the Stanton number at the leading-edge increases as the Reynolds number decreases, as it is documented in the literature.
Embodied, Symbolic and Formal Thinking in Linear Algebra
Stewart, Sepideh; Thomas, Michael O. J.
2007-01-01
Students often find their first university linear algebra experience very challenging. While coping with procedural aspects of the subject, solving linear systems and manipulating matrices, they may struggle with crucial conceptual ideas underpinning them, making it very difficult to progress in more advanced courses. This research has sought to…
Linear algebra meets Lie algebra: the Kostant-Wallach theory
Shomron, Noam; Parlett, Beresford N.
2008-01-01
In two languages, Linear Algebra and Lie Algebra, we describe the results of Kostant and Wallach on the fibre of matrices with prescribed eigenvalues of all leading principal submatrices. In addition, we present a brief introduction to basic notions in Algebraic Geometry, Integrable Systems, and Lie Algebra aimed at specialists in Linear Algebra.
Comments on new iterative methods for solving linear systems
Wang Ke
2017-06-01
Full Text Available Some new iterative methods were presented by Du, Zheng and Wang for solving linear systems in [3], where it is shown that the new methods, comparing to the classical Jacobi or Gauss-Seidel method, can be applied to more systems and have faster convergence. This note shows that their methods are suitable for more matrices than positive matrices which the authors suggested through further analysis and numerical examples.
Stoll, R R
1968-01-01
Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understand
Meromorphic functions and linear algebra
Nevanlinna, Olavi
2003-01-01
This volume describes for the first time in monograph form important applications in numerical methods of linear algebra. The author presents new material and extended results from recent papers in a very readable style. The main goal of the book is to study the behavior of the resolvent of a matrix under the perturbation by low rank matrices. Whereas the eigenvalues (the poles of the resolvent) and the pseudospectra (the sets where the resolvent takes large values) can move dramatically under such perturbations, the growth of the resolvent as a matrix-valued meromorphic function remains essen
On Skew Circulant Type Matrices Involving Any Continuous Fibonacci Numbers
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.
Matrix Operations for Engineers and Scientists An Essential Guide in Linear Algebra
Jeffrey, Alan
2010-01-01
Engineers and scientists need to have an introduction to the basics of linear algebra in a context they understand. Computer algebra systems make the manipulation of matrices and the determination of their properties a simple matter, and in practical applications such software is often essential. However, using this tool when learning about matrices, without first gaining a proper understanding of the underlying theory, limits the ability to use matrices and to apply them to new problems. This book explains matrices in the detail required by engineering or science students, and it discusses linear systems of ordinary differential equations. These students require a straightforward introduction to linear algebra illustrated by applications to which they can relate. It caters of the needs of undergraduate engineers in all disciplines, and provides considerable detail where it is likely to be helpful. According to the author the best way to understand the theory of matrices is by working simple exercises designe...
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.
Solow, Daniel
2014-01-01
This text covers the basic theory and computation for a first course in linear programming, including substantial material on mathematical proof techniques and sophisticated computation methods. Includes Appendix on using Excel. 1984 edition.
Liesen, Jörg
2015-01-01
This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exerc...
Searle, Shayle R
2012-01-01
This 1971 classic on linear models is once again available--as a Wiley Classics Library Edition. It features material that can be understood by any statistician who understands matrix algebra and basic statistical methods.
Probabilistic Signal Recovery and Random Matrices
2016-12-08
that classical methods for linear regression (such as Lasso) are applicable for non- linear data. This surprising finding has already found several...we studied the complexity of convex sets. In numerical linear algebra , we analyzed the fastest known randomized approximation algorithm for...and perfect matchings In numerical linear algebra , we studied the fastest known randomized approximation algorithm for computing the permanents of
Christofilos, N.C.; Polk, I.J.
1959-02-17
Improvements in linear particle accelerators are described. A drift tube system for a linear ion accelerator reduces gap capacity between adjacent drift tube ends. This is accomplished by reducing the ratio of the diameter of the drift tube to the diameter of the resonant cavity. Concentration of magnetic field intensity at the longitudinal midpoint of the external sunface of each drift tube is reduced by increasing the external drift tube diameter at the longitudinal center region.
Evolutionary Games with Randomly Changing Payoff Matrices
Yakushkina, Tatiana; Saakian, David B.; Bratus, Alexander; Hu, Chin-Kun
2015-06-01
Evolutionary games are used in various fields stretching from economics to biology. In most of these games a constant payoff matrix is assumed, although some works also consider dynamic payoff matrices. In this article we assume a possibility of switching the system between two regimes with different sets of payoff matrices. Potentially such a model can qualitatively describe the development of bacterial or cancer cells with a mutator gene present. A finite population evolutionary game is studied. The model describes the simplest version of annealed disorder in the payoff matrix and is exactly solvable at the large population limit. We analyze the dynamics of the model, and derive the equations for both the maximum and the variance of the distribution using the Hamilton-Jacobi equation formalism.
Introduction to random matrices theory and practice
Livan, Giacomo; Vivo, Pierpaolo
2018-01-01
Modern developments of Random Matrix Theory as well as pedagogical approaches to the standard core of the discipline are surprisingly hard to find in a well-organized, readable and user-friendly fashion. This slim and agile book, written in a pedagogical and hands-on style, without sacrificing formal rigor fills this gap. It brings Ph.D. students in Physics, as well as more senior practitioners, through the standard tools and results on random matrices, with an eye on most recent developments that are not usually covered in introductory texts. The focus is mainly on random matrices with real spectrum. The main guiding threads throughout the book are the Gaussian Ensembles. In particular, Wigner’s semicircle law is derived multiple times to illustrate several techniques (e.g., Coulomb gas approach, replica theory). Most chapters are accompanied by Matlab codes (stored in an online repository) to guide readers through the numerical check of most analytical results.
The recurrence sequences via Sylvester matrices
Karaduman, Erdal; Deveci, Ömür
2017-07-01
In this work, we define the Pell-Jacobsthal-Slyvester sequence and the Jacobsthal-Pell-Slyvester sequence by using the Slyvester matrices which are obtained from the characteristic polynomials of the Pell and Jacobsthal sequences and then, we study the sequences defined modulo m. Also, we obtain the cyclic groups and the semigroups from the generating matrices of these sequences when read modulo m and then, we derive the relationships among the orders of the cyclic groups and the periods of the sequences. Furthermore, we redefine Pell-Jacobsthal-Slyvester sequence and the Jacobsthal-Pell-Slyvester sequence by means of the elements of the groups and then, we examine them in the finite groups.
Radiation-induced transformations of isolated organic molecules in solid rare gas matrices
Feldman, V.I.
1998-01-01
Complete text of publication follows. The studies of radiation-chemical behaviour of isolated organic molecules in rigid inert media are of considerable interest for radiation chemistry and general structural chemistry. Previous efforts were limited to the ESR studies of radicals resulting from some small hydrocarbon molecules in frozen rare gas solutions. Recently, we developed an approach to the radiation chemistry of isolated organic molecules using classic matrix isolation procedure for sample preparation and a combination of ESR and IR spectroscopy for characterization of paramagnetic and diamagnetic species resulting form electron irradiation or organic molecules in solid rare gas matrices at 10-15 K. The results obtained reveal high efficiency of energy transfer from rare gas matrix to organic molecules. The total radiation-chemical yields of degradation of organic molecules in argon and xenon matrices were measured directly by IR spectroscopy. The studies of the effect of electron scavengers on the radiolysis of organic molecules in solid rare gases show that the main primary process is positive hole transfer from matrix to additive molecule. ESR spectra of a number of radical cations (alkanes, ethers, arenes) were first characterized in a low-disturbing environment. It was found that the electronic characteristics (IP, polarizability) of the matrix used had crucial effect on trapping and degradation of primary organic radical cations. Using matrices with various IP provides an unique possibility to examine the chemical meaning of excess energy resulting from exothermic positive hole transfer, that is, to follow the fate of excited cations in condensed phase
Joint Matrices Decompositions and Blind Source Separation
Chabriel, G.; Kleinsteuber, M.; Moreau, E.; Shen, H.; Tichavský, Petr; Yeredor, A.
2014-01-01
Roč. 31, č. 3 (2014), s. 34-43 ISSN 1053-5888 R&D Projects: GA ČR GA102/09/1278 Institutional support: RVO:67985556 Keywords : joint matrices decomposition * tensor decomposition * blind source separation Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 5.852, year: 2014 http://library.utia.cas.cz/separaty/2014/SI/tichavsky-0427607.pdf
Tensor Permutation Matrices in Finite Dimensions
Christian, Rakotonirina
2005-01-01
We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows us to construct a tensor permutation matrix, which is a generalisation of tensor commutation matrix, has been established. The expression of an element of a tensor commutation matrix has been generalised in the case of any element of a tensor permutation ma...
Fast Approximate Joint Diagonalization Incorporating Weight Matrices
Tichavský, Petr; Yeredor, A.
2009-01-01
Roč. 57, č. 3 (2009), s. 878-891 ISSN 1053-587X R&D Projects: GA MŠk 1M0572 Institutional research plan: CEZ:AV0Z10750506 Keywords : autoregressive processes * blind source separation * nonstationary random processes Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 2.212, year: 2009 http://library.utia.cas.cz/separaty/2009/SI/tichavsky-fast approximate joint diagonalization incorporating weight matrices.pdf
Photoluminescence of nanocrystals embedded in oxide matrices
Estrada, C.; Gonzalez, J.A.; Kunold, A.; Reyes-Esqueda, J.A.; Pereyra, P.
2006-12-01
We used the theory of finite periodic systems to explain the photoluminescence spectra dependence on the average diameter of nanocrystals embedded in oxide matrices. Because of the broad matrix band gap, the photoluminescence response is basically determined by isolated nanocrystals and sequences of a few of them. With this model we were able to reproduce the shape and displacement of the experimentally observed photoluminescence spectra. (author)
Equiangular tight frames and unistochastic matrices
Goyeneche, D.; Turek, Ondřej
2017-01-01
Roč. 50, č. 24 (2017), č. článku 245304. ISSN 1751-8113 R&D Projects: GA ČR GA17-01706S Institutional support: RVO:61389005 Keywords : equiangular tight frames * unistochastic matrices * SIC POVM Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 1.857, year: 2016
Simplifications of rational matrices by using UML
Tasić, Milan B.; Stanimirović, Ivan P.
2013-01-01
The simplification process on rational matrices consists of simplifying each entry represented by a rational function. We follow the classic approach of dividing the numerator and denominator polynomials by their common GCD polynomial, and provide the activity diagram in UML for this process. A rational matrix representation as the quotient of a polynomial matrix and a polynomial is also discussed here and illustrated via activity diagrams. Also, a class diagram giving the links between the c...
PHAGOCYTOSIS AND REMODELING OF COLLAGEN MATRICES
Abraham, Leah C.; Dice, J Fred.; Lee, Kyongbum; Kaplan, David L.
2007-01-01
The biodegradation of collagen and the deposition of new collagen-based extracellular matrices are of central importance in tissue remodeling and function. Similarly, for collagen-based biomaterials used in tissue engineering, the degradation of collagen scaffolds with accompanying cellular infiltration and generation of new extracellular matrix is critical for integration of in vitro grown tissues in vivo. In earlier studies we observed significant impact of collagen structure on primary lun...
Preconditioners for regularized saddle point matrices
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
Non linear viscoelastic models
Agerkvist, Finn T.
2011-01-01
Viscoelastic eects are often present in loudspeaker suspensions, this can be seen in the displacement transfer function which often shows a frequency dependent value below the resonance frequency. In this paper nonlinear versions of the standard linear solid model (SLS) are investigated....... The simulations show that the nonlinear version of the Maxwell SLS model can result in a time dependent small signal stiness while the Kelvin Voight version does not....
Quantitative analysis of eyes and other optical systems in linear optics.
Harris, William F; Evans, Tanya; van Gool, Radboud D
2017-05-01
To show that 14-dimensional spaces of augmented point P and angle Q characteristics, matrices obtained from the ray transference, are suitable for quantitative analysis although only the latter define an inner-product space and only on it can one define distances and angles. The paper examines the nature of the spaces and their relationships to other spaces including symmetric dioptric power space. The paper makes use of linear optics, a three-dimensional generalization of Gaussian optics. Symmetric 2 × 2 dioptric power matrices F define a three-dimensional inner-product space which provides a sound basis for quantitative analysis (calculation of changes, arithmetic means, etc.) of refractive errors and thin systems. For general systems the optical character is defined by the dimensionally-heterogeneous 4 × 4 symplectic matrix S, the transference, or if explicit allowance is made for heterocentricity, the 5 × 5 augmented symplectic matrix T. Ordinary quantitative analysis cannot be performed on them because matrices of neither of these types constitute vector spaces. Suitable transformations have been proposed but because the transforms are dimensionally heterogeneous the spaces are not naturally inner-product spaces. The paper obtains 14-dimensional spaces of augmented point P and angle Q characteristics. The 14-dimensional space defined by the augmented angle characteristics Q is dimensionally homogenous and an inner-product space. A 10-dimensional subspace of the space of augmented point characteristics P is also an inner-product space. The spaces are suitable for quantitative analysis of the optical character of eyes and many other systems. Distances and angles can be defined in the inner-product spaces. The optical systems may have multiple separated astigmatic and decentred refracting elements. © 2017 The Authors Ophthalmic & Physiological Optics © 2017 The College of Optometrists.
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.
Exact closed-form expression for the inverse moments of one-sided correlated Gram matrices
Elkhalil, Khalil; Kammoun, Abla; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim
2016-01-01
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.
Matrix Tricks for Linear Statistical Models
Puntanen, Simo; Styan, George PH
2011-01-01
In teaching linear statistical models to first-year graduate students or to final-year undergraduate students there is no way to proceed smoothly without matrices and related concepts of linear algebra; their use is really essential. Our experience is that making some particular matrix tricks very familiar to students can substantially increase their insight into linear statistical models (and also multivariate statistical analysis). In matrix algebra, there are handy, sometimes even very simple "tricks" which simplify and clarify the treatment of a problem - both for the student and
Group inverses of M-matrices and their applications
Kirkland, Stephen J
2013-01-01
Group inverses for singular M-matrices are useful tools not only in matrix analysis, but also in the analysis of stochastic processes, graph theory, electrical networks, and demographic models. Group Inverses of M-Matrices and Their Applications highlights the importance and utility of the group inverses of M-matrices in several application areas. After introducing sample problems associated with Leslie matrices and stochastic matrices, the authors develop the basic algebraic and spectral properties of the group inverse of a general matrix. They then derive formulas for derivatives of matrix f
Hg-Xe exciplex formation in mixed Xe/Ar matrices: molecular dynamics and luminescence study.
Lozada-García, Rolando; Rojas-Lorenzo, Germán; Crépin, Claudine; Ryan, Maryanne; McCaffrey, John G
2015-03-19
Luminescence of Hg((3)P1) atoms trapped in mixed Ar/Xe matrices containing a small amount of Xe is reported. Broad emission bands, strongly red-shifted from absorption are recorded which are assigned to strong complexes formed between the excited mercury Hg* and xenon atoms. Molecular dynamics calculations are performed on simulated Xe/Ar samples doped with Hg to follow the behavior of Hg* in the mixed rare gas matrices leading to exciplex formation. The role of Xe atoms in the first solvation shell (SS1) around Hg was investigated in detail, revealing the formation of two kinds of triatomic exciplexes; namely, Xe-Hg*-Xe and Ar-Hg*-Xe. The first species exists only when two xenon atoms are present in SS1 with specific geometries allowing the formation of a linear or quasi-linear exciplex. In the other geometries, or in the presence of only one Xe in SS1, a linear Ar-Hg*-Xe exciplex is formed. The two kinds of exciplexes have different emission bands, the most red-shifted being that involving two Xe atoms, whose emission is very close to that observed in pure Xe matrices. Simulations give a direct access to the analysis of the experimental absorption, emission, and excitation spectra, together with the dynamics of exciplexes formation.
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
Lemieux, M.A.; Breton, P.; Tremblay, A.M.S.
1985-01-01
It is shown that the Negative Eigenvalue Theorem and transfer matrix methods may be considered within a unified framework and generalized to compute projected densities of states or, more generally, any linear combination of matrix elements of the inverse of large symmetric random matrices. As examples of applications, extensive simulations for one- and two-mode behaviour in the Raman spectrum of one-dimensional mixed crystals and a finite-size analysis of critical exponents for the central force percolation universality class are presented
Olive, David J
2017-01-01
This text covers both multiple linear regression and some experimental design models. The text uses the response plot to visualize the model and to detect outliers, does not assume that the error distribution has a known parametric distribution, develops prediction intervals that work when the error distribution is unknown, suggests bootstrap hypothesis tests that may be useful for inference after variable selection, and develops prediction regions and large sample theory for the multivariate linear regression model that has m response variables. A relationship between multivariate prediction regions and confidence regions provides a simple way to bootstrap confidence regions. These confidence regions often provide a practical method for testing hypotheses. There is also a chapter on generalized linear models and generalized additive models. There are many R functions to produce response and residual plots, to simulate prediction intervals and hypothesis tests, to detect outliers, and to choose response trans...
Alcaraz, J.
2001-01-01
After several years of study e''+ e''- linear colliders in the TeV range have emerged as the major and optimal high-energy physics projects for the post-LHC era. These notes summarize the present status form the main accelerator and detector features to their physics potential. The LHC era. These notes summarize the present status, from the main accelerator and detector features to their physics potential. The LHC is expected to provide first discoveries in the new energy domain, whereas an e''+ e''- linear collider in the 500 GeV-1 TeV will be able to complement it to an unprecedented level of precision in any possible areas: Higgs, signals beyond the SM and electroweak measurements. It is evident that the Linear Collider program will constitute a major step in the understanding of the nature of the new physics beyond the Standard Model. (Author) 22 refs
Edwards, Harold M
1995-01-01
In his new undergraduate textbook, Harold M Edwards proposes a radically new and thoroughly algorithmic approach to linear algebra Originally inspired by the constructive philosophy of mathematics championed in the 19th century by Leopold Kronecker, the approach is well suited to students in the computer-dominated late 20th century Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples, making the study of linear algebra a truly interactive experience Designed for a one-semester course, this text adopts an algorithmic approach to linear algebra giving the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject Students at all levels will find much interactive instruction in this text while teachers will find stimulating examples and methods of approach to the subject
Zyoud, Ahed; Al-Kerm, Rola S.; Al-Kerm, Rana S.; Waseem, Mansur; Mohammed, H.S. Helal; Park, DaeHoon; Campet, Guy; Sabli, Nordin; Hilal, Hikmat S.
2015-01-01
Enhancement of hole-transfer across CuSe electrode/liquid junction can be facilitated by coating with metalloporphyrin complexes embedded inside polyethylene matrices. - Highlights: • CuSe films were electrochemically deposited onto FTO/Glass • Annealing CuSe film electrodes enhanced PEC characteristics • PEC characteristics were further enhanced by metalloporphyrin/polyethylene matrices, yielding ∼15% efficiency • Matrix behavior as charge transfer mediator enhanced electrode conversion efficiency and stability - Abstract: Electrodeposited CuSe film electrodes have been prepared onto FTO/glass by a facile method based on earlier methods described for other systems. The films were characterized, modified by annealing and further characterized. The films were then modified by coating with tetra(-4-pyridyl) pophyrinato-manganese (MnTPyP) complexes embedded inside commercial polyethylene (PE) matrices. The effects of modifications on different film properties, such as X-ray diffraction (XRD) patterns, surface morphology, photoluminescence (PL) spectra and electronic absorption spectra were investigated. Compared with other thin film electrode systems, very high photoelectrochemical (PEC) conversion efficiency values have been observed here. Pre-annealing the CuSe films at 150°C for 2 h, followed by attaching the MnTPyP/PE matrices remarkably enhanced their PEC characteristics. The conversion efficiency was significantly enhanced, from less than 1.0% to more than 15%. Fill factor (FF) was also enhanced from ∼30% to ∼80%. Values of open-circuit potential (V OC ) and short-circuit current (J SC ) were significantly enhanced. While annealing affects uniformity, particle inter-connection and surface texture of the CuSe films, the MnTPyP complex species behaves as an additional charge-transfer mediator across the film/electrolyte junction. Optimization of PEC characteristics, using different deposition times, different annealing temperatures, different
DeAngelis, Paul L
2002-11-01
Glycosaminoglycans (linear polysaccharides with a repeating disaccharide backbone containing an amino sugar) are essential components of extracellular matrices of animals. These complex molecules play important structural, adhesion, and signaling roles in mammals. Direct detection of glycosaminoglycans has been reported in a variety of organisms, but perhaps more definitive tests for the glycosyltransferase genes should be utilized to clarify the distribution of glycosaminoglycans in metazoans. Recently, glycosyltransferases that form the hyaluronan, heparin/heparan, or chondroitin backbone were identified at the molecular level. The three types of glycosyltransferases appear to have evolved independently based on sequence comparisons and other characteristics. All metazoans appear to possess heparin/heparan. Chondroitin is found in some worms, arthropods, and higher animals. Hyaluronan is found only in two of the three main branches of chordates. The presence of several types of glycosaminoglycans in the body allows multiple communication channels and adhesion systems to operate simultaneously. Certain pathogenic bacteria produce extracellular coatings, called capsules, which are composed of glycosaminoglycans that increase their virulence during infection. The capsule helps shield the microbe from the host defenses and/or modulates host physiology. The bacterial and animal polysaccharides are chemically identical or at least very similar. Therefore, no immune response is generated, in contrast to the vast majority of capsular polymers from other bacteria. In microbial systems, it appears that in most cases functional convergent evolution of glycosaminoglycan glycosyltransferases occurred, rather than direct horizontal gene transfer from their vertebrate hosts. Copyright 2002 Wiley-Liss, Inc.
Carla Regina Amorim dos Anjos Queiroz
2015-03-01
Full Text Available Pereskia aculeata Mill., popularly known in Brazil as “Ora-pro-nobis”, is an unconventional edible vegetable. Taking into account its potential for agronomic cultivation, this study aimed to evaluate the growth response of this plant under intermittent drought through controlled reductions in the substrate matric potential, in a greenhouse. Treatments consisted of adding to the pots a volume of water to raise the matric potential to -5 kPa, according to the water retention curve in the substrate, whenever the mean substrate matric potential reached values between -10 kPa and -70 kPa, depending on the treatment. At 140 days after transplanting, leaf area and dry mass of leaves, stems and roots were determined. The intermittent reduction of the matric potential in the root zone of “Ora-pro-nobis” affected less the dry mass accumulation in leaves (reduction of 21.4% than in stems (reduction of 48.1% and roots (reduction of 63.7%, and that is interesting because leaves are the main commercial product of this plant. The treatment also modified the proportionality of dry mass allocation among plant parts and reduced the photosynthetic efficiency of leaves, fact evidenced by the linear increase of the specific leaf area (0.63 cm2 g-1kPa-1 and leaf area ratio (0.39 cm-2 g-1kPa-1, although not affecting directly the leaf area.
A Geršgorin-type eigenvalue localization set with n parameters for stochastic matrices
Wang Xiaoxiao
2018-04-01
Full Text Available A set in the complex plane which involves n parameters in [0, 1] is given to localize all eigenvalues different from 1 for stochastic matrices. As an application of this set, an upper bound for the moduli of the subdominant eigenvalues of a stochastic matrix is obtained. Lastly, we fix n parameters in [0, 1] to give a new set including all eigenvalues different from 1, which is tighter than those provided by Shen et al. (Linear Algebra Appl. 447 (2014 74-87 and Li et al. (Linear and Multilinear Algebra 63(11 (2015 2159-2170 for estimating the moduli of subdominant eigenvalues.
Multivariate covariance generalized linear models
Bonat, W. H.; Jørgensen, Bent
2016-01-01
are fitted by using an efficient Newton scoring algorithm based on quasi-likelihood and Pearson estimating functions, using only second-moment assumptions. This provides a unified approach to a wide variety of types of response variables and covariance structures, including multivariate extensions......We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models, designed to handle multivariate response variables, along with a wide range of temporal and spatial correlation structures defined in terms of a covariance link...... function combined with a matrix linear predictor involving known matrices. The method is motivated by three data examples that are not easily handled by existing methods. The first example concerns multivariate count data, the second involves response variables of mixed types, combined with repeated...
Computational linear and commutative algebra
Kreuzer, Martin
2016-01-01
This book combines, in a novel and general way, an extensive development of the theory of families of commuting matrices with applications to zero-dimensional commutative rings, primary decompositions and polynomial system solving. It integrates the Linear Algebra of the Third Millennium, developed exclusively here, with classical algorithmic and algebraic techniques. Even the experienced reader will be pleasantly surprised to discover new and unexpected aspects in a variety of subjects including eigenvalues and eigenspaces of linear maps, joint eigenspaces of commuting families of endomorphisms, multiplication maps of zero-dimensional affine algebras, computation of primary decompositions and maximal ideals, and solution of polynomial systems. This book completes a trilogy initiated by the uncharacteristically witty books Computational Commutative Algebra 1 and 2 by the same authors. The material treated here is not available in book form, and much of it is not available at all. The authors continue to prese...
Identification of general linear mechanical systems
Sirlin, S. W.; Longman, R. W.; Juang, J. N.
1983-01-01
Previous work in identification theory has been concerned with the general first order time derivative form. Linear mechanical systems, a large and important class, naturally have a second order form. This paper utilizes this additional structural information for the purpose of identification. A realization is obtained from input-output data, and then knowledge of the system input, output, and inertia matrices is used to determine a set of linear equations whereby we identify the remaining unknown system matrices. Necessary and sufficient conditions on the number, type and placement of sensors and actuators are given which guarantee identificability, and less stringent conditions are given which guarantee generic identifiability. Both a priori identifiability and a posteriori identifiability are considered, i.e., identifiability being insured prior to obtaining data, and identifiability being assured with a given data set.
Kazemi, Elahe; Haji Shabani, Ali Mohammad; Dadfarnia, Shayessteh; Abbasi, Amir; Rashidian Vaziri, Mohammad Reza; Behjat, Abbas
2016-01-01
This study aims at developing a novel, sensitive, fast, simple and convenient method for separation and preconcentration of trace amounts of fluoxetine before its spectrophotometric determination. The method is based on combination of magnetic mixed hemimicelles solid phase extraction and dispersive micro solid phase extraction using 1-hexadecyl-3-methylimidazolium bromide coated magnetic graphene as a sorbent. The magnetic graphene was synthesized by a simple coprecipitation method and characterized by X-ray diffraction (XRD), Fourier transform infrared (FT-IR) spectroscopy and scanning electron microscopy (SEM). The retained analyte was eluted using a 100 μL mixture of methanol/acetic acid (9:1) and converted into fluoxetine-β-cyclodextrin inclusion complex. The analyte was then quantified by fiber optic linear array spectrophotometry as well as mode-mismatched thermal lens spectroscopy (TLS). The factors affecting the separation, preconcentration and determination of fluoxetine were investigated and optimized. With a 50 mL sample and under optimized conditions using the spectrophotometry technique, the method exhibited a linear dynamic range of 0.4–60.0 μg L"−"1, a detection limit of 0.21 μg L"−"1, an enrichment factor of 167, and a relative standard deviation of 2.1% and 3.8% (n = 6) at 60 μg L"−"1 level of fluoxetine for intra- and inter-day analyses, respectively. However, with thermal lens spectrometry and a sample volume of 10 mL, the method exhibited a linear dynamic range of 0.05–300 μg L"−"1, a detection limit of 0.016 μg L"−"1 and a relative standard deviation of 3.8% and 5.6% (n = 6) at 60 μg L"−"1 level of fluoxetine for intra- and inter-day analyses, respectively. The method was successfully applied to determine fluoxetine in pharmaceutical formulation, human urine and environmental water samples. - Graphical abstract: A novel, sensitive, fast, simple and convenient mixed hemimicelles dispersive micro solid
Kazemi, Elahe; Haji Shabani, Ali Mohammad [Department of Chemistry, Yazd University, Safaieh, 89195-741, Yazd (Iran, Islamic Republic of); Dadfarnia, Shayessteh, E-mail: sdadfarnia@yazd.ac.ir [Department of Chemistry, Yazd University, Safaieh, 89195-741, Yazd (Iran, Islamic Republic of); Abbasi, Amir [Department of Physics, Yazd University, Safaieh, 89195-741, Yazd (Iran, Islamic Republic of); Rashidian Vaziri, Mohammad Reza [Laser and Optics Research School, 14155-1339, Tehran (Iran, Islamic Republic of); Behjat, Abbas [Department of Physics, Yazd University, Safaieh, 89195-741, Yazd (Iran, Islamic Republic of)
2016-01-28
This study aims at developing a novel, sensitive, fast, simple and convenient method for separation and preconcentration of trace amounts of fluoxetine before its spectrophotometric determination. The method is based on combination of magnetic mixed hemimicelles solid phase extraction and dispersive micro solid phase extraction using 1-hexadecyl-3-methylimidazolium bromide coated magnetic graphene as a sorbent. The magnetic graphene was synthesized by a simple coprecipitation method and characterized by X-ray diffraction (XRD), Fourier transform infrared (FT-IR) spectroscopy and scanning electron microscopy (SEM). The retained analyte was eluted using a 100 μL mixture of methanol/acetic acid (9:1) and converted into fluoxetine-β-cyclodextrin inclusion complex. The analyte was then quantified by fiber optic linear array spectrophotometry as well as mode-mismatched thermal lens spectroscopy (TLS). The factors affecting the separation, preconcentration and determination of fluoxetine were investigated and optimized. With a 50 mL sample and under optimized conditions using the spectrophotometry technique, the method exhibited a linear dynamic range of 0.4–60.0 μg L{sup −1}, a detection limit of 0.21 μg L{sup −1}, an enrichment factor of 167, and a relative standard deviation of 2.1% and 3.8% (n = 6) at 60 μg L{sup −1} level of fluoxetine for intra- and inter-day analyses, respectively. However, with thermal lens spectrometry and a sample volume of 10 mL, the method exhibited a linear dynamic range of 0.05–300 μg L{sup −1}, a detection limit of 0.016 μg L{sup −1} and a relative standard deviation of 3.8% and 5.6% (n = 6) at 60 μg L{sup −1} level of fluoxetine for intra- and inter-day analyses, respectively. The method was successfully applied to determine fluoxetine in pharmaceutical formulation, human urine and environmental water samples. - Graphical abstract: A novel, sensitive, fast, simple and convenient mixed hemimicelles
Answers to selected problems in multivariable calculus with linear algebra and series
Trench, William F
1972-01-01
Answers to Selected Problems in Multivariable Calculus with Linear Algebra and Series contains the answers to selected problems in linear algebra, the calculus of several variables, and series. Topics covered range from vectors and vector spaces to linear matrices and analytic geometry, as well as differential calculus of real-valued functions. Theorems and definitions are included, most of which are followed by worked-out illustrative examples.The problems and corresponding solutions deal with linear equations and matrices, including determinants; vector spaces and linear transformations; eig
Determination of coefficient matrices for ARMA model
Tran Dinh Tri.
1990-10-01
A new recursive algorithm for determining coefficient matrices of ARMA model from measured data is presented. The Yule-Walker equations for the case of ARMA model are derived from the ARMA innovation equation. The recursive algorithm is based on choosing appropriate form of the operator functions and suitable representation of the (n+1)-th order operator functions according to ones with the lower order. Two cases, when the order of the AR part is equal to one of the MA part, and the optimal case, were considered. (author) 5 refs
Algebraic Graph Theory Morphisms, Monoids and Matrices
Knauer, Ulrich
2011-01-01
This is a highly self-contained book about algebraic graph theory which iswritten with a view to keep the lively and unconventional atmosphere of a spoken text to communicate the enthusiasm the author feels about this subject. The focus is on homomorphisms and endomorphisms, matrices and eigenvalues. Graph models are extremely useful for almost all applications and applicators as they play an important role as structuring tools. They allow to model net structures -like roads, computers, telephones -instances of abstract data structures -likelists, stacks, trees -and functional or object orient
Coherence and extensions of stochastic matrices
Angelo Gilio
1995-11-01
Full Text Available In this paper a review of some general results on coherence of conditional probability assessments is given. Then, a necessary and sufficient condition on coherence of two finite families of discrete conditianal probability distributions, represented by two stochastic matrices P and Q, is obtained. Moreover, the possible extensions of the assessment (P,Q to the marginal distributions are examined and explicit formulas for them are given in some special case. Finally, a general algorithm to check coherence of (P,Q and to derive its extensions is proposed.
Spurny, F.; Pachnerovy Brabcovy, K.; Ploc, O.; Ambrozovy, I.; Mrazova, Z.
2011-01-01
Active mobile dosimetry unit (Liulin), passive plastic nuclear track detectors (PNTD) and thermoluminescent detectors (TLD) were exposed in a C290 MeV/n beam at HIMAC-BIO (NIRS (Japan)). Two different types of beam configuration were used-monoenergetic beam (MONO) and spread-out Bragg peak (SOBP); the detectors were placed at several depths from the entrance up to the depths behind the Bragg peak. Relative response of TLDs in beams has been studied as a function of the depth, and it was re-proved that it can depend on the linear energy transfer (LET). Liulin measures energy deposition in Si; the spectra of energy deposited in Si can be transformed to the spectra of lineal energy or LET. PNTDs are able to determine the LET of registered particles directly. The limitation of both methods is in the range in which they can determine the LET-Liulin is able to measure perpendicularly incident charged particles up to ∼35 keV/μm (in water), PNTD can measure from ∼7 to 400 keV/μm, independently of the registration angle. The results from both methods are compared and combined for both beams' configuration, and a good agreement is observed. (authors)
Karloff, Howard
1991-01-01
To this reviewer’s knowledge, this is the first book accessible to the upper division undergraduate or beginning graduate student that surveys linear programming from the Simplex Method…via the Ellipsoid algorithm to Karmarkar’s algorithm. Moreover, its point of view is algorithmic and thus it provides both a history and a case history of work in complexity theory. The presentation is admirable; Karloff's style is informal (even humorous at times) without sacrificing anything necessary for understanding. Diagrams (including horizontal brackets that group terms) aid in providing clarity. The end-of-chapter notes are helpful...Recommended highly for acquisition, since it is not only a textbook, but can also be used for independent reading and study. —Choice Reviews The reader will be well served by reading the monograph from cover to cover. The author succeeds in providing a concise, readable, understandable introduction to modern linear programming. —Mathematics of Computing This is a textbook intend...
Sasaki, K.; Miyakoshi, H. (Akita Univ., Akita (Japan). Mining College); Kinoshita, H.; Onozuka, T. (Hanaoka Mining Co. Ltd., Akita (Japan))
1990-09-25
In this report, the method of analyzing mine ventilation networks is explained in which the direct matric operation method is applied to the solution of the linear equation system introduced from the fundamental equation of the nodal head method. In other words, the fundamental equation was expressed by genelarized equation composition by using connecting functions between nodes and the algorism of a computer program was clarified. And the calculation method necessary for other ventilation netwrks analysis was shown in a concrete form. For solving the linear equation system, the matric operation method based on the modified Choleski's method was used in order to speed up the calculation and stabilize the convergence process of the solution. As examples, calculation was made on the ventilation networks of total numbers of the nodes of 8, 14, 51 and 141. From these ventilation network analyses, using a linear equation system concerning the nodal pressure correction, it was found that in the system with convergence acceleration coefficient of 1.4, the number of sequential repeating frequency of approximation Mc which was required for convergence was in the order of Mc {approx equal} 13 (cycle) for the condition that the fan pressure was constant and the convergence condition was {vert bar} AQi {vert bar}{sub max} {lt} 0.1m {sup 3}/min. 14 refs., 12 figs., 3 tabs.
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.
Virial expansion for almost diagonal random matrices
Yevtushenko, Oleg; Kravtsov, Vladimir E
2003-01-01
Energy level statistics of Hermitian random matrices H-circumflex with Gaussian independent random entries H i≥j is studied for a generic ensemble of almost diagonal random matrices with (vertical bar H ii vertical bar 2 ) ∼ 1 and (vertical bar H i≠j vertical bar 2 ) bF(vertical bar i - j vertical bar) parallel 1. We perform a regular expansion of the spectral form-factor K(τ) = 1 + bK 1 (τ) + b 2 K 2 (τ) + c in powers of b parallel 1 with the coefficients K m (τ) that take into account interaction of (m + 1) energy levels. To calculate K m (τ), we develop a diagrammatic technique which is based on the Trotter formula and on the combinatorial problem of graph edges colouring with (m + 1) colours. Expressions for K 1 (τ) and K 2 (τ) in terms of infinite series are found for a generic function F(vertical bar i - j vertical bar ) in the Gaussian orthogonal ensemble (GOE), the Gaussian unitary ensemble (GUE) and in the crossover between them (the almost unitary Gaussian ensemble). The Rosenzweig-Porter and power-law banded matrix ensembles are considered as examples
Generalized Eigenvalues for pairs on heritian matrices
Rublein, George
1988-01-01
A study was made of certain special cases of a generalized eigenvalue problem. Let A and B be nxn matrics. One may construct a certain polynomial, P(A,B, lambda) which specializes to the characteristic polynomial of B when A equals I. In particular, when B is hermitian, that characteristic polynomial, P(I,B, lambda) has real roots, and one can ask: are the roots of P(A,B, lambda) real when B is hermitian. We consider the case where A is positive definite and show that when N equals 3, the roots are indeed real. The basic tools needed in the proof are Shur's theorem on majorization for eigenvalues of hermitian matrices and the interlacing theorem for the eigenvalues of a positive definite hermitian matrix and one of its principal (n-1)x(n-1) minors. The method of proof first reduces the general problem to one where the diagonal of B has a certain structure: either diag (B) = diag (1,1,1) or diag (1,1,-1), or else the 2 x 2 principal minors of B are all 1. According as B has one of these three structures, we use an appropriate method to replace A by a positive diagonal matrix. Since it can be easily verified that P(D,B, lambda) has real roots, the result follows. For other configurations of B, a scaling and a continuity argument are used to prove the result in general.
Universality for 1d Random Band Matrices: Sigma-Model Approximation
Shcherbina, Mariya; Shcherbina, Tatyana
2018-02-01
The paper continues the development of the rigorous supersymmetric transfer matrix approach to the random band matrices started in (J Stat Phys 164:1233-1260, 2016; Commun Math Phys 351:1009-1044, 2017). We consider random Hermitian block band matrices consisting of W× W random Gaussian blocks (parametrized by j,k \\in Λ =[1,n]^d\\cap Z^d ) with a fixed entry's variance J_{jk}=δ _{j,k}W^{-1}+β Δ _{j,k}W^{-2} , β >0 in each block. Taking the limit W→ ∞ with fixed n and β , we derive the sigma-model approximation of the second correlation function similar to Efetov's one. Then, considering the limit β , n→ ∞, we prove that in the dimension d=1 the behaviour of the sigma-model approximation in the bulk of the spectrum, as β ≫ n , is determined by the classical Wigner-Dyson statistics.
Meet and Join Matrices in the Poset of Exponential Divisors
... exponential divisor ( G C E D ) and the least common exponential multiple ( L C E M ) do not always exist. In this paper we embed this poset in a lattice. As an application we study the G C E D and L C E M matrices, analogues of G C D and L C M matrices, which are both special cases of meet and join matrices on lattices.
The 'golden' matrices and a new kind of cryptography
Stakhov, A.P.
2007-01-01
We consider a new class of square matrices called the 'golden' matrices. They are a generalization of the classical Fibonacci Q-matrix for continuous domain. The 'golden' matrices can be used for creation of a new kind of cryptography called the 'golden' cryptography. The method is very fast and simple for technical realization and can be used for cryptographic protection of digital signals (telecommunication and measurement systems)
Generalized Perron--Frobenius Theorem for Nonsquare Matrices
Avin, Chen; Borokhovich, Michael; Haddad, Yoram; Kantor, Erez; Lotker, Zvi; Parter, Merav; Peleg, David
2013-01-01
The celebrated Perron--Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields of science and engineering, including dynamical systems theory, economics, statistics and optimization. However, many real-life scenarios give rise to nonsquare matrices. A natural question is whether the...
Exploring linear algebra labs and projects with Mathematica
Arangala, Crista
2014-01-01
Matrix Operations Lab 0: An Introduction to Mathematica Lab 1: Matrix Basics and Operations Lab 2: A Matrix Representation of Linear Systems Lab 3: Powers, Inverses, and Special Matrices Lab 4: Graph Theory and Adjacency Matrices Lab 5: Permutations and Determinants Lab 6: 4 x 4 Determinants and Beyond Project Set 1 Invertibility Lab 7: Singular or Nonsingular? Why Singularity Matters Lab 8: Mod It Out, Matrices with Entries in ZpLab 9: It's a Complex World Lab 10: Declaring Independence: Is It Linear? Project Set 2 Vector Spaces Lab 11: Vector Spaces and SubspacesLab 12: Basing It All on Just a Few Vectors Lab 13: Linear Transformations Lab 14: Eigenvalues and Eigenspaces Lab 15: Markov Chains, An Application of Eigenvalues Project Set 3 Orthogonality Lab 16: Inner Product Spaces Lab 17: The Geometry of Vector and Inner Product SpacesLab 18: Orthogonal Matrices, QR Decomposition, and Least Squares Regression Lab 19: Symmetric Matrices and Quadratic Forms Project Set 4 Matrix Decomposition with Applications L...
Scaling Sparse Matrices for Optimization Algorithms
Gajulapalli Ravindra S; Lasdon Leon S
2006-01-01
To iteratively solve large scale optimization problems in various contexts like planning, operations, design etc., we need to generate descent directions that are based on linear system solutions. Irrespective of the optimization algorithm or the solution method employed for the linear systems, ill conditioning introduced by problem characteristics or the algorithm or both need to be addressed. In [GL01] we used an intuitive heuristic approach in scaling linear systems that improved performan...
Intrinsic Density Matrices of the Nuclear Shell Model
Deveikis, A.; Kamuntavichius, G.
1996-01-01
A new method for calculation of shell model intrinsic density matrices, defined as two-particle density matrices integrated over the centre-of-mass position vector of two last particles and complemented with isospin variables, has been developed. The intrinsic density matrices obtained are completely antisymmetric, translation-invariant, and do not employ a group-theoretical classification of antisymmetric states. They are used for exact realistic density matrix expansion within the framework of the reduced Hamiltonian method. The procedures based on precise arithmetic for calculation of the intrinsic density matrices that involve no numerical diagonalization or orthogonalization have been developed and implemented in the computer code. (author). 11 refs., 2 tabs
Noble, J. H.; Lubasch, M.; Stevens, J.; Jentschura, U. D.
2017-12-01
We describe a matrix diagonalization algorithm for complex symmetric (not Hermitian) matrices, A ̲ =A̲T, which is based on a two-step algorithm involving generalized Householder reflections based on the indefinite inner product 〈 u ̲ , v ̲ 〉 ∗ =∑iuivi. This inner product is linear in both arguments and avoids complex conjugation. The complex symmetric input matrix is transformed to tridiagonal form using generalized Householder transformations (first step). An iterative, generalized QL decomposition of the tridiagonal matrix employing an implicit shift converges toward diagonal form (second step). The QL algorithm employs iterative deflation techniques when a machine-precision zero is encountered "prematurely" on the super-/sub-diagonal. The algorithm allows for a reliable and computationally efficient computation of resonance and antiresonance energies which emerge from complex-scaled Hamiltonians, and for the numerical determination of the real energy eigenvalues of pseudo-Hermitian and PT-symmetric Hamilton matrices. Numerical reference values are provided.
Ogawa, Yasuhiro
2016-02-25
Most radiation biologists/radiation oncologists have long accepted the concept that the biologic effects of radiation principally involve damage to deoxyribonucleic acid (DNA), which is the critical target, as described in "Radiobiology for the Radiologist", by E.J. Hall and A.J. Giaccia [1]. Although the concepts of direct and indirect effects of radiation are fully applicable to low-LET (linear energy transfer) radioresistant tumor cells/normal tissues such as osteosarcoma cells and chondrocytes, it is believed that radiation-associated damage to DNA does not play a major role in the mechanism of cell death in low-LET radiosensitive tumors/normal tissues such as malignant lymphoma cells and lymphocytes. Hall and Giaccia describe lymphocytes as very radiosensitive, based largely on apoptosis subsequent to irradiation. As described in this review, apoptosis of lymphocytes and lymphoma cells is actually induced by the "hydrogen peroxide (H₂O₂) effect", which I propose in this review article for the first time. The mechanism of lymphocyte death via the H₂O₂ effect represents an ideal model to develop the enhancement method of radiosensitivity for radiation therapy of malignant neoplasms. In terms of imitating the high radiosensitivity of lymphocytes, osteosarcoma cells (representative of low-LET radioresistant cells) might be the ideal model for indicating the conversion of cells from radioresistant to radiosensitive utilizing the H₂O₂ effect. External beam radiation such as X-rays and high-energy electrons for use in modern radiotherapy are generally produced using a linear accelerator. We theorized that when tumors are irradiated in the presence of H₂O₂, the activities of anti-oxidative enzymes such as peroxidases and catalase are blocked and oxygen molecules are produced at the same time via the H₂O₂ effect, resulting in oxidative damage to low-LET radioresistant tumor cells, thereby rendering them highly sensitive to irradiation. In this
Yasuhiro Ogawa
2016-02-01
Full Text Available Most radiation biologists/radiation oncologists have long accepted the concept that the biologic effects of radiation principally involve damage to deoxyribonucleic acid (DNA, which is the critical target, as described in “Radiobiology for the Radiologist”, by E.J. Hall and A.J. Giaccia [1]. Although the concepts of direct and indirect effects of radiation are fully applicable to low-LET (linear energy transfer radioresistant tumor cells/normal tissues such as osteosarcoma cells and chondrocytes, it is believed that radiation-associated damage to DNA does not play a major role in the mechanism of cell death in low-LET radiosensitive tumors/normal tissues such as malignant lymphoma cells and lymphocytes. Hall and Giaccia describe lymphocytes as very radiosensitive, based largely on apoptosis subsequent to irradiation. As described in this review, apoptosis of lymphocytes and lymphoma cells is actually induced by the “hydrogen peroxide (H2O2 effect”, which I propose in this review article for the first time. The mechanism of lymphocyte death via the H2O2 effect represents an ideal model to develop the enhancement method of radiosensitivity for radiation therapy of malignant neoplasms. In terms of imitating the high radiosensitivity of lymphocytes, osteosarcoma cells (representative of low-LET radioresistant cells might be the ideal model for indicating the conversion of cells from radioresistant to radiosensitive utilizing the H2O2 effect. External beam radiation such as X-rays and high-energy electrons for use in modern radiotherapy are generally produced using a linear accelerator. We theorized that when tumors are irradiated in the presence of H2O2, the activities of anti-oxidative enzymes such as peroxidases and catalase are blocked and oxygen molecules are produced at the same time via the H2O2 effect, resulting in oxidative damage to low-LET radioresistant tumor cells, thereby rendering them highly sensitive to irradiation. In this
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
Perturbation analysis of linear control problems
Petkov, Petko; Konstantinov, Mihail
2017-01-01
The paper presents a brief overview of the technique of splitting operators, proposed by the authors and intended for perturbation analysis of control problems involving unitary and orthogonal matrices. Combined with the technique of Lyapunov majorants and the implementation of the Banach and Schauder fixed point principles, it allows to obtain rigorous non-local perturbation bounds for a set of sensitivity analysis problems. Among them are the reduction of linear systems into orthogonal canonical forms, the feedback synthesis problem and pole assignment problem in particular, as well as other important problems in control theory and linear algebra. Key words: perturbation analysis, canonical forms, feedback synthesis
Korff, Christian
2003-01-01
The construction of auxiliary matrices for the six-vertex model at a root of unity is investigated from a quantum group theoretic point of view. Employing the concept of intertwiners associated with the quantum loop algebra U q (s-tilde l-tilde 2 ) at q N = 1, a three-parameter family of auxiliary matrices is constructed. The elements of this family satisfy a functional relation with the transfer matrix allowing one to solve the eigenvalue problem of the model and to derive the Bethe ansatz equations. This functional relation is obtained from the decomposition of a tensor product of evaluation representations and involves auxiliary matrices with different parameters. Because of this dependence on additional parameters, the auxiliary matrices break in general the finite symmetries of the six-vertex model, such as spin-reversal or spin-conservation. More importantly, they also lift the extra degeneracies of the transfer matrix due to the loop symmetry present at rational coupling values. The extra parameters in the auxiliary matrices are shown to be directly related to the elements in the enlarged centre Z of the algebra U q (s-tilde l-tilde 2 ) at q N = 1. This connection provides a geometric interpretation of the enhanced symmetry of the six-vertex model at rational coupling. The parameters labelling the auxiliary matrices can be interpreted as coordinates on a hypersurface Spec Z subset of C 4 which remains invariant under the action of an infinite-dimensional group G of analytic transformations, called the quantum coadjoint action
Extended linear chain compounds
Linear chain substances span a large cross section of contemporary chemistry ranging from covalent polymers, to organic charge transfer com plexes to nonstoichiometric transition metal coordination complexes. Their commonality, which coalesced intense interest in the theoretical and exper imental solid state physics/chemistry communities, was based on the obser vation that these inorganic and organic polymeric substrates exhibit striking metal-like electrical and optical properties. Exploitation and extension of these systems has led to the systematic study of both the chemistry and physics of highly and poorly conducting linear chain substances. To gain a salient understanding of these complex materials rich in anomalous aniso tropic electrical, optical, magnetic, and mechanical properties, the conver gence of diverse skills and talents was required. The constructive blending of traditionally segregated disciplines such as synthetic and physical organic, inorganic, and polymer chemistry, crystallog...
Reduction of Linear Programming to Linear Approximation
Vaserstein, Leonid N.
2006-01-01
It is well known that every Chebyshev linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to a Chebyshev linear approximation problem.
Freund, Roland
1988-01-01
Conjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.
Trupin-Wasselin, V
2000-07-11
The effect of ionizing radiations on aqueous solutions leads to water ionization and then to the formation of radical species and molecular products (e{sup -}{sub aq}, H{sup .}, OH{sup .}, H{sub 2}O{sub 2}, H{sub 2}). It has been shown that the stopping power, characterized by the LET value (Linear Energy Transfer) becomes different when the nature of the ionizing radiations is different. Few data are nowadays available for high LET radiations such as protons and high energy heavy ions. These particles have been used to better understand the primary processes in radiation chemistry. The yield of a chemical dosimeter (the Fricke dosimeter) and those of the hydrogen peroxide have been determined for different LET. The effect of the dose rate on the Fricke dosimeter yield and on the H{sub 2}O{sub 2} yield has been studied too. When the dose rate increases, an increase of the molecular products yield is observed. At very high dose rate, this yield decreases on account of the attack of the molecular products by radicals. The H{sub 2}O{sub 2} yield in alkaline medium decreases when the pH reaches 12. This decrease can be explained by a slowing down of the H{sub 2}O{sub 2} formation velocity in alkaline medium. Superoxide radical has also been studied in this work. A new detection method: the time-resolved chemiluminescence has been perfected for this radical. This technique is more sensitive than the absorption spectroscopy. Experiments with heavy ions have allowed to determine the O{sub 2}{sup .-} yield directly in the irradiation cell. The experimental results have been compared with those obtained with a Monte Carlo simulation code. (O.M.)
Equiangular tight frames and unistochastic matrices
Goyeneche, Dardo; Turek, Ondřej
2017-01-01
We demonstrate that a complex equiangular tight frame composed of N vectors in dimension d , denoted ETF ( d , N ), exists if and only if a certain bistochastic matrix, univocally determined by N and d , belongs to a special class of unistochastic matrices. This connection allows us to find new complex ETFs in infinitely many dimensions and to derive a method to introduce non-trivial free parameters in ETFs. We present an explicit six-parametric family of complex ETF(6,16), which defines a family of symmetric POVMs. Minimal and maximal possible average entanglement of the vectors within this qubit–qutrit family are described. Furthermore, we propose an efficient numerical procedure to compute the unitary matrix underlying a unistochastic matrix, which we apply to find all existing classes of complex ETFs containing up to 20 vectors. (paper)
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.
Sparse random matrices: The eigenvalue spectrum revisited
Semerjian, Guilhem; Cugliandolo, Leticia F.
2003-08-01
We revisit the derivation of the density of states of sparse random matrices. We derive a recursion relation that allows one to compute the spectrum of the matrix of incidence for finite trees that determines completely the low concentration limit. Using the iterative scheme introduced by Biroli and Monasson [J. Phys. A 32, L255 (1999)] we find an approximate expression for the density of states expected to hold exactly in the opposite limit of large but finite concentration. The combination of the two methods yields a very simple geometric interpretation of the tails of the spectrum. We test the analytic results with numerical simulations and we suggest an indirect numerical method to explore the tails of the spectrum. (author)
From Pauli Matrices to Quantum Ito Formula
Pautrat, Yan
2005-01-01
This paper answers important questions raised by the recent description, by Attal, of a robust and explicit method to approximate basic objects of quantum stochastic calculus on bosonic Fock space by analogues on the state space of quantum spin chains. The existence of that method justifies a detailed investigation of discrete-time quantum stochastic calculus. Here we fully define and study that theory and obtain in particular a discrete-time quantum Ito formula, which one can see as summarizing the commutation relations of Pauli matrices.An apparent flaw in that approximation method is the difference in the quantum Ito formulas, discrete and continuous, which suggests that the discrete quantum stochastic calculus differs fundamentally from the continuous one and is therefore not a suitable object to approximate subtle phenomena. We show that flaw is only apparent by proving that the continuous-time quantum Ito formula is actually a consequence of its discrete-time counterpart
Viscous hydrophilic injection matrices for serial crystallography
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
Semiparametric estimation of covariance matrices for longitudinal data.
Fan, Jianqing; Wu, Yichao
2008-12-01
Estimation of longitudinal data covariance structure poses significant challenges because the data are usually collected at irregular time points. A viable semiparametric model for covariance matrices was proposed in Fan, Huang and Li (2007) that allows one to estimate the variance function nonparametrically and to estimate the correlation function parametrically via aggregating information from irregular and sparse data points within each subject. However, the asymptotic properties of their quasi-maximum likelihood estimator (QMLE) of parameters in the covariance model are largely unknown. In the current work, we address this problem in the context of more general models for the conditional mean function including parametric, nonparametric, or semi-parametric. We also consider the possibility of rough mean regression function and introduce the difference-based method to reduce biases in the context of varying-coefficient partially linear mean regression models. This provides a more robust estimator of the covariance function under a wider range of situations. Under some technical conditions, consistency and asymptotic normality are obtained for the QMLE of the parameters in the correlation function. Simulation studies and a real data example are used to illustrate the proposed approach.
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.
Deterministic matrices matching the compressed sensing phase transitions of Gaussian random matrices
Monajemi, Hatef; Jafarpour, Sina; Gavish, Matan; Donoho, David L.; Ambikasaran, Sivaram; Bacallado, Sergio; Bharadia, Dinesh; Chen, Yuxin; Choi, Young; Chowdhury, Mainak; Chowdhury, Soham; Damle, Anil; Fithian, Will; Goetz, Georges; Grosenick, Logan
2012-01-01
In compressed sensing, one takes samples of an N-dimensional vector using an matrix A, obtaining undersampled measurements . For random matrices with independent standard Gaussian entries, it is known that, when is k-sparse, there is a precisely determined phase transition: for a certain region in the (,)-phase diagram, convex optimization typically finds the sparsest solution, whereas outside that region, it typically fails. It has been shown empirically that the same property—with the ...
Binary Positive Semidefinite Matrices and Associated Integer Polytopes
Letchford, Adam N.; Sørensen, Michael Malmros
2012-01-01
We consider the positive semidefinite (psd) matrices with binary entries, along with the corresponding integer polytopes. We begin by establishing some basic properties of these matrices and polytopes. Then, we show that several families of integer polytopes in the literature-the cut, boolean qua...
CONVERGENCE OF POWERS OF CONTROLLABLE INTUITIONISTIC FUZZY MATRICES
Riyaz Ahmad Padder; P. Murugadas
2016-01-01
Convergences of powers of controllable intuitionistic fuzzy matrices have been stud¬ied. It is shown that they oscillate with period equal to 2, in general. Some equalities and sequences of inequalities about powers of controllable intuitionistic fuzzy matrices have been obtained.
Propositional matrices as alternative representation of truth values ...
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 ...
Korff, C
2003-01-01
The construction of auxiliary matrices for the six-vertex model at a root of unity is investigated from a quantum group theoretic point of view. Employing the concept of intertwiners associated with the quantum loop algebra U sub q (s-tilde l-tilde sub 2) at q sup N = 1, a three-parameter family of auxiliary matrices is constructed. The elements of this family satisfy a functional relation with the transfer matrix allowing one to solve the eigenvalue problem of the model and to derive the Bethe ansatz equations. This functional relation is obtained from the decomposition of a tensor product of evaluation representations and involves auxiliary matrices with different parameters. Because of this dependence on additional parameters, the auxiliary matrices break in general the finite symmetries of the six-vertex model, such as spin-reversal or spin-conservation. More importantly, they also lift the extra degeneracies of the transfer matrix due to the loop symmetry present at rational coupling values. The extra pa...
Numerical linear algebra theory and applications
Beilina, Larisa; Karchevskii, Mikhail
2017-01-01
This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigen problems. Numerical algorithms illustrated by computer programs written in MATLAB® are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level.
Abel-grassmann's groupoids of modulo matrices
Javaid, Q.; Awan, M.D.; Naqvi, S.H.A.
2016-01-01
The binary operation of usual addition is associative in all matrices over R. However, a binary operation of addition in matrices over Z/sub n/ of a nonassociative structures of AG-groupoids and AG-groups are defined and investigated here. It is shown that both these structures exist for every integer n >≥ 3. Various properties of these structures are explored like: (i) Every AG-groupoid of matrices over Z/sub n/ is transitively commutative AG-groupoid and is a cancellative AG-groupoid if n is prime. (ii) Every AG-groupoid of matrices over Z/sub n/ of Type-II is a T/sup 3/-AG-groupoid. (iii) An AG-groupoid of matrices over Z/sub n/ ; G /sub nAG/(t,u), is an AG-band, if t+u=1(mod n). (author)
Stability and response bounds of non-conservative linear systems
Pommer, Christian
2003-01-01
For a linear system of second order differential equations the stability is studied by Lyapunov's direct method. The Lyapunov matrix equation is solved and a sufficient condition for stability is expressed by the system matrices. For a system which satisfies the condition for stability the Lyapunov...
TRANSFERENCE BEFORE TRANSFERENCE.
Bonaminio, Vincenzo
2017-10-01
This paper is predominantly a clinical presentation that describes the transmigration of one patient's transference to another, with the analyst functioning as a sort of transponder. It involves an apparently accidental episode in which there was an unconscious intersection between two patients. The author's aim is to show how transference from one case may affect transference in another, a phenomenon the author calls transference before transference. The author believes that this idea may serve as a tool for understanding the unconscious work that takes place in the clinical situation. In a clinical example, the analyst finds himself caught up in an enactment involving two patients in which he becomes the medium of what happens in session. © 2017 The Psychoanalytic Quarterly, Inc.
Tanwiwat Jaikuna
2017-02-01
Full Text Available Purpose: To develop an in-house software program that is able to calculate and generate the biological dose distribution and biological dose volume histogram by physical dose conversion using the linear-quadratic-linear (LQL model. Material and methods : The Isobio software was developed using MATLAB version 2014b to calculate and generate the biological dose distribution and biological dose volume histograms. The physical dose from each voxel in treatment planning was extracted through Computational Environment for Radiotherapy Research (CERR, and the accuracy was verified by the differentiation between the dose volume histogram from CERR and the treatment planning system. An equivalent dose in 2 Gy fraction (EQD2 was calculated using biological effective dose (BED based on the LQL model. The software calculation and the manual calculation were compared for EQD2 verification with pair t-test statistical analysis using IBM SPSS Statistics version 22 (64-bit. Results: Two and three-dimensional biological dose distribution and biological dose volume histogram were displayed correctly by the Isobio software. Different physical doses were found between CERR and treatment planning system (TPS in Oncentra, with 3.33% in high-risk clinical target volume (HR-CTV determined by D90%, 0.56% in the bladder, 1.74% in the rectum when determined by D2cc, and less than 1% in Pinnacle. The difference in the EQD2 between the software calculation and the manual calculation was not significantly different with 0.00% at p-values 0.820, 0.095, and 0.593 for external beam radiation therapy (EBRT and 0.240, 0.320, and 0.849 for brachytherapy (BT in HR-CTV, bladder, and rectum, respectively. Conclusions : The Isobio software is a feasible tool to generate the biological dose distribution and biological dose volume histogram for treatment plan evaluation in both EBRT and BT.
Computational aspects of linear control
2002-01-01
Many devices (we say dynamical systems or simply systems) behave like black boxes: they receive an input, this input is transformed following some laws (usually a differential equation) and an output is observed. The problem is to regulate the input in order to control the output, that is for obtaining a desired output. Such a mechanism, where the input is modified according to the output measured, is called feedback. The study and design of such automatic processes is called control theory. As we will see, the term system embraces any device and control theory has a wide variety of applications in the real world. Control theory is an interdisci plinary domain at the junction of differential and difference equations, system theory and statistics. Moreover, the solution of a control problem involves many topics of numerical analysis and leads to many interesting computational problems: linear algebra (QR, SVD, projections, Schur complement, structured matrices, localization of eigenvalues, computation of the...
Probing the Locality of Excited States with Linear Algebra.
Etienne, Thibaud
2015-04-14
This article reports a novel theoretical approach related to the analysis of molecular excited states. The strategy introduced here involves gathering two pieces of physical information, coming from Hilbert and direct space operations, into a general, unique quantum mechanical descriptor of electronic transitions' locality. Moreover, the projection of Hilbert and direct space-derived indices in an Argand plane delivers a straightforward way to visually probe the ability of a dye to undergo a long- or short-range charge-transfer. This information can be applied, for instance, to the analysis of the electronic response of families of dyes to light absorption by unveiling the trend of a given push-pull chromophore to increase the electronic cloud polarization magnitude of its main transition with respect to the size extension of its conjugated spacer. We finally demonstrate that all the quantities reported in this article can be reliably approximated by a linear algebraic derivation, based on the contraction of detachment/attachment density matrices from canonical to atomic space. This alternative derivation has the remarkable advantage of a very low computational cost with respect to the previously used numerical integrations, making fast and accurate characterization of large molecular systems' excited states easily affordable.
Andersen, Stig Kildegård; Carlsen, Henrik; Thomsen, Per Grove
2003-01-01
The objective of this study has been to create a model for studying effects of temperature fluctuations in regenerator matrices on Stirling engine performance. A one-dimensional model with axial discretisation of engine components has been formulated using a fixed Eulerian grid. The model contains...... that adjusts solutions so that they satisfy the necessary cyclic boundary conditions as well as integral conditions for cyclic heat transfer for walls in the engine and for the mean cycle pressure. It has been found that it is possible to accurately solve the stiff ODE system that describes the coupled...
a Continuous-Time Positive Linear System
Kyungsup Kim
2013-01-01
Full Text Available This paper discusses a computational method to construct positive realizations with sparse matrices for continuous-time positive linear systems with multiple complex poles. To construct a positive realization of a continuous-time system, we use a Markov sequence similar to the impulse response sequence that is used in the discrete-time case. The existence of the proposed positive realization can be analyzed with the concept of a polyhedral convex cone. We provide a constructive algorithm to compute positive realizations with sparse matrices of some positive systems under certain conditions. A sufficient condition for the existence of a positive realization, under which the proposed constructive algorithm works well, is analyzed.
Stochastic equivalent linearization in 3-D hysteretic frames
Casciati, F.; Faravelli, L.
1987-01-01
Stochastic equivalent linearization technique for hysteretic systems is extended to study the dynamic response of 3-D frames with hysteretic constitutive laws in the potential plastic hinges. The constitutive law is idealized by an appropriate endochronic model. A general purpose finite element code is adopted in order to generate the matrices by which the equations of motion to be linearized are built. (orig./HP)
Linear matrix differential equations of higher-order and applications
Mustapha Rachidi
2008-07-01
Full Text Available In this article, we study linear differential equations of higher-order whose coefficients are square matrices. The combinatorial method for computing the matrix powers and exponential is adopted. New formulas representing auxiliary results are obtained. This allows us to prove properties of a large class of linear matrix differential equations of higher-order, in particular results of Apostol and Kolodner are recovered. Also illustrative examples and applications are presented.
A turbulent mixing Reynolds stress model fitted to match linear interaction analysis predictions
Griffond, J; Soulard, O; Souffland, D
2010-01-01
To predict the evolution of turbulent mixing zones developing in shock tube experiments with different gases, a turbulence model must be able to reliably evaluate the production due to the shock-turbulence interaction. In the limit of homogeneous weak turbulence, 'linear interaction analysis' (LIA) can be applied. This theory relies on Kovasznay's decomposition and allows the computation of waves transmitted or produced at the shock front. With assumptions about the composition of the upstream turbulent mixture, one can connect the second-order moments downstream from the shock front to those upstream through a transfer matrix, depending on shock strength. The purpose of this work is to provide a turbulence model that matches LIA results for the shock-turbulent mixture interaction. Reynolds stress models (RSMs) with additional equations for the density-velocity correlation and the density variance are considered here. The turbulent states upstream and downstream from the shock front calculated with these models can also be related through a transfer matrix, provided that the numerical implementation is based on a pseudo-pressure formulation. Then, the RSM should be modified in such a way that its transfer matrix matches the LIA one. Using the pseudo-pressure to introduce ad hoc production terms, we are able to obtain a close agreement between LIA and RSM matrices for any shock strength and thus improve the capabilities of the RSM.
Dynamics of unsymmetric piecewise-linear/non-linear systems using finite elements in time
Wang, Yu
1995-08-01
The dynamic response and stability of a single-degree-of-freedom system with unsymmetric piecewise-linear/non-linear stiffness are analyzed using the finite element method in the time domain. Based on a Hamilton's weak principle, this method provides a simple and efficient approach for predicting all possible fundamental and sub-periodic responses. The stability of the steady state response is determined by using Floquet's theory without any special effort for calculating transition matrices. This method is applied to a number of examples, demonstrating its effectiveness even for a strongly non-linear problem involving both clearance and continuous stiffness non-linearities. Close agreement is found between available published findings and the predictions of the finite element in time approach, which appears to be an efficient and reliable alternative technique for non-linear dynamic response and stability analysis of periodic systems.
Litvinenko, Alexander
2017-09-26
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 Mat\\\\\\'ern 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.
Shun-ichi Amari
2014-04-01
Full Text Available Information geometry studies the dually flat structure of a manifold, highlighted by the generalized Pythagorean theorem. The present paper studies a class of Bregman divergences called the (ρ,τ-divergence. A (ρ,τ -divergence generates a dually flat structure in the manifold of positive measures, as well as in the manifold of positive-definite matrices. The class is composed of decomposable divergences, which are written as a sum of componentwise divergences. Conversely, a decomposable dually flat divergence is shown to be a (ρ,τ -divergence. A (ρ,τ -divergence is determined from two monotone scalar functions, ρ and τ. The class includes the KL-divergence, α-, β- and (α, β-divergences as special cases. The transformation between an affine parameter and its dual is easily calculated in the case of a decomposable divergence. Therefore, such a divergence is useful for obtaining the center for a cluster of points, which will be applied to classification and information retrieval in vision. For the manifold of positive-definite matrices, in addition to the dually flatness and decomposability, we require the invariance under linear transformations, in particular under orthogonal transformations. This opens a way to define a new class of divergences, called the (ρ,τ -structure in the manifold of positive-definite matrices.
Litvinenko, Alexander
2017-09-24
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 Mat\\\\\\'ern 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 ($\\\\mathcal{H}$-) 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.
Substituted amylose matrices for oral drug delivery
Moghadam, S H; Wang, H W; El-Leithy, E Saddar; Chebli, C; Cartilier, L
2007-01-01
High amylose corn starch was used to obtain substituted amylose (SA) polymers by chemically modifying hydroxyl groups by an etherification process using 1,2-epoxypropanol. Tablets for drug-controlled release were prepared by direct compression and their release properties assessed by an in vitro dissolution test (USP XXIII no 2). The polymer swelling was characterized by measuring gravimetrically the water uptake ability of polymer tablets. SA hydrophilic matrix tablets present sequentially a burst effect, typical of hydrophilic matrices, and a near constant release, typical of reservoir systems. After the burst effect, surface pores disappear progressively by molecular association of amylose chains; this allows the creation of a polymer layer acting as a diffusion barrier and explains the peculiar behaviour of SA polymers. Several formulation parameters such as compression force, drug loading, tablet weight and insoluble diluent concentration were investigated. On the other hand, tablet thickness, scanning electron microscope analysis and mercury intrusion porosimetry showed that the high crushing strength values observed for SA tablets were due to an unusual melting process occurring during tabletting although the tablet external layer went only through densification, deformation and partial melting. In contrast, HPMC tablets did not show any traces of a melting process
Neutrino mass matrices with vanishing determinant
Chauhan, Bhag C.; Pulido, Joao; Picariello, Marco
2006-01-01
We investigate the prospects for neutrinoless double beta decay, texture zeros. and equalities between neutrino mass matrix elements in scenarios with vanishing determinant mass matrices for vanishing and finite θ 13 mixing angles in normal and inverse mass hierarchies. For normal hierarchy and both zero and finite θ 13 it is found that neutrinoless double beta decay cannot be observed by any of the present or next generation experiments, while for inverse hierarchy it is, on the contrary, accessible to experiments. Regarding texture zeros and equalities between mass matrix elements, we find that in both normal and inverse hierarchies with θ 13 =0 no texture zeros nor any such equalities can exist apart from the obvious ones. For θ 13 ≠0 some texture zeros become possible. In normal hierarchy two texture zeros occur if 8.1x10 -2 ≤sinθ 13 ≤9.1x10 -2 while in inverse hierarchy three are possible, one with sinθ 13 ≥7x10 -3 and two others with sinθ 13 ≥0.18. All equalities between mass matrix elements are impossible with θ 13 ≠0
Calculating scattering matrices by wave function matching
Zwierzycki, M.; Khomyakov, P.A.; Starikov, A.A.; Talanana, M.; Xu, P.X.; Karpan, V.M.; Marushchenko, I.; Brocks, G.; Kelly, P.J.; Xia, K.; Turek, I.; Bauer, G.E.W.
2008-01-01
The conductance of nanoscale structures can be conveniently related to their scattering properties expressed in terms of transmission and reflection coefficients. Wave function matching (WFM) is a transparent technique for calculating transmission and reflection matrices for any Hamiltonian that can be represented in tight-binding form. A first-principles Kohn-Sham Hamiltonian represented on a localized orbital basis or on a real space grid has such a form. WFM is based upon direct matching of the scattering-region wave function to the Bloch modes of ideal leads used to probe the scattering region. The purpose of this paper is to give a pedagogical introduction to WFM and present some illustrative examples of its use in practice. We briefly discuss WFM for calculating the conductance of atomic wires, using a real space grid implementation. A tight-binding muffin-tin orbital implementation very suitable for studying spin-dependent transport in layered magnetic materials is illustrated by looking at spin-dependent transmission through ideal and disordered interfaces. (copyright 2008 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Probing the Topology of Density Matrices
Charles-Edouard Bardyn
2018-02-01
Full Text Available The mixedness of a quantum state is usually seen as an adversary to topological quantization of observables. For example, exact quantization of the charge transported in a so-called Thouless adiabatic pump is lifted at any finite temperature in symmetry-protected topological insulators. Here, we show that certain directly observable many-body correlators preserve the integrity of topological invariants for mixed Gaussian quantum states in one dimension. Our approach relies on the expectation value of the many-body momentum-translation operator and leads to a physical observable—the “ensemble geometric phase” (EGP—which represents a bona fide geometric phase for mixed quantum states, in the thermodynamic limit. In cyclic protocols, the EGP provides a topologically quantized observable that detects encircled spectral singularities (“purity-gap” closing points of density matrices. While we identify the many-body nature of the EGP as a key ingredient, we propose a conceptually simple, interferometric setup to directly measure the latter in experiments with mesoscopic ensembles of ultracold atoms.
Visualizing complex (hydrological) systems with correlation matrices
Haas, J. C.
2016-12-01
When trying to understand or visualize the connections of different aspects of a complex system, this often requires deeper understanding to start with, or - in the case of geo data - complicated GIS software. To our knowledge, correlation matrices have rarely been used in hydrology (e.g. Stoll et al., 2011; van Loon and Laaha, 2015), yet they do provide an interesting option for data visualization and analysis. We present a simple, python based way - using a river catchment as an example - to visualize correlations and similarities in an easy and colorful way. We apply existing and easy to use python packages from various disciplines not necessarily linked to the Earth sciences and can thus quickly show how different aquifers work or react, and identify outliers, enabling this system to also be used for quality control of large datasets. Going beyond earlier work, we add a temporal and spatial element, enabling us to visualize how a system reacts to local phenomena such as for example a river, or changes over time, by visualizing the passing of time in an animated movie. References: van Loon, A.F., Laaha, G.: Hydrological drought severity explained by climate and catchment characteristics, Journal of Hydrology 526, 3-14, 2015, Drought processes, modeling, and mitigation Stoll, S., Hendricks Franssen, H. J., Barthel, R., Kinzelbach, W.: What can we learn from long-term groundwater data to improve climate change impact studies?, Hydrology and Earth System Sciences 15(12), 3861-3875, 2011
Decellularized matrices for cardiovascular tissue engineering.
Moroni, Francesco; Mirabella, Teodelinda
2014-01-01
Cardiovascular disease (CVD) is one of the leading causes of death in the Western world. The replacement of damaged vessels and valves has been practiced since the 1950's. Synthetic grafts, usually made of bio-inert materials, are long-lasting and mechanically relevant, but fail when it comes to "biointegration". Decellularized matrices, instead, can be considered biological grafts capable of stimulating in vivo migration and proliferation of endothelial cells (ECs), recruitment and differentiation of mural cells, finally, culminating in the formation of a biointegrated tissue. Decellularization protocols employ osmotic shock, ionic and non-ionic detergents, proteolitic digestions and DNase/RNase treatments; most of them effectively eliminate the cellular component, but show limitations in preserving the native structure of the extracellular matrix (ECM). In this review, we examine the current state of the art relative to decellularization techniques and biological performance of decellularized heart, valves and big vessels. Furthermore, we focus on the relevance of ECM components, native and resulting from decellularization, in mediating in vivo host response and determining repair and regeneration, as opposed to graft corruption.
On some Toeplitz matrices and their inversions
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.
Moncouyoux, J.P.
1995-01-01
The confinement by vitrification of high-level radioactive wastes is studied in the CEA for fifteen years. These studies have lead to the preparation of glassy matrices by innovating processes. These processes can be applied to non-radioactive toxic materials treatment too. In this work are more particularly described the glassy matrix long-dated behaviour and the different vitrification processes used (by direct induction in cold crucible, by transferred arc plasma). (O.L.). 1 tab
Tavichakorntrakool, Ratree; Prasongwattana, Vitoon; Sungkeeree, Seksit; Saisud, Phitsamai; Sribenjalux, Pipat; Pimratana, Chaowat; Bovornpadungkitti, Sombat; Sriboonlue, Pote; Thongboonkerd, Visith
2012-11-01
Urinary tract infections are generally known to be associated with nephrolithiasis, particularly struvite stone, in which the most common microbe found is urea-splitting bacterium, i.e. Proteus mirabilis. However, our observation indicated that it might not be the case of stone formers in Thailand. We therefore extensively characterized microorganisms associated with all types of kidney stones. A total of 100 kidney stone formers (59 males and 41 females) admitted for elective percutaneous nephrolithotomy were recruited and microorganisms isolated from catheterized urine and cortex and nidus of their stones were analyzed. From 100 stone formers recruited, 36 cases had a total of 45 bacterial isolates cultivated from their catheterized urine and/or stone matrices. Among these 36 cases, chemical analysis by Fourier-transformed infrared spectroscopy revealed that 8 had the previously classified 'infection-induced stones', whereas the other 28 cases had the previously classified 'metabolic stones'. Calcium oxalate (in either pure or mixed form) was the most common and found in 64 and 75% of the stone formers with and without bacterial isolates, respectively. Escherichia coli was the most common bacterium (approximately one-third of all bacterial isolates) found in urine and stone matrices (both nidus and periphery). Linear regression analysis showed significant correlation (r = 0.860, P stone matrices. Multidrug resistance was frequently found in these isolated bacteria. Moreover, urea test revealed that only 31% were urea-splitting bacteria, whereas the majority (69%) had negative urea test. Our data indicate that microorganisms are associated with almost all chemical types of kidney stones and urea-splitting bacteria are not the major causative microorganisms found in urine and stone matrices of the stone formers in Thailand. These data may lead to rethinking and a new roadmap for future research regarding the role of microorganisms in kidney stone formation.
Dynamics with Matrices Possessing Kronecker Product Structure
Łoś, M.
2015-06-01
In this paper we present an application of Alternating Direction Implicit (ADI) algorithm for solution of non-stationary PDE-s using isogeometric finite element method. We show that ADI algorithm has a linear computational cost at every time step. We illustrate this approach by solving two example non-stationary three-dimensional problems using explicit Euler and Newmark time-stepping scheme: heat equation and linear elasticity equations for a cube. The stability of the simulation is controlled by monitoring the energy of the solution.
Dynamics with Matrices Possessing Kronecker Product Structure
Łoś, M.; Wó zniak, M.; Paszynśki, M.; Dalcin, L.; Calo, Victor M.
2015-01-01
In this paper we present an application of Alternating Direction Implicit (ADI) algorithm for solution of non-stationary PDE-s using isogeometric finite element method. We show that ADI algorithm has a linear computational cost at every time step. We illustrate this approach by solving two example non-stationary three-dimensional problems using explicit Euler and Newmark time-stepping scheme: heat equation and linear elasticity equations for a cube. The stability of the simulation is controlled by monitoring the energy of the solution.
Haiqing Zhang
2014-01-01
Full Text Available Satisfying consistency requirements of pairwise comparison matrix (PCM is a critical step in decision making methodologies. An algorithm has been proposed to find a new modified consistent PCM in which it can replace the original inconsistent PCM in analytic hierarchy process (AHP or in fuzzy AHP. This paper defines the modified consistent PCM by the original inconsistent PCM and an adjustable consistent PCM combined. The algorithm adopts a segment tree to gradually approach the greatest lower bound of the distance with the original PCM to obtain the middle value of an adjustable PCM. It also proposes a theorem to obtain the lower value and the upper value of an adjustable PCM based on two constraints. The experiments for crisp elements show that the proposed approach can preserve more of the original information than previous works of the same consistent value. The convergence rate of our algorithm is significantly faster than previous works with respect to different parameters. The experiments for fuzzy elements show that our method could obtain suitable modified fuzzy PCMs.
Information geometry of density matrices and state estimation
Brody, Dorje C
2011-01-01
Given a pure state vector |x) and a density matrix ρ-hat, the function p(x|ρ-hat)= defines a probability density on the space of pure states parameterised by density matrices. The associated Fisher-Rao information measure is used to define a unitary invariant Riemannian metric on the space of density matrices. An alternative derivation of the metric, based on square-root density matrices and trace norms, is provided. This is applied to the problem of quantum-state estimation. In the simplest case of unitary parameter estimation, new higher-order corrections to the uncertainty relations, applicable to general mixed states, are derived. (fast track communication)
Chain of matrices, loop equations and topological recursion
Orantin, Nicolas
2009-01-01
Random matrices are used in fields as different as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces. Both of them are based on the study of a matrix integral. However, this term can be confusing since the definition of a matrix integral in these two applications is not the same. These two definitions, perturbative and non-perturbative, are discussed in this chapter as well as their relation. The so-called loop equations satisfied by integrals over random matrices coupled in chain is discussed as well as their recursive solution in the perturbative case when the matrices are Hermitean.
M. De la Sen
2017-01-01
Full Text Available This paper formulates an “ad hoc” robust version under parametrical disturbances of the discrete version of the Kalman-Yakubovich-Popov Lemma for a class of positive hybrid dynamic linear systems which consist of a continuous-time system coupled with a discrete-time or a digital one. An extended discrete system, whose state vector contains both the digital one and the discretization of the continuous-time one at sampling instants, is a key analysis element in the formulation. The hyperstability and asymptotic hyperstability properties of the studied class of positive hybrid systems under feedback from any member of a nonlinear (and, eventually, time-varying class of controllers, which satisfies a Popov’s-type inequality, are also investigated as linked to the positive realness of the associated transfer matrices.
Miniature linear cooler development
Pruitt, G.R.
1993-01-01
An overview is presented of the status of a family of miniature linear coolers currently under development by Hughes Aircraft Co. for use in hand held, volume limited or power limited infrared applications. These coolers, representing the latest additions to the Hughes family of TOP trademark [twin-opposed piston] linear coolers, have been fabricated and tested in three different configurations. Each configuration is designed to utilize a common compressor assembly resulting in reduced manufacturing costs. The baseline compressor has been integrated with two different expander configurations and has been operated with two different levels of input power. These various configuration combinations offer a wide range of performance and interface characteristics which may be tailored to applications requiring limited power and size without significantly compromising cooler capacity or cooldown characteristics. Key cooler characteristics and test data are summarized for three combinations of cooler configurations which are representative of the versatility of this linear cooler design. Configurations reviewed include the shortened coldfinger [1.50 to 1.75 inches long], limited input power [less than 17 Watts] for low power availability applications; the shortened coldfinger with higher input power for lightweight, higher performance applications; and coldfingers compatible with DoD 0.4 Watt Common Module coolers for wider range retrofit capability. Typical weight of these miniature linear coolers is less than 500 grams for the compressor, expander and interconnecting transfer line. Cooling capacity at 80K at room ambient conditions ranges from 400 mW to greater than 550 mW. Steady state power requirements for maintaining a heat load of 150 mW at 80K has been shown to be less than 8 Watts. Ongoing reliability growth testing is summarized including a review of the latest test article results
Matrices over runtime systems at exascale
Agullo, Emmanuel; Bosilca, George; Bramas, Bé renger; Castagnede, Cedric; Coulaud, Olivier; Darve, Eric F.; Dongarra, Jack; Faverge, Mathieu; Furmento, Nathalie; Giraud, Luc; Lacoste, Xavier; Langou, Julien; Ltaief, Hatem; Messner, Matthias; Namyst, Raymond; Ramet, Pierre; Takahashi, Toru; Thibault, Samuel; Tomov, Stanimire Z.; Yamazaki, Ichitaro
2012-01-01
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
Lambda-matrices and vibrating systems
Lancaster, Peter
2002-01-01
Features aspects and solutions of problems of linear vibrating systems with a finite number of degrees of freedom. Starts with development of necessary tools in matrix theory, followed by numerical procedures for relevant matrix formulations and relevant theory of differential equations. Minimum of mathematical abstraction; assumes a familiarity with matrix theory, elementary calculus. 1966 edition.
Modular Extracellular Matrices: Solutions for the Puzzle
Serban, Monica A.; Prestwich, Glenn D.
2008-01-01
The common technique of growing cells in two-dimensions (2-D) is gradually being replaced by culturing cells on matrices with more appropriate composition and stiffness, or by encapsulation of cells in three-dimensions (3-D). The universal acceptance of the new 3-D paradigm has been constrained by the absence of a commercially available, biocompatible material that offers ease of use, experimental flexibility, and a seamless transition from in vitro to in vivo applications. The challenge – the puzzle that needs a solution – is to replicate the complexity of the native extracellular matrix (ECM) environment with the minimum number of components necessary to allow cells to rebuild and replicate a given tissue. For use in drug discovery, toxicology, cell banking, and ultimately in reparative medicine, the ideal matrix would therefore need to be highly reproducible, manufacturable, approvable, and affordable. Herein we describe the development of a set of modular components that can be assembled into biomimetic materials that meet these requirements. These semi-synthetic ECMs, or sECMs, are based on hyaluronan derivatives that form covalently crosslinked, biodegradable hydrogels suitable for 3-D culture of primary and stem cells in vitro, and for tissue formation in vivo. The sECMs can be engineered to provide appropriate biological cues needed to recapitulate the complexity of a given ECM environment. Specific applications for different sECM compositions include stem cell expansion with control of differentiation, scar-free wound healing, growth factor delivery, cell delivery for osteochondral defect and liver repair, and development of vascularized tumor xenografts for personalized chemotherapy. PMID:18442709
Comparison of eigensolvers for symmetric band matrices.
Moldaschl, Michael; Gansterer, Wilfried N
2014-09-15
We compare different algorithms for computing eigenvalues and eigenvectors of a symmetric band matrix across a wide range of synthetic test problems. Of particular interest is a comparison of state-of-the-art tridiagonalization-based methods as implemented in Lapack or Plasma on the one hand, and the block divide-and-conquer (BD&C) algorithm as well as the block twisted factorization (BTF) method on the other hand. The BD&C algorithm does not require tridiagonalization of the original band matrix at all, and the current version of the BTF method tridiagonalizes the original band matrix only for computing the eigenvalues. Avoiding the tridiagonalization process sidesteps the cost of backtransformation of the eigenvectors. Beyond that, we discovered another disadvantage of the backtransformation process for band matrices: In several scenarios, a lot of gradual underflow is observed in the (optional) accumulation of the transformation matrix and in the (obligatory) backtransformation step. According to the IEEE 754 standard for floating-point arithmetic, this implies many operations with subnormal (denormalized) numbers, which causes severe slowdowns compared to the other algorithms without backtransformation of the eigenvectors. We illustrate that in these cases the performance of existing methods from Lapack and Plasma reaches a competitive level only if subnormal numbers are disabled (and thus the IEEE standard is violated). Overall, our performance studies illustrate that if the problem size is large enough relative to the bandwidth, BD&C tends to achieve the highest performance of all methods if the spectrum to be computed is clustered. For test problems with well separated eigenvalues, the BTF method tends to become the fastest algorithm with growing problem size.
MATXTST, Basic Operations for Covariance Matrices
Geraldo, Luiz P.; Smith, Donald
1989-01-01
1 - Description of program or function: MATXTST and MATXTST1 perform the following operations for a covariance matrix: - test for singularity; - test for positive definiteness; - compute the inverse if the matrix is non-singular; - compute the determinant; - determine the number of positive, negative, and zero eigenvalues; - examine all possible 3 X 3 cross correlations within a sub-matrix corresponding to a leading principal minor which is non-positive definite. While the two programs utilize the same input, the calculational procedures employed are somewhat different and their functions are complementary. The available input options include: i) the full covariance matrix, ii) the basic variables plus the relative covariance matrix, or iii) uncertainties in the basic variables plus the correlation matrix. 2 - Method of solution: MATXTST employs LINPACK subroutines SPOFA and SPODI to test for positive definiteness and to perform further optional calculations. Subroutine SPOFA factors a symmetric matrix M using the Cholesky algorithm to determine the elements of a matrix R which satisfies the relation M=R'R, where R' is the transposed matrix of R. Each leading principal minor of M is tested until the first one is found which is not positive definite. MATXTST1 uses LINPACK subroutines SSICO, SSIFA, and SSIDI to estimate whether the matrix is near to singularity or not (SSICO), and to perform the matrix diagonalization process (SSIFA). The algorithm used in SSIFA is generalization of the Method of Lagrange Reduction. SSIDI is used to compute the determinant and inertia of the matrix. 3 - Restrictions on the complexity of the problem: Matrices of sizes up to 50 X 50 elements can be treated by present versions of the programs
Sosa, Natalia; Gerbino, Esteban; Golowczyc, Marina A.; Schebor, Carolina; Gómez-Zavaglia, Andrea; Tymczyszyn, E. Elizabeth
2016-01-01
In this work maltodextrins were added to commercial galacto-oligosaccharides (GOS) in a 1:1 ratio and their thermophysical characteristics were analyzed. GOS:MD solutions were then used as matrices during spray-drying of Lactobacillus plantarum CIDCA 83114. The obtained powders were equilibrated at different relative humidities (RH) and stored at 5 and 20°C for 12 weeks, or at 30°C for 6 weeks. The Tgs of GOS:MD matrices were about 20–30°C higher than those of GOS at RH within 11 and 52%. A linear relation between the spin-spin relaxation time (T2) and T-Tg parameter was observed for GOS:MD matrices equilibrated at 11, 22, 33, and 44% RH at 5, 20, and 30°C. Spray-drying of L. plantarum CIDCA 83114 in GOS:MD matrices allowed the recovery of 93% microorganisms. In contrast, only 64% microorganisms were recovered when no GOS were included in the dehydration medium. Survival of L. plantarum CIDCA 83114 during storage showed the best performance for bacteria stored at 5°C. In a further step, the slopes of the linear regressions provided information about the rate of microbial inactivation for each storage condition (k values). This information can be useful to calculate the shelf-life of spray-dried starters stored at different temperatures and RH. Using GOS:MD matrices as a dehydration medium enhanced the recovery of L. plantarum CIDCA 83114 after spray-drying. This strategy allowed for the first time the spray-drying stabilization of a potentially probiotic strain in the presence of GOS. PMID:27199918
Natalia eSosa
2016-05-01
Full Text Available In this work maltodextrins were added to commercial GOS in a 1:1 ratio and their thermophysical characteristics were analyzed. GOS:MD solutions were then used as matrices during spray-drying of L. plantarum CIDCA 83114. The obtained powders were equilibrated at different relative humidities (RH and stored at 5 and 20ºC for 12 weeks, or at 30ºC for 6 weeks.The Tgs of GOS:MD matrices were about 20-30oC higher than those of GOS at RH within 11 and 52%. A linear relation between the spin-spin relaxation time (T2 and T-Tg parameter was observed for GOS:MD matrices equilibrated at 11, 22, 33 and 44% RH at 5, 20 and 30ºC.Spray-drying of L. plantarum CIDCA 83114 in GOS:MD matrices allowed the recovery of 93% microorganisms. In contrast, only 64% microorganisms were recovered when no MD were included in the dehydration medium. Survival of L. plantarum CIDCA 83114 during storage showed the best performance for bacteria stored at 5oC. In a further step, the slopes of the linear regressions provided information about the rate of microbial inactivation for each storage condition (k values. This information can be useful to calculate the shelf-life of spray-dried starters stored at different temperatures and RH. Using GOS:MD matrices as a dehydration medium enhanced the recovery of L. plantarum CIDCA 83114 after spray-drying. This strategy allowed for the first time the spray-drying stabilization of a potentially probiotic strain in the presence of GOS.
Joint Estimation of Multiple Precision Matrices with Common Structures.
Lee, Wonyul; Liu, Yufeng
Estimation of inverse covariance matrices, known as precision matrices, is important in various areas of statistical analysis. In this article, we consider estimation of multiple precision matrices sharing some common structures. In this setting, estimating each precision matrix separately can be suboptimal as it ignores potential common structures. This article proposes a new approach to parameterize each precision matrix as a sum of common and unique components and estimate multiple precision matrices in a constrained l 1 minimization framework. We establish both estimation and selection consistency of the proposed estimator in the high dimensional setting. The proposed estimator achieves a faster convergence rate for the common structure in certain cases. Our numerical examples demonstrate that our new estimator can perform better than several existing methods in terms of the entropy loss and Frobenius loss. An application to a glioblastoma cancer data set reveals some interesting gene networks across multiple cancer subtypes.
Finiteness properties of congruence classes of infinite matrices
Eggermont, R.H.
2014-01-01
We look at spaces of infinite-by-infinite matrices, and consider closed subsets that are stable under simultaneous row and column operations. We prove that up to symmetry, any of these closed subsets is defined by finitely many equations.
Flexible Bayesian Dynamic Modeling of Covariance and Correlation Matrices
Lan, Shiwei; Holbrook, Andrew; Fortin, Norbert J.; Ombao, Hernando; Shahbaba, Babak
2017-01-01
Modeling covariance (and correlation) matrices is a challenging problem due to the large dimensionality and positive-definiteness constraint. In this paper, we propose a novel Bayesian framework based on decomposing the covariance matrix
A canonical form of the equation of motion of linear dynamical systems
Kawano, Daniel T.; Salsa, Rubens Goncalves; Ma, Fai; Morzfeld, Matthias
2018-03-01
The equation of motion of a discrete linear system has the form of a second-order ordinary differential equation with three real and square coefficient matrices. It is shown that, for almost all linear systems, such an equation can always be converted by an invertible transformation into a canonical form specified by two diagonal coefficient matrices associated with the generalized acceleration and displacement. This canonical form of the equation of motion is unique up to an equivalence class for non-defective systems. As an important by-product, a damped linear system that possesses three symmetric and positive definite coefficients can always be recast as an undamped and decoupled system.
Procrustes Problems for General, Triangular, and Symmetric Toeplitz Matrices
Juan Yang
2013-01-01
Full Text Available The Toeplitz Procrustes problems are the least squares problems for the matrix equation AX=B over some Toeplitz matrix sets. In this paper the necessary and sufficient conditions are obtained about the existence and uniqueness for the solutions of the Toeplitz Procrustes problems when the unknown matrices are constrained to the general, the triangular, and the symmetric Toeplitz matrices, respectively. The algorithms are designed and the numerical examples show that these algorithms are feasible.
An introduction to the theory of canonical matrices
Turnbull, H W
2004-01-01
Thorough and self-contained, this penetrating study of the theory of canonical matrices presents a detailed consideration of all the theory's principal features. Topics include elementary transformations and bilinear and quadratic forms; canonical reduction of equivalent matrices; subgroups of the group of equivalent transformations; and rational and classical canonical forms. The final chapters explore several methods of canonical reduction, including those of unitary and orthogonal transformations. 1952 edition. Index. Appendix. Historical notes. Bibliographies. 275 problems.
Dynamical correlations for circular ensembles of random matrices
Nagao, Taro; Forrester, Peter
2003-01-01
Circular Brownian motion models of random matrices were introduced by Dyson and describe the parametric eigenparameter correlations of unitary random matrices. For symmetric unitary, self-dual quaternion unitary and an analogue of antisymmetric Hermitian matrix initial conditions, Brownian dynamics toward the unitary symmetry is analyzed. The dynamical correlation functions of arbitrary number of Brownian particles at arbitrary number of times are shown to be written in the forms of quaternion determinants, similarly as in the case of Hermitian random matrix models
Complementary Set Matrices Satisfying a Column Correlation Constraint
Wu, Di; Spasojevic, Predrag
2006-01-01
Motivated by the problem of reducing the peak to average power ratio (PAPR) of transmitted signals, we consider a design of complementary set matrices whose column sequences satisfy a correlation constraint. The design algorithm recursively builds a collection of $2^{t+1}$ mutually orthogonal (MO) complementary set matrices starting from a companion pair of sequences. We relate correlation properties of column sequences to that of the companion pair and illustrate how to select an appropriate...
Open vessel microwave digestion of food matrices (T6)
Rhodes, L.; LeBlanc, G.
2002-01-01
Full text: Advancements in the field of open vessel microwave digestion continue to provide solutions for industries requiring acid digestion of large sample sizes. Those interesting in digesting food matrices are particularly interested in working with large amounts of sample and then diluting small final volumes. This paper will show the advantages of instantaneous regent addition and post-digestion evaporation when performing an open vessel digestion and evaporation methods for various food matrices will be presented along with analyte recovery data. (author)
Quantum Algorithms for Weighing Matrices and Quadratic Residues
van Dam, Wim
2000-01-01
In this article we investigate how we can employ the structure of combinatorial objects like Hadamard matrices and weighing matrices to device new quantum algorithms. We show how the properties of a weighing matrix can be used to construct a problem for which the quantum query complexity is ignificantly lower than the classical one. It is pointed out that this scheme captures both Bernstein & Vazirani's inner-product protocol, as well as Grover's search algorithm. In the second part of the ar...
Asymptotic Distribution of Eigenvalues of Weakly Dilute Wishart Matrices
Khorunzhy, A. [Institute for Low Temperature Physics (Ukraine)], E-mail: khorunjy@ilt.kharkov.ua; Rodgers, G. J. [Brunel University, Uxbridge, Department of Mathematics and Statistics (United Kingdom)], E-mail: g.j.rodgers@brunel.ac.uk
2000-03-15
We study the eigenvalue distribution of large random matrices that are randomly diluted. We consider two random matrix ensembles that in the pure (nondilute) case have a limiting eigenvalue distribution with a singular component at the origin. These include the Wishart random matrix ensemble and Gaussian random matrices with correlated entries. Our results show that the singularity in the eigenvalue distribution is rather unstable under dilution and that even weak dilution destroys it.