Kramerov, Dmitri A; Vassetzky, Nikita S
2011-01-01
Short interspersed elements (SINEs) are mobile genetic elements that invade the genomes of many eukaryotes. Since their discovery about 30 years ago, many gaps in our understanding of the biology and function of SINEs have been filled. This review summarizes the past and recent advances in the studies of SINEs. The structure and origin of SINEs as well as the processes involved in their amplification, transcription, RNA processing, reverse transcription, and integration of a SINE copy into the genome are considered. Then we focus on the significance of SINEs for the host genomes. While these genomic parasites can be deleterious to the cell, the long-term being in the genome has made SINEs a valuable source of genetic variation providing regulatory elements for gene expression, alternative splice sites, polyadenylation signals, and even functional RNA genes. Copyright © 2011 John Wiley & Sons, Ltd.
Approximate Implicitization Using Linear Algebra
Oliver J. D. Barrowclough
2012-01-01
Full Text Available We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD systems. We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms. We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.
Non-Linear Approximation of Bayesian Update
Litvinenko, Alexander
2016-06-23
We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.
Approximation Limits of Linear Programs (Beyond Hierarchies)
Braun, Gábor; Pokutta, Sebastian; Steurer, David
2012-01-01
We develop a framework for approximation limits of polynomial-size linear programs from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any linear program as opposed to only programs generated by hierarchies. Using our framework, we prove that O(n^{1/2-eps})-approximations for CLIQUE require linear programs of size 2^{n^\\Omega(eps)}. (This lower bound applies to linear programs using a certain encoding of CLIQUE as a linear optimization problem.) Moreover, we establish a similar result for approximations of semidefinite programs by linear programs. Our main ingredient is a quantitative improvement of Razborov's rectangle corruption lemma for the high error regime, which gives strong lower bounds on the nonnegative rank of certain perturbations of the unique disjointness matrix.
From B(a)cklund Transformation to a Linear System of Sine-Gordon Theory in Superspace
M. Siddiq; M. Hassan
2005-01-01
@@ A systematic approach is presented to find a linear system associated with the sine-Gordon equation from a given set of super Riccati systems. The Riccati system is shown to be related to the super B(a)cklund transformation and the linear eigenvalue problem.
Discrete cosine and sine transforms general properties, fast algorithms and integer approximations
Britanak, Vladimir; Rao, K R; Rao, K R
2006-01-01
The Discrete Cosine Transform (DCT) is used in many applications by the scientific, engineering and research communities and in data compression in particular. Fast algorithms and applications of the DCT Type II (DCT-II) have become the heart of many established international image/video coding standards. Since then other forms of the DCT and Discrete Sine Transform (DST) have been investigated in detail. This new edition presents the complete set of DCT and DST discrete trigonometric transforms, including their definitions, general mathematical properties, and relations to the optimal Karhune
Analytical Ballistic Trajectories with Approximately Linear Drag
Giliam J. P. de Carpentier
2014-01-01
Full Text Available This paper introduces a practical analytical approximation of projectile trajectories in 2D and 3D roughly based on a linear drag model and explores a variety of different planning algorithms for these trajectories. Although the trajectories are only approximate, they still capture many of the characteristics of a real projectile in free fall under the influence of an invariant wind, gravitational pull, and terminal velocity, while the required math for these trajectories and planners is still simple enough to efficiently run on almost all modern hardware devices. Together, these properties make the proposed approach particularly useful for real-time applications where accuracy and performance need to be carefully balanced, such as in computer games.
Spectral clustering based on local linear approximations
Arias-Castro, Ery; Lerman, Gilad
2010-01-01
In the context of clustering, we assume a generative model where each cluster is the result of sampling points in the neighborhood of an embedded smooth surface, possibly contaminated with outliers. We consider a prototype for a higher-order spectral clustering method based on the residual from a local linear approximation. In an asymptotic setting where the number of points becomes large, we obtain theoretical guaranties for this algorithm and show that, both in terms of separation and robustness to outliers, it outperforms the standard spectral clustering algorithm based on pairwise distances of Ng, Jordan and Weiss (NIPS, 2001). Under some conditions on the dimension of, and the incidence angle at, an intersection, the algorithm is able to recover the intersecting clusters. The optimal choice for some of the tuning parameters depends on the dimension and thickness of the clusters. We provide estimators that come close enough for our purposes. We discuss the cases of clusters of mixed dimensions and of clus...
Basicity of Systems of Sines with Linear Phase in Weighted Sobolev Spaces
V. F. Salmanov
2013-01-01
Full Text Available The perturbed systems of sines, which appear when solving some partial differential equations by the Fourier method, are considered in this paper. Basis properties of these systems in weighted Sobolev spaces of functions are studied.
Hydration thermodynamics beyond the linear response approximation
Raineri, Fernando O.
2016-10-01
The solvation energetics associated with the transformation of a solute molecule at infinite dilution in water from an initial state A to a final state B is reconsidered. The two solute states have different potentials energies of interaction, {{\\Psi}\\text{A}} and {{\\Psi}\\text{B}} , with the solvent environment. Throughout the A \\to B transformation of the solute, the solvation system is described by a Hamiltonian H≤ft(ξ \\right) that changes linearly with the coupling parameter ξ. By focusing on the characterization of the probability density {{\\wp}ξ}≤ft( y\\right) that the dimensionless perturbational solute-solvent interaction energy Y=β ≤ft({{\\Psi}\\text{B}}-{{\\Psi}\\text{A}}\\right) has numerical value y when the coupling parameter is ξ, we derive a hierarchy of differential equation relations between the ξ-dependent cumulant functions of various orders in the expansion of the appropriate cumulant generating function. On the basis of this theoretical framework we then introduce an inherently nonlinear solvation model for which we are able to find analytical results for both {{\\wp}ξ} ≤ft( y\\right) and for the solvation thermodynamic functions. The solvation model is based on the premise that there is an upper or a lower bound (depending on the nature of the interactions considered) to the amplitude of the fluctuations of Y in the solution system at equilibrium. The results reveal essential differences in behavior for the model when compared with the linear response approximation to solvation, particularly with regards to the probability density {{\\wp}ξ} ≤ft( y\\right) . The analytical expressions for the solvation properties show, however, that the linear response behavior is recovered from the new model when the room for the thermal fluctuations in Y is not restricted by the existence of a nearby bound. We compare the predictions of the model with the results from molecular dynamics computer simulations for aqueous solvation, in
Least Square Approximation by Linear Combinations of Multi(Poles).
1983-04-01
ID-R134 069 LEAST SQUARE APPROXIMATION BY LINEAR COMBINATIONS OF i/i MULTI(POLES). 1U OHIO STATE UNIV COLUMBUS DEPT OF GEODETIC SCIENCE AND SURVEY...TR-83-0 117 LEAST SQUARE APPROXIMATION BY LINEAR COMBINATIONS OF (MULTI)POLES WILLI FREEDEN DEPARTMENT OF GEODETIC SCIENCE AND SURVEYING THE OHIO...Subtitle) S. TYPE OF REPORT & PERIOD COVERED LEAST SQUARE APPROXIMATION BY LINEAR Scientific Report No. 3 COMBINATIONS OF (MULTI)POLES 6. PERFORMING ORG
The best simultaneous approximation in linear 2-normed spaces
Acikgoz, Mehmet
2012-01-01
In this paper, we shall investigate and analyse a new study on the best simultaneous approximation in the context of linear 2-normed spaces inspired by Elumalai and his coworkers in Elumalai. The basis of this investigation is to extend and refinement the definition of the classical aproximation, best approximation and some related concepts to linear 2-normed spaces.
CHARACTERIZATION OF BEST APPROXIMATIONS IN METRIC LINEAR SPACES
Sizwe Mabizela
2003-01-01
Let (X,d) be a real metric linear space, with translation-invariant metric d and G a linear subspace of X. In this paper we use functionals in the Lipschitz dual of X to characterize those elements of G which are best approximations to elements of X. We also give simultaneous characterization of elements of best approximation and also consider elements of e-approximation.
Linear approximation of the first eigenvalue on compact manifolds
CHEN; Mufa(陈木法); E.; Scacciatelli; YAO; Liang(姚亮)
2002-01-01
For compact, connected Riemannian manifolds with Ricci curvature bounded below by a constant, what is the linear approximation of the first eigenvalue of Laplacian? The answer is presented with computer assisted proof and the result is optimal in certain sense.
Approximate Method for Solving the Linear Fuzzy Delay Differential Equations
S. Narayanamoorthy
2015-01-01
Full Text Available We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.
Generating exact solutions to Einstein's equation using linearized approximations
Harte, Abraham I.; Vines, Justin
2016-10-01
We show that certain solutions to the linearized Einstein equation can—by the application of a particular type of linearized gauge transformation—be straightforwardly transformed into solutions of the exact Einstein equation. In cases with nontrivial matter content, the exact stress-energy tensor of the transformed metric has the same eigenvalues and eigenvectors as the linearized stress-energy tensor of the initial approximation. When our gauge exists, the tensorial structure of transformed metric perturbations identically eliminates all nonlinearities in Einstein's equation. As examples, we derive the exact Kerr and gravitational plane wave metrics from standard harmonic-gauge approximations.
Generating exact solutions to Einstein's equation using linearized approximations
Harte, Abraham I
2016-01-01
We show that certain solutions to the linearized Einstein equation can---by the application of a particular type of linearized gauge transformation---be straightforwardly transformed into solutions of the exact Einstein equation. In cases with nontrivial matter content, the exact stress-energy tensor of the transformed metric has the same eigenvalues and eigenvectors as the linearized stress-energy tensor of the initial approximation. When our gauge exists, the tensorial structure of transformed metric perturbations identically eliminates all nonlinearities in Einstein's equation. As examples, we derive the exact Kerr and gravitational plane wave metrics from standard harmonic-gauge approximations.
Semigroup theory and numerical approximation for equations in linear viscoelasticity
Fabiano, R. H.; Ito, K.
1990-01-01
A class of abstract integrodifferential equations used to model linear viscoelastic beams is investigated analytically, applying a Hilbert-space approach. The basic equation is rewritten as a Cauchy problem, and its well-posedness is demonstrated. Finite-dimensional subspaces of the state space and an estimate of the state operator are obtained; approximation schemes for the equations are constructed; and the convergence is proved using the Trotter-Kato theorem of linear semigroup theory. The actual convergence behavior of different approximations is demonstrated in numerical computations, and the results are presented in tables.
Linear approximation for measurement errors in phase shifting interferometry
van Wingerden, Johannes; Frankena, Hans J.; Smorenburg, Cornelis
1991-07-01
This paper shows how measurement errors in phase shifting interferometry (PSI) can be described to a high degree of accuracy in a linear approximation. System error sources considered here are light source instability, imperfect reference phase shifting, mechanical vibrations, nonlinearity of the detector, and quantization of the detector signal. The measurement inaccuracies resulting from these errors are calculated in linear approximation for several formulas commonly used for PSI. The results are presented in tables for easy calculation of the measurement error magnitudes for known system errors. In addition, this paper discusses the measurement error reduction which can be achieved by choosing an appropriate phase calculation formula.
Linear low-rank approximation and nonlinear dimensionality reduction
ZHANG Zhenyue; ZHA Hongyuan
2004-01-01
We present our recent work on both linear and nonlinear data reduction methods and algorithms: for the linear case we discuss results on structure analysis of SVD of column-partitioned matrices and sparse low-rank approximation; for the nonlinear case we investigate methods for nonlinear dimensionality reduction and manifold learning. The problems we address have attracted great deal of interest in data mining and machine learning.
The Log-Linear Return Approximation, Bubbles, and Predictability
Engsted, Tom; Pedersen, Thomas Quistgaard; Tanggaard, Carsten
2012-01-01
We study in detail the log-linear return approximation introduced by Campbell and Shiller (1988a). First, we derive an upper bound for the mean approximation error, given stationarity of the log dividend-price ratio. Next, we simulate various rational bubbles which have explosive conditional....... Finally, we show that a bubble model in which expected returns are constant can explain the predictability of stock returns from the dividend-price ratio that many previous studies have documented....
Iterative linear system solvers with approximate matrix-vector products
Eshof, J. van den; Sleijpen, G.L.G.; Gijzen, M.B. van
2003-01-01
There are classes of linear problems for which a matrix-vector product is a time consuming operation because an expensive approximation method is required to compute it to a given accuracy. One important example is simulations in lattice QCD with Neuberger fermions where a matrix multiply
Non-Linear Integral Equation and excited-states scaling functions in the sine-Gordon model
Destri, C
1997-01-01
The NLIE (the non-linear integral equation equivalent to the Bethe Ansatz equations for finite size) is generalized to excited states, that is states with holes and complex roots over the antiferromagnetic ground state. We consider the sine-Gordon/massive Thirring model (sG/mT) in a periodic box of length L using the light-cone approach, in which the sG/mT model is obtained as the continuum limit of an inhomogeneous six vertex model. This NLIE is an useful starting point to compute the spectrum of excited states both analytically in the large L (perturbative) and small L (conformal) regimes as well as numerically. We derive the conformal weights of the Bethe states with holes and non-string complex roots (close and wide roots) in the UV limit. These weights agree with the Coulomb gas description, yielding a UV conformal spectrum related by duality to the IR conformal spectrum of the six vertex model.
Optimal approximation of linear systems by artificial immune response
无
2006-01-01
This paper puts forward a novel artificial immune response algorithm for optimal approximation of linear systems. A quaternion model of artificial immune response is proposed for engineering computing. The model abstracts four elements, namely, antigen, antibody, reaction rules among antibodies, and driving algorithm describing how the rules are applied to antibodies, to simulate the process of immune response. Some reaction rules including clonal selection rules, immunological memory rules and immune regulation rules are introduced. Using the theorem of Markov chain, it is proofed that the new model is convergent. The experimental study on the optimal approximation of a stable linear system and an unstable one show that the approximate models searched by the new model have better performance indices than those obtained by some existing algorithms including the differential evolution algorithm and the multi-agent genetic algorithm.
Born approximation in linear-time invariant system
Gumjudpai, Burin
2015-01-01
Linear-time invariant (LTI) oscillation systems such as forced mechanical vibration, series RLC and parallel RLC circuits can be solved by using simplest initial conditions or employing of Green's function of which knowledge of initial condition of the force term is needed. Here we show a mathematical connection of the LTI system and the Helmholtz equation form of the time-independent Schr\\"{o}dinger equation in quantum mechanical scattering problem. We apply Born approximation in quantum mechanics to obtain LTI general solution in form of infinite Born series which can be expressed as a series of one-dimensional Feynman graphs. Conditions corresponding to the approximation are given for the case of harmonic driving force. The Born series of the harmonic forced oscillation case are derived by directly applying the approximation to the LTI system or by transforming the LTI system to Helmholtz equation prior to doing the approximation.
Generalised quasi-linear approximation of the HMRI
Child, Adam; Marston, Brad; Tobias, Steven
2016-01-01
Motivated by recent advances in Direct Statistical Simulation (DSS) of astrophysical phenomena such as out of equilibrium jets, we perform a Direct Numerical Simulation (DNS) of the helical magnetorotational instability (HMRI) under the generalised quasilinear approximation (GQL). This approximation generalises the quasilinear approximation (QL) to include the self-consistent interaction of large-scale modes, interpolating between fully nonlinear DNS and QL DNS whilst still remaining formally linear in the small scales. In this paper we address whether GQL can more accurately describe low-order statistics of axisymmetric HMRI when compared with QL by performing DNS under various degrees of GQL approximation. We utilise various diagnostics, such as energy spectra in addition to first and second cumulants, for calculations performed for a range of Reynolds and Hartmann numbers (describing rotation and imposed magnetic field strength respectively). We find that GQL performs significantly better than QL in descri...
Optimal Piecewise-Linear Approximation of the Quadratic Chaotic Dynamics
J. Petrzela
2012-04-01
Full Text Available This paper shows the influence of piecewise-linear approximation on the global dynamics associated with autonomous third-order dynamical systems with the quadratic vector fields. The novel method for optimal nonlinear function approximation preserving the system behavior is proposed and experimentally verified. This approach is based on the calculation of the state attractor metric dimension inside a stochastic optimization routine. The approximated systems are compared to the original by means of the numerical integration. Real electronic circuits representing individual dynamical systems are derived using classical as well as integrator-based synthesis and verified by time-domain analysis in Orcad Pspice simulator. The universality of the proposed method is briefly discussed, especially from the viewpoint of the higher-order dynamical systems. Future topics and perspectives are also provided
A Linear-Time Approximation of the Earth Mover's Distance
Jang, Min-Hee; Faloutsos, Christos; Park, Sunju
2011-01-01
Color descriptors are one of the important features used in content-based image retrieval. The Dominant Color Descriptor (DCD) represents a few perceptually dominant colors in an image through color quantization. For image retrieval based on DCD, the earth mover's distance and the optimal color composition distance are proposed to measure the dissimilarity between two images. Although providing good retrieval results, both methods are too time-consuming to be used in a large image database. To solve the problem, we propose a new distance function that calculates an approximate earth mover's distance in linear time. To calculate the dissimilarity in linear time, the proposed approach employs the space-filling curve for multidimensional color space. To improve the accuracy, the proposed approach uses multiple curves and adjusts the color positions. As a result, our approach achieves order-of-magnitude time improvement but incurs small errors. We have performed extensive experiments to show the effectiveness and...
Linear approximation model network and its formation via evolutionary computation
Yun Li; Kay Chen Tan
2000-04-01
To overcome the deficiency of `local model network' (LMN) techniques, an alternative `linear approximation model' (LAM) network approach is proposed. Such a network models a nonlinear or practical system with multiple linear models fitted along operating trajectories, where individual models are simply networked through output or parameter interpolation. The linear models are valid for the entire operating trajectory and hence overcome the local validity of LMN models, which impose the predetermination of a scheduling variable that predicts characteristic changes of the nonlinear system. LAMs can be evolved fromsampled step response data directly, eliminating the need forlocal linearisation upon a pre-model using derivatives of the nonlinear system. The structural difference between a LAM network and an LMN isthat the overall model of the latteris a parameter-varying system and hence nonlinear,while the formerremains linear time-invariant (LTI). Hence, existing LTI and transfer function theory applies to a LAM network, which is therefore easy to use for control system design. Validation results show that the proposed method offers a simple, transparent and accurate multivariable modelling technique for nonlinear systems.
Stochastic analysis of Chemical Reaction Networks using Linear Noise Approximation.
Cardelli, Luca; Kwiatkowska, Marta; Laurenti, Luca
2016-11-01
Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analyzed through solving the Chemical Master Equation (CME) or performing extensive simulations. Analysing stochasticity is often needed, particularly when some molecules occur in low numbers. Unfortunately, both approaches become infeasible if the system is complex and/or it cannot be ensured that initial populations are small. We develop a probabilistic logic for CRNs that enables stochastic analysis of the evolution of populations of molecular species. We present an approximate model checking algorithm based on the Linear Noise Approximation (LNA) of the CME, whose computational complexity is independent of the population size of each species and polynomial in the number of different species. The algorithm requires the solution of first order polynomial differential equations. We prove that our approach is valid for any CRN close enough to the thermodynamical limit. However, we show on four case studies that it can still provide good approximation even for low molecule counts. Our approach enables rigorous analysis of CRNs that are not analyzable by solving the CME, but are far from the deterministic limit. Moreover, it can be used for a fast approximate stochastic characterization of a CRN.
Linear $\\Sigma$ Model in the Gaussian Functional Approximation
Nakamura, I
2001-01-01
We apply a self-consistent relativistic mean-field variational ``Gaussian functional'' (or Hartree) approximation to the linear $\\sigma$ model with spontaneously and explicitly broken chiral O(4) symmetry. We set up the self-consistency, or ``gap'' and the Bethe-Salpeter equations. We check and confirm the chiral Ward-Takahashi identities, among them the Nambu-Goldstone theorem and the (partial) axial current conservation [CAC], both in and away from the chiral limit. With explicit chiral symmetry breaking we confirm the Dashen relation for the pion mass and partial CAC. We solve numerically the gap and Bethe-Salpeter equations, discuss the solutions' properties and the particle content of the theory.
Goal-oriented reduced basis approximation for linear elastodynamic problems
Hoang, Khac Chi; Bordas, Stephane P A
2013-01-01
In this paper, we study numerically the linear damped second-order hyperbolic partial differential equation (PDE) with affine parameter dependence using a goal-oriented approach by finite element (FE) and reduced basis (RB) methods. The main contribution of this paper is the "goal-oriented" proper orthogonal decomposition (POD)-Greedy sampling procedure within the RB approximation context. This proposed procedure makes use of the information of the solution of the associated dual (or adjoint) problem and the primal residual similarly to the well-known dual-weighted residual (DWR) technique developed earlier. First, we introduce the RB recipe: Galerkin projection onto a space $Y_N$ spanned by solutions of the governing PDE at $N$ selected points in parameter space. This set of $N$ parameter points is constructed very optimally by the proposed goal-oriented POD-Greedy sampling procedure. Second, based on the affine parameter dependence, we make use of the offline-online computational procedures: in the offline ...
Linear low-rank approximation and nonlinear dimensionality reduction
无
2004-01-01
［1］Bishop, C. M., Svensen, M., Williams, C. K. I., GTM: the generative topographic mapping, Neural Computation,1998, 10: 215-234.［2］Freedman, D., Efficient simplicial reconstructions of manifolds from their samples, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2002, 24: 1349-1357.［3］Hinton, G., Roweis, S., Stochastic neighbor embedding, Neural Information Processing Systems, 2003, 15:833-840.［4］Kohonen, T., Self-organizing Maps, 3rd ed., Berlin: Springer-Verlag, 2000.［5］Ramsay, J. O., Silverman, B. W., Applied Functional Data Analysis, Berlin: Springer-Verlag, 2002.［6］Roweis, S., Saul, L., Nonlinear dimensionality reduction by locally linear embedding, Science, 2000, 290:2323-2326.［7］Tenenbaum, J., De Silva, V., Langford, J., A global geometric framework for nonlinear dimension reduction,Science, 2000, 290:2319-2323.［8］Xu, G., Kailath, T., Fast subspace decompsotion, IEEE Transactions on Signal Processing, 1994, 42: 539-551.［9］Xu, G., Zha, H., Golub, G. et al., Fast algorithms for updating signal subspaces, IEEE Transactions on Circuits and Systems, 1994, 41: 537-549.［10］Zha, H., Marques, O., Simon, H., Large-scale SVD and subspace-based methods for information retrieval, Proceedings of Irregular '98, Lecture Notes in Computer Science, 1998, 1457: 29-42.［11］Zhang, Z., Zha, H., Structure and perturbation analysis of truncated SVDs for column-partitioned matrices,SIAM Journal on Matrix Analysis and Applications, 2001, 22: 1245-1262.［12］Zhang, Z., Zha, H., Simon, H., Low-rank approximations with sparse factors I: basic algorithms and error analysis, SIAM Journal on Matrix Analysis and Applications, 2002, 23: 706-727.［13］Stewart, G. W., Four algorithms for the efficient computation of truncated pivoted QR approximation to a sparse matrix, Numerische Mathematik, 1999, 83:313-323.［14］Golub, G., Van Loan, C., Matrix Computations, 3nd ed., Baltimore, Maryland: Johns Hopkins University Press,1996.
Approximate Solution Methods for Linear Stochastic Difference Equations. I. Moments
Roerdink, J.B.T.M.
1983-01-01
The cumulant expansion for linear stochastic differential equations is extended to the case of linear stochastic difference equations. We consider a vector difference equation, which contains a deterministic matrix A0 and a random perturbation matrix A1(t). The expansion proceeds in powers of ατc, w
Time signal filtering by relative neighborhood graph localized linear approximation
Sørensen, John Aasted
1994-01-01
A time signal filtering algorithm based on the relative neighborhood graph (RNG) used for localization of linear filters is proposed. The filter is constructed from a training signal during two stages. During the first stage an RNG is constructed. During the second stage, localized linear filters...
H2-optimal approximation of MIMO linear dynamical systems
Van Dooren, Paul; Absil, P -A
2008-01-01
We consider the problem of approximating a multiple-input multiple-output (MIMO) $p\\times m$ rational transfer function $H(s)$ of high degree by another $p\\times m$ rational transfer function $\\hat H(s)$ of much smaller degree, so that the ${\\cal H}_2$ norm of the approximation error is minimized. We characterize the stationary points of the ${\\cal H}_2$ norm of the approximation error by tangential interpolation conditions and also extend these results to the discrete-time case. We analyze whether it is reasonable to assume that lower-order models can always be approximated arbitrarily closely by imposing only first-order interpolation conditions. Finally, we analyze the ${\\cal H}_2$ norm of the approximation error for a simple case in order to illustrate the complexity of the minimization problem.
Approximate inverse preconditioning of iterative methods for nonsymmetric linear systems
Benzi, M. [Universita di Bologna (Italy); Tuma, M. [Inst. of Computer Sciences, Prague (Czech Republic)
1996-12-31
A method for computing an incomplete factorization of the inverse of a nonsymmetric matrix A is presented. The resulting factorized sparse approximate inverse is used as a preconditioner in the iterative solution of Ax = b by Krylov subspace methods.
Weighted least squares stationary approximations to linear systems.
Bierman, G. J.
1972-01-01
Investigation of the problem of replacing a certain time-varying linear system by a stationary one. Several quadratic criteria are proposed to aid in determining suitable candidate systems. One criterion for choosing the matrix B (in the stationary system) is initial-condition dependent, and another bounds the 'worst case' homogeneous system performance. Both of these criteria produce weighted least square fits.
An inhomogeneous wave equation and non-linear Diophantine approximation
Beresnevich, V.; Dodson, M. M.; Kristensen, S.;
2008-01-01
A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution...... is studied. Both the Lebesgue and Hausdorff measures of this set are obtained....
An Adaptive Linear Approximation Algorithm for Copositive Programs
Bundfuss, Stefan; Dur, Mirjam
2009-01-01
We study linear optimization problems over the cone of copositive matrices. These problems appear in nonconvex quadratic and binary optimization; for instance, the maximum clique problem and other combinatorial problems can be reformulated as such problems. We present new polyhedral inner and outer
Optimal angle reduction - a behavioral approach to linear system approximation
Roorda, Berend; Fuhrmann, P.A.
2001-01-01
We investigate the problem of optimal state reduction under minimization of the angle between system behaviors. The angle is defined in a worst-case sense, as the largest angle that can occur between a system trajectory and its optimal approximation in the reduced-order model. This problem is analyz
Locally linear approximation for Kernel methods : the Railway Kernel
Muñoz, Alberto; González, Javier
2008-01-01
In this paper we present a new kernel, the Railway Kernel, that works properly for general (nonlinear) classification problems, with the interesting property that acts locally as a linear kernel. In this way, we avoid potential problems due to the use of a general purpose kernel, like the RBF kernel, as the high dimension of the induced feature space. As a consequence, following our methodology the number of support vectors is much lower and, therefore, the generalization capability of the pr...
The Nonclassical Diffusion Approximation to the Nonclassical Linear Boltzmann Equation
Vasques, Richard
2015-01-01
We show that, by correctly selecting the probability distribution function $p(s)$ for a particle's distance-to-collision, the nonclassical diffusion equation can be represented exactly by the nonclassical linear Boltzmann equation for an infinite homogeneous medium. This choice of $p(s)$ preserves the $true$ mean-squared free path of the system, which sheds new light on the results obtained in previous work.
Error Analysis on Plane-to-Plane Linear Approximate Coordinate Transformation
Q. F. Zhang; Q. Y. Peng; J. H. Fan
2014-09-01
In this paper, the error analysis has been done for the linear approximate transformation between two tangent planes in celestial sphere in a simple case. The results demonstrate that the error from the linear transformation does not meet the requirement of high-precision astrometry under some conditions, so the linear approximate transformation should be taken seriously.
Functional noncoding sequences derived from SINEs in the mammalian genome.
Nishihara, Hidenori; Smit, Arian F A; Okada, Norihiro
2006-07-01
Recent comparative analyses of mammalian sequences have revealed that a large number of nonprotein-coding genomic regions are under strong selective constraint. Here, we report that some of these loci have been derived from a newly defined family of ancient SINEs (short interspersed repetitive elements). This is a surprising result, as SINEs and other transposable elements are commonly thought to be genomic parasites. We named the ancient SINE family AmnSINE1, for Amniota SINE1, because we found it to be present in mammals as well as in birds, and some copies predate the mammalian-bird split 310 million years ago (Mya). AmnSINE1 has a chimeric structure of a 5S rRNA and a tRNA-derived SINE, and is related to five tRNA-derived SINE families that we characterized here in the coelacanth, dogfish shark, hagfish, and amphioxus genomes. All of the newly described SINE families have a common central domain that is also shared by zebrafish SINE3, and we collectively name them the DeuSINE (Deuterostomia SINE) superfamily. Notably, of the approximately 1000 still identifiable copies of AmnSINE1 in the human genome, 105 correspond to loci phylogenetically highly conserved among mammalian orthologs. The conservation is strongest over the central domain. Thus, AmnSINE1 appears to be the best example of a transposable element of which a significant fraction of the copies have acquired genomic functionality.
Ito, Kazufumi; Teglas, Russell
1987-01-01
The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.
Ito, K.; Teglas, R.
1984-01-01
The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.
A. Kitipongwatana
2014-06-01
Full Text Available In this article, an excited oscillator which is analyzed by using a multi-time linear analytical model is proposed. An obtained closed-form solution can be exploited not only to explain phenomena in the beat and locked states that are mostly studied in literature but also in an additional state called the non-locked state. With the proposed analysis, it is found that the non-locked state of the oscillator behaves similarly to the up-conversion process. It provides a new point-of-view to the phase noise oscillator. Moreover, our principle indicates that the important factor defining the behavior in each state and state transition is the transfer function of the system. The proposed mathematical model is verified by the experimental and numerical results.
正弦型非线性调频键控及性能分析%Approach to sine non-linear chirp keying modulation and performance analysis
孙志国; 曹雪; 周彬; 宁晓燕; 熊磊
2013-01-01
以正弦型非线性调频信号为载波样本,提出一种非单频波带通调制方法——正弦型非线性调频键控(sine non-linear chirp keying,SNCK).通过调整时间-带宽积和频率变化曲线频率等参数,SNCK可实现满足不同信道环境和服务质量需求的无线通信.同时,由于采用非单频波作为载波样本,SNCK具有较好的多普勒频移抑制能力.构建SNCK的数学模型,分析已调信号正交化设计方法、频域特征及信道适应能力等性能.理论分析和实验结果表明:相较于甚小线性调频键控,SNCK具有相近的高白噪声抑制能力和频域能量集中度；相较于最小频移键控,SNCK具有更强的多普勒频移抑制能力.SNCK可作为通信终端高速率运动场景下的变速率无线通信系统的带通调制方案.%A new kind of non-single frequency wave band pass modulation method named sine non-linear chirp keying (SNCK) is proposed which uses sinusoidal non-linear chirp signals as carriers. Adjusting parame-ters such as time-bandwidth product or the frequencies of frequency variation curve, SNCK can be used in wire-less communication systems with different qualities of service or channel characters. More importantly, SNCK has a strong ability to suppress Doppler frequency shift by using non-single frequency wave as carriers. The mathematical model of SNCK is set up, the design method of orthogonalization is given, and the performances, such as frequency domain energy concentration of modulation signals and adaptabilities of channels, are ana-lyzed. Theoretical analysis and experimental results show that SNCK has the same suppression ability of aver-age Gaussian white noise and frequency domain energy concentration compared with the very minimum chirp ke-ying (VMCK), and a stronger Doppler frequency shift suppression ability than the minimum shift keying (MSK). SNCK can be used as a kind of band pass modulation scheme for variable rate wireless communication
Atomic core-ionization energies; approximately piecewise-linear and linear relationships
Avery, James Emil; Avery, John Scales
2008-01-01
In the Generalized Sturmian Method, solutions to the many-particle Schr\\"odinger equation are built up from isoenergetic sets of solutions to an approximate Schr\\"odinger equation with a weighted potential $\\beta_\
Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes
Zhang, H.W.; Schäffer, Hemming Andreas
2007-01-01
An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....
Approximate controllability of infinite dimensional linear systems in nonreflexive state spaces
Xin YU; Chao XU
2005-01-01
This paper deals with the problem of approximate controllability of infinite dimensional linear systems in nonreflexive state spaces.A necessary and sufficient condition for approximate controllability via Lp([0,T],U),1≤p<∞ is obtained,where Lp([0,T],U) is the control function space.
Gibson, J. S.; Rosen, I. G.
1988-01-01
An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.
Approximation of Functions of Two Variables by Certain Linear Positive Operators
Fatma Taşdelen; Ali Olgun; Gülen Bascanbaz-Tunca
2007-08-01
We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using modulus of continuity. Moreover we define an th order generalization of these operators and observe its approximation properties. Furthermore, we study the convergence of the linear positive operators in a weighted space of functions of two variables and find the rate of this convergence using weighted modulus of continuity.
Fixed-dimensional parallel linear programming via relative {Epsilon}-approximations
Goodrich, M.T.
1996-12-31
We show that linear programming in IR{sup d} can be solved deterministically in O((log log n){sup d}) time using linear work in the PRAM model of computation, for any fixed constant d. Our method is developed for the CRCW variant of the PRAM parallel computation model, and can be easily implemented to run in O(log n(log log n){sup d-1}) time using linear work on an EREW PRAM. A key component in these algorithms is a new, efficient parallel method for constructing E-nets and E-approximations (which have wide applicability in computational geometry). In addition, we introduce a new deterministic set approximation for range spaces with finite VC-exponent, which we call the {delta}-relative {epsilon}-approximation, and we show how such approximations can be efficiently constructed in parallel.
Vladimirov, Igor G
2012-01-01
This paper extends the energy-based version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential equations with non-quadratic Hamiltonians. The linearization proceeds by approximating the actual Hamiltonian of the quantum system by a quadratic function of its observables which corresponds to the Hamiltonian of a quantum harmonic oscillator. This approximation is carried out in a mean square optimal sense with respect to a Gaussian reference quantum state and leads to a self-consistent linearization procedure where the mean vector and quantum covariance matrix of the system observables evolve in time according to the effective linear dynamics. We demonstrate the proposed Hamiltonian-based Gaussian linearization for the quantum Duffing oscillator whose Hamiltonian is a quadro-quartic polynomial of the momentum and position operators. The results of the paper are applicable t...
Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures
Gibson, J. S.; Adamian, A.
1988-01-01
An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.
Potential function methods for approximately solving linear programming problems theory and practice
Bienstock, Daniel
2002-01-01
Potential Function Methods For Approximately Solving Linear Programming Problems breaks new ground in linear programming theory. The book draws on the research developments in three broad areas: linear and integer programming, numerical analysis, and the computational architectures which enable speedy, high-level algorithm design. During the last ten years, a new body of research within the field of optimization research has emerged, which seeks to develop good approximation algorithms for classes of linear programming problems. This work both has roots in fundamental areas of mathematical programming and is also framed in the context of the modern theory of algorithms. The result of this work, in which Daniel Bienstock has been very much involved, has been a family of algorithms with solid theoretical foundations and with growing experimental success. This book will examine these algorithms, starting with some of the very earliest examples, and through the latest theoretical and computational developments.
Linear Time Approximation Schemes for the Gale-Berlekamp Game and Related Minimization Problems
Karpinski, Marek
2008-01-01
We design a linear time approximation scheme for the Gale-Berlekamp Switching Game and generalize it to a wider class of dense fragile minimization problems including the Nearest Codeword Problem (NCP) and Unique Games Problem. Further applications include, among other things, finding a constrained form of matrix rigidity and maximum likelihood decoding of an error correcting code. As another application of our method we give the first linear time approximation schemes for correlation clustering with a fixed number of clusters and its hierarchical generalization. Our results depend on a new technique for dealing with small objective function values of optimization problems and could be of independent interest.
Pladdy, Christopher; Nerayanuru, Sreenivasa M.; Fimoff, Mark; Özen, Serdar; Zoltowski, Michael
2004-01-01
We present a low complexity approximate method for semi-blind best linear unbiased estimation (BLUE) of a channel impulse response vector (CIR) for a communication system, which utilizes a periodically transmitted training sequence, within a continuous stream of information symbols. The algorithm achieves slightly degraded results at a much lower complexity than directly computing the BLUE CIR estimate. In addition, the inverse matrix required to invert the weighted normal equations to solve ...
Approximation of the solution of certain nonlinear ODEs with linear complexity
Dratman, Ezequiel
2010-03-01
We study the positive stationary solutions of a standard finite-difference discretization of the semilinear heat equation with nonlinear Neumann boundary conditions. We prove that there exists a unique solution of such a discretization, which approximates the unique positive stationary solution of the "continuous" equation. Furthermore, we exhibit an algorithm computing an [epsilon]-approximation of such a solution by means of a homotopy continuation method. The cost of our algorithm is linear in the number of nodes involved in the discretization and the logarithm of the number of digits of approximation required.
The Cosmic Linear Anisotropy Solving System (CLASS). Part II: Approximation schemes
Blas, Diego; Lesgourgues, Julien [Institut de Théorie des Phénomènes Physiques, École Polytechnique Fédérale de Lausanne, CH-1015, Lausanne (Switzerland); Tram, Thomas, E-mail: diego.blas@epfl.ch, E-mail: julien.lesgourgues@cern.ch, E-mail: tram@phys.au.dk [CERN, Theory Division, CH-1211 Geneva 23 (Switzerland)
2011-07-01
Boltzmann codes are used extensively by several groups for constraining cosmological parameters with Cosmic Microwave Background and Large Scale Structure data. This activity is computationally expensive, since a typical project requires from 10{sup 4} to 10{sup 5} Boltzmann code executions. The newly released code CLASS (Cosmic Linear Anisotropy Solving System) incorporates improved approximation schemes leading to a simultaneous gain in speed and precision. We describe here the three approximations used by CLASS for basic ΛCDM models, namely: a baryon-photon tight-coupling approximation which can be set to first order, second order or to a compromise between the two; an ultra-relativistic fluid approximation which had not been implemented in public distributions before; and finally a radiation streaming approximation taking reionisation into account.
Moses, Tim
2013-01-01
The purpose of this study was to evaluate the use of adjoined and piecewise linear approximations (APLAs) of raw equipercentile equating functions as a postsmoothing equating method. APLAs are less familiar than other postsmoothing equating methods (i.e., cubic splines), but their use has been described in historical equating practices of…
Approximation of a switched linear system by a nonswitched homogeneous polynomial system
无
2006-01-01
It is shown that given a switched linear control system which satisfy the controllability rank condition, it is possible to construct a non-switched homogenous polynomial control system in such a way that the trajectories of the latter may be arbitrarily well approximated norm on finite time intervals.
Bose-Einstein Condensation in Linear Sigma Model at Hartree Approximation
M. Agop; SHU Song; Camelia Popa; LI Jia-Rong; Anca Harabagiu
2008-01-01
The BEC of charged pions is investigated in the framework of O(4) linear sigma model. By using Cornwall Jackiw Tomboulis formalism, we have derived the gap equations for the effective masses of the mesons at finite tempera-ture and finite isospin density. The critical temperature and phase diagram of BEC are discussed in the non-chiral limit at Hartree approximation.
Approximate solutions of non-linear circular orbit relative motion in curvilinear coordinates
Bombardelli, Claudio; Gonzalo, Juan Luis; Roa, Javier
2016-07-01
A compact, time-explicit, approximate solution of the highly non-linear relative motion in curvilinear coordinates is provided under the assumption of circular orbit for the chief spacecraft. The rather compact, three-dimensional solution is obtained by algebraic manipulation of the individual Keplerian motions in curvilinear, rather than Cartesian coordinates, and provides analytical expressions for the secular, constant and periodic terms of each coordinate as a function of the initial relative motion conditions or relative orbital elements. Numerical test cases are conducted to show that the approximate solution can be effectively employed to extend the classical linear Clohessy-Wiltshire solution to include non-linear relative motion without significant loss of accuracy up to a limit of 0.4-0.45 in eccentricity and 40-45° in relative inclination for the follower. A very simple, quadratic extension of the classical Clohessy-Wiltshire solution in curvilinear coordinates is also presented.
Approximate solutions of non-linear circular orbit relative motion in curvilinear coordinates
Bombardelli, Claudio; Gonzalo, Juan Luis; Roa, Javier
2017-01-01
A compact, time-explicit, approximate solution of the highly non-linear relative motion in curvilinear coordinates is provided under the assumption of circular orbit for the chief spacecraft. The rather compact, three-dimensional solution is obtained by algebraic manipulation of the individual Keplerian motions in curvilinear, rather than Cartesian coordinates, and provides analytical expressions for the secular, constant and periodic terms of each coordinate as a function of the initial relative motion conditions or relative orbital elements. Numerical test cases are conducted to show that the approximate solution can be effectively employed to extend the classical linear Clohessy-Wiltshire solution to include non-linear relative motion without significant loss of accuracy up to a limit of 0.4-0.45 in eccentricity and 40-45° in relative inclination for the follower. A very simple, quadratic extension of the classical Clohessy-Wiltshire solution in curvilinear coordinates is also presented.
Near-linear time medial axis approximation of smooth curves in $\\mathbb{R}^3$
Christian Scheffer
2016-10-01
Full Text Available We present the first algorithm to approximate the medial axis $M_{\\gamma}$ of a smooth, closed curve $\\gamma \\subset \\mathbb{R}^3$ in near-linear time. Our algorithm works on a sufficiently dense \\eps-sample and comes with a convergence guarantee for the non-discrete, but continuous approximation object. As our approach also works correctly for a set of curves, we discuss the following application of the medial axis: The medial axis of two curves $\\gamma_1$ and $\\gamma_2$ can be applied to compute piecewise-linear simplifications of $\\gamma_1$ and $\\gamma_2$. In particular, a controllable tradeoff between the degree of simplification and the degree of falsification of the summed Fr\\'{e}chet distance between $\\gamma_1$ and $\\gamma_2$ is obtained. Finally, we show that for simplifying $\\gamma_1$ and $\\gamma_2$, our approximation, instead of $M_{\\gamma}$, can be applied while guaranteeing the same result.
SINEs as driving forces in genome evolution.
Schmitz, J
2012-01-01
SINEs are short interspersed elements derived from cellular RNAs that repetitively retropose via RNA intermediates and integrate more or less randomly back into the genome. SINEs propagate almost entirely vertically within their host cells and, once established in the germline, are passed on from generation to generation. As non-autonomous elements, their reverse transcription (from RNA to cDNA) and genomic integration depends on the activity of the enzymatic machinery of autonomous retrotransposons, such as long interspersed elements (LINEs). SINEs are widely distributed in eukaryotes, but are especially effectively propagated in mammalian species. For example, more than a million Alu-SINE copies populate the human genome (approximately 13% of genomic space), and few master copies of them are still active. In the organisms where they occur, SINEs are a challenge to genomic integrity, but in the long term also can serve as beneficial building blocks for evolution, contributing to phenotypic heterogeneity and modifying gene regulatory networks. They substantially expand the genomic space and introduce structural variation to the genome. SINEs have the potential to mutate genes, to alter gene expression, and to generate new parts of genes. A balanced distribution and controlled activity of such properties is crucial to maintaining the organism's dynamic and thriving evolution.
A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces
Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at [University of Innsbruck, Department of Mathematics (Austria); Tuffaha, Amjad, E-mail: atufaha@aus.edu [American University of Sharjah, Department of Mathematics (United Arab Emirates)
2017-06-15
We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solution of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.
Maximum error-bounded Piecewise Linear Representation for online stream approximation
Xie, Qing
2014-04-04
Given a time series data stream, the generation of error-bounded Piecewise Linear Representation (error-bounded PLR) is to construct a number of consecutive line segments to approximate the stream, such that the approximation error does not exceed a prescribed error bound. In this work, we consider the error bound in L∞ norm as approximation criterion, which constrains the approximation error on each corresponding data point, and aim on designing algorithms to generate the minimal number of segments. In the literature, the optimal approximation algorithms are effectively designed based on transformed space other than time-value space, while desirable optimal solutions based on original time domain (i.e., time-value space) are still lacked. In this article, we proposed two linear-time algorithms to construct error-bounded PLR for data stream based on time domain, which are named OptimalPLR and GreedyPLR, respectively. The OptimalPLR is an optimal algorithm that generates minimal number of line segments for the stream approximation, and the GreedyPLR is an alternative solution for the requirements of high efficiency and resource-constrained environment. In order to evaluate the superiority of OptimalPLR, we theoretically analyzed and compared OptimalPLR with the state-of-art optimal solution in transformed space, which also achieves linear complexity. We successfully proved the theoretical equivalence between time-value space and such transformed space, and also discovered the superiority of OptimalPLR on processing efficiency in practice. The extensive results of empirical evaluation support and demonstrate the effectiveness and efficiency of our proposed algorithms.
An Automated Algorithm for Approximation of Temporal Video Data Using Linear B'EZIER Fitting
Murtaza Ali Khan
2010-05-01
Full Text Available This paper presents an efficient method for approximation of temporal video data using linear Bezierfitting. For a given sequence of frames, the proposed method estimates the intensity variations of eachpixel in temporal dimension using linear Bezier fitting in Euclidean space. Fitting of each segmentensures upper bound of specified mean squared error. Break and fit criteria is employed to minimize thenumber of segments required to fit the data. The proposed method is well suitable for lossy compressionof temporal video data and automates the fitting process of each pixel. Experimental results show that theproposed method yields good results both in terms of objective and subjective quality measurementparameters without causing any blocking artifacts.
Linear power spectra in cold+hot dark matter models analytical approximations and applications
Ma Chung Pei
1996-01-01
This paper presents simple analytic approximations to the linear power spectra, linear growth rates, and rms mass fluctuations for both components in a family of cold+hot dark matter (CDM+HDM) models that are of current cosmological interest. The formulas are valid for a wide range of wavenumber, neutrino fraction, redshift, and Hubble constant: k\\lo 10\\,h Mpc^{-1}, 0.05\\lo \\onu\\lo 0.3, 0\\le z\\lo 15, and 0.5\\lo h \\lo 0.8. A new, redshift-dependent shape parameter \\Gamma_\
The O(N) linear sigma model at finite temperature beyond the Hartree approximation
Baacke, J
2003-01-01
We study the O(N) linear sigma model with spontaneous symmetry breaking, using a Hartree-like ansatz with a classical field and variational masses. We go beyond the Hartree approximation by including the two-loop contribution, the sunset diagram, using the 2PPI expansion. We have computed numerically the effective potential at finite temperature. We find a phase transition of second order, while it is first order in the one-loop Hartree approximation. We also discuss some implications of the fact that in this order, the decay of the sigma into two pions affects the thermal diagrams.
O(N) linear sigma model beyond the Hartree approximation at finite temperature
Baacke, J; Michalski, Stefan
2003-01-01
We study the O(N) linear sigma model with spontaneous symmetry breaking at finite temperature in the framework of the two-particle point-irreducible (2PPI) effective action. We go beyond the Hartree approximation by including the two-loop contribution, i.e., the sunset diagram. A phase transition of second order is found, whereas it is of first order in the one-loop Hartree approximation. Furthermore, we show the temperature-dependence of the variational mass parameters and comment on their relation to the physical sigma and pion masses.
Derrida, Bernard; Hakim, Vincent; Zeitak, Reuven
1996-09-01
The fraction r\\(t\\) of spins which have never flipped up to time t is studied within a linear diffusion approximation to phase ordering. Numerical simulations show that r\\(t\\) decays with time like a power law with a nontrivial exponent θ which depends on the space dimension. The dynamics is a special case of a stationary Gaussian process of known correlation function. The exponent θ is given by the asymptotic decay of the probability distribution of intervals between consecutive zero crossings. An approximation based on the assumption that successive zero crossings are independent random variables gives values of θ in close agreement with the results of simulations.
Pedro Mayorga
2016-11-01
Full Text Available Linear systems with tridiagonal structures are very common in problems related not only to engineering, but chem-istry, biomedical or finance, for example, real time cubic B-Spline interpolation of ND-images, real time processing of Electrocardio-graphy (ECG and hand drawing recognition. In those problems which the matrix is positive definite, it is possible to optimize the solution in O(n?? time. This paper describes such systems whose size grows over time and proposes an approximation in ???????? time of such systems based on a series of previous approximations. In addition, it is described the development of the method and is proved that the proposed solution converges linearly to the optimal. A real-time cubic B-Spline interpolation of an ECG is computed with this proposal, for this application the proposed method shows a global relative error near to ????-6 and its computation is faster than traditional methods, as shown in the experiments.
Analyses of Valid Range for the Linear Approximation in a Single-Mode Laser
CHENGQing-Hua; CAOLi; WANGJun; WUDa-Jin
2004-01-01
Using the linear approximation method, we calculated the steady-state mean normalized intensity fluctuation for a loss-noise model of a single-mode laser driven by a pump noise and a quantum noise, whose real part and imaginary part are cross-correlated. We analyzed the valid range for the linear approximation method by studying the influences on the steady-state mean normalized intensity fluctuation by the cross-correlation coefficient, the intensities of the quantum and pump noise, the net gain, and the amplitude and frequency of the input signal, and we found that the valid range becomes wider when the cross-correlation between the real and imaginary part of quantum noise is weaker, the noise intensities of quantum and pump are weaker, the laser system is far from the threshold and the signal has smaller amplitude and higher frequency.
TAO Liang; LUO Bin
2005-01-01
An efficient algorithm for the representation and approximation of linear time-varying systems is presented via the fast real-valued discrete Gabor transform. Compared with the existing algorithm based on the traditional complex-valued discrete Gabor transform, the proposed algorithm runs faster, can more easily be implemented in software or hardware, and leads to a more compact representation. Simulation results are given for demonstration.
无
2006-01-01
A new method of resolving overlapped peak, Fourier self-deconvolution (FSD) using approximation CN obtained from frequency domain wavelet transform of F(ω) yielded by Fourier transform of overlapped peak signals f(t) as the linear function, was presented in this paper.Compared with classical FSD, the new method exhibits excellent resolution for different overlapped peak signals such as HPLC signals, and have some characteristics such as an extensive applicability for any overlapped peak shape signals and a simple operation because of no selection procedure of the linear function. Its excellent resolution for those different overlapped peak signals is mainly because F(ω) obtained from Fourier transform of f(t) and CN obtained from wavelet transform of F(ω) have the similar linearity and peak width. The effect of those fake peaks can be eliminated by the algorithm proposed by authors. This method has good potential in the process of different overlapped peak signals.
Yunfeng Wu
2014-01-01
Full Text Available This paper presents a novel adaptive linear and normalized combination (ALNC method that can be used to combine the component radial basis function networks (RBFNs to implement better function approximation and regression tasks. The optimization of the fusion weights is obtained by solving a constrained quadratic programming problem. According to the instantaneous errors generated by the component RBFNs, the ALNC is able to perform the selective ensemble of multiple leaners by adaptively adjusting the fusion weights from one instance to another. The results of the experiments on eight synthetic function approximation and six benchmark regression data sets show that the ALNC method can effectively help the ensemble system achieve a higher accuracy (measured in terms of mean-squared error and the better fidelity (characterized by normalized correlation coefficient of approximation, in relation to the popular simple average, weighted average, and the Bagging methods.
d'Eon, Eugene
2013-01-01
We derive new diffusion solutions to the monoenergetic generalized linear Boltzmann transport equation (GLBE) for the stationary collision density and scalar flux about an isotropic point source in an infinite $d$-dimensional absorbing medium with isotropic scattering. We consider both classical transport theory with exponentially-distributed free paths in arbitrary dimensions as well as a number of non-classical transport theories (non-exponential random flights) that describe a broader class of transport processes within partially-correlated random media. New rigorous asymptotic diffusion approximations are derived where possible. We also generalize Grosjean's moment-preserving approach of separating the first (or uncollided) distribution from the collided portion and approximating only the latter using diffusion. We find that for any spatial dimension and for many free-path distributions Grosjean's approach produces compact, analytic approximations that are, overall, more accurate for high absorption and f...
RCS estimation of linear and planar dipole phased arrays approximate model
Singh, Hema; Jha, Rakesh Mohan
2016-01-01
In this book, the RCS of a parallel-fed linear and planar dipole array is derived using an approximate method. The signal propagation within the phased array system determines the radar cross section (RCS) of phased array. The reflection and transmission coefficients for a signal at different levels of the phased-in scattering array system depend on the impedance mismatch and the design parameters. Moreover the mutual coupling effect in between the antenna elements is an important factor. A phased array system comprises of radiating elements followed by phase shifters, couplers, and terminating load impedance. These components lead to respective impedances towards the incoming signal that travels through them before reaching receive port of the array system. In this book, the RCS is approximated in terms of array factor, neglecting the phase terms. The mutual coupling effect is taken into account. The dependence of the RCS pattern on the design parameters is analyzed. The approximate model is established as a...
Approximate linear confidence and curvature of a kinetic model of dodecanedioic acid in humans.
Panunzi, Simona; De Gaetano, Andrea; Mingrone, Geltrude
2005-11-01
Dicarboxylic acids with an even number of carbon atoms have been proposed as an alternate energy substrate for enteral or parenteral nutrition in the acutely ill patient, due to their water solubility and their yielding TCA cycle intermediates upon beta-oxidation. In the present work, a nonlinear compartmental model of the kinetics of dodecanedioic acid is developed, and its parameters are estimated from time concentration experimental observations obtained from six healthy volunteers undergoing a per os administration of 3 g of the substance. Although the model is linear in the transfer of the free substance from plasma to the tissues, the exchange between gut and plasma compartments is represented as a saturable function. Albumin binding is then incorporated to obtain the final model in terms of the measured total concentrations. Estimates of the model's structural parameters were computed for each experimental subject, and the usual single-subject approximate confidence regions for the parameters were derived by inversion of the Hessian at the optimum. To verify the applicability of this approximation, the nonlinearity of the expectation surface at the optimum was measured by computing the normal (intrinsic) component of curvature. Because the model curvature was excessive in all subjects, the usual approximation could not be trusted to provide acceptable approximations to the parameter confidence regions. A suitable Monte Carlo simulation yielded empirical joint parameter distributions from which the approximate parameter variances could finally be obtained.
The Signal Generator of Triphase Sine Wave
RAOMin; MAOSaofu
2003-01-01
In the process of developing and adjusting the product in this project, we need some signal sources, which usually afford square or sine wave. Generally the square ware is used for digit logic, but for the analog signal wave is used to judge the linearity's qualities and other functions of the electric circuit. However the common ready-made signal sourceis all unidirectional sine wave, the signal sources whose phase shift can arbitrarily be regulatedand which have precise phase are still not available one the current market.
AN AUTOMATED ALGORITHM FOR APPROXIMATION OF TEMPORAL VIDEO DATA USING LINEAR BEZIER FITTING
Murtaza Ali Khan
2010-05-01
Full Text Available This paper presents an efficient method for approximation of temporal video data using linear Bezier fitting. For a given sequence of frames, the proposed method estimates the intensity variations of each pixel in temporal dimension using linear Bezier fitting in Euclidean space. Fitting of each segment ensures upper bound of specified mean squared error. Break and fit criteria is employed to minimize the number of segments required to fit the data. The proposed method is well suitable for lossy compression of temporal video data and automates the fitting process of each pixel. Experimental results show that the proposed method yields good results both in terms of objective and subjective quality measurement parameters without causing any blocking artifacts.
The dynamics of a spinning particle in a linear in spin Hamiltonian approximation
Lukes-Gerakopoulos, Georgios; Patsis, Panos A; Seyrich, Jonathan
2016-01-01
We investigate for order and chaos the dynamical system of a spinning test particle of mass $m$ moving in the spacetime background of a Kerr black hole of mass M. This system is approximated in our investigation by the linear in spin Hamiltonian function provided in [E. Barausse, and A. Buonanno, Phys.Rev. D 81, 084024 (2010)]. We study the corresponding phase space by using 2D projections on a surface of section and the method of color and rotation on a 4D Poincar\\'e section. Various topological structures coming from the non-integrability of the linear in spin Hamiltonian are found and discussed. Moreover, an interesting result is that from the value of the dimensionless spin $S/(m M)=10^{-4}$ of the particle and below, the impact of the non-integrability of the system on the motion of the particle seems to be negligible.
MetaSINEs: Broad Distribution of a Novel SINE Superfamily in Animals
Nishihara, Hidenori; Plazzi, Federico; Passamonti, Marco; Okada, Norihiro
2016-01-01
SINEs (short interspersed elements) are transposable elements that typically originate independently in each taxonomic clade (order/family). However, some SINE families share a highly similar central sequence and are thus categorized as a SINE superfamily. Although only four SINE superfamilies (CORE-SINEs, V-SINEs, DeuSINEs, and Ceph-SINEs) have been reported so far, it is expected that new SINE superfamilies would be discovered by deep exploration of new SINEs in metazoan genomes. Here we de...
Xuefei Shi
2014-01-01
Full Text Available We consider a single machine scheduling problem with multiple maintenance activities, where the maintenance duration function is of the linear form ft=a+bt with a≥0 and b>1. We propose an approximation algorithm named FFD-LS2I with a worst-case bound of 2 for problem. We also show that there is no polynomial time approximation algorithm with a worst-case bound less than 2 for the problem with b≥0 unless P=NP, which implies that the FFD-LS2I algorithm is the best possible algorithm for the case b>1 and that the FFD-LS algorithm, which is proposed in the literature, is the best possible algorithm for the case b≤1 both from the worst-case bound point of view.
Mohammad Javad Namazifar
2015-09-01
Full Text Available The Freeze-Tag Problem (FTP arises in the study of swarm robotics. The FTP is a combinatorial optimization problem that starts by locating a set of robots in a Euclidean plane. Here, we are given a swarm of n asleep (frozen or inactive robots and a single awake (active robot. In order to activate an inactive robot in FTP, the active robot should either be in the physical proximity to the inactive robot or ``touch`` it. The new activated robot starts moving and can wake up other inactive robots. The goal is to ﬁnd an optimal activating schedule with the minimum time required for activating all robots. In general, FTP is an NP-Hard problem and in the Euclidean space is an open problem. In this paper, we present a recursive approximation algorithm with a constant approximation factor and a linear running time for the Euclidean Freeze-Tag Problem.
Phase patterns in finite oscillator networks with insights from the piecewise linear approximation
Goldstein, Daniel
2015-03-01
Recent experiments on spatially extend arrays of droplets containing Belousov-Zhabotinsky reactants have shown a rich variety of spatio-temporal patterns. Motivated by this experimental set up, we study a simple model of chemical oscillators in the highly nonlinear excitable regime in order to gain insight into the mechanism giving rise to the observed multistable attractors. When coupled, these two attractors have different preferred phase synchronizations, leading to complex behavior. We study rings of coupled oscillators and observe a rich array of oscillating patterns. We combine Turing analysis and a piecewise linear approximation to better understand the observed patterns.
Brett, Tobias; Galla, Tobias
2013-06-21
We develop a systematic approach to the linear-noise approximation for stochastic reaction systems with distributed delays. Unlike most existing work our formalism does not rely on a master equation; instead it is based upon a dynamical generating functional describing the probability measure over all possible paths of the dynamics. We derive general expressions for the chemical Langevin equation for a broad class of non-Markovian systems with distributed delay. Exemplars of a model of gene regulation with delayed autoinhibition and a model of epidemic spread with delayed recovery provide evidence of the applicability of our results.
Hardware Efficient Approximative Matrix Inversion for Linear Pre-Coding in Massive MIMO
Prabhu, Hemanth; Edfors, Ove; Rodrigues, Joachim; Liu, Liang; Rusek, Fredrik
2014-01-01
This paper describes a hardware efficient linear pre-coder for Massive MIMO Base Stations (BSs) comprising a very large number of antennas, say, in the order of 100s, serving multiple users simultaneously. To avoid hardware demanding direct matrix inversions required for the Zero-Forcing (ZF) pre-coder, we use low complexity Neumann series based approximations. Furthermore, we propose a method to speed-up the convergence of the Neumann series by using tri-diagonal pre-condition matrices, whic...
A novel impact identification algorithm based on a linear approximation with maximum entropy
Sanchez, N.; Meruane, V.; Ortiz-Bernardin, A.
2016-09-01
This article presents a novel impact identification algorithm that uses a linear approximation handled by a statistical inference model based on the maximum-entropy principle, termed linear approximation with maximum entropy (LME). Unlike other regression algorithms as artificial neural networks (ANNs) and support vector machines, the proposed algorithm requires only parameter to be selected and the impact is identified after solving a convex optimization problem that has a unique solution. In addition, with LME data is processed in a period of time that is comparable to the one of other algorithms. The performance of the proposed methodology is validated by considering an experimental aluminum plate. Time varying strain data is measured using four piezoceramic sensors bonded to the plate. To demonstrate the potential of the proposed approach over existing ones, results obtained via LME are compared with those of ANN and least square support vector machines. The results demonstrate that with a low number of sensors it is possible to accurately locate and quantify impacts on a structure and that LME outperforms other impact identification algorithms.
Xin-Jia Meng
2015-01-01
Full Text Available Multidisciplinary reliability is an important part of the reliability-based multidisciplinary design optimization (RBMDO. However, it usually has a considerable amount of calculation. The purpose of this paper is to improve the computational efficiency of multidisciplinary inverse reliability analysis. A multidisciplinary inverse reliability analysis method based on collaborative optimization with combination of linear approximations (CLA-CO is proposed in this paper. In the proposed method, the multidisciplinary reliability assessment problem is first transformed into a problem of most probable failure point (MPP search of inverse reliability, and then the process of searching for MPP of multidisciplinary inverse reliability is performed based on the framework of CLA-CO. This method improves the MPP searching process through two elements. One is treating the discipline analyses as the equality constraints in the subsystem optimization, and the other is using linear approximations corresponding to subsystem responses as the replacement of the consistency equality constraint in system optimization. With these two elements, the proposed method realizes the parallel analysis of each discipline, and it also has a higher computational efficiency. Additionally, there are no difficulties in applying the proposed method to problems with nonnormal distribution variables. One mathematical test problem and an electronic packaging problem are used to demonstrate the effectiveness of the proposed method.
Approximation by random weighting method for M-test in linear models
Xiao-yan WU; Ya-ning YANG; Lin-cheng ZHAO
2007-01-01
The M-test has been in common use and widely studied in testing the linear hypotheses in linear models. However, the critical value for the test is usually related to the quantities of the unknown error distribution and the estimate of the nuisance parameters may be rather involved, not only for the M-test method but also for the existing bootstrap methods. In this paper we suggest a random weighting resampling method for approximating the null distribution of the M-test statistic.It is shown that, under both the null and the local alternatives, the random weighting statistic has the same asymptotic distribution as the null distribution of the M-test. The critical values of the M-test can therefore be obtained by the random weighting method without estimating the nuisance parameters. A distinguished feature of the proposed method is that the approximation is valid even the null hypothesis is not true and the power evaluation is possible under the local alternatives.
Approximation by random weighting method for M-test in linear models
2007-01-01
The M-test has been in common use and widely studied in testing the linear hypotheses in linear models. However, the critical value for the test is usually related to the quantities of the unknown error distribution and the estimate of the nuisance parameters may be rather involved, not only for the M-test method but also for the existing bootstrap methods. In this paper we suggest a random weighting resampling method for approximating the null distribution of the M-test statistic. It is shown that, under both the null and the local alternatives, the random weighting statistic has the same asymptotic distribution as the null distribution of the M-test. The critical values of the M-test can therefore be obtained by the random weighting method without estimating the nuisance parameters. A distinguished feature of the proposed method is that the approximation is valid even the null hypothesis is not true and the power evaluation is possible under the local alternatives.
Dynamics of global atmospheric CO2 concentration from 1850 to 2010: a linear approximation
Wang, W.; Nemani, R.
2014-09-01
The increase in anthropogenic CO2 emissions largely followed an exponential path between 1850 and 2010, and the corresponding increases in atmospheric CO2 concentration were almost constantly proportional to the emissions by the so-called "airborne fraction". These observations suggest that the dynamics of atmospheric CO2 concentration through this time period may be properly approximated as a linear system. We demonstrate this hypothesis by deriving a linear box-model to describe carbon exchanges between the atmosphere and the surface reservoirs under the influence of disturbances such as anthropogenic CO2 emissions and global temperature changes. We show that the box model accurately simulates the observed atmospheric CO2 concentrations and growth rates across interannual to multi-decadal time scales. The model also allows us to analytically examine the dynamics of such changes/variations, linking its characteristic disturbance-response functions to bio-geophysically meaningful parameters. In particular, our results suggest that the elevated atmospheric CO2 concentrations have significantly promoted the gross carbon uptake by the terrestrial biosphere. However, such "fertilization" effects are partially offset by enhanced carbon release from surface reservoirs promoted by warmer temperatures. The result of these interactions appears to be a decline in net efficiency in sequestering atmospheric CO2 by ∼30% since 1960s. We believe that the linear modeling framework outlined in this paper provides a convenient tool to diagnose the observed atmospheric CO2 dynamics and monitor their future changes.
Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.
Talaei, Behzad; Jagannathan, Sarangapani; Singler, John
2017-03-02
This paper develops a near optimal boundary control method for distributed parameter systems governed by uncertain linear 1-D parabolic partial differential equations (PDE) by using approximate dynamic programming. A quadratic surface integral is proposed to express the optimal cost functional for the infinite-dimensional state space. Accordingly, the Hamilton-Jacobi-Bellman (HJB) equation is formulated in the infinite-dimensional domain without using any model reduction. Subsequently, a neural network identifier is developed to estimate the unknown spatially varying coefficient in PDE dynamics. Novel tuning law is proposed to guarantee the boundedness of identifier approximation error in the PDE domain. A radial basis network (RBN) is subsequently proposed to generate an approximate solution for the optimal surface kernel function online. The tuning law for near optimal RBN weights is created, such that the HJB equation error is minimized while the dynamics are identified and closed-loop system remains stable. Ultimate boundedness (UB) of the closed-loop system is verified by using the Lyapunov theory. The performance of the proposed controller is successfully confirmed by simulation on an unstable diffusion-reaction process.
A linearly approximated iterative Gaussian decomposition method for waveform LiDAR processing
Mountrakis, Giorgos; Li, Yuguang
2017-07-01
Full-waveform LiDAR (FWL) decomposition results often act as the basis for key LiDAR-derived products, for example canopy height, biomass and carbon pool estimation, leaf area index calculation and under canopy detection. To date, the prevailing method for FWL product creation is the Gaussian Decomposition (GD) based on a non-linear Levenberg-Marquardt (LM) optimization for Gaussian node parameter estimation. GD follows a ;greedy; approach that may leave weak nodes undetected, merge multiple nodes into one or separate a noisy single node into multiple ones. In this manuscript, we propose an alternative decomposition method called Linearly Approximated Iterative Gaussian Decomposition (LAIGD method). The novelty of the LAIGD method is that it follows a multi-step ;slow-and-steady; iterative structure, where new Gaussian nodes are quickly discovered and adjusted using a linear fitting technique before they are forwarded for a non-linear optimization. Two experiments were conducted, one using real full-waveform data from NASA's land, vegetation, and ice sensor (LVIS) and another using synthetic data containing different number of nodes and degrees of overlap to assess performance in variable signal complexity. LVIS data revealed considerable improvements in RMSE (44.8% lower), RSE (56.3% lower) and rRMSE (74.3% lower) values compared to the benchmark GD method. These results were further confirmed with the synthetic data. Furthermore, the proposed multi-step method reduces execution times in half, an important consideration as there are plans for global coverage with the upcoming Global Ecosystem Dynamics Investigation LiDAR sensor on the International Space Station.
Approximating high-dimensional dynamics by barycentric coordinates with linear programming
Hirata, Yoshito, E-mail: yoshito@sat.t.u-tokyo.ac.jp; Aihara, Kazuyuki; Suzuki, Hideyuki [Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505 (Japan); Department of Mathematical Informatics, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656 (Japan); CREST, JST, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012 (Japan); Shiro, Masanori [Department of Mathematical Informatics, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656 (Japan); Mathematical Neuroinformatics Group, Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568 (Japan); Takahashi, Nozomu; Mas, Paloma [Center for Research in Agricultural Genomics (CRAG), Consorci CSIC-IRTA-UAB-UB, Barcelona 08193 (Spain)
2015-01-15
The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.
Optimal inference strategies and their implications for the linear noise approximation
Hartich, David
2016-01-01
We study the information loss of a class of inference strategies that is solely based on time averaging. For an array of independent binary sensors (e.g., receptors) measuring a weak random signal (e.g., ligand concentration) this information loss is up to 0.5 bit per measurement irrespective of the number of sensors. We derive a condition related to the local detailed balance relation that determines whether or not such a loss of information occurs. Specifically, if the free energy difference arising from the signal is symmetrically distributed among the forward and backward rates, time integration mechanisms will capture the full information about the signal. As an implication, for the linear noise approximation, we can identify the same loss of information, arising from its inherent simplification of the dynamics.
Fast Evaluation of Fluctuations in Biochemical Networks With the Linear Noise Approximation
Elf, Johan; Ehrenberg, Måns
2003-01-01
Biochemical networks in single cells can display large fluctuations in molecule numbers, making mesoscopic approaches necessary for correct system descriptions. We present a general method that allows rapid characterization of the stochastic properties of intracellular networks. The starting point is a macroscopic description that identifies the system's elementary reactions in terms of rate laws and stoichiometries. From this formulation follows directly the stationary solution of the linear noise approximation (LNA) of the Master equation for all the components in the network. The method complements bifurcation studies of the system's parameter dependence by providing estimates of sizes, correlations, and time scales of stochastic fluctuations. We describe how the LNA can give precise system descriptions also near macroscopic instabilities by suitable variable changes and elimination of fast variables. PMID:14597656
Approximating high-dimensional dynamics by barycentric coordinates with linear programming.
Hirata, Yoshito; Shiro, Masanori; Takahashi, Nozomu; Aihara, Kazuyuki; Suzuki, Hideyuki; Mas, Paloma
2015-01-01
The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.
Frommer, A; Lippert, Th; Rittich, H
2012-01-01
The Lanczos process constructs a sequence of orthonormal vectors v_m spanning a nested sequence of Krylov subspaces generated by a hermitian matrix A and some starting vector b. In this paper we show how to cheaply recover a secondary Lanczos process, starting at an arbitrary Lanczos vector v_m and how to use this secondary process to efficiently obtain computable error estimates and error bounds for the Lanczos approximations to a solution of a linear system Ax = b as well as, more generally, for the Lanczos approximations to the action of a rational matrix function on a vector. Our approach uses the relation between the Lanczos process and quadrature as developed by Golub and Meurant. It is different from methods known so far because of its use of the secondary Lanczos process. With our approach, it is now in particular possible to efficiently obtain upper bounds for the error in the 2-norm, provided a lower bound on the smallest eigenvalue of A is known. This holds for the error of the cg iterates as well ...
Liu, Y.; Li, T.; Zhu, C.; Zhang, R.; Wu, Y.
2015-12-01
Three-dimensional (3-D) electromagnetic (EM) forward modelling and inversion continues to be an important issue for the correct interpretation of EM data.To this end,approximate solutions have been developed that allow the construction of relatively fast forward modelling and inversion schemes.We have developed an improved quasi-linear approximation which is more appropriate in solving the linear equation for greatly shortening calculation time.We achieved this by using green's function properties.Then we introduced the improved quasi-linear approximation to spectral induced polarization (SIP) to tackle the problem of the resolution and the efficiency.The localized quasi-linear (LQL) approximation theory is appropriate for multisource array-type surveys assuming that the normal field is slowly varying within the inhomogeneity domain.However,the normal field of attenuates severely which dose not satisfy the assumption of the LQL approximation.As a consenquence,the imaginary part is not accurate when LQL approximation is adopted for the simulation.The improved quasi-linear approximation provide a new approach with the same resolution of QL approximation and much less calculation time.We have also constructed three-dimensional SIP forward modeling based on improved quasi-linear approximation method.It only takes 0.8s for forward modeling when inhomogeneity domain is divided into 2000 blocks.Beyond that, we have introduced the Cole-Cole model to the algorithm and complete the three-dimensional complex resistivity conjugate gradient inversion with parameter restraint.The model trial results show that this method can obtain good inversion results in physical parameters such as zero frequency resistivity, polarization.The results demonstrate the stability and the efficiency of the improved quasi-linear approximation and the method may be a practical solution for3-D EM forward modelling and inversion of SIP.
Vortex Strings and Nonabelian sine-Gordon Theories
Park, Q H
1999-01-01
We generalize the Lund-Regge model for vortex string dynamics in 4-dimensional Minkowski space to the arbitrary n-dimensional case. The n-dimensional vortex equation is identified with a nonabelian sine-Gordon equation and its integrability is proven by finding the associated linear equations of the inverse scattering. An explicit expression of vortex coordinates in terms of the variables of the nonabelian sine-Gordon system is derived. In particular, we obtain the n-dimensional vortex soliton solution of the Hasimoto-type from the one soliton solution of the nonabelian sine-Gordon equation.
Linear noise approximation for oscillations in a stochastic inhibitory network with delay
Dumont, Grégory; Northoff, Georg; Longtin, André
2014-07-01
Understanding neural variability is currently one of the biggest challenges in neuroscience. Using theory and computational modeling, we study the behavior of a globally coupled inhibitory neural network, in which each neuron follows a purely stochastic two-state spiking process. We investigate the role of both this intrinsic randomness and the conduction delay on the emergence of fast (e.g., gamma) oscillations. Toward that end, we expand the recently proposed linear noise approximation (LNA) technique to this non-Markovian "delay" case. The analysis first leads to a nonlinear delay-differential equation (DDE) with multiplicative noise for the mean activity. The LNA then yields two coupled DDEs, one of which is driven by additive Gaussian white noise. These equations on their own provide an excellent approximation to the full network dynamics, which are much longer to integrate. They further allow us to compute a theoretical expression for the power spectrum of the population activity. Our analytical result is in good agreement with the power spectrum obtained via numerical simulations of the full network dynamics, for the large range of parameters where both the intrinsic stochasticity and the conduction delay are necessary for the occurrence of oscillations. The intrinsic noise arises from the probabilistic description of each neuron, yet it is expressed at the system activity level, and it can only be controlled by the system size. In fact, its effect on the fluctuations in system activity disappears in the infinite network size limit, but the characteristics of the oscillatory activity depend on all model parameters including the system size. Using the Hilbert transform, we further show that the intrinsic noise causes sporadic strong fluctuations in the phase of the gamma rhythm.
Non-linear effects in the post-Newtonian approximation of a spherically symmetric field
Gambi, J.M.; Zamorano, P. [Madrid Univ. Carlos 3, Madrid (Spain). Dept. de Matematicas; Romero, P.; Garcia del Pino, M.L. [Madrid Univ. Complutense, Madrid (Spain). Dept. de Astronomia y Geodesia
2000-02-01
Conditions for the compatibility of the exterior metric of a spherically symmetric object with the field equations for the empty space and equations of motion and of trajectories for test particles, written in polar Gaussian and Fermi coordinates, are obtained to show that, although their explicit exact solutions cannot be derived in these coordinates, the post-Newtonian limits of these solutions can, nevertheless, be obtained. With these limits, it is next shown that the cited post-Newtonian equations do not fit into the standard post-Newtonian approximation either. It is then shown that these coordinates can, nevertheless, be included in a more general formalism together with the usual post-Newtonian (standard, harmonic, Painleve and isotropic) coordinates so that their respective equations of motion may be compared to each other and, finally, it is demonstrated that the only non-linear term taken in the Christoffel symbols with these usual coordinates in the standard post-Newtonian equations of motion to explain some known perturbations is not needed when polar Gaussian or Fermi coordinates are used to explain also those perturbations. In fact, it is demonstrated that these are the only coordinates for which that term becomes zero.
Lenoir, A; Pélissier, T; Bousquet-Antonelli, C; Deragon, J M
2005-01-01
Brassica oleracea and Arabidopsis thaliana belong to the Brassicaceae(Cruciferae) family and diverged 16 to 19 million years ago. Although the genome size of B. oleracea (approximately 600 million base pairs) is more than four times that of A. thaliana (approximately 130 million base pairs), their gene content is believed to be very similar with more than 85% sequence identity in the coding region. Therefore, this important difference in genome size is likely to reflect a different rate of non-coding DNA accumulation. Transposable elements (TEs) constitute a major fraction of non-coding DNA in plant species. A different rate in TE accumulation between two closely related species can result in significant genome size variations in a short evolutionary period. Short interspersed elements (SINEs) are non-autonomous retroposons that have invaded the genome of most eukaryote species. Several SINE families are present in B. oleracea and A. thaliana and we found that two of them (called RathE1 and RathE2) are present in both species. In this study, the tempo of evolution of RathE1 and RathE2 SINE families in both species was compared. We observed that most B. oleracea RathE2 SINEs are "young" (close to the consensus sequence) and abundant while elements from this family are more degenerated and much less abundant in A. thaliana. However, the situation is different for the RathE1 SINE family for which the youngest elements are found in A. thaliana. Surprisingly, no SINE was found to occupy the same (orthologous) genomic locus in both species suggesting that either these SINE families were not amplified at a significant rate in the common ancestor of the two species or that older elements were lost and only the recent (lineage-specific) insertions remain. To test this latter hypothesis, loci containing a recently inserted SINE in the A. thaliana col-0 ecotype were selected and characterized in several other A. thaliana ecotypes. In addition to the expected SINE containing
Investigation on the MOC with a linear source approximation scheme in three-dimensional assembly
Zhu, Chenglin; Cao, Xinrong [Harbin Engineering University, Haribin (China)
2014-08-15
Method of characteristics (MOC) for solving neutron transport equation has already become one of the fundamental methods for lattice calculation of nuclear design code system. At present, MOC has three schemes to deal with the neutron source of the transport equation: the flat source approximation of the step characteristics (SC) scheme, the diamond difference (DD) scheme and the linear source (LS) characteristics scheme. The MOC for SC scheme and DD scheme need large storage space and long computing time when they are used to calculate large-scale three-dimensional neutron transport problems. In this paper, a LS scheme and its correction for negative source distribution were developed and added to DRAGON code. This new scheme was compared with the SC scheme and DD scheme which had been applied in this code. As an open source code, DRAGON could solve three-dimensional assembly with MOC method. Detailed calculation is conducted on two-dimensional VVER-1000 assembly under three schemes of MOC. The numerical results indicate that coarse mesh could be used in the LS scheme with the same accuracy. And the LS scheme applied in DRAGON is effective and expected results are achieved. Then three-dimensional cell problem and VVER-1000 assembly are calculated with LS scheme and SC scheme. The results show that less memory and shorter computational time are employed in LS scheme compared with SC scheme. It is concluded that by using LS scheme, DRAGON is able to calculate large-scale three-dimensional problems with less storage space and shorter computing time.
Comparison of renormalization group schemes for sine-Gordon type models
Nandori, I; Sailer, K; Trombettoni, A
2009-01-01
We consider the scheme-dependence of the renormalization group (RG) flow obtained in the local potential approximation for two-dimensional periodic, sine-Gordon type field-theoric models with possible inclusion of explicit mass terms. For sine-Gordon type models showing up a Kosterlitz-Thouless-Berezinskii type phase transition the Wegner-Houghton, the Polchinski, the functional Callan-Symanzik and the effective average action RG methods give qualitatively the same result and the critical frequency (temperature) can be obtained scheme-independently from the RG equations linearized around the Gaussian fixed point. For the massive sine-Gordon model which undergoes an Ising type phase transition, the Wegner-Houghton, the functional Callan-Symanzik and the effective average action RG methods provide the same scheme-independent phase structure and value for the critical ratio, in agreement with the results of lattice methods. It is also shown that RG equations linearized around the Gaussian fixed point produce sch...
Sauria SINEs: Novel short interspersed retroposable elements that are widespread in reptile genomes.
Piskurek, Oliver; Austin, Christopher C; Okada, Norihiro
2006-05-01
SINEs are short interspersed retrotransposable elements that invade new genomic sites. Their retrotransposition depends on reverse transcriptase and endonuclease activities encoded by partner LINEs (long interspersed elements). Recent genomic research has demonstrated that retroposons account for at least 40% of the human genome. Hitherto, more than 30 families of SINEs have been characterized in mammalian genomes, comprising approximately 4600 extant species; the distribution and extent of SINEs in reptilian genomes, however, are poorly documented. With more than 7400 species of lizards and snakes, Squamata constitutes the largest and most diverse group of living reptiles. We have discovered and characterized a novel SINE family, Sauria SINEs, whose members are widely distributed among genomes of lizards, snakes, and tuataras. Sauria SINEs comprise a 5' tRNA-related region, a tRNA-unrelated region, and a 3' tail region (containing short tandem repeats) derived from LINEs. We distinguished eight Sauria SINE subfamilies in genomes of four major squamate lineages and investigated their evolutionary relationships. Our data illustrate the overall efficacy of Sauria SINEs as novel retrotransposable markers for elucidation of squamate evolutionary history. We show that all Sauria SINEs share an identical 3' sequence with Bov-B LINEs and propose that they utilize the enzymatic machinery of Bov-B LINEs for their own retrotransposition. This finding, along with the ubiquity of Bov-B LINEs previously demonstrated in squamate genomes, suggests that these LINEs have been an active partner of Sauria SINEs since this SINE family was generated more than 200 million years ago.
Plane wave holonomies in quantum gravity. II. A sine wave solution
Neville, Donald E.
2015-08-01
This paper constructs an approximate sinusoidal wave packet solution to the equations of canonical gravity. The theory uses holonomy-flux variables with support on a lattice (LHF =lattice-holonomy flux ). There is an SU(2) holonomy on each edge of the LHF simplex, and the goal is to study the behavior of these holonomies under the influence of a passing gravitational wave. The equations are solved in a small sine approximation: holonomies are expanded in powers of sines and terms beyond sin2 are dropped; also, fields vary slowly from vertex to vertex. The wave is unidirectional and linearly polarized. The Hilbert space is spanned by a set of coherent states tailored to the symmetry of the plane wave case. Fixing the spatial diffeomorphisms is equivalent to fixing the spatial interval between vertices of the loop quantum gravity lattice. This spacing can be chosen such that the eigenvalues of the triad operators are large, as required in the small sine limit, even though the holonomies are not large. Appendices compute the energy of the wave, estimate the lifetime of the coherent state packet, discuss circular polarization and coarse-graining, and determine the behavior of the spinors used in the U(N) SHO realization of LQG.
Sine-wave speech recognition in a tonal language.
Feng, Yan-Mei; Xu, Li; Zhou, Ning; Yang, Guang; Yin, Shan-Kai
2012-02-01
It is hypothesized that in sine-wave replicas of natural speech, lexical tone recognition would be severely impaired due to the loss of F0 information, but the linguistic information at the sentence level could be retrieved even with limited tone information. Forty-one native Mandarin-Chinese-speaking listeners participated in the experiments. Results showed that sine-wave tone-recognition performance was on average only 32.7% correct. However, sine-wave sentence-recognition performance was very accurate, approximately 92% correct on average. Therefore the functional load of lexical tones on sentence recognition is limited, and the high-level recognition of sine-wave sentences is likely attributed to the perceptual organization that is influenced by top-down processes. © 2012 Acoustical Society of America
Prendiville, Julie S; Tucker, Lori B; Cabral, David A; Crawford, Richard I
2004-01-01
The characteristic rash of systemic juvenile idiopathic arthritis is a transient erythematous eruption associated with a quotidian spiking fever. Usually asymptomatic, it can be pruritic, with dermatographism at sites of scratching or pressure. An illness similar to this entity in adults is designated adult-onset Still disease. The relationship between the pediatric and adult disease is uncertain and differences in case definition have evolved. Specifically, a sustained arthritis for at least 6 weeks is required for a diagnosis of systemic juvenile idiopathic arthritis, whereas transient arthritis and arthralgia are accepted criteria in adult-onset Still disease. We describe five patients less than 16 years of age who presented with an acute illness characterized by fever and a distinctive skin eruption. Intense pruritus and linear erythematous lesions flared with a spiking fever, usually in the late afternoon and evening. Periorbital edema/erythema and nonlinear urticarial lesions were also seen. Two children had splinter hemorrhages of the nail beds and one girl developed a fixed, scaling, pigmented, linear eruption. Severe malaise, myalgia, arthralgia, and leukocytosis were present in every patient. Other systemic manifestations included sore throat, transient arthritis, abdominal pain, lymphadenopathy, hepatomegaly, splenomegaly, hyperferritinemia, and hepatic dysfunction. No patient had a sustained arthritis. The course of the disease was variable. One patient, diagnosed with macrophage activation syndrome, recovered on oral naproxen. Two patients responded to systemic corticosteroid therapy. One girl developed status epilepticus and died from aspiration and asphyxia. A boy with severe hepatitis developed renal failure and thrombotic thrombocytopenic purpura and was treated with plasmapheresis, dialysis, and systemic corticosteroids; he had recurrent episodes of rash and fever into adult life. These children did not fulfill the case definition of systemic
Approximating the Pareto Set of Multiobjective Linear Programs via Robust Optimization
Gorissen, B.L.; den Hertog, D.
2012-01-01
Abstract: The Pareto set of a multiobjective optimization problem consists of the solutions for which one or more objectives can not be improved without deteriorating one or more other objectives. We consider problems with linear objectives and linear constraints and use Adjustable Robust Optimizati
Huffman Coding with Letter Costs: A Linear-Time Approximation Scheme
Golin, Mordecai; Mathieu, Claire; Young, Neal E.
2002-01-01
We give a polynomial-time approximation scheme for the generalization of Huffman Coding in which codeword letters have non-uniform costs (as in Morse code, where the dash is twice as long as the dot). The algorithm computes a (1+epsilon)-approximate solution in time O(n + f(epsilon) log^3 n), where n is the input size.
Koleski, Goce; Fournier, Jean-Baptiste
2016-05-01
The linear response approximation, used within effective field theory to calculate mediated interactions between inclusions, is studied for an exactly solvable one-dimensional model. We show that it works poorly in the case of inclusions imposing absolute deformations to the field, while it works well for massless theories in the case of inclusions imposing relative deformations to the field.
无
2006-01-01
We determine the asymptotic order of entropy number and optimal non - linear approximations of anisotropic periodic Besov class of Brpθ(Td) (1≤p≤∞, 1≤θ≤∞ ) by manifolds of finite pseudo-dimension in the metric Lq (Td), 1≤ q≤∞, where Td is the d-dimensional torus.
Senjean, Bruno; Jensen, Hans Jørgen Aa; Fromager, Emmanuel
2015-01-01
The computation of excitation energies in range-separated ensemble density-functional theory (DFT) is discussed. The latter approach is appealing as it enables the rigorous formulation of a multi-determinant state-averaged DFT method. In the exact theory, the short-range density functional, that complements the long-range wavefunction-based ensemble energy contribution, should vary with the ensemble weights even when the density is held fixed. This weight dependence ensures that the range-separated ensemble energy varies linearly with the ensemble weights. When the (weight-independent) ground-state short-range exchange-correlation functional is used in this context, curvature appears thus leading to an approximate weight-dependent excitation energy. In order to obtain unambiguous approximate excitation energies, we simply propose to interpolate linearly the ensemble energy between equiensembles. It is shown that such a linear interpolation method (LIM) effectively introduces weight dependence effects. LIM has...
Analysis of the linear approximation of seismic inversions for various structural pairs
Buldgen, G; Dupret, M A
2016-01-01
Thanks to space-based photometry missions CoRoT and Kepler, we benefit from a wealth of seismic data for stars other than the sun. In the future, K2, Tess, and Plato will complement this data and provide observations in addition to those already at hand. The availability of this data leads to questions on how it is feasible to extend linear structural inversion techniques to stars other than the sun. Linked to this problem is the question of the validity of the linear assumption. In this study, we analyse its limitations with respect to changes of structural variables.We wish to provide a more extended theoretical background to structural linear inversions by doing a study of the validity of the linear assumption for various structural variables. First, we recall the origins of the linear assumption for structural stellar inversions and explain its importance for asteroseismic studies. We recall the impact of unknown structural quantities such as the mass and the radius of the star on structural inversion res...
Kovács, M; Lindgren, F
2012-01-01
We present an abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise. First, an abstract representation formula is derived for sufficiently smooth test functions. The formula is then applied to the wave equation, where the spatial approximation is done via the standard continuous finite element method and the time discretization via an I-stable rational approximation to the exponential function. It is found that the rate of weak convergence is twice that of strong convergence. Furthermore, in contrast to the parabolic case, higher order schemes in time, such as the Crank-Nicolson scheme, are worthwhile to use if the solution is not very regular. Finally we apply the theory to parabolic equations and detail a weak error estimate for the linearized Cahn-Hilliard-Cook equation as well as comment on the stochastic heat equation.
Ergodic theory and Diophantine approximation for translation surfaces and linear forms
Athreya, Jayadev; Parrish, Andrew; Tseng, Jimmy
2016-08-01
We derive results on the distribution of directions of saddle connections on translation surfaces using only the Birkhoff ergodic theorem applied to the geodesic flow on the moduli space of translation surfaces. Our techniques, together with an approximation argument, also give an alternative proof of a weak version of a classical theorem in multi-dimensional Diophantine approximation due to Schmidt (1960 Can. J. Math. 12 619-31, 1964 Trans. Am. Math. Soc. 110 493-518). The approximation argument allows us to deduce the Birkhoff genericity of almost all lattices in a certain submanifold of the space of unimodular lattices from the Birkhoff genericity of almost all lattices in the whole space and similarly for the space of affine unimodular lattices.
Knoester, Jasper; Mukamel, Shaul
1989-01-01
Reduced equations of motion for material and radiation field variables in a molecular crystal are presented that allow us to calculate linear- and nonlinear-optical susceptibilities, accounting in a systematic way for intermolecular interactions. These equations are derived starting from the multipo
Krykunov, Mykhaylo; Autschbach, Jochen
2007-01-14
We report implementations and results of time-dependent density functional calculations (i) of the frequency-dependent magnetic dipole-magnetic dipole polarizability, (ii) of the (observable) translationally invariant linear magnetic response, and (iii) of a linear intensity differential (LID) which includes the dynamic dipole magnetizability. The density functional calculations utilized density fitting. For achieving gauge-origin independence we have employed time-periodic magnetic-field-dependent basis functions as well as the dipole velocity gauge, and have included explicit density-fit related derivatives of the Coulomb potential. We present the results of calculations of static and dynamic magnetic dipole-magnetic dipole polarizabilities for a set of small molecules, the LID for the SF6 molecule, and dispersion curves for M-hexahelicene of the origin invariant linear magnetic response as well as of three dynamic polarizabilities: magnetic dipole-magnetic dipole, electric dipole-electric dipole, and electric dipole-magnetic dipole. We have also performed comparison of the linear magnetic response and magnetic dipole-magnetic dipole polarizability over a wide range of frequencies for H2O and SF6.
Analysis of the linear approximation of seismic inversions for various structural pairs
Buldgen, G.; Reese, D. R.; Dupret, M. A.
2017-01-01
Context. Thanks to the space-based photometry missions CoRoT and Kepler, we now benefit from a wealth of seismic data for stars other than the sun. In the future, K2, Tess, and Plato will complement this data and provide observations in addition to those already at hand. The availability of this data leads to questions on how it is feasible to extend kernel-based, linear structural inversion techniques to stars other than the sun. Linked to the inversion problem is the question of the validity of the linear assumption. In this study, we analyse the limitations of this assumption with respect to changes of structural variables. Aims: We wish to provide a more extended theoretical background to structural linear inversions by doing a study of the validity of the linear assumption for various structural variables. We thus point towards limitations in inversion techniques in the asteroseismic and helioseismic cases. Methods: First, we recall the origins of the linear assumption for structural stellar inversions and explain its importance for asteroseismic studies. We also briefly recall the impact of unknown structural quantities such as the mass and the radius of the star on structural inversion results. We then explain how kernels for new structural variables can be derived using two methods, one suited to asteroseismic targets, the other to helioseismic targets. For this second method, we present a new structural pair, namely the (A,Y) structural kernels. The kernels are then tested in various numerical experiments that enable us to evaluate the weaknesses of different structural pairs and the domains of validity of their respective linear regime. Results: The numerical tests we carry out allow us to disentangle the impact of various uncertainties in stellar models on the verification of the linear integral relations. We show the importance of metallicity, the impact of the equation of state, extra-mixing, and inaccuracies in the microphysics on the verification of
Isolation and characterization of active LINE and SINEs from the eel.
Kajikawa, Masaki; Ichiyanagi, Kenji; Tanaka, Nozomu; Okada, Norihiro
2005-03-01
Long interspersed elements (LINEs) and short interspersed elements (SINEs) are retrotransposons. These elements can mobilize by the "copy-and-paste" mechanism, in which their own RNA is reverse-transcribed into complementary DNA (cDNA). LINEs and SINEs not only are components of eukaryotic genomes but also drivers of genomic evolution. Thus, studies of the amplification mechanism of LINEs and SINEs are important for understanding eukaryotic genome evolution. Here we report the characterization of one LINE family (UnaL2) and two SINE families (UnaSINE1 and UnaSINE2) from the eel (Anguilla japonica) genome. UnaL2 is approximately 3.6 kilobases (kb) and encodes only one open reading frame (ORF). UnaL2 belongs to the stringent type--thought to be a major group of LINEs--and can mobilize in HeLa cells. We also show that UnaL2 and the two UnaSINEs have similar 3' tails, and that both UnaSINE1 and UnaSINE2 can be mobilized by UnaL2 in HeLa cells. These elements are thus useful for delineating the amplification mechanism of stringent type LINEs as well as that of SINEs.
Limitations caused by distortion in room impulse response measurements by swept sine technique
Stojic, Branko; Ciric, Dejan; Markovic, Milos
2011-01-01
by the distortion in room impulse response measurements by swept sine technique are analyzed here by the simulations and measurements. For the investigation, both linear and exponential swept sines are used as an excitation signal. In the simulations, this signal is modified by the nonlinearity model in the time...... of a measured response can be limited in a similar way as in maximum length sequence technique, although the saturation level (maximum dynamic range) is higher for swept sine technique. Thus, swept sine technique is also vulnerable to a certain extent to distortion that limits the quality of measured impulse...
Study of models of the sine-Gordon type in flat and curved spacetime
Bazeia, D. [Universidade de Sao Paulo, Instituto de Fisica, Sao Paulo, SP (Brazil); Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil); Universidade Federal de Campina Grande, Departamento de Fisica, Campina Grande, PB (Brazil); Losano, L. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil); Universidade Federal de Campina Grande, Departamento de Fisica, Campina Grande, PB (Brazil); Menezes, R. [Universidade Federal de Campina Grande, Departamento de Fisica, Campina Grande, PB (Brazil); Rocha, Roldao da [Universidade Federal do ABC, Centro de Matematica, Computacao e Cognicao, Santo Andre, SP (Brazil)
2013-07-15
We study a new family of models of the sine-Gordon type, starting from the sine-Gordon model, including the double sine-Gordon, the triple one, and so on. The models appears as deformations of the starting model, with the deformation controlled by two parameters, one very small, used to control a linear expansion on it, and the other, which specifies the particular model in the family of models. We investigate the presence of topological defects, showing how the solutions can be constructed explicitly from the topological defects of the sine-Gordon model itself. In particular, we delve into the double sine-Gordon model in a braneworld scenario with a single extra dimension of infinite extent, showing that a stable gravity scenario is admissible. Also, we briefly show that the deformation procedure can be used iteratively, leading to a diversity of possibilities to construct families of models of the sine-Gordon type. (orig.)
Approximating electronically excited states with equation-of-motion linear coupled-cluster theory
Byrd, Jason N.; Rishi, Varun; Perera, Ajith; Bartlett, Rodney J.
2015-10-01
A new perturbative approach to canonical equation-of-motion coupled-cluster theory is presented using coupled-cluster perturbation theory. A second-order Møller-Plesset partitioning of the Hamiltonian is used to obtain the well known equation-of-motion many-body perturbation theory equations and two new equation-of-motion methods based on the linear coupled-cluster doubles and linear coupled-cluster singles and doubles wavefunctions. These new methods are benchmarked against very accurate theoretical and experimental spectra from 25 small organic molecules. It is found that the proposed methods have excellent agreement with canonical equation-of-motion coupled-cluster singles and doubles state for state orderings and relative excited state energies as well as acceptable quantitative agreement for absolute excitation energies compared with the best estimate theory and experimental spectra.
Saligrama, V
2008-01-01
We consider the classical Compressed Sensing problem. We have a large under-determined set of noisy measurements Y=GX+N, where X is a sparse signal and G is drawn from a random ensemble. In this paper we focus on a quantized linear programming solution for support recovery. Our solution of the problem amounts to solving $\\min \\|Z\\|_1 ~ s.t. ~ Y=G Z$, and quantizing/thresholding the resulting solution $Z$. We show that this scheme is guaranteed to perfectly reconstruct a discrete signal or control the element-wise reconstruction error for a continuous signal for specific values of sparsity. We show that in the linear regime when the sparsity, $k$, increases linearly with signal dimension, $n$, the sign pattern of $X$ can be recovered with $SNR=O(\\log n)$ and $m= O(k)$ measurements. Our proof technique is based on perturbation of the noiseless $\\ell_1$ problem. Consequently, the achievable sparsity level in the noisy problem is comparable to that of the noiseless problem. Our result offers a sharp characterizat...
Key-frame retrieval from MPEG video based on linear approximation of content curve
Kim, Tae-hee; Lee, Woong-hee; Jeong, Dong-seok
2003-01-01
In general, video is too much lengthy for browsing the contents. So, there are many efforts being made for browsing the content of the video fast and effectively. Video summary is the one of techniques related to those efforts. Video summary comprises a number of key-frames. Therefore, we propose a method to extract key-frames from the video in MPEG compressed domain. Proposed method extracts the simple 2D content curve reflecting the variation of the video content from the MPEG video in the compressed domain, approximates the curve to polygonal lines and then extracts key-frames from the approximated lines effectively and rapidly. Also, proposed method let the user set the number of key-frames.
Approximation of Integrable Functions by General Linear Operators of Their Fourier Series
W(l)odzimierz (L)ENSKI; Bogdan SZAL
2012-01-01
The pointwise estimates of the deviation Tn,A,Bf(·) -f(·) in terms of moduli of continuity (w).f and w.f there are proved.Analogical results on norm approximation with remarks and corollaries are also given.In the results there are used the essentially weaker conditions than these in [Mittal,M.L.:J.Math.Anal.Appl.,220,434-450 (1998) Theorem 1,p.437].
Łenski Włodzimierz
2014-12-01
Full Text Available The pointwise estimates of the deviations r T͂n,A,Bf (· - f͂͂ (· and T͂n,A,Bf (· - f͂͂ (·,ε in terms of moduli of continuity ω̃f and r ω̃f are proved. Analogical results on norm approximation with remarks and corollary are also given. These results generalized a theorem of Mittal [3, Theorem 1, p. 437].
Ringham, Brandy M; Kreidler, Sarah M; Muller, Keith E; Glueck, Deborah H
2016-07-30
Multilevel and longitudinal studies are frequently subject to missing data. For example, biomarker studies for oral cancer may involve multiple assays for each participant. Assays may fail, resulting in missing data values that can be assumed to be missing completely at random. Catellier and Muller proposed a data analytic technique to account for data missing at random in multilevel and longitudinal studies. They suggested modifying the degrees of freedom for both the Hotelling-Lawley trace F statistic and its null case reference distribution. We propose parallel adjustments to approximate power for this multivariate test in studies with missing data. The power approximations use a modified non-central F statistic, which is a function of (i) the expected number of complete cases, (ii) the expected number of non-missing pairs of responses, or (iii) the trimmed sample size, which is the planned sample size reduced by the anticipated proportion of missing data. The accuracy of the method is assessed by comparing the theoretical results to the Monte Carlo simulated power for the Catellier and Muller multivariate test. Over all experimental conditions, the closest approximation to the empirical power of the Catellier and Muller multivariate test is obtained by adjusting power calculations with the expected number of complete cases. The utility of the method is demonstrated with a multivariate power analysis for a hypothetical oral cancer biomarkers study. We describe how to implement the method using standard, commercially available software products and give example code. Copyright © 2015 John Wiley & Sons, Ltd.
Tractable Latent State Filtering for Non-Linear DSGE Models Using a Second-Order Approximation
Kollmann, Robert
2013-01-01
This paper develops a novel approach for estimating latent state variables of Dynamic Stochastic General Equilibrium (DSGE) models that are solved using a second-order accurate approximation. I apply the Kalman filter to a state-space representation of the second-order solution based on the ‘pruning’ scheme of Kim, Kim, Schaumburg and Sims (2008). By contrast to particle filters, no stochastic simulations are needed for the filter here--the present method is thus much faster. In Monte Carlo e...
Approximating electronically excited states with equation-of-motion linear coupled-cluster theory
Byrd, Jason N; Perera, Ajith; Bartlett, Rodney J
2015-01-01
A new perturbative approach to canonical equation-of-motion coupled-cluster theory is presented using coupled-cluster perturbation theory. A second-order M{\\o}ller-Plesset partitioning of the Hamiltonian is used to obtain the well known equation-of-motion many-body perturbation theory (EOM-MBPT(2)) equations and two new equation-of-motion methods based on the linear coupled-cluster doubles (EOM-LCCD) and linear coupled-cluster singles and doubles (EOM-LCCSD) wavefunctions. This is achieved by performing a short-circuiting procedure on the MBPT(2) similarity transformed Hamiltonian. These new methods are benchmarked against very accurate theoretical and experimental spectra from 25 small organic molecules. It is found that the proposed methods have excellent agreement with canonical EOM-CCSD state for state orderings and relative excited state energies as well as acceptable quantitative agreement for absolute excitation energies compared with the best estimate theory and experimental spectra.
Lie-heng Wang
2000-01-01
In this paper, the linear finite element approximation to the elastic contact problem with curved contact boundary is considered. The error bound O(h1-2) is obtained with requirements of two times continuously differentiable for contact boundary and the usual regular triangulation, while I.Hlavacek et. al. obtained the error bound O(h ) with requirements of three times continuously differentiable for contact boundary and extra regularities of triangulation (c.f. [2]).
Study on Linear Approximation of 2-round Trivium%2轮Trivium的线性逼近研究
欧智慧; 赵亚群
2013-01-01
Trivium is an important international sequence cryptography. Jia Yan-yan(Journal of Electronics&Information Technology, 2011, (6)) attacks 2-round Trivium by utilizing a simple and multiple linear cryptanalysis. In the light of few linear approximation and little deviation in their papers. This paper presents a method to conduct linear cryptanalysis of 2-round Trivium by changing clock number and linear approximations of the first round, and proposes a linear approximation with deviation 2-29 and 8 linear approximations with deviation 2-30. Moreover, utilizing the algorithm of Jia Yan-yan paper attacks 2-round Trivium by simple and multiple linear cryptanalysis. Study result shows that, in order to identify a secret key given, the method can supply the success rate with 1/16 of data amount compared with the foregone data amount required, namely, the number of chosen Initial Vector(IV) are 258 and 257, respectively.%Trivium是国际重要的序列密码，贾艳艳等人曾提出对2轮Trivium进行单线性和多线性密码攻击(电子与信息学报，2011年第1期)。针对其中的线性近似方程个数少和偏差小问题，提出通过改变第1轮Trivium所占的时钟数和线性逼近式的方法对2轮进行线性逼近，给出一个偏差为2-29的线性符合和8个偏差为2-30的线性符合，并利用贾艳艳文中算法对2轮Trivium进行单线性和多线性密码攻击。研究结果表明，在相同攻击成功概率的前提下，所需的数据量均为上文中所需数据量的1/16，即需要选择初始化向量的个数分别为258和257。
Attraction and Stability of Nonlinear Ode's using Continuous Piecewise Linear Approximations
Garcia, Andres; Agamennoni, Osvaldo
2010-04-01
In this paper, several results concerning attraction and asymptotic stability in the large of nonlinear ordinary differential equations are presented. The main result is very simple to apply yielding a sufficient condition under which the equilibrium point (assuming a unique equilibrium) is attractive and also provides a variety of options among them the classical linearization and other existing results are special cases of the this main theorem in this paper including and extension of the well known Markus-Yamabe conjecture. Several application examples are presented in order to analyze the advantages and drawbacks of the proposed result and to compare such results with successful existing techniques for analysis available in the literature nowadays.
Attraction and Stability of Nonlinear Ode's using Continuous Piecewise Linear Approximations
Garcia, Andres
2010-01-01
In this paper, several results concerning attraction and asymptotic stability in the large of nonlinear ordinary differential equations are presented. The main result is very simple to apply yielding a sufficient condition under which the equilibrium point (assuming a unique equilibrium) is attractive and also provides a variety of options among them the classical linearization and other existing results are special cases of the this main theorem in this paper including and extension of the well known Markus-Yamabe conjecture. Several application examples are presented in order to analyze the advantages and drawbacks of the proposed result and to compare such results with successful existing techniques for analysis available in the literature nowadays.
Dimmelmeier, H; Font, J A; Dimmelmeier, Harald; Stergioulas, Nikolaos; Font, Jose A.
2005-01-01
We study non-linear axisymmetric pulsations of rotating relativistic stars using a general relativistic hydrodynamics code under the assumption of a conformal flatness. We compare our results to previous simulations where the spacetime dynamics was neglected. The pulsations are studied along various sequences of both uniformly and differentially rotating relativistic polytropes with index N = 1. We identify several modes, including the lowest-order l = 0, 2, and 4 axisymmetric modes, as well as several axisymmetric inertial modes. Differential rotation significantly lowers mode frequencies, increasing prospects for detection by current gravitational wave interferometers. We observe an extended avoided crossing between the l = 0 and l = 4 first overtones, which is important for correctly identifying mode frequencies in case of detection. For uniformly rotating stars near the mass-shedding limit, we confirm the existence of the mass-shedding-induced damping of pulsations, though the effect is not as strong as i...
Carlberg, Kevin
2010-10-28
A Petrov-Galerkin projection method is proposed for reducing the dimension of a discrete non-linear static or dynamic computational model in view of enabling its processing in real time. The right reduced-order basis is chosen to be invariant and is constructed using the Proper Orthogonal Decomposition method. The left reduced-order basis is selected to minimize the two-norm of the residual arising at each Newton iteration. Thus, this basis is iteration-dependent, enables capturing of non-linearities, and leads to the globally convergent Gauss-Newton method. To avoid the significant computational cost of assembling the reduced-order operators, the residual and action of the Jacobian on the right reduced-order basis are each approximated by the product of an invariant, large-scale matrix, and an iteration-dependent, smaller one. The invariant matrix is computed using a data compression procedure that meets proposed consistency requirements. The iteration-dependent matrix is computed to enable the least-squares reconstruction of some entries of the approximated quantities. The results obtained for the solution of a turbulent flow problem and several non-linear structural dynamics problems highlight the merit of the proposed consistency requirements. They also demonstrate the potential of this method to significantly reduce the computational cost associated with high-dimensional non-linear models while retaining their accuracy. © 2010 John Wiley & Sons, Ltd.
Tal-Ezer, Hillel
1987-01-01
During the process of solving a mathematical model numerically, there is often a need to operate on a vector v by an operator which can be expressed as f(A) while A is NxN matrix (ex: exp(A), sin(A), A sup -1). Except for very simple matrices, it is impractical to construct the matrix f(A) explicitly. Usually an approximation to it is used. In the present research, an algorithm is developed which uses a polynomial approximation to f(A). It is reduced to a problem of approximating f(z) by a polynomial in z while z belongs to the domain D in the complex plane which includes all the eigenvalues of A. This problem of approximation is approached by interpolating the function f(z) in a certain set of points which is known to have some maximal properties. The approximation thus achieved is almost best. Implementing the algorithm to some practical problem is described. Since a solution to a linear system Ax = b is x= A sup -1 b, an iterative solution to it can be regarded as a polynomial approximation to f(A) = A sup -1. Implementing the algorithm in this case is also described.
Losa, C; Dossing, T; Vigezzi, E; Broglia, R A
2010-01-01
We present a calculation of the properties of vibrational states in deformed, axially--symmetric even--even nuclei, within the framework of a fully self--consistent Quasparticle Random Phase Approximation (QRPA). The same Skyrme energy density and density-dependent pairing functionals are used to calculate the mean field and the residual interaction in the particle-hole and particle-particle channels. We have tested our software in the case of spherical nuclei against fully self consistent calculations published in the literature, finding excellent agreement. We investigate the consequences of neglecting the spin-orbit and Coulomb residual interactions in QRPA. Furthermore we discuss the improvement obtained in the QRPA result associated with the removal of spurious modes. Isoscalar and isovector responses in the deformed ${}^{24}{}^{-}{}^{26}$Mg, ${}^{34}$Mg isotopes are presented and compared to experimental findings.
Markov chain Monte Carlo inference for Markov jump processes via the linear noise approximation.
Stathopoulos, Vassilios; Girolami, Mark A
2013-02-13
Bayesian analysis for Markov jump processes (MJPs) is a non-trivial and challenging problem. Although exact inference is theoretically possible, it is computationally demanding, thus its applicability is limited to a small class of problems. In this paper, we describe the application of Riemann manifold Markov chain Monte Carlo (MCMC) methods using an approximation to the likelihood of the MJP that is valid when the system modelled is near its thermodynamic limit. The proposed approach is both statistically and computationally efficient whereas the convergence rate and mixing of the chains allow for fast MCMC inference. The methodology is evaluated using numerical simulations on two problems from chemical kinetics and one from systems biology.
Migliano, P.; Zarzoso, D.; Artola, F. J.; Camenen, Y.; Garbet, X.
2017-09-01
The analytical treatment of plasma kinetic linear instabilities in toroidal geometry is commonly tackled employing a power series expansion of the resonant part of the dispersion relation. This expansion is valid under the assumption that the modulus of the mode frequency is smaller than the magnitude of the frequencies characterising the system (the drift, bounce and transit frequencies for example). We will refer to this approximation as high frequency approximation (HFA). In this paper the linear plasma dispersion relation is derived in the framework of the gyro-kinetic model, for the electrostatic case, in the local limit, in the absence of collisions, for a non rotating plasma, considering adiabatic electrons, in toroidal circular geometry, neglecting the parallel dynamics effect. A systematic analysis of the meaning and limitations of the HFA is performed. As already known, the HFA is not valid for tokamak relevant parameters. A new way to approximate the resonant part of the dispersion relation, called here Improved high frequency approximation (IHFA), is therefore proposed. A quantitative analysis of the ion temperature gradient (ITG) instability is presented. The IHFA is shown to be applicable to the treatment of the ITG instability in tokamaks.
Sines and Cosines. Part 1 of 3
Apostol, Tom M. (Editor)
1992-01-01
Applying the concept of similarities, the mathematical principles of circular motion and sine and cosine waves are presented utilizing both film footage and computer animation in this 'Project Mathematics' series video. Concepts presented include: the symmetry of sine waves; the cosine (complementary sine) and cosine waves; the use of sines and cosines on coordinate systems; the relationship they have to each other; the definitions and uses of periodic waves, square waves, sawtooth waves; the Gibbs phenomena; the use of sines and cosines as ratios; and the terminology related to sines and cosines (frequency, overtone, octave, intensity, and amplitude).
Bidifferential Calculus, Matrix SIT and Sine-Gordon Equations
A. Dimakis
2011-01-01
Full Text Available We express a matrix version of the self-induced transparency (SIT equations in the bidifferential calculus framework. An infinite family of exact solutions is then obtained by application of a general result that generates exact solutions from solutions of a linear system of arbitrary matrix size. A side result is a solution formula for the sine-Gordon equation.
Ogiwara, Ikuo; Miya, Masaki; Ohshima, Kazuhiko; Okada, Norihiro
2002-02-01
We have identified a new superfamily of vertebrate short interspersed repetitive elements (SINEs), designated V-SINEs, that are widespread in fishes and frogs. Each V-SINE includes a central conserved domain preceded by a 5'-end tRNA-related region and followed by a potentially recombinogenic (TG)(n) tract, with a 3' tail derived from the 3' untranslated region (UTR) of the corresponding partner long interspersed repetitive element (LINE) that encodes a functional reverse transcriptase. The central domain is strongly conserved and is even found in SINEs in the lamprey genome, suggesting that V-SINEs might be approximately 550 Myr old or older in view of the timing of divergence of the lamprey lineage from the bony fish lineage. The central conserved domain might have been subject to some form of positive selection. Although the contemporary 3' tails of V-SINEs differ from one another, it is possible that the original 3' tail might have been replaced, via recombination, by the 3' tails of more active partner LINEs, thereby retaining retropositional activity and the ability to survive for long periods on the evolutionary time scale. It seems plausible that V-SINEs may have some function(s) that have been maintained by the coevolution of SINEs and LINEs during the evolution of vertebrates.
Abundant Interaction Solutions of Sine-Gordon Equation
DaZhao Lü
2012-01-01
Full Text Available With the help of computer symbolic computation software (e.g., Maple, abundant interaction solutions of sine-Gordon equation are obtained by means of a constructed Wronskian form expansion method. The method is based upon the forms and structures of Wronskian solutions of sine-Gordon equation, and the functions used in the Wronskian determinants do not satisfy linear partial differential equations. Such interaction solutions are difficultly obtained via other methods. And the method can be automatically carried out in computer.
Ibáñez, Javier; Hernández, Vicente
2011-03-01
Differential Matrix Riccati Equations (DMREs) appear in several branches of science such as applied physics and engineering. For example, these equations play a fundamental role in control theory, optimal control, filtering and estimation, decoupling and order reduction, etc. In this paper a new method based on a theorem proved in this paper is described for solving DMREs by a piecewise-linearized approach. This method is applied for developing two block-oriented algorithms based on diagonal Padé approximants. MATLAB versions of the above algorithms are developed, comparing, under equal conditions, accuracy and computational costs with other piecewise-linearized algorithms implemented by the authors. Experimental results show the advantages of solving stiff or non-stiff DMREs by the implemented algorithms.
Memon, Sajid
2012-01-01
In this article, a posteriori error estimates are derived for mixed finite element Galerkin approximations to second order linear parabolic initial and boundary value problems. Using mixed elliptic reconstructions, a posteriori error estimates in L∞(L2)- and L2(L2)-norms for the solution as well as its flux are proved for the semidiscrete scheme. Finally, based on a backward Euler method, a completely discrete scheme is analyzed and a posteriori error bounds are derived, which improves upon earlier results on a posteriori estimates of mixed finite element approximations to parabolic problems. Results of numerical experiments verifying the efficiency of the estimators have also been provided. © 2012 Society for Industrial and Applied Mathematics.
2轮Trivium的多线性密码分析%Linear Cryptanalysis of 2-round Trivium with Multiple Approximations
贾艳艳; 胡予濮; 杨文峰; 高军涛
2011-01-01
Trivium has successfully been chosen as one of the final ciphers by eSTREAM. It has a simple and elegant structure. Although Trivium has attached a lot of interest, it remains unbroken. By finding more linear approximations, a linear cryptanalysis of 2-round Trivium is made by utilizing multiple approximations and a more efficient distinguishing attack is proposed. Compared with current single linear cryptanalysis, this method allows for a reduction in the amount of data required for a successful attack. That is to say, if n linear approximations can be found, this method can supply the success rate with 1/n of the data amount required by a simple linear cryptanalysis. This study shows that there are still some defects in the design of stream cipher Trivium, further safety analysis are needed before its going into the implementation.%作为欧洲流密码发展计划eSTREAM的7个最终获选算法之一,Trivium的安全性考察表明至今为止还没有出现有效的攻击算法.该文针对2轮Trivium,通过找出更多线性逼近方程,对其进行了多线性密码分析,提出了一种更有效的区分攻击算法.与现有的单线性密码分析算法相比,该算法攻击成功所需的数据量明显减少,即:若能找到n个线性近似方程,在达到相同攻击成功概率的前提下,多线性密码分析所需的数据量只有单线性密码分析的1/n.该研究结果表明,Trivium的设计还存在一定的缺陷,投入实用之前还需要实施进一步的安全性分析.
Wang, Junping
2011-01-01
This paper derives some maximum principles for P1-conforming finite element approximations of quasi-linear second order elliptic equations. The results are extensions of the classical maximum principles in the theory of partial differential equations to finite element methods. The mathematical tools are also extensions of the variational approach that was used in classical PDE theories. The maximum principles for finite element approximations are valid with some geometric conditions that are applied to the angles of each element. For the general quasi-linear elliptic equation, each triangle or tetrahedron needs to be $O(h^\\alpha)$-acute in the sense that each angle $\\alpha_{ij}$ (for triangle) or interior dihedral angle $\\alpha_{ij}$ (for tetrahedron) must satisfy $\\alpha_{ij}\\le \\pi/2-\\gamma h^\\alpha$ for some $\\alpha\\ge 0$ and $\\gamma>0$. For the Poisson problem where the differential operator is given by Laplacian, the angle requirement is the same as the classical one: either all the triangles are non-obt...
Chi-Chang Chen
2015-01-01
Full Text Available The relay node placement problem in wireless sensor network (WSN aims at deploying the minimum number of relay nodes over the network so that each sensor can communicate with at least one relay node. When the deployed relay nodes are homogeneous and their communication ranges are circular, one way to solve the WSN relay node placement problem is to solve the minimum geometric disk cover (MGDC problem first and place the relay nodes at the centers of the covering disks and then, if necessary, deploy additional relay nodes to meet the connection requirement of relay nodes. It is known that the MGDC problem is NP-complete. A novel linear time approximation algorithm for the MGDC problem is proposed, which identifies covering disks using the regular hexagon tessellation of the plane with bounded area. The approximation ratio of the proposed algorithm is (5+ϵ, where 0<ϵ≤15. Experimental results show that the worst case is rare, and on average the proposed algorithm uses less than 1.7 times the optimal disks of the MGDC problem. In cases where quick deployment is necessary, this study provides a fast 7-approximation algorithm which uses on average less than twice the optimal number of relay nodes in the simulation.
Georgoulis, M K
2007-01-01
We self-consistently derive the magnetic energy and relative magnetic helicity budgets of a three-dimensional linear force-free magnetic structure rooted in a lower boundary plane. For the potential magnetic energy we derive a general expression that gives results practically equivalent to those of the magnetic Virial theorem. All magnetic energy and helicity budgets are formulated in terms of surface integrals applied to the lower boundary, thus avoiding computationally intensive three-dimensional magnetic field extrapolations. We analytically and numerically connect our derivations with classical expressions for the magnetic energy and helicity, thus presenting a so-far lacking unified treatment of the energy/helicity budgets in the constant-alpha approximation. Applying our derivations to photospheric vector magnetograms of an eruptive and a noneruptive solar active regions, we find that the most profound quantitative difference between these regions lies in the estimated free magnetic energy and relative ...
Klabucar, D; Mekterovic, D; Podobnik, B
2003-01-01
If instantons are introduced into the MIT bag model in such a way that bag radii are allowed to vary, the MIT bag interior can accommodate instanton density which is by an order of magnitude larger than in the case when the radii are fixed (although it is still significantly smaller than in the nonperturbative QCD vacuum). The instanton contribution to baryon mass shifts is also correspondingly larger. The instanton-induced part of the scalar strangeness of the nucleon MIT bag is an order of magnitude larger than found previously, within the linearized approximation. The decrease of the model radii (which is associated with the increase of the instanton density) is very favorable from the standpoint of nuclear physics.
Generalized sine-Gordon solitons
Santos, C dos [Centro de Fisica e Departamento de Fisica e Astronomia, Faculdade de Ciencias da Universidade do Porto, 4169-007 Porto (Portugal); Rubiera-Garcia, D, E-mail: cssilva@fc.up.pt, E-mail: rubieradiego@gmail.com [Departamento de Fisica, Universidad de Oviedo, Avenida Calvo Sotelo 18, 33007 Oviedo, Asturias (Spain)
2011-10-21
In this paper, we construct analytical self-dual soliton solutions in (1+1) dimensions for two families of models which can be seen as generalizations of the sine-Gordon system but where the kinetic term is non-canonical. For that purpose we use a projection method applied to the sine-Gordon soliton. We focus our attention on the wall and lump-like soliton solutions of these k-field models. These solutions and their potentials reduce to those of the Klein-Gordon kink and the standard lump for the case of a canonical kinetic term. As we increase the nonlinearity on the kinetic term the corresponding potentials get modified and the nature of the soliton may change, in particular, undergoing a topology modification. The procedure constructed here is shown to be a sort of generalization of the deformation method for a specific class of k-field models. (paper)
Holota, Petr; Nesvadba, Otakar
2017-04-01
The aim of this paper is to discuss the solution of the linearized gravimetric boundary value problem by means of the method of successive approximations. We start with the relation between the geometry of the solution domain and the structure of Laplace's operator. Similarly as in other branches of engineering and mathematical physics a transformation of coordinates is used that offers a possibility to solve an alternative between the boundary complexity and the complexity of the coefficients of the partial differential equation governing the solution. Laplace's operator has a relatively simple structure in terms of ellipsoidal coordinates which are frequently used in geodesy. However, the physical surface of the Earth substantially differs from an oblate ellipsoid of revolution, even if it is optimally fitted. Therefore, an alternative is discussed. A system of general curvilinear coordinates such that the physical surface of the Earth is imbedded in the family of coordinate surfaces is used. Clearly, the structure of Laplace's operator is more complicated in this case. It was deduced by means of tensor calculus and in a sense it represents the topography of the physical surface of the Earth. Nevertheless, the construction of the respective Green's function is more simple, if the solution domain is transformed. This enables the use of the classical Green's function method together with the method of successive approximations for the solution of the linear gravimetric boundary value problem expressed in terms of new coordinates. The structure of iteration steps is analyzed and where useful also modified by means of the integration by parts. Comparison with other methods is discussed.
Bajnok, Z; Takács, G
2002-01-01
We review our recent results on the on-shell description of sine-Gordon model with integrable boundary conditions. We determined the spectrum of boundary states together with their reflection factors by closing the boundary bootstrap and checked these results against WKB quantization and numerical finite volume spectra obtained from the truncated conformal space approach. The relation between a boundary resonance state and the semiclassical instability of a static classical solution is analyzed in detail.
Liu, Jian; Miller, William H.
2007-07-10
The linearized approximation to the semiclassical initial value representation (LSC-IVR) has been used together with the thermal Gaussian approximation (TGA) (TGA/LSC-IVR) to simulate quantum dynamical effects in realistic models of two condensed phase systems. This represents the first study of dynamical properties of the Ne13 Lennard-Jones (LJ) cluster in its liquid-solid phase transition region (temperature from 4 K to 14 K). Calculation of the force autocorrelation function shows considerable differences from that given by classical mechanics, namely that the cluster is much more mobile (liquid-like) than in the classical case. Liquid para-hydrogen at two thermodynamic state points (25 K and 14 K under nearly zero external pressure) has also been studied. The momentum autocorrelation function obtained from the TGA/LSC-IVR approach shows very good agreement with recent accurate path integral Monte Carlo (PIMC) results at 25 K. The self-diffusion constants calculated by the TGA/LSC-IVR are in reasonable agreement with those from experiment and from other theoretical calculations. These applications demonstrate the TGA/LSC-IVR to be a practical and versatile method for quantum dynamics simulations of condensed phase systems.
PCR-based approach to SINE isolation: simple and complex SINEs.
Borodulina, Olga R; Kramerov, Dmitri A
2005-04-11
Highly repeated copies of short interspersed elements (SINEs) occur in eukaryotic genomes. The distribution of each SINE family is usually restricted to some genera, families, or orders. SINEs have an RNA polymerase III internal promoter, which is composed of boxes A and B. Here we propose a method for isolation of novel SINE families based on genomic DNA PCR with oligonucleotide identical to box A as a primer. Cloning of the size-heterogeneous PCR-products and sequencing of their terminal regions allow determination of SINE structure. Using this approach, two novel SINE families, Rhin-1 and Das-1, from the genomes of great horseshoe bat (Rhinolophus ferrumequinum) and nine-banded armadillo (Dasypus novemcinctus), respectively, were isolated and studied. The distribution of Rhin-1 is restricted to two of six bat families tested. Copies of this SINE are characterized by frequent internal insertions and significant length (200-270 bp). Das-1 being only 90 bp in length is one of the shortest SINEs known. Most of Das-1 nucleotide sequences demonstrate significant similarity to alanine tRNA which appears to be an evolutionary progenitor of this SINE. Together with three other known SINEs (ID, Vic-1, and CYN), Das-1 constitutes a group of simple SINEs. Interestingly, three SINE families of this group are alanine tRNA-derived. Most probably, this tRNA gave rise to short and simple but successful SINEs several times during mammalian evolution.
Deterministic approach for multiple-source tsunami hazard assessment for Sines, Portugal
Wronna, M.; Omira, R.; Baptista, M. A.
2015-11-01
In this paper, we present a deterministic approach to tsunami hazard assessment for the city and harbour of Sines, Portugal, one of the test sites of project ASTARTE (Assessment, STrategy And Risk Reduction for Tsunamis in Europe). Sines has one of the most important deep-water ports, which has oil-bearing, petrochemical, liquid-bulk, coal, and container terminals. The port and its industrial infrastructures face the ocean southwest towards the main seismogenic sources. This work considers two different seismic zones: the Southwest Iberian Margin and the Gloria Fault. Within these two regions, we selected a total of six scenarios to assess the tsunami impact at the test site. The tsunami simulations are computed using NSWING, a Non-linear Shallow Water model wIth Nested Grids. In this study, the static effect of tides is analysed for three different tidal stages: MLLW (mean lower low water), MSL (mean sea level), and MHHW (mean higher high water). For each scenario, the tsunami hazard is described by maximum values of wave height, flow depth, drawback, maximum inundation area and run-up. Synthetic waveforms are computed at virtual tide gauges at specific locations outside and inside the harbour. The final results describe the impact at the Sines test site considering the single scenarios at mean sea level, the aggregate scenario, and the influence of the tide on the aggregate scenario. The results confirm the composite source of Horseshoe and Marques de Pombal faults as the worst-case scenario, with wave heights of over 10 m, which reach the coast approximately 22 min after the rupture. It dominates the aggregate scenario by about 60 % of the impact area at the test site, considering maximum wave height and maximum flow depth. The HSMPF scenario inundates a total area of 3.5 km2.
Ngui, Dianah, E-mail: ngui.diana@ku.ac.ke [Kenyatta University, P.O. Box 43844-00100, Nairobi (Kenya); Kenya Institute for Public Policy Research and Analysis, P.O. Box, 56445-00200, Nairobi (Kenya); Mutua, John [Energy Regulatory Commission, P.O. Box 42681-00100, Nairobi (Kenya); Osiolo, Hellen; Aligula, Eric [Kenya Institute for Public Policy Research and Analysis, P.O. Box, 56445-00200, Nairobi (Kenya)
2011-11-15
This paper estimates price and fuel expenditure elasticities of demand by applying the linear Approximate Almost Ideal Demand system (LA-AIDS) to 3665 households sampled across Kenya in 2009. The results indicate that motor spirit premium (MSP), automotive gas oil (AGO) and lubricants are price elastic while fuel wood, kerosene, charcoal, liquefied petroleum gas (LPG) and electricity are price inelastic. Kerosene is income elastic while fuel wood, charcoal, LPG, electricity, MSP and AGO are income inelastic. The results also reveal fuel stack behaviour, that is, multiple fuel use among the households. Main policy implications of the results include increasing the penetration of alternative fuels as well as provision of more fiscal incentives to increase usage of cleaner fuels. This not withstanding however, the household income should be increased beyond a certain point for the household to completely shift and use a new fuel. - Highlights: > Fuel wood, kerosene, charcoal, LPG and electricity are price inelastic. > Kerosene is income elastic. > Fuel wood, charcoal, electricity, LPG, MSP and AGO are income inelastic. > Results reveal fuel stack behaviour among the households. > Income should be increased beyond a certain point to facilitate fuel switch.
Bioinformatic analysis of Entamoeba histolytica SINE1 elements
Butcher Sarah A
2010-05-01
Full Text Available Abstract Background Invasive amoebiasis, caused by infection with the human parasite Entamoeba histolytica remains a major cause of morbidity and mortality in some less-developed countries. Genetically E. histolytica exhibits a number of unusual features including having approximately 20% of its genome comprised of repetitive elements. These include a number of families of SINEs - non-autonomous elements which can, however, move with the help of partner LINEs. In many eukaryotes SINE mobility has had a profound effect on gene expression; in this study we concentrated on one such element - EhSINE1, looking in particular for evidence of recent transposition. Results EhSINE1s were detected in the newly reassembled E. histolytica genome by searching with a Hidden Markov Model developed to encapsulate the key features of this element; 393 were detected. Examination of their sequences revealed that some had an internal structure showing one to four 26-27 nt repeats. Members of the different classes differ in a number of ways and in particular those with two internal repeats show the properties expected of fairly recently transposed SINEs - they are the most homogeneous in length and sequence, they have the longest (i.e. the least decayed target site duplications and are the most likely to show evidence (in a cDNA library of active transcription. Furthermore we were able to identify 15 EhSINE1s (6 pairs and one triplet which appeared to be identical or very nearly so but inserted into different sites in the genome; these provide good evidence that if mobility has now ceased it has only done so very recently. Conclusions Of the many families of repetitive elements present in the genome of E. histolytica we have examined in detail just one - EhSINE1. We have shown that there is evidence for waves of transposition at different points in the past and no evidence that mobility has entirely ceased. There are many aspects of the biology of this parasite which
Thomas Philipp
2012-05-01
Full Text Available Abstract Background It is well known that the deterministic dynamics of biochemical reaction networks can be more easily studied if timescale separation conditions are invoked (the quasi-steady-state assumption. In this case the deterministic dynamics of a large network of elementary reactions are well described by the dynamics of a smaller network of effective reactions. Each of the latter represents a group of elementary reactions in the large network and has associated with it an effective macroscopic rate law. A popular method to achieve model reduction in the presence of intrinsic noise consists of using the effective macroscopic rate laws to heuristically deduce effective probabilities for the effective reactions which then enables simulation via the stochastic simulation algorithm (SSA. The validity of this heuristic SSA method is a priori doubtful because the reaction probabilities for the SSA have only been rigorously derived from microscopic physics arguments for elementary reactions. Results We here obtain, by rigorous means and in closed-form, a reduced linear Langevin equation description of the stochastic dynamics of monostable biochemical networks in conditions characterized by small intrinsic noise and timescale separation. The slow-scale linear noise approximation (ssLNA, as the new method is called, is used to calculate the intrinsic noise statistics of enzyme and gene networks. The results agree very well with SSA simulations of the non-reduced network of elementary reactions. In contrast the conventional heuristic SSA is shown to overestimate the size of noise for Michaelis-Menten kinetics, considerably under-estimate the size of noise for Hill-type kinetics and in some cases even miss the prediction of noise-induced oscillations. Conclusions A new general method, the ssLNA, is derived and shown to correctly describe the statistics of intrinsic noise about the macroscopic concentrations under timescale separation conditions
Evolutionary applications of MIRs and SINEs
Buchanan, F; Crawford, A; Strobeck, C; Palsboll, P; Plante, Y
It is believed that short interspersed elements (SINEs) are irreversibly inserted into genomes. We use this concept to try to deduce the evolution of whales using sequence and hybridization studies. The observation that microsatellites are associated with SINEs lead us to screen sequences
Evolutionary applications of MIRs and SINEs
Buchanan, F; Crawford, A; Strobeck, C; Palsboll, P; Plante, Y
1999-01-01
It is believed that short interspersed elements (SINEs) are irreversibly inserted into genomes. We use this concept to try to deduce the evolution of whales using sequence and hybridization studies. The observation that microsatellites are associated with SINEs lead us to screen sequences surroundin
Limitations caused by distortion in room impulse response measurements by swept sine technique
Stojic, Branko; Ciric, Dejan; Markovic, Milos
2011-01-01
of a measured response can be limited in a similar way as in maximum length sequence technique, although the saturation level (maximum dynamic range) is higher for swept sine technique. Thus, swept sine technique is also vulnerable to a certain extent to distortion that limits the quality of measured impulse......The significance of a room impulse response implies the requirement that its measurement should have a high level of accuracy in certain applications. One of the common problems in a measurement process is nonlinearity leading to the distortion of a room impulse response. Limitations caused...... by the distortion in room impulse response measurements by swept sine technique are analyzed here by the simulations and measurements. For the investigation, both linear and exponential swept sines are used as an excitation signal. In the simulations, this signal is modified by the nonlinearity model in the time...
Static Properties of the Multiple-Sine-Gordon Systems
Peyravi, M; Montakhab, Afshin
2010-01-01
In this paper, we examine some basic properties of the multiple-Sine-Gordon (MSG) systems, which constitute a generalization of the celebrated sine-Gordon (SG) system. We start by showing how MSG systems can be viewed as a general class of periodic functions. Next, periodic and step-like solutions of these systems are discussed in some details. In particular, we study the static properties of such systems by considering slope and phase diagrams. We also use concepts like energy density and pressure to characterize and distinguish such solutions. We interpret these solutions as an interacting many body system, in which kinks and antikinks behave as extended particles. Finally, we provide a linear stability analysis of periodic solutions which indicates short wavelength solutions to be stable.
Métris, Aline; George, Susie M; Ropers, Delphine
2017-01-02
Addition of salt to food is one of the most ancient and most common methods of food preservation. However, little is known of how bacterial cells adapt to such conditions. We propose to use piecewise linear approximations to model the regulatory adaptation of Escherichiacoli to osmotic stress. We apply the method to eight selected genes representing the functions known to be at play during osmotic adaptation. The network is centred on the general stress response factor, sigma S, and also includes a module representing the catabolic repressor CRP-cAMP. Glutamate, potassium and supercoiling are combined to represent the intracellular regulatory signal during osmotic stress induced by salt. The output is a module where growth is represented by the concentration of stable RNAs and the transcription of the osmotic gene osmY. The time course of gene expression of transport of osmoprotectant represented by the symporter proP and of the osmY is successfully reproduced by the network. The behaviour of the rpoS mutant predicted by the model is in agreement with experimental data. We discuss the application of the model to food-borne pathogens such as Salmonella; although the genes considered have orthologs, it seems that supercoiling is not regulated in the same way. The model is limited to a few selected genes, but the regulatory interactions are numerous and span different time scales. In addition, they seem to be condition specific: the links that are important during the transition from exponential to stationary phase are not all needed during osmotic stress. This model is one of the first steps towards modelling adaptation to stress in food safety and has scope to be extended to other genes and pathways, other stresses relevant to the food industry, and food-borne pathogens. The method offers a good compromise between systems of ordinary differential equations, which would be unmanageable because of the size of the system and for which insufficient data are available
Köylüoglu, H. U.; Nielsen, Søren R. K.; Cakmak, A. S.
Geometrically non-linear multi-degree-of-freedom (MDOF) systems subject to random excitation are considered. New semi-analytical approximate forward difference equations for the lower order non-stationary statistical moments of the response are derived from the stochastic differential equations...... of motion, and, the accuracy of these equations is numerically investigated. For stationary excitations, the proposed method computes the stationary statistical moments of the response from the solution of non-linear algebraic equations....
A ROM-less direct digital frequency synthesizer based on hybrid polynomial approximation.
Omran, Qahtan Khalaf; Islam, Mohammad Tariqul; Misran, Norbahiah; Faruque, Mohammad Rashed Iqbal
2014-01-01
In this paper, a novel design approach for a phase to sinusoid amplitude converter (PSAC) has been investigated. Two segments have been used to approximate the first sine quadrant. A first linear segment is used to fit the region near the zero point, while a second fourth-order parabolic segment is used to approximate the rest of the sine curve. The phase sample, where the polynomial changed, was chosen in such a way as to achieve the maximum spurious free dynamic range (SFDR). The invented direct digital frequency synthesizer (DDFS) has been encoded in VHDL and post simulation was carried out. The synthesized architecture exhibits a promising result of 90 dBc SFDR. The targeted structure is expected to show advantages for perceptible reduction of hardware resources and power consumption as well as high clock speeds.
Avramopoulos, A; Papadopoulos, M G; Reis, H
2007-03-15
A discrete model based on the multipolar expansion including terms up to hexadecapoles was employed to describe the electrostatic interactions in liquid acetonitrile. Liquid structures obtained form molecular dynamics simulations with different classical, nonpolarizable potentials were used to analyze the electrostatic interactions. The computed average local field was employed for the determination of the environmental effects on the linear and nonlinear electrical molecular properties. Dipole-dipole interactions yield the dominant contribution to the local field, whereas higher multipolar contributions are small but not negligible. Using the effective in-phase properties, macroscopic linear and nonlinear susceptibilities of the liquid were computed. Depending on the partial charges describing the Coulomb interactions of the force field employed, either the linear properties (refractive index and dielectric constant) were reproduced in good agreement with experiment or the nonlinear properties [third-harmonic generation (THG) and electric field induced second-harmonic (EFISH) generation] and the bulk density but never both sets of properties together. It is concluded that the partial charges of the force fields investigated are not suitable for reliable dielectric properties. New methods are probably necessary for the determination of partial charges, which should take into account the collective and long-range nature of electrostatic interactions more precisely.
Experimental Study of Turbulent Wake Behind a Sine Shaped Island in a Shallow-Water Layer
李玲; 李玉梁; 陈嘉范
2002-01-01
A series of experiments is conducted to study shallow-water flow in the wake of a sine shaped island. Digital particle imaging velocimetry (DPIV) is used to measure velocities in the turbulent wake behind a sine shaped island for different characteristic coefficients S. Flow streamlines are given for the wake flows. The measured results show that the characteristic coefficient S is uniquely related to the flow pattern around a sine shaped island in a shallow water layer. An S value of approximately 0.20 is the critical value for transition from a vortex street to unsteady flow and a value of approximately 0.40 is the critical value for transition from unsteady flow to steady flow.
Standard Sine Fitting Algorithms Applied To Blade Tip Timing Data
Kaźmierczak Krzysztof
2014-12-01
Full Text Available Blade Tip Timing (BTT is a non-intrusive method to measure blade vibration in turbomachinery. Time of Arrival (TOA is recorded when a blade is passing a stationary sensor. The measurement data, in form of undersampled (aliased tip-deflection signal, are difficult to analyze with standard signal processing methods like digital filters or Fourier Transform. Several indirect methods are applied to process TOA sequences, such as reconstruction of aliased spectrum and Least-Squares Fitting to harmonic oscillator model. We used standard sine fitting algorithms provided by IEEE-STD-1057 to estimate blade vibration parameters. Blade-tip displacement was simulated in time domain using SDOF model, sampled by stationary sensors and then processed by the sinefit.m toolkit. We evaluated several configurations of different sensor placement, noise level and number of data. Results of the linear sine fitting, performed with the frequency known a priori, were compared with the non-linear ones. Some of non-linear iterations were not convergent. The algorithms and testing results are aimed to be used in analysis of asynchronous blade vibration.
SINEBase: a database and tool for SINE analysis.
Vassetzky, Nikita S; Kramerov, Dmitri A
2013-01-01
SINEBase (http://sines.eimb.ru) integrates the revisited body of knowledge about short interspersed elements (SINEs). A set of formal definitions concerning SINEs was introduced. All available sequence data were screened through these definitions and the genetic elements misidentified as SINEs were discarded. As a result, 175 SINE families have been recognized in animals, flowering plants and green algae. These families were classified by the modular structure of their nucleotide sequences and the frequencies of different patterns were evaluated. These data formed the basis for the database of SINEs. The SINEBase website can be used in two ways: first, to explore the database of SINE families, and second, to analyse candidate SINE sequences using specifically developed tools. This article presents an overview of the database and the process of SINE identification and analysis.
Chi-Chang Wang
2013-09-01
Full Text Available This paper seeks to use the proposed residual correction method in coordination with the monotone iterative technique to obtain upper and lower approximate solutions of singularly perturbed non-linear boundary value problems. First, the monotonicity of a non-linear differential equation is reinforced using the monotone iterative technique, then the cubic-spline method is applied to discretize and convert the differential equation into the mathematical programming problems of an inequation, and finally based on the residual correction concept, complex constraint solution problems are transformed into simpler questions of equational iteration. As verified by the four examples given in this paper, the method proposed hereof can be utilized to fast obtain the upper and lower solutions of questions of this kind, and to easily identify the error range between mean approximate solutions and exact solutions.
Grima, Ramon
2015-10-01
It is well known that the linear-noise approximation (LNA) agrees with the chemical master equation, up to second-order moments, for chemical systems composed of zero and first-order reactions. Here we show that this is also a property of the LNA for a subset of chemical systems with second-order reactions. This agreement is independent of the number of interacting molecules.
Discretizing of linear systems with time-delay Using method of Euler’s and Tustin’s approximations
Bemri H’mida
2015-03-01
Full Text Available Delays deteriorate the control performance and could destabilize the overall system in the theory of discretetime signals and dynamic systems. Whenever a computer is used in measurement, signal processing or control applications, the data as seen from the computer and systems involved are naturally discrete-time because a computer executes program code at discrete points of time. Theory of discrete-time dynamic signals and systems is useful in design and analysis of control systems, signal filters, state estimators and model estimation from time-series of process data system identification. In this paper, a new approximated discretization method and digital design for control systems with delays is proposed. System is transformed to a discrete-time model with time delays. To implement the digital modeling, we used the z-transfer functions matrix which is a useful model type of discrete-time systems, being analogous to the Laplace-transform for continuous-time systems. The most important use of the z-transform is for defining z-transfer functions matrix is employed to obtain an extended discrete-time. The proposed method can closely approximate the step response of the original continuous timedelayed control system by choosing various of energy loss level. Illustrative example is simulated to demonstrate the effectiveness of the developed method.
Pham, Ninh Dang; Pagh, Rasmus
2012-01-01
Outlier mining in d-dimensional point sets is a fundamental and well studied data mining task due to its variety of applications. Most such applications arise in high-dimensional domains. A bottleneck of existing approaches is that implicit or explicit assessments on concepts of distance or nearest...... neighbor are deteriorated in high-dimensional data. Following up on the work of Kriegel et al. (KDD '08), we investigate the use of angle-based outlier factor in mining high-dimensional outliers. While their algorithm runs in cubic time (with a quadratic time heuristic), we propose a novel random...... projection-based technique that is able to estimate the angle-based outlier factor for all data points in time near-linear in the size of the data. Also, our approach is suitable to be performed in parallel environment to achieve a parallel speedup. We introduce a theoretical analysis of the quality...
Churakov, Gennady; Smit, Arian F A; Brosius, Jürgen; Schmitz, Jürgen
2005-04-01
About half of the mammalian genome is composed of retroposons. Long interspersed elements (LINEs) and short interspersed elements (SINEs) are the most abundant repetitive elements and account for about 21% and 13% of the human genome, respectively. SINEs have been detected in all major mammalian lineages, except for the South American order Xenarthra, also termed Edentata (armadillos, anteaters, and sloths). Investigating this order, we discovered a novel high-copy-number family of tRNA derived SINEs in the nine-banded armadillo Dasypus novemcinctus, a species that successfully crossed the Central American land bridge to North America in the Pliocene. A specific computer algorithm was developed, and we detected and extracted 687 specific SINEs from databases. Termed DAS-SINEs, we further divided them into six distinct subfamilies. We extracted tRNA(Ala)-derived monomers, two types of dimers, and three subfamilies of chimeric fusion products of a tRNA(Ala) domain and an approximately 180-nt sequence of thus far unidentified origin. Comparisons of secondary structures of the DAS-SINEs' tRNA domains suggest selective pressure to maintain a tRNA-like D-arm structure in the respective founder RNAs, as shown by compensatory mutations. By analysis of subfamily-specific genetic variability, comparison of the proportion of direct repeats, and analysis of self-integrations as well as key events of dimerization and deletions or insertions, we were able to delineate the evolutionary history of the DAS-SINE subfamilies.
Gravity localization in sine-Gordon braneworlds
Cruz, W T; Sousa, L J S; Almeida, C A S
2016-01-01
In this work we study two types of five-dimensional braneworld models given by sine-Gordon potentials. In both scenarios, the thick brane is generated by a real scalar field coupled to gravity. We focus our investigation on the localization of graviton field and the behaviour of the massive spectrum. In particular, we analyse the localization of massive modes by means of a relative probability method in a Quantum Mechanics context. Initially, considering a scalar field sine-Gordon potential, we find a resonance to the graviton at zero mode. However, when we consider a double sine-Gordon potential, the brane structure is changed allowing the existence of massless and massive resonant states. The new results show how the existence of an internal structure can aid in the emergence of massive resonant modes on the brane.
Gravity localization in sine-Gordon braneworlds
Cruz, W.T., E-mail: wilamicruz@gmail.com [Instituto Federal de Educação, Ciência e Tecnologia do Ceará (IFCE), Campus Juazeiro do Norte, 63040-540 Juazeiro do Norte, Ceará (Brazil); Maluf, R.V., E-mail: r.v.maluf@fisica.ufc.br [Departamento de Física, Universidade Federal do Ceará (UFC), C.P. 6030, 60455-760 Fortaleza, Ceará (Brazil); Sousa, L.J.S., E-mail: luisjose@fisica.ufc.br [Instituto Federal de Educação, Ciência e Tecnologia do Ceará (IFCE), Campus Canindé, 62700-000 Canindé, Ceará (Brazil); Almeida, C.A.S., E-mail: carlos@fisica.ufc.br [Departamento de Física, Universidade Federal do Ceará (UFC), C.P. 6030, 60455-760 Fortaleza, Ceará (Brazil)
2016-01-15
In this work we study two types of five-dimensional braneworld models given by sine-Gordon potentials. In both scenarios, the thick brane is generated by a real scalar field coupled to gravity. We focus our investigation on the localization of graviton field and the behaviour of the massive spectrum. In particular, we analyse the localization of massive modes by means of a relative probability method in a Quantum Mechanics context. Initially, considering a scalar field sine-Gordon potential, we find a localized state to the graviton at zero mode. However, when we consider a double sine-Gordon potential, the brane structure is changed allowing the existence of massive resonant states. The new results show how the existence of an internal structure can aid in the emergence of massive resonant modes on the brane.
Gulati, Mamta; Saini, Tarun Deep
2016-07-01
The short-wave asymptotics (WKB) of spiral density waves in self-gravitating stellar discs is well suited for the study of the dynamics of tightly-wound wavepackets. But the textbook WKB theory is not well adapted to the study of the linear eigenmodes in a collisionless self-gravitating disc because of the transcendental nature of the dispersion relation. We present a modified WKB theory of spiral density waves, for collisionless discs in the epicyclic limit, in which the perturbed gravitational potential is related to the perturbed surface density by the Poisson integral in Kalnaj's logarithmic spiral form. An integral equation is obtained for the surface density perturbation, which is seen to also reduce to the standard WKB dispersion relation. Although our formulation is general and applies to all discs, we present our analysis only for nearly Keplerian, low-mass, self-gravitating discs revolving around massive central objects, and derive an integral equation governing the slow precessional modes of such discs. For a prograde disc, the integral kernel turns out be real and symmetric, implying that all slow modes are stable. We apply the slow mode integral equation to two unperturbed disc profiles, the Jalali-Tremaine annular discs, and the Kuzmin disc. We determine eigenvalues and eigenfunctions for both m = 1 and m = 2 slow modes for these profiles and discuss their properties. Our results compare well with those of Jalali-Tremaine.
Gulati, Mamta
2016-01-01
The short--wave asymptotics (WKB) of spiral density waves in self-gravitating stellar discs is well suited for the study of the dynamics of tightly--wound wavepackets. But the textbook WKB theory is not well adapted to the study of the linear eigenmodes in a collisionless self-gravitating disc because of the transcendental nature of the dispersion relation. We present a modified WKB of spiral density waves, for collisionless discs in the epicyclic limit, in which the perturbed gravitational potential is related to the perturbed surface density by the Poisson integral in Kalnaj's logarithmic spiral form. An integral equation is obtained for the surface density perturbation, which is seen to also reduce to the standard WKB dispersion relation. We specialize to a low mass (or Keplerian) self-gravitating disc around a massive black hole, and derive an integral equation governing the eigenspectra and eigenfunctions of slow precessional modes. For a prograde disc, the integral kernel turns out be real and symmetric...
张珺; 郭宇锋; 徐跃; 林宏; 杨慧; 洪洋; 姚佳飞
2015-01-01
A novel one-dimensional (1D) analytical model is proposed for quantifying the breakdown voltage of reduced surface field (RESURF) lateral power device fabricated on silicon on an insulator (SOI) substrate. We assume that the charges in the depletion region contribute to the lateral PN junctions along the diagonal of the area shared by the lateral and vertical depletion regions. Based on the assumption, the lateral PN junction behaves as a linearly graded junction, thus resulting in a reduced surface electric field and high breakdown voltage. Using the proposed model, the breakdown voltage as a function of device parameters is investigated and compared with the numerical simulation by the TCAD tools. The analytical results are shown to be in fair agreement with the numerical results. Finally, a new RESURF criterion is derived which offers a useful scheme to optimize the structure parameters. This simple 1D model provides a clear physical insight into the RESURF effect and a new explanation on the improvement in breakdown voltage in an SOI RESURF device.
On the Monge-Ampère equivalent of the sine-Gordon equation
Ferapontov, E V
1994-01-01
Surfaces of constant negative curvature in Euclidean space can be described by either the sine-Gordon equation for the angle between asymptotic directions, or a Monge-Ampère equation for the graph of the surface. We present the explicit form of the correspondence between these two integrable non-linear partial differential equations using their well-known properties in differential geometry. We find that the cotangent of the angle between asymptotic directions is directly related to the mean curvature of the surface. This is a Bäcklund-type transformation between the sine-Gordon and Monge-Ampère equations.
Identification of novel SINEs from Cyprinidae and their evolutionary significance
HAN Yawei; HE Shunping; CHEN Yiyu
2007-01-01
Short interspersed nuclear elements (SINEs) are widespread among eukaryotic genomes. They are repetitive DNA sequences that have been amplified by retrotransposition. In this study, a class of SINEs were isolated from the Opsariichthys bidens genome, and named Opsar. Sequence analysis confirmed that Opsar is a new class of typical SINEs derived from tRNA molecules. With the tRNA-derived region of Opsar and through BLASTN search, we further identified Zb-SINEs from the zebrafish genome, which includes two groups: Zb-SINE-A and Zb-SINE-B. The Zb-SINE-A group comprises subfamilies of -A1-A5, and the Zb-SINE-B group is a dimer of the tRNAAla-derived region and shares a similar dimeric composition to Alu. Zb-SINEs are composed of three distinct regions:a 5' end tRNA-derived region, a tRNA-unrelated region and a 3' end AT-rich region. The flanking regions are AT rich. The average length of Zb-SINEs elements is about 340 bp. Zb-SINEs account for as much as 0.1% of the whole zebrafish genome. About 70 % of the Zb-SINEs are on chromosomes 11, 18, and 19. These Zb-SINEs were characterized by PCR and dot hybridization. The distribution pattern of Zb-SINEs in genome strongly supports the master genes model. The tRNA-derived regions of Opsar and Zb-SINEs were compared with the tRNAAla gene, and they showed 76 % similarity, indicating that Opsar and Zb-SINEs originated from an inactive tRNAAlasequence or a tRNAAla-like sequence. In view of the evolutionary status of zebrafish in the Cyprinidae, we deduced that Zb-SINEs were a very old class of interspersed sequences.
Newly discovered young CORE-SINEs in marsupial genomes.
Munemasa, Maruo; Nikaido, Masato; Nishihara, Hidenori; Donnellan, Stephen; Austin, Christopher C; Okada, Norihiro
2008-01-15
Although recent mammalian genome projects have uncovered a large part of genomic component of various groups, several repetitive sequences still remain to be characterized and classified for particular groups. The short interspersed repetitive elements (SINEs) distributed among marsupial genomes are one example. We have identified and characterized two new SINEs from marsupial genomes that belong to the CORE-SINE family, characterized by a highly conserved "CORE" domain. PCR and genomic dot blot analyses revealed that the distribution of each SINE shows distinct patterns among the marsupial genomes, implying different timing of their retroposition during the evolution of marsupials. The members of Mar3 (Marsupialia 3) SINE are distributed throughout the genomes of all marsupials, whereas the Mac1 (Macropodoidea 1) SINE is distributed specifically in the genomes of kangaroos. Sequence alignment of the Mar3 SINEs revealed that they can be further divided into four subgroups, each of which has diagnostic nucleotides. The insertion patterns of each SINE at particular genomic loci, together with the distribution patterns of each SINE, suggest that the Mar3 SINEs have intensively amplified after the radiation of diprotodontians, whereas the Mac1 SINE has amplified only slightly after the divergence of hypsiprimnodons from other macropods. By compiling the information of CORE-SINEs characterized to date, we propose a comprehensive picture of how SINE evolution occurred in the genomes of marsupials.
Carnivore-specific SINEs (Can-SINEs): distribution, evolution, and genomic impact.
Walters-Conte, Kathryn B; Johnson, Diana L E; Allard, Marc W; Pecon-Slattery, Jill
2011-01-01
Short interspersed nuclear elements (SINEs) are a type of class 1 transposable element (retrotransposon) with features that allow investigators to resolve evolutionary relationships between populations and species while providing insight into genome composition and function. Characterization of a Carnivora-specific SINE family, Can-SINEs, has, has aided comparative genomic studies by providing rare genomic changes, and neutral sequence variants often needed to resolve difficult evolutionary questions. In addition, Can-SINEs constitute a significant source of functional diversity with Carnivora. Publication of the whole-genome sequence of domestic dog, domestic cat, and giant panda serves as a valuable resource in comparative genomic inferences gleaned from Can-SINEs. In anticipation of forthcoming studies bolstered by new genomic data, this review describes the discovery and characterization of Can-SINE motifs as well as describes composition, distribution, and effect on genome function. As the contribution of noncoding sequences to genomic diversity becomes more apparent, SINEs and other transposable elements will play an increasingly large role in mammalian comparative genomics.
Sine-Bar Attachment For Machine Tools
Mann, Franklin D.
1988-01-01
Sine-bar attachment for collets, spindles, and chucks helps machinists set up quickly for precise angular cuts that require greater precision than provided by graduations of machine tools. Machinist uses attachment to index head, carriage of milling machine or lathe relative to table or turning axis of tool. Attachment accurate to 1 minute or arc depending on length of sine bar and precision of gauge blocks in setup. Attachment installs quickly and easily on almost any type of lathe or mill. Requires no special clamps or fixtures, and eliminates many trial-and-error measurements. More stable than improvised setups and not jarred out of position readily.
Sines and Cosines. Part 3 of 3
Apostol, Tom M. (Editor)
1994-01-01
In this 'Project Mathematics' series video, the addition formulas of sines and cosines are explained and their real life applications are demonstrated. Both film footage and computer animation is used. Several mathematical concepts are discussed and include: Ptolemy's theorem concerned with quadrilaterals; the difference between a central angle and an inscribed angle; sines and chord lengths; special angles; subtraction formulas; and a application to simple harmonic motion. A brief history of the city Alexandria, its mathematicians, and their contribution to the field of mathematics is shown.
Sine-Bar Attachment For Machine Tools
Mann, Franklin D.
1988-01-01
Sine-bar attachment for collets, spindles, and chucks helps machinists set up quickly for precise angular cuts that require greater precision than provided by graduations of machine tools. Machinist uses attachment to index head, carriage of milling machine or lathe relative to table or turning axis of tool. Attachment accurate to 1 minute or arc depending on length of sine bar and precision of gauge blocks in setup. Attachment installs quickly and easily on almost any type of lathe or mill. Requires no special clamps or fixtures, and eliminates many trial-and-error measurements. More stable than improvised setups and not jarred out of position readily.
BoS: a large and diverse family of short interspersed elements (SINEs) in Brassica oleracea.
Zhang, Xiaoyu; Wessler, Susan R
2005-05-01
Short interspersed elements (SINEs) are nonautonomous non-LTR retrotransposons that populate eukaryotic genomes. Numerous SINE families have been identified in animals, whereas only a few have been described in plants. Here we describe a new family of SINEs, named BoS, that is widespread in Brassicaceae and present at approximately 2000 copies in Brassica oleracea. In addition to sharing a modular structure and target site preference with previously described SINEs, BoS elements have several unusual features. First, the head regions of BoS RNAs can adopt a distinct hairpin-like secondary structure. Second, with 15 distinct subfamilies, BoS represents one of the most diverse SINE families described to date. Third, several of the subfamilies have a mosaic structure that has arisen through the exchange of sequences between existing subfamilies, possibly during retrotransposition. Analysis of BoS subfamilies indicate that they were active during various time periods through the evolution of Brassicaceae and that active elements may still reside in some Brassica species. As such, BoS elements may be a valuable tool as phylogenetic makers for resolving outstanding issues in the evolution of species in the Brassicaceae family.
Peng, Degao; van Aggelen, Helen; Steinmann, Stephan; Yang, Yang; Yang, Weitao; Duke University Team
2014-03-01
The particle-particle random-phase approximation (pp-RPA) recently attracts extensive interests in quantum chemistry recently. Pp-RPA is a versatile model to calculate ground-state correlation energies, and double ionization potential/double electron affinity. We inspect particle-particle random-phase approximation in different perspectives to further understand its theoretical fundamentals. Viewed as summation of all ladder diagrams, the pp-RPA correlation energy is proved to be analytically equivalent to the ladder coupled-cluster doubles (ladder-CCD) theory. With this equivalence, we can make use of various well-established coupled-cluster techniques to study pp-RPA. Furthermore, we establish linear-response time-dependent density-functional theory with pairing fields (TDDFT-PF), where pp-RPA can be interpreted as the mean-field approximation to a general theory. TDDFT-PF is closely related to the density-functional theory of superconductors, but is applied to normal systems to capture exact N plus/minus 2 excitations. In the linear-response regime, both the adiabatic and non-adiabatic TDDFT-PF equations are established. This sets the fundamentals for further density-functional developments aiming for pp-RPA. These theoretical perspectives will be very helpful for future study.
Another Method to Find the Derivative of Sine
Zhang Yuanyi
2005-01-01
@@ 1 Introduction It is very important to find the derivative of sine in mathematics. For each derivative of trigonometric functions is begin with sine. The sketch of its proof is transforming two subtracted sine functions into the form of multiplication[1][2][3][4][5][6].But this method appears the form of fraction, so it is difficult for the beginners and the self - learners to understand the increment of the sine function △y[1
Zuehlsdorff, Tim J; Payne, Mike C; Haynes, Peter D
2015-01-01
We present a solution of the full TDDFT eigenvalue equation in the linear response formalism exhibiting a linear-scaling computational complexity with system size, without relying on the simplifying Tamm-Dancoff approximation (TDA). The implementation relies on representing the occupied and unoccupied subspace with two different sets of in situ optimised localised functions, yielding a very compact and efficient representation of the transition density matrix of the excitation with the accuracy associated with a systematic basis set. The TDDFT eigenvalue equation is solved using a preconditioned conjugate-gradients algorithm that is very memory-efficient. The algorithm is validated on a test molecule and a good agreement with results obtained from standard quantum chemistry packages is found, with the preconditioner yielding a significant improvement in convergence rates. The method developed in this work is then used to reproduce experimental results of the absorption spectrum of bacteriochlorophyll (BChl) i...
Benjamin Banneker and the Law of Sines
Mahoney, John F.
2005-01-01
Benjamin Banneker, a self-taught mathematician, surveyor and astronomer published annual almanacs containing his astronomical observations and predictions. Banneker who also used logarithms to apply the Law of Sines believed that the method used to solve a mathematical problem depends on the tools available.
Ferranti, Francesco; Rolain, Yves
2017-01-01
This paper proposes a novel state-space matrix interpolation technique to generate linear parameter-varying (LPV) models starting from a set of local linear time-invariant (LTI) models estimated at fixed operating conditions. Since the state-space representation of LTI models is unique up to a similarity transformation, the state-space matrices need to be represented in a common state-space form. This is needed to avoid potentially large variations as a function of the scheduling parameters of the state-space matrices to be interpolated due to underlying similarity transformations, which might degrade the accuracy of the interpolation significantly. Underlying linear state coordinate transformations for a set of local LTI models are extracted by the computation of similarity transformation matrices by means of linear least-squares approximations. These matrices are then used to transform the local LTI state-space matrices into a form suitable to achieve accurate interpolation results. The proposed LPV modeling technique is validated by pertinent numerical results.
李春先; 方卯发
2003-01-01
We present the linear entropy dynarmics of the field state in the dispersive cavity in the Jaynes-Cummings model with an intensity-dependent coupling in the dispersive approximation, and investigate the influence of dissipation on entanglement between the field and the atoms. We show that the coherence properties of the field are also affected by the cavity when the nonlinear process of the field interacting with the atoms with an intensity-dependent coupling is involved, and find that the dissipation constant, the intensity of the field and the atomic distribution angle have different influence on the coherence properties of the field.
Dilogarithm Identities for Sine-Gordon and Reduced Sine-Gordon Y-Systems
Tomoki Nakanishi
2010-10-01
Full Text Available We study the family of Y-systems and T-systems associated with the sine-Gordon models and the reduced sine-Gordon models for the parameter of continued fractions with two terms. We formulate these systems by cluster algebras, which turn out to be of finite type, and prove their periodicities and the associated dilogarithm identities which have been conjectured earlier. In particular, this provides new examples of periodicities of seeds.
Ben-David, Smadar; Yaakov, Beery; Kashkush, Khalil
2013-10-01
Short interspersed nuclear elements (SINEs) are non-autonomous non-LTR retroelements that are present in most eukaryotic species. While SINEs have been intensively investigated in humans and other animal systems, they are poorly studied in plants, especially in wheat (Triticum aestivum). We used quantitative PCR of various wheat species to determine the copy number of a wheat SINE family, termed Au SINE, combined with computer-assisted analyses of the publicly available 454 pyrosequencing database of T. aestivum. In addition, we utilized site-specific PCR on 57 Au SINE insertions, transposon methylation display and transposon display on newly formed wheat polyploids to assess retrotranspositional activity, epigenetic status and genetic rearrangements in Au SINE, respectively. We retrieved 3706 different insertions of Au SINE from the 454 pyrosequencing database of T. aestivum, and found that most of the elements are inserted in A/T-rich regions, while approximately 38% of the insertions are associated with transcribed regions, including known wheat genes. We observed typical retrotransposition of Au SINE in the second generation of a newly formed wheat allohexaploid, and massive hypermethylation in CCGG sites surrounding Au SINE in the third generation. Finally, we observed huge differences in the copy numbers in diploid Triticum and Aegilops species, and a significant increase in the copy numbers in natural wheat polyploids, but no significant increase in the copy number of Au SINE in the first four generations for two of three newly formed allopolyploid species used in this study. Our data indicate that SINEs may play a prominent role in the genomic evolution of wheat through stress-induced activation. © 2013 Ben-Gurion University The Plant Journal © 2013 John Wiley & Sons Ltd.
Zuehlsdorff, T. J., E-mail: tjz21@cam.ac.uk; Payne, M. C. [Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE (United Kingdom); Hine, N. D. M. [Department of Physics, University of Warwick, Coventry CV4 7AL (United Kingdom); Haynes, P. D. [Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ (United Kingdom); Department of Physics, Imperial College London, Exhibition Road, London SW7 2AZ (United Kingdom); Thomas Young Centre for Theory and Simulation of Materials, Imperial College London, Exhibition Road, London SW7 2AZ (United Kingdom)
2015-11-28
We present a solution of the full time-dependent density-functional theory (TDDFT) eigenvalue equation in the linear response formalism exhibiting a linear-scaling computational complexity with system size, without relying on the simplifying Tamm-Dancoff approximation (TDA). The implementation relies on representing the occupied and unoccupied subspaces with two different sets of in situ optimised localised functions, yielding a very compact and efficient representation of the transition density matrix of the excitation with the accuracy associated with a systematic basis set. The TDDFT eigenvalue equation is solved using a preconditioned conjugate gradient algorithm that is very memory-efficient. The algorithm is validated on a small test molecule and a good agreement with results obtained from standard quantum chemistry packages is found, with the preconditioner yielding a significant improvement in convergence rates. The method developed in this work is then used to reproduce experimental results of the absorption spectrum of bacteriochlorophyll in an organic solvent, where it is demonstrated that the TDA fails to reproduce the main features of the low energy spectrum, while the full TDDFT equation yields results in good qualitative agreement with experimental data. Furthermore, the need for explicitly including parts of the solvent into the TDDFT calculations is highlighted, making the treatment of large system sizes necessary that are well within reach of the capabilities of the algorithm introduced here. Finally, the linear-scaling properties of the algorithm are demonstrated by computing the lowest excitation energy of bacteriochlorophyll in solution. The largest systems considered in this work are of the same order of magnitude as a variety of widely studied pigment-protein complexes, opening up the possibility of studying their properties without having to resort to any semiclassical approximations to parts of the protein environment.
Zuehlsdorff, T. J.; Hine, N. D. M.; Payne, M. C.; Haynes, P. D.
2015-11-01
We present a solution of the full time-dependent density-functional theory (TDDFT) eigenvalue equation in the linear response formalism exhibiting a linear-scaling computational complexity with system size, without relying on the simplifying Tamm-Dancoff approximation (TDA). The implementation relies on representing the occupied and unoccupied subspaces with two different sets of in situ optimised localised functions, yielding a very compact and efficient representation of the transition density matrix of the excitation with the accuracy associated with a systematic basis set. The TDDFT eigenvalue equation is solved using a preconditioned conjugate gradient algorithm that is very memory-efficient. The algorithm is validated on a small test molecule and a good agreement with results obtained from standard quantum chemistry packages is found, with the preconditioner yielding a significant improvement in convergence rates. The method developed in this work is then used to reproduce experimental results of the absorption spectrum of bacteriochlorophyll in an organic solvent, where it is demonstrated that the TDA fails to reproduce the main features of the low energy spectrum, while the full TDDFT equation yields results in good qualitative agreement with experimental data. Furthermore, the need for explicitly including parts of the solvent into the TDDFT calculations is highlighted, making the treatment of large system sizes necessary that are well within reach of the capabilities of the algorithm introduced here. Finally, the linear-scaling properties of the algorithm are demonstrated by computing the lowest excitation energy of bacteriochlorophyll in solution. The largest systems considered in this work are of the same order of magnitude as a variety of widely studied pigment-protein complexes, opening up the possibility of studying their properties without having to resort to any semiclassical approximations to parts of the protein environment.
Short interspersed elements (SINEs) of the Geomyoidea superfamily rodents.
Gogolevsky, Konstantin P; Kramerov, Dmitri A
2006-05-24
A new short interspersed element (SINE) was isolated from the genome of desert kangaroo rat (Dipodomys deserti) using single-primer PCR. This SINE consists of two monomers: the left monomer (IDL) resembles rodent ID element and other tRNAAla(CGC)-derived SINEs, whereas the right one (Geo) shows no similarity with known SINE sequences. PCR and hybridization analyses demonstrated that IDL-Geo SINE is restricted to the rodent superfamily Geomyoidea (families Geomyidea and Heteromyidea). Isolation and analysis of IDL-Geo from California pocket mouse (Chaetodipus californicus) and Botta's pocket gopher (Thomomys bottae) revealed some species-specific features of this SINE family. The structure and evolution of known dimeric SINEs are discussed.
Synchronisation in Coupled Sine Circle Maps
Chatterjee, N; Chatterjee, Nandini; Gupte, Neelima
1995-01-01
We study the spatially synchronized and temporally periodic solutions of a 1-d lattice of coupled sine circle maps. We carry out an analytic stability analysis of this spatially synchronized and temporally periodic case and obtain the stability matrix in a neat block diagonal form. We find spatially synchronized behaviour over a substantial range of parameter space. We have also extended the analysis to higher spatial periods with similar results. Numerical simulations for various temporal periods of the synchronized solution, reveal that the entire structure of the Arnold tongues and the devil's staircase seen in the case of the single circle map can also be observed for the synchronized coupled sine circle map lattice. Our formalism should be useful in the study of spatially periodic behaviour in other coupled map lattices.
Jung Nikolai H
2012-11-01
Full Text Available Abstract Background Transcranial magnetic stimulation (TMS commonly uses so-called monophasic pulses where the initial rapidly changing current flow is followed by a critically dampened return current. It has been shown that a monophasic TMS pulse preferentially excites different cortical circuits in the human motor hand area (M1-HAND, if the induced tissue current has a posterior-to-anterior (PA or anterior-to-posterior (AP direction. Here we tested whether similar direction-specific effects could be elicited in M1-HAND using TMS pulses with a half-sine wave configuration. Results In 10 young participants, we applied half-sine pulses to the right M1-HAND which elicited PA or AP currents with respect to the orientation of the central sulcus. Measurements of the motor evoked potential (MEP revealed that PA half-sine stimulation resulted in lower resting motor threshold (RMT than AP stimulation. When stimulus intensity (SI was gradually increased as percentage of maximal stimulator output, the stimulus–response curve (SRC of MEP amplitude showed a leftward shift for PA as opposed to AP half-sine stimulation. Further, MEP latencies were approximately 1 ms shorter for PA relative to AP half-sine stimulation across the entire SI range tested. When adjusting SI to the respective RMT of PA and AP stimulation, the direction-specific differences in MEP latencies persisted, while the gain function of MEP amplitudes was comparable for PA and AP stimulation. Conclusions Using half-sine pulse configuration, single-pulse TMS elicits consistent direction-specific effects in M1-HAND that are similar to TMS with monophasic pulses. The longer MEP latency for AP half-sine stimulation suggests that PA and AP half-sine stimulation preferentially activates different sets of cortical neurons that are involved in the generation of different corticospinal descending volleys.
Dermatomyositis Sine Myositis with Membranoproliferative Glomerulonephritis
Mohammad Bagher Owlia
2012-01-01
Full Text Available Dermatomyositis (DM is an autoimmune disease that is characterized by involvement of proximal musculature and skin. We report a 52-year-old woman with a 6-year history of dermatomyositis sine myositis, who developed lower extremity edema and proteinuria. Pathological examination of renal biopsy showed membranoproliferative glomerulonephritis. She received steroid, cyclophosphamide, and mycophenolate mofetil. Over the 9 to 10 months after the beginning of treatment, the proteinuria was improved.
Exact renormalization group and Sine Gordon theory
Oak, Prafulla; Sathiapalan, B.
2017-07-01
The exact renormalization group is used to study the RG flow of quantities in field theories. The basic idea is to write an evolution operator for the flow and evaluate it in perturbation theory. This is easier than directly solving the differential equation. This is illustrated by reproducing known results in four dimensional ϕ 4 field theory and the two dimensional Sine-Gordon theory. It is shown that the calculation of beta function is somewhat simplified. The technique is also used to calculate the c-function in two dimensional Sine-Gordon theory. This agrees with other prescriptions for calculating c-functions in the literature. If one extrapolates the connection between central charge of a CFT and entanglement entropy in two dimensions, to the c-function of the perturbed CFT, then one gets a value for the entanglement entropy in Sine-Gordon theory that is in exact agreement with earlier calculations (including one using holography) in arXiv:1610.04233.
Lin Shao
2016-01-01
Full Text Available Due to large numbers of antennas and users, matrix inversion is complicated in linear precoding techniques for massive MIMO systems. Several approximated matrix inversion methods, including the Neumann series, have been proposed to reduce the complexity. However, the Neumann series does not converge fast enough. In this paper, to speed up convergence, a new joint Newton iteration and Neumann series method is proposed, with the first iteration result of Newton iteration method being employed to reconstruct the Neumann series. Then, a high probability convergence condition is established, which can offer useful guidelines for practical massive MIMO systems. Finally, simulation examples are given to demonstrate that the new joint Newton iteration and Neumann series method has a faster convergence rate compared to the previous Neumann series, with almost no increase in complexity when the iteration number is greater than or equal to 2.
Samuelson, Paul A.
1978-01-01
In the usual Darwinian case in which struggle for existence leads to density limitations on the environment's carrying capacity, R. A. Fisher's reproductive-value concept reduces to zero for every initial age group. To salvage some meaning for Fisher's notion, two variant reproductive-value concepts are defined here: an “incipient reproductive-value function,” applicable to a system's early dilute stage when density effects are still ignorable; and a “second-order penultimate reproductive-value function,” linking to a system's initial conditions near equilibrium its much later small deviations from carrying-capacity equilibrium. Also, slowly changing age-structured mortality and fertility parameters of Lotka and Mendelian mating systems are shown to suggest linear reproductive-value surrogates that provide approximations for truly nonlinear diploid and haploid models. PMID:16592600
Lorin, E.; Yang, X.; Antoine, X.
2016-06-01
The paper is devoted to develop efficient domain decomposition methods for the linear Schrödinger equation beyond the semiclassical regime, which does not carry a small enough rescaled Planck constant for asymptotic methods (e.g. geometric optics) to produce a good accuracy, but which is too computationally expensive if direct methods (e.g. finite difference) are applied. This belongs to the category of computing middle-frequency wave propagation, where neither asymptotic nor direct methods can be directly used with both efficiency and accuracy. Motivated by recent works of the authors on absorbing boundary conditions (Antoine et al. (2014) [13] and Yang and Zhang (2014) [43]), we introduce Semiclassical Schwarz Waveform Relaxation methods (SSWR), which are seamless integrations of semiclassical approximation to Schwarz Waveform Relaxation methods. Two versions are proposed respectively based on Herman-Kluk propagation and geometric optics, and we prove the convergence and provide numerical evidence of efficiency and accuracy of these methods.
de Vega, H J; Sanchez, N G
2010-01-01
We combine observed properties of galaxies as the core density and radius with the theoretical linear evolution of density fluctuations computed from first principles since the end of inflation till today. The halo radius r_0 is computed in terms of cosmological parameters. The theoretical density profiles rho(r)/rho(0) have an universal shape as a function of r/r_0 which reproduces the observations. We show that the linear approximation to the Boltzmann-Vlasov equation is valid for very large galaxies and correctly provides universal quantities which are common to all galaxies, as the surface density and density profile. By matching the theoretically computed surface density to its observed value we obtain (i) the decreasing of the phase-space density during the MD era (ii) the mass of the dark matter particle which turns to be between 1 and 2 keV and the decoupling temperature T_d which turns to be above 100 GeV (iii) the core vs. cusp discrimination: keV dark matter particles produce cored density profiles...
Tetsu, Hiroyuki; Nakamoto, Taishi, E-mail: h.tetsu@geo.titech.ac.jp [Earth and Planetary Sciences, Tokyo Institute of Technology, Tokyo 152-8551 (Japan)
2016-03-15
Radiation is an important process of energy transport, a force, and a basis for synthetic observations, so radiation hydrodynamics (RHD) calculations have occupied an important place in astrophysics. However, although the progress in computational technology is remarkable, their high numerical cost is still a persistent problem. In this work, we compare the following schemes used to solve the nonlinear simultaneous equations of an RHD algorithm with the flux-limited diffusion approximation: the Newton–Raphson (NR) method, operator splitting, and linearization (LIN), from the perspective of the computational cost involved. For operator splitting, in addition to the traditional simple operator splitting (SOS) scheme, we examined the scheme developed by Douglas and Rachford (DROS). We solve three test problems (the thermal relaxation mode, the relaxation and the propagation of linear waves, and radiating shock) using these schemes and then compare their dependence on the time step size. As a result, we find the conditions of the time step size necessary for adopting each scheme. The LIN scheme is superior to other schemes if the ratio of radiation pressure to gas pressure is sufficiently low. On the other hand, DROS can be the most efficient scheme if the ratio is high. Although the NR scheme can be adopted independently of the regime, especially in a problem that involves optically thin regions, the convergence tends to be worse. In all cases, SOS is not practical.
Conserved domains and SINE diversity during animal evolution.
Luchetti, Andrea; Mantovani, Barbara
2013-10-01
Eukaryotic genomes harbour a number of mobile genetic elements (MGEs); moving from one genomic location to another, they are known to impact on the host genome. Short interspersed elements (SINEs) are well-represented, non-autonomous retroelements and they are likely the most diversified MGEs. In some instances, sequence domains conserved across unrelated SINEs have been identified; remarkably, one of these, called Nin, has been conserved since the Radiata-Bilateria splitting. Here we report on two new domains: Inv, derived from Nin, identified in insects and in deuterostomes, and Pln, restricted to polyneopteran insects. The identification of Inv and Pln sequences allowed us to retrieve new SINEs, two in insects and one in a hemichordate. The diverse structural combination of the different domains in different SINE families, during metazoan evolution, offers a clearer view of SINE diversity and their frequent de novo emergence through module exchange, possibly underlying the high evolutionary success of SINEs. © 2013 Elsevier Inc. All rights reserved.
Multiple sine, multiple elliptic gamma functions and rational cones
Tizzano, Luigi
2015-01-01
We define generalizations of the multiple elliptic gamma functions and the multiple sine functions, labelled by rational cones in $\\mathbb{R}^r$. For $r=2,3$ we prove that the generalized multiple elliptic gamma functions enjoy a modular property determined by the cone. This generalizes the modular properties of the elliptic gamma function studied by Felder and Varchenko. The generalized multiple sine enjoy a related infinite product representation, generalizing the results of Narukawa for the ordinary multiple sine functions.
Bov-B-mobilized SINEs in vertebrate genomes.
Gogolevsky, Konstantin P; Vassetzky, Nikita S; Kramerov, Dmitri A
2008-01-15
Two new short retroposon families (SINEs) have been found in the genome of springhare Pedetes capensis (Rodentia). One of them, Ped-1, originated from 5S rRNA, while the other one, Ped-2, originated from tRNA-derived SINE ID. In contrast to most currently active mammalian SINEs mobilized by L1 long retrotransposon (LINE), Ped-1 and Ped-2 are mobilized by Bov-B, a LINE family of the widely distributed RTE clade. The 3' part of these SINEs originates from two sequences in the 5' and 3' regions of Bov-B. Such bipartite structure of the LINE-derived part has been revealed in all Bov-B-mobilized SINEs known to date (AfroSINE, Bov-tA, Mar-1, and Ped-1/2), which distinguishes them from other SINEs with only a 3' LINE-derived part. Structural analysis and the distribution of Bov-B LINEs and partner SINEs supports the horizontal transfer of Bov-B, while the SINEs emerged independently in lineages with this LINE.
Jithinraj, P K; Roy, Ushasi; Gopalakrishnan, Manoj
2014-03-07
Zero-order ultrasensitivity (ZOU) is a long known and interesting phenomenon in enzyme networks. Here, a substrate is reversibly modified by two antagonistic enzymes (a 'push-pull' system) and the fraction in modified state undergoes a sharp switching from near-zero to near-unity at a critical value of the ratio of the enzyme concentrations, under saturation conditions. ZOU and its extensions have been studied for several decades now, ever since the seminal paper of Goldbeter and Koshland (1981); however, a complete probabilistic treatment, important for the study of fluctuations in finite populations, is still lacking. In this paper, we study ZOU using a modular approach, akin to the total quasi-steady state approximation (tQSSA). This approach leads to a set of Fokker-Planck (drift-diffusion) equations for the probability distributions of the intermediate enzyme-bound complexes, as well as the modified/unmodified fractions of substrate molecules. We obtain explicit expressions for various average fractions and their fluctuations in the linear noise approximation (LNA). The emergence of a 'critical point' for the switching transition is rigorously established. New analytical results are derived for the average and variance of the fractional substrate concentration in various chemical states in the near-critical regime. For the total fraction in the modified state, the variance is shown to be a maximum near the critical point and decays algebraically away from it, similar to a second-order phase transition. The new analytical results are compared with existing ones as well as detailed numerical simulations using a Gillespie algorithm.
Sines and Cosines. Part 2 of 3
Apostol, Tom M. (Editor)
1993-01-01
The Law of Sines and the Law of Cosines are introduced and demonstrated in this 'Project Mathematics' series video using both film footage and computer animation. This video deals primarily with the mathematical field of Trigonometry and explains how these laws were developed and their applications. One significant use is geographical and geological surveying. This includes both the triangulation method and the spirit leveling method. With these methods, it is shown how the height of the tallest mountain in the world, Mt. Everest, was determined.
Gildeberto S. Cardoso
2011-01-01
Full Text Available This paper presents a study of linear control systems based on exact feedback linearization and approximate feedback linearization. As exact feedback linearization is applied, a linear controller can perform the control objectives. The approximate feedback linearization is required when a nonlinear system presents a noninvolutive property. It uses a Taylor series expansion in order to compute a nonlinear transformation of coordinates to satisfy the involutivity conditions.
Kulyanitsa, A. L.; Rukhovich, A. D.; Rukhovich, D. D.; Koroleva, P. V.; Rukhovich, D. I.; Simakova, M. S.
2017-04-01
The concept of soil line can be to describe the temporal distribution of spectral characteristics of the bare soil surface. In this case, the soil line can be referred to as the multi-temporal soil line, or simply temporal soil line (TSL). In order to create TSL for 8000 regular lattice points for the territory of three regions of Tula oblast, we used 34 Landsat images obtained in the period from 1985 to 2014 after their certain transformation. As Landsat images are the matrices of the values of spectral brightness, this transformation is the normalization of matrices. There are several methods of normalization that move, rotate, and scale the spectral plane. In our study, we applied the method of piecewise linear approximation to the spectral neighborhood of soil line in order to assess the quality of normalization mathematically. This approach allowed us to range normalization methods according to their quality as follows: classic normalization > successive application of the turn and shift > successive application of the atmospheric correction and shift > atmospheric correction > shift > turn > raw data. The normalized data allowed us to create the maps of the distribution of a and b coefficients of the TSL. The map of b coefficient is characterized by the high correlation with the ground-truth data obtained from 1899 soil pits described during the soil surveys performed by the local institute for land management (GIPROZEM).
Johnson, Joseph F
2011-01-01
We give Sir James Jeans's notion of 'normal state' a mathematically precise definition. We prove that normal cells of trajectories exist in the Hamiltonian heat-bath model of an assembly of linearly coupled oscillators that generates the Ornstein--Uhlenbeck process in the limit of an infinite number of degrees of freedom. This, in some special cases, verifies some far-reaching conjectures of Khintchine on the weak ergodicity of a dynamical system with a large number of degrees of freedom. In order to estimate the theoretical auto-correlation function of a time series from the sample auto-correlation function of one of its realisations, it is usually assumed without justification that the time series is ergodic. Khintchine's conjectures about dynamical systems with large numbers of degrees of freedom justifies, even in the absence of ergodicity, approximately the same conclusions. Para emplear el correlograma de los valores muestrales de un proceso estoc\\'astico para estimar su funci\\'on te\\'orica de autocorre...
The Geometrodynamics of Sine-Gordon Solitons
Gegenberg, J
1998-01-01
The relationship between N-soliton solutions to the Euclidean sine-Gordon equation and Lorentzian black holes in Jackiw-Teitelboim dilaton gravity is investigated, with emphasis on the important role played by the dilaton in determining the black hole geometry. We show how an N-soliton solution can be used to construct ``sine-Gordon'' coordinates for a black hole of mass M, and construct the transformation to more standard ``Schwarzchild-like'' coordinates. For N=1 and 2, we find explicit closed form solutions to the dilaton equations of motion in soliton coordinates, and find the relationship between the soliton parameters and the black hole mass. Remarkably, the black hole mass is non-negative for arbitrary soliton parameters. In the one-soliton case the coordinates are shown to cover smoothly a region containing the whole interior of the black hole as well as a finite neighbourhood outside the horizon. A Hamiltonian analysis is performed for slicings that approach the soliton coordinates on the interior, a...
Bunched soliton states in weakly coupled sine-Gordon systems
Grønbech-Jensen, N.; Samuelsen, Mogens Rugholm; Lomdahl, P. S.
1990-01-01
The interaction between solitons of two weakly coupled sine-Gordon systems is considered. In particular, the stability of bunched states is investigated, and perturbation results are compared with numerical results.......The interaction between solitons of two weakly coupled sine-Gordon systems is considered. In particular, the stability of bunched states is investigated, and perturbation results are compared with numerical results....
Radial sine-Gordon kinks as sources of fast breathers
Caputo, Jean Guy; Sørensen, Mads Peter
2013-01-01
We consider radial sine-Gordon kinks in two, three, and higher dimensions. A full two-dimensional simulation showing that azimuthal perturbations remain small allows us to reduce the problem to the one-dimensional radial sine-Gordon equation. We solve this equation on an interval [r, r1] and abso...
有理三角曲面的分片线性逼近%Piecewise Linear Approximation of Rational Triangular Surfaces
周联; 王国瑾
2012-01-01
Piecewise linear approximation of rational triangular surfaces is useful in surfaces intersection, surfaces rendering and mesh generation. The approximation error bound is usually estimated based on the information about second-order derivative bounds of the rational triangular surfaces. But the derivative bounds of rational triangular surfaces are difficult and less effective to be estimated. To solve this problem, using homogeneous coordinates and inequality method, we present an algorithm to estimate subdivision depths for rational triangular surfaces which are defined in any arbitrary triangle. The estimation is performed on the polynomial surfaces, of which the given rational surfaces are the images under the standard perspective projection. It is more efficient than evaluating the derivative bounds of the given surfaces directly. The subdivison depth is obtained in advance, however, it guarantees the required flatness of the given surface after the subdivision. Moreover, using Mobius reparameterization technique, the variance of the log weights of rational triangular Bezier surfaces is minimized, which can obviously improve the efficiency of the algorithm. In particular, the optimal reparameterization is solved explicitly, so reparameterization hardly increases operating times. Numerical examples suggest that this algorithm not only possesses more powerful properties, but also is more effective compared with any other old methods.%有理三角曲面的分片线性逼近在参数曲面的求交、绘制等方面有着重要应用.已有研究主要采用曲面的二阶导矢界来估计逼近误差,而有理曲面的导矢界估计是一项困难的工作.为解决上述问题,利用齐次坐标,给出了一种定义域为任意三角形的有理三角曲面的分片线性逼近算法.该算法有效地避免了有理三角曲面的导矢界估计,并且离散段数可先验地给出.此外,通过重新参数化技术来缩小有理三角Bézier曲面的权
Origin and evolution of SINEs in eukaryotic genomes.
Kramerov, D A; Vassetzky, N S
2011-12-01
Short interspersed elements (SINEs) are one of the two most prolific mobile genomic elements in most of the higher eukaryotes. Although their biology is still not thoroughly understood, unusual life cycle of these simple elements amplified as genomic parasites makes their evolution unique in many ways. In contrast to most genetic elements including other transposons, SINEs emerged de novo many times in evolution from available molecules (for example, tRNA). The involvement of reverse transcription in their amplification cycle, huge number of genomic copies and modular structure allow variation mechanisms in SINEs uncommon or rare in other genetic elements (module exchange between SINE families, dimerization, and so on.). Overall, SINE evolution includes their emergence, progressive optimization and counteraction to the cell's defense against mobile genetic elements.
Matveev, Vitaliy; Nishihara, Hidenori; Okada, Norihiro
2007-08-01
Short interspersed elements (SINEs) constitute a group of retroposons propagating in the genome via a mechanism of reverse transcription, in which they depend on the enzymatic machinery of long retroposons (LINEs). Over 70 SINE families have been described to date from the genomes of various eukaryotes. Here, we characterize two novel SINEs from salmons (Actinopterygii: Salmonoidei). The first family, termed SlmI, was shown to be widespread among all genera of the suborder. These SINEs have a tRNA(Leu)-related promoter region at their 5'-end, a unique central conserved domain with a subfamily-specific region, and an end with RSg-1-LINE-derived 3'-terminus preceding the A/T-rich tail. The same LINE-related segment is also shared by two other salmonid SINEs: HpaI and OS-SINE1. The structural peculiarities and overall sequence identity of the SlmI 3'-terminus suggest that it has been acquired from HpaI SINEs but not directly from the partner LINE. This region plays a crucial role in the process of retrotransposition of short interspersed elements, and the case of its SINE-to-SINE transmission is the first recorded to date. Possible scenarios and potential evolutionary implications of the observed interaction between short retroposons are discussed. Apart from the above, we found a copy of the SlmI SINE in the GenBank entry for the blood fluke, Schistosoma japonicum (Trematoda: Strigeiformes) -- a trematode causing one of the most important human helminth infections, with its genome known to host other groups of salmonoid retroposons. In the present article, we suggest our views with regard to possible ways in which such an intensive horizontal transfer of salmonoid retroposons to the schistosomal genome occurs. The second novel SINE family, termed SlmII, originates from one of the SlmI subfamilies, with which it shares the same tRNA-related region, central domain, and a part of RSg-1-derived segment, but has a different 3'-tail of unidentified origin. Its distribution
Efficient Sampling of Band-limited Signals from Sine Wave Crossings
Selva, J
2010-01-01
This paper presents an efficient method for reconstructing a band-limited signal in the discrete domain from its crossings with a sine wave. The method makes it possible to design A/D converters that only deliver the crossing timings, which are then used to interpolate the input signal at arbitrary instants. Potentially, it may allow for reductions in power consumption and complexity, as well as for an increase in the achievable sampling bandwidth. The reconstruction in the discrete domain is based on a recently-proposed modification of the Lagrange interpolator, which is readily implementable with linear complexity and efficiently, given that it re-uses known schemes for variable fractional-delay (VFD) filters. As a spin-off, the method allows one to perform spectral analysis from sine wave crossings with the complexity of the FFT. Finally, the results in the paper are validated in a numerical example.
Kondo, Kenichi
2013-11-01
Ultradiscretization with negative values is a long-standing problem and several attempts have been made to solve it. Among others, we focus on the symmetrized max-plus algebra, with which we ultradiscretize the discrete sine-Gordon equation. Another ultradiscretization of the discrete sine-Gordon equation has already been proposed by previous studies, but the equation and the solutions obtained here are considered to directly correspond to the discrete counterpart. We also propose a noncommutative discrete analogue of the sine-Gordon equation, reveal its relations to other integrable systems including the noncommutative discrete KP equation, and construct multisoliton solutions by a repeated application of Darboux transformations. Moreover, we derive a noncommutative ultradiscrete analogue of the sine-Gordon equation and its 1-soliton and 2-soliton solutions, using the symmetrized max-plus algebra. As a result, we have a complete set of commutative and noncommutative versions of continuous, discrete, and ultradiscrete sine-Gordon equations.
Kenichi Kondo
2013-11-01
Full Text Available Ultradiscretization with negative values is a long-standing problem and several attempts have been made to solve it. Among others, we focus on the symmetrized max-plus algebra, with which we ultradiscretize the discrete sine-Gordon equation. Another ultradiscretization of the discrete sine-Gordon equation has already been proposed by previous studies, but the equation and the solutions obtained here are considered to directly correspond to the discrete counterpart. We also propose a noncommutative discrete analogue of the sine-Gordon equation, reveal its relations to other integrable systems including the noncommutative discrete KP equation, and construct multisoliton solutions by a repeated application of Darboux transformations. Moreover, we derive a noncommutative ultradiscrete analogue of the sine-Gordon equation and its 1-soliton and 2-soliton solutions, using the symmetrized max-plus algebra. As a result, we have a complete set of commutative and noncommutative versions of continuous, discrete, and ultradiscrete sine-Gordon equations.
Ultrashort light bullets described by the two-dimensional sine-Gordon equation
Leblond, Hervé; 10.1103/PHYSREVA.81.063815
2011-01-01
By using a reductive perturbation technique applied to a two-level model, this study puts forward a generic two-dimensional sine-Gordon evolution equation governing the propagation of femtosecond spatiotemporal optical solitons in Kerr media beyond the slowly varying envelope approximation. Direct numerical simulations show that, in contrast to the long-wave approximation, no collapse occurs, and that robust (2+1)-dimensional ultrashort light bullets may form from adequately chosen few-cycle input spatiotemporal wave forms. In contrast to the case of quadratic nonlinearity, the light bullets oscillate in both space and time and are therefore not steady-state lumps.
Possible involvement of SINEs in mammalian-specific brain formation.
Sasaki, Takeshi; Nishihara, Hidenori; Hirakawa, Mika; Fujimura, Koji; Tanaka, Mikiko; Kokubo, Nobuhiro; Kimura-Yoshida, Chiharu; Matsuo, Isao; Sumiyama, Kenta; Saitou, Naruya; Shimogori, Tomomi; Okada, Norihiro
2008-03-18
Retroposons, such as short interspersed elements (SINEs) and long interspersed elements (LINEs), are the major constituents of higher vertebrate genomes. Although there are many examples of retroposons' acquiring function, none has been implicated in the morphological innovations specific to a certain taxonomic group. We previously characterized a SINE family, AmnSINE1, members of which constitute a part of conserved noncoding elements (CNEs) in mammalian genomes. We proposed that this family acquired genomic functionality or was exapted after retropositioning in a mammalian ancestor. Here we identified 53 new AmnSINE1 loci and refined 124 total loci, two of which were further analyzed. Using a mouse enhancer assay, we demonstrate that one SINE locus, AS071, 178 kbp from the gene FGF8 (fibroblast growth factor 8), is an enhancer that recapitulates FGF8 expression in two regions of the developing forebrain, namely the diencephalon and the hypothalamus. Our gain-of-function analysis revealed that FGF8 expression in the diencephalon controls patterning of thalamic nuclei, which act as a relay center of the neocortex, suggesting a role for FGF8 in mammalian-specific forebrain patterning. Furthermore, we demonstrated that the locus, AS021, 392 kbp from the gene SATB2, controls gene expression in the lateral telencephalon, which is thought to be a signaling center during development. These results suggest important roles for SINEs in the development of the mammalian neuronal network, a part of which was initiated with the exaptation of AmnSINE1 in a common mammalian ancestor.
SINEs, evolution and genome structure in the opossum.
Gu, Wanjun; Ray, David A; Walker, Jerilyn A; Barnes, Erin W; Gentles, Andrew J; Samollow, Paul B; Jurka, Jerzy; Batzer, Mark A; Pollock, David D
2007-07-01
Short INterspersed Elements (SINEs) are non-autonomous retrotransposons, usually between 100 and 500 base pairs (bp) in length, which are ubiquitous components of eukaryotic genomes. Their activity, distribution, and evolution can be highly informative on genomic structure and evolutionary processes. To determine recent activity, we amplified more than one hundred SINE1 loci in a panel of 43 M. domestica individuals derived from five diverse geographic locations. The SINE1 family has expanded recently enough that many loci were polymorphic, and the SINE1 insertion-based genetic distances among populations reflected geographic distance. Genome-wide comparisons of SINE1 densities and GC content revealed that high SINE1 density is associated with high GC content in a few long and many short spans. Young SINE1s, whether fixed or polymorphic, showed an unbiased GC content preference for insertion, indicating that the GC preference accumulates over long time periods, possibly in periodic bursts. SINE1 evolution is thus broadly similar to human Alu evolution, although it has an independent origin. High GC content adjacent to SINE1s is strongly correlated with bias towards higher AT to GC substitutions and lower GC to AT substitutions. This is consistent with biased gene conversion, and also indicates that like chickens, but unlike eutherian mammals, GC content heterogeneity (isochore structure) is reinforced by substitution processes in the M. domestica genome. Nevertheless, both high and low GC content regions are apparently headed towards lower GC content equilibria, possibly due to a relative shift to lower recombination rates in the recent Monodelphis ancestral lineage. Like eutherians, metatherian (marsupial) mammals have evolved high CpG substitution rates, but this is apparently a convergence in process rather than a shared ancestral state.
SINE TRANSFORM MATRIX FOR SOLVING TOEPLITZ MATRIX PROBLEMS
Li-zhi Cheng
2001-01-01
In recent papers, some authors studied the solutions of symmetricpositive definite(SPD) Toeplitz systems Tn x = b by the conjugate gradient method(CG) with different sine trans- forms based preconditioners. In this paper, we first discuss the properties of eigenvalues for the main known circulant, skew circulant and sine transform based preconditioners. A counter example shows that E.Boman's preconditioner is only positive semi-definite for the banded Toeplitz matrix. To use preconditioner effectively, then we propose a modified Boman's preconditioner and a new Cesaro sum type sine transform based preconditioner. Finally, the results of numerical experimentation with these two preconditioners are pre- sented.
张秀玲
1999-01-01
A method of approaching to the infinite-dimensional linear operators by the finite-dimensional operators is discussed. It is shown that,for every infinite-dimensional operator A and every natural number n,there exists an n-dimensional optimal approximation to A. The norm error is found and the necessary and sufficient condition for such n-dimensional optimal approximations to be unique is obtained.
M.L.B. Simas
2005-03-01
Full Text Available An assumption commonly made in the study of visual perception is that the lower the contrast threshold for a given stimulus, the more sensitive and selective will be the mechanism that processes it. On the basis of this consideration, we investigated contrast thresholds for two classes of stimuli: sine-wave gratings and radial frequency stimuli (i.e., j0 targets or stimuli modulated by spherical Bessel functions. Employing a suprathreshold summation method, we measured the selectivity of spatial and radial frequency filters using either sine-wave gratings or j0 target contrast profiles at either 1 or 4 cycles per degree of visual angle (cpd, as the test frequencies. Thus, in a forced-choice trial, observers chose between a background spatial (or radial frequency alone and the given background stimulus plus the test frequency (1 or 4 cpd sine-wave grating or radial frequency. Contrary to our expectations, the results showed elevated thresholds (i.e., inhibition for sine-wave gratings and decreased thresholds (i.e., summation for radial frequencies when background and test frequencies were identical. This was true for both 1- and 4-cpd test frequencies. This finding suggests that sine-wave gratings and radial frequency stimuli are processed by different quasi-linear systems, one working at low luminance and contrast level (sine-wave gratings and the other at high luminance and contrast levels (radial frequency stimuli. We think that this interpretation is consistent with distinct foveal only and foveal-parafoveal mechanisms involving striate and/or other higher visual areas (i.e., V2 and V4.
The Perception of "Sine-Wave Speech" by Adults with Developmental Dyslexia.
Rosner, Burton S.; Talcott, Joel B.; Witton, Caroline; Hogg, James D.; Richardson, Alexandra J.; Hansen, Peter C.; Stein, John F.
2003-01-01
"Sine-wave speech" sentences contain only four frequency-modulated sine waves, lacking many acoustic cues present in natural speech. Adults with (n=19) and without (n=14) dyslexia were asked to reproduce orally sine-wave utterances in successive trials. Results suggest comprehension of sine-wave sentences is impaired in some adults with…
Short interspersed elements (SINEs) are a major source of canine genomic diversity.
Wang, Wei; Kirkness, Ewen F
2005-12-01
SINEs are retrotransposons that have enjoyed remarkable reproductive success during the course of mammalian evolution, and have played a major role in shaping mammalian genomes. Previously, an analysis of survey-sequence data from an individual dog (a poodle) indicated that canine genomes harbor a high frequency of alleles that differ only by the absence or presence of a SINEC_Cf repeat. Comparison of this survey-sequence data with a draft genome sequence of a distinct dog (a boxer) has confirmed this prediction, and revealed the chromosomal coordinates for >10,000 loci that are bimorphic for SINEC_Cf insertions. Analysis of SINE insertion sites from the genomes of nine additional dogs indicates that 3%-5% are absent from either the poodle or boxer genome sequences--suggesting that an additional 10,000 bimorphic loci could be readily identified in the general dog population. We describe a methodology that can be used to identify these loci, and could be adapted to exploit these bimorphic loci for genotyping purposes. Approximately half of all annotated canine genes contain SINEC_Cf repeats, and these elements are occasionally transcribed. When transcribed in the antisense orientation, they provide splice acceptor sites that can result in incorporation of novel exons. The high frequency of bimorphic SINE insertions in the dog population is predicted to provide numerous examples of allele-specific transcription patterns that will be valuable for the study of differential gene expression among multiple dog breeds.
Bunched soliton states in weakly coupled sine-Gordon systems
Gronbech-Jensen, N.; Samuelsen, M.R. (Physics Laboratory I, The Technical University of Denmark, DK-2800 Lyngby (Denmark)); Lomdahl, P.S. (Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM (USA)); Blackburn, J.A. (Department of Physics and Computing, Wilfrid Laurier University, Waterloo, Ontario (Canada))
1990-09-01
The interaction between solitons of two weakly coupled sine-Gordon systems is considered. In particular, the stability of bunched states is investigated, and perturbation results are compared with numerical results.
Sine-Gordon Theory : Entanglement entropy and holography
Banerjee, Pinaki; Sathiapalan, B
2016-01-01
We compute entanglement entropy of sine-Gordon theory for a single interval using both field theoretic and holographic techniques. The results match for near-marginal perturbations up to leading order in the coupling.
A unified approach in seeking the solitary wave solutions to sine-Gordon type equations
Xie Yuan-Xi; Tang Jia-Shi
2005-01-01
By utilizing the solutions of an auxiliary ordinary differential equation introduced in this paper, we present a simple and direct method to uniformly construct the exact solitary wave solutions for sine-Gordon type equations.As illustrative examples, the exact solitary wave solutions of some physically significant sine-Gordon type equations,including the sine-Gordon equation, double sine-Gordon equation and mKdV-sine-Gordon equation, are investigated by means of this method.
Borodulina, O R; Kramerov, D A
2001-10-01
Four tRNA-related SINE families were isolated from the genome of the shrew Sorex araneus (SOR element), mole Mogera robusta (TAL element), and hedgehog Mesechinus dauuricus (ERI-1 and ERI-2 elements). Each of these SINEs families is specific for a single Insectivora family: SOR, for Soricidae (shrews); TAL, for Talpidae (moles and desmans); ERI-1 and ERI-2, for Erinaceidae (hedgehogs). There is a long polypyrimidine region (TC-motif) in TAL, ERI-1, and ERI-2 elements located immediately upstream of an A-rich tail with polyadenylation signals (AATAAA) and an RNA polymerase III terminator (T(4-6)) or TCT(3-4)). Ten out of 14 analyzed mammalian tRNA-related SINE families have an A-rich tail similar to that of TAL, ERI-1, and ERI-2 elements. These elements were assigned to class T+. The other four SINEs including SOR element have no polyadenylation signal and transcription terminator in their A-rich tail and were assigned to class T-. Class T+ SINEs occur only in mammals, and most of them have a long polypyrimidine region. Possible models of retroposition of class T+ and T- SINEs are discussed.
Guinea pig ID-like families of SINEs.
Kass, David H; Schaetz, Brian A; Beitler, Lindsey; Bonney, Kevin M; Jamison, Nicole; Wiesner, Cathy
2009-05-01
Previous studies have indicated a paucity of SINEs within the genomes of the guinea pig and nutria, representatives of the Hystricognathi suborder of rodents. More recent work has shown that the guinea pig genome contains a large number of B1 elements, expanding to various levels among different rodents. In this work we utilized A-B PCR and screened GenBank with sequences from isolated clones to identify potentially uncharacterized SINEs within the guinea pig genome, and identified numerous sequences with a high degree of similarity (>92%) specific to the guinea pig. The presence of A-tails and flanking direct repeats associated with these sequences supported the identification of a full-length SINE, with a consensus sequence notably distinct from other rodent SINEs. Although most similar to the ID SINE, it clearly was not derived from the known ID master gene (BC1), hence we refer to this element as guinea pig ID-like (GPIDL). Using the consensus to screen the guinea pig genomic database (Assembly CavPor2) with Ensembl BlastView, we estimated at least 100,000 copies, which contrasts markedly to just over 100 copies of ID elements. Additionally we provided evidence of recent integrations of GPIDL as two of seven analyzed conserved GPIDL-containing loci demonstrated presence/absence variants in Cavia porcellus and C. aperea. Using intra-IDL PCR and sequence analyses we also provide evidence that GPIDL is derived from a hystricognath-specific SINE family. These results demonstrate that this SINE family continues to contribute to the dynamics of genomes of hystricognath rodents.
Le Thi Phuong Ngoc
2016-01-01
Full Text Available This paper is devoted to the study of a nonlinear Carrier wave equation in an annular membrane associated with Robin-Dirichlet conditions. Existence and uniqueness of a weak solution are proved by using the linearization method for nonlinear terms combined with the Faedo-Galerkin method and the weak compact method. Furthermore, an asymptotic expansion of a weak solution of high order in a small parameter is established.
Ahlkrona, Josefin; Kirchner, Nina; Zwinger, Thomas
2015-01-01
We propose and implement a new method, called the Ice Sheet Coupled Approximation Levels (ISCAL) method, for simulation of ice sheet flow in large domains under long time-intervals. The method couples the exact, full Stokes (FS) equations with the Shallow Ice Approximation (SIA). The part of the domain where SIA is applied is determined automatically and dynamically based on estimates of the modeling error. For a three dimensional model problem where the number of degrees of freedom is comparable to a real world application, ISCAL performs almost an order of magnitude faster with a low reduction in accuracy compared to a monolithic FS. Furthermore, ISCAL is shown to be able to detect rapid dynamic changes in the flow. Three different error estimations are applied and compared. Finally, ISCAL is applied to the Greenland Ice Sheet, proving ISCAL to be a potential valuable tool for the ice sheet modeling community.
Ahlkrona, Josefin; Lötstedt, Per; Kirchner, Nina; Zwinger, Thomas
2016-03-01
We propose and implement a new method, called the Ice Sheet Coupled Approximation Levels (ISCAL) method, for simulation of ice sheet flow in large domains during long time-intervals. The method couples the full Stokes (FS) equations with the Shallow Ice Approximation (SIA). The part of the domain where SIA is applied is determined automatically and dynamically based on estimates of the modeling error. For a three dimensional model problem, ISCAL computes the solution substantially faster with a low reduction in accuracy compared to a monolithic FS. Furthermore, ISCAL is shown to be able to detect rapid dynamic changes in the flow. Three different error estimations are applied and compared. Finally, ISCAL is applied to the Greenland Ice Sheet on a quasi-uniform grid, proving ISCAL to be a potential valuable tool for the ice sheet modeling community.
Recombinant SINEs are formed at high frequency during induced retrotransposition in vivo.
Yadav, Vijay Pal; Mandal, Prabhat Kumar; Bhattacharya, Alok; Bhattacharya, Sudha
2012-05-22
Non-long terminal repeat Retrotransposons are referred to as long interspersed nuclear elements (LINEs) and their non-autonomous partners are short interspersed nuclear elements (SINEs). It is believed that an active SINE copy, upon retrotransposition, generates near identical copies of itself, which subsequently accumulate mutations resulting in sequence polymorphism. Here we show that when a retrotransposition-competent cell line of the parasitic protist Entamoeba histolytica, transfected with a marked SINE copy, is induced to retrotranspose, >20% of the newly retrotransposed copies are neither identical to the marked SINE nor to the mobilized resident SINEs. Rather they are recombinants of resident SINEs and the marked SINE. They are a consequence of retrotransposition and not DNA recombination, as they are absent in cells not expressing the retrotransposition functions. This high-frequency recombination provides a new explanation for the existence of mosaic SINEs, which may impact on genetic analysis of SINE lineages, and measurement of phylogenetic distances.
唐功友; 王海红
2005-01-01
A successive approximation approach for designing optimal controllers is presented for discrete linear time-delay systems with a quadratic performance index. By using the successive approximation approach, the original optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems without time-delay and timeadvance terms. The optimal control law obtained consists of an accurate feedback terms and a time-delay compensation term which is the limit of the solution sequence of the adjoint equations.By using a finite-step iteration of the time-delay compensation term of the optimal solution sequence,a suboptimal control law is obtained. Simulation examples axe employed to test the validity of the proposed approach.
任传荣; 康丽英
2007-01-01
In this paper, a parallel machine scheduling problem was considered, where the processing time of a job is a simple linear function of its starting time. The objective is to minimize makespan. A fully polynomial time approximation scheme for the problem of scheduling n deteriorating jobs on two identical machines was worked out. Furthermore, the result was generalized to the case of a fixed number of machines.
Lagrangian formulation of symmetric space sine-Gordon models
Bakas, Ioannis; Shin, H J; Park, Q Han
1996-01-01
The symmetric space sine-Gordon models arise by conformal reduction of ordinary 2-dim \\sigma-models, and they are integrable exhibiting a black-hole type metric in target space. We provide a Lagrangian formulation of these systems by considering a triplet of Lie groups F \\supset G \\supset H. We show that for every symmetric space F/G, the generalized sine-Gordon models can be derived from the G/H WZW action, plus a potential term that is algebraically specified. Thus, the symmetric space sine-Gordon models describe certain integrable perturbations of coset conformal field theories at the classical level. We also briefly discuss their vacuum structure, Backlund transformations, and soliton solutions.
Deragon, Jean-Marc; Zhang, Xiaoyu
2006-12-01
Short interspersed elements (SINEs) are a class of dispersed mobile sequences that use RNA as an intermediate in an amplification process called retroposition. The presence-absence of a SINE at a given locus has been used as a meaningful classification criterion to evaluate phylogenetic relations among species. We review here recent developments in the characterisation of plant SINEs and their use as molecular makers to retrace phylogenetic relations among wild and cultivated Oryza and Brassica species. In Brassicaceae, further use of SINE markers is limited by our partial knowledge of endogenous SINE families (their origin and evolution histories) and by the absence of a clear classification. To solve this problem, phylogenetic relations among all known Brassicaceae SINEs were analyzed and a new classification, grouping SINEs in 15 different families, is proposed. The relative age and size of each Brassicaceae SINE family was evaluated and new phylogenetically supported subfamilies were described. We also present evidence suggesting that new potentially active SINEs recently emerged in Brassica oleracea from the shuffling of preexisting SINE portions. Finally, the comparative evolution history of SINE families present in Arabidopsis thaliana and Brassica oleracea revealed that SINEs were in general more active in the Brassica lineage. The importance of these new data for the use of Brassicaceae SINEs as molecular markers in future applications is discussed.
SINE retrotransposons cause epigenetic reprogramming of adjacent gene promoters.
Estécio, Marcos R H; Gallegos, Juan; Dekmezian, Mhair; Lu, Yue; Liang, Shoudan; Issa, Jean-Pierre J
2012-10-01
Almost half of the human genome and as much as 40% of the mouse genome is composed of repetitive DNA sequences. The majority of these repeats are retrotransposons of the SINE and LINE families, and such repeats are generally repressed by epigenetic mechanisms. It has been proposed that these elements can act as methylation centers from which DNA methylation spreads into gene promoters in cancer. Contradictory to a methylation center function, we have found that retrotransposons are enriched near promoter CpG islands that stay methylation-free in cancer. Clearly, it is important to determine which influence, if any, these repetitive elements have on nearby gene promoters. Using an in vitro system, we confirm here that SINE B1 elements can influence the activity of downstream gene promoters, with acquisition of DNA methylation and loss of activating histone marks, thus resulting in a repressed state. SINE sequences themselves did not immediately acquire DNA methylation but were marked by H3K9me2 and H3K27me3. Moreover, our bisulfite sequencing data did not support that gain of DNA methylation in gene promoters occurred by methylation spreading from SINE B1 repeats. Genome-wide analysis of SINE repeats distribution showed that their enrichment is directly correlated with the presence of USF1, USF2, and CTCF binding, proteins with insulator function. In summary, our work supports the concept that SINE repeats interfere negatively with gene expression and that their presence near gene promoters is counter-selected, except when the promoter is protected by an insulator element.
Sudden interaction quench in the quantum sine-Gordon model
Sabio, Javier [Instituto de Ciencia de Materiales de Madrid (CSIC), Sor Juana Ines de la Cruz 3, E-28049 Madrid (Spain); Kehrein, Stefan, E-mail: javier.sabio@icmm.csic.e [Arnold-Sommerfeld-Center for Theoretical Physics, Center for NanoSciences and Department fuer Physik, Ludwig-Maximilians-Universitaet Muenchen, Theresienstrasse 37, 80333 Muenchen (Germany)
2010-05-15
We study a sudden interaction quench in the weak-coupling regime of the quantum sine-Gordon model. The real time dynamics of the bosonic mode occupation numbers is calculated using the flow equation method. While we cannot prove results for the asymptotic long-time limit, we can establish the existence of an extended regime in time where the mode occupation numbers relax to twice their equilibrium values. This factor two indicates a non-equilibrium distribution and is a universal feature of weak interaction quenches. The weak-coupling quantum sine-Gordon model therefore turns out to be on the borderline between thermalization and non-thermalization.
On the Stability of the Generalized Sine Functional Equations
Gwang Hui KIM
2009-01-01
The aim of this paper is to study the stability problem of the generalized sine functional equations as follows:g(x)f(y)=f(x+y/2)2-f(x-y/2)2,f(x)g(y)=f(x+y/2)2-f(x-y/2)2,g(x)g(y)=f(x+y/2)2-f(x-y/2)2.Namely, we have generalized the Hyers-Ulam stability of the (pexiderized) sine functional equation.
Ii, Barry Moore; Autschbach, Jochen
2013-11-12
The lowest-energy/longest-wavelength electronic singlet excitation energies of linear cyanine dyes are examined, using time-dependent density functional theory (TDDFT) and selected wave function methods in comparison with literature data. Variations of the bond-length alternation obtained with different optimized structures produce small differences of the excitation energy in the limit of an infinite chain. Hybrid functionals with range-separated exchange are optimally 'tuned', which is shown to minimize the delocalization error (DE) in the cyanine π systems. Much unlike the case of charge-transfer excitations, small DEs are not strongly correlated with better performance. A representative cyanine is analyzed in detail. Compared with accurate benchmark data, TDDFT with 'pure' local functionals gives too high singlet excitation energies for all systems, but DFT-based ΔSCF calculations with a local functional severely underestimates the energies. TDDFT strongly overestimates the difference between singlet and triplet excitation energies. An analysis points to systematically much too small magnitudes of integrals from the DFT components of the exchange-correlation response kernel as the likely culprit. The findings support previous suggestions that the differential correlation energy between the ground and excited state is not correctly produced by TDDFT with most functionals.
Achieser, N I
2004-01-01
A pioneer of many modern developments in approximation theory, N. I. Achieser designed this graduate-level text from the standpoint of functional analysis. The first two chapters address approximation problems in linear normalized spaces and the ideas of P. L. Tchebysheff. Chapter III examines the elements of harmonic analysis, and Chapter IV, integral transcendental functions of the exponential type. The final two chapters explore the best harmonic approximation of functions and Wiener's theorem on approximation. Professor Achieser concludes this exemplary text with an extensive section of pr
5S rRNA-derived and tRNA-derived SINEs in fruit bats.
Gogolevsky, Konstantin P; Vassetzky, Nikita S; Kramerov, Dmitri A
2009-05-01
Most short retroposons (SINEs) descend from cellular tRNA of 7SL RNA. Here, four new SINEs were found in megabats (Megachiroptera) but neither in microbats nor in other mammals. Two of them, MEG-RS and MEG-RL, descend from another cellular RNA, 5S rRNA; one (MEG-T2) is a tRNA-derived SINE; and MEG-TR is a hybrid tRNA/5S rRNA SINE. Insertion locus analysis suggests that these SINEs were active in the recent fruit bat evolution. Analysis of MEG-RS and MEG-RL in comparison with other few 5S rRNA-derived SINEs demonstrates that the internal RNA polymerase III promoter is their most invariant region, while the secondary structure is more variable. The mechanisms underlying the modular structure of these and other SINEs as well as their variation are discussed. The scenario of evolution of MEG SINEs is proposed.
Oscillating and rotating sine-Gordon system
Olsen, O. H.; Samuelsen, Mogens Rugholm
1986-01-01
on the rate of change of the vacuum. For small rates a parametric excitation of standing waves is found, and for larger rates the system linearizes. In the case of oscillating vacuum a perturbation approach explains the behavior perfectly, while for small rates of increasing vacuum the system reduces...
Emotional intelligence : Sine qua non of leadership or folderol?
Walter, Frank; Cole, Michael S.; Humphrey, Ronald H.
Emotional intelligence (EI) is a divisive topic for many individuals interested in the subject of leadership. Whereas practitioner-oriented publications have claimed that EI is the sine qua non of leadership, academics continue to discuss EI's relevance for understanding leadership emergence,
Nonlinear dynamics of a parametrically driven sine-Gordon system
Grønbech-Jensen, Niels; Kivshar, Yuri S.; Samuelsen, Mogens Rugholm
1993-01-01
We consider a sine-Gordon system, driven by an ac parametric force in the presence of loss. It is demonstrated that a breather can be maintained in a steady state at half of the external frequency. In the small-amplitude limit the effect is described by an effective nonlinear Schrodinger equation...
Prediction and phylogenetic analysis of mammalian short interspersed elements (SINEs).
Rogozin, I B; Mayorov, V I; Lavrentieva, M V; Milanesi, L; Adkison, L R
2000-09-01
The presence of repetitive elements can create serious problems for sequence analysis, especially in the case of homology searches in nucleotide sequence databases. Repetitive elements should be treated carefully by using special programs and databases. In this paper, various aspects of SINE (short interspersed repetitive element) identification, analysis and evolution are discussed.
Phonons and solitons in the "thermal" sine-Gordon system
Salerno, Mario; Jørgensen, E.; Samuelsen, Mogens Rugholm
1984-01-01
Standard methods of stochastic processes are used to study the coupling of the sine-Gordon system with a heat reservoir. As a result we find thermal phonons with an average energy of kB T per mode. The translational mode (zero mode) is found to carry an average energy of 1 / 2kBT. This last value...
The Sine Method: An Alternative Height Measurement Technique
Don C. Bragg; Lee E. Frelich; Robert T. Leverett; Will Blozan; Dale J. Luthringer
2011-01-01
Height is one of the most important dimensions of trees, but few observers are fully aware of the consequences of the misapplication of conventional height measurement techniques. A new approach, the sine method, can improve height measurement by being less sensitive to the requirements of conventional techniques (similar triangles and the tangent method). We studied...
Soliton annihilation in the perturbed sine-Gordon system
Pedersen, Niels Falsig; Samuelsen, Mogens Rugholm; Welner, D.
1984-01-01
Fluxon-antifluxon annihilation in the perturbed sine-Gordon equation with loss and driving terms is investigated. For the infinite line we find a simple analytic expression for the threshold driving term corresponding to annihilation. With the application of the results to a Josephson junction...
Perturbation analysis of a parametrically changed sine-Gordon equation
Sakai, S.; Samuelsen, Mogens Rugholm; Olsen, O. H.
1987-01-01
A long Josephson junction with a spatially varying inductance is a physical manifestation of a modified sine-Gordon equation with parametric perturbation. Soliton propagation in such Josephson junctions is discussed. First, for an adiabatic model where the inductance changes smoothly compared...
Experimental Investigation of Trapped Sine-Gordon Solitons
Davidson, A.; Dueholm, B.; Kryger, B.
1985-01-01
We have observed for the first time a single sine-Gordon soliton trapped in an annular Josephson junction. This system offers a unique possibility to study undisturbed soliton motion. In the context of perturbation theory, the soliton may be viewed as a relativistic particle moving under a uniform...
Rotationally symmetric numerical solutions to the sine-Gordon equation
Olsen, O. H.; Samuelsen, Mogens Rugholm
1981-01-01
We examine numerically the properties of solutions to the spherically symmetric sine-Gordon equation given an initial profile which coincides with the one-dimensional breather solution and refer to such solutions as ring waves. Expanding ring waves either exhibit a return effect or expand towards...
Complex sine-Gordon Equation in Coherent Optical Pulse Propagation
Park, Q H
1999-01-01
It is shown that the McCall-Hahn theory of self-induced transparency in coherent optical pulse propagation can be identified with the complex sine-Gordon theory in the sharp line limit. We reformulate the theory in terms of the deformed gauged Wess-Zumino-Witten sigma model and address various new aspects of self-induced transparency.
Sine-wave three phase resonance inverter for operation of ...
naeema
Sine-wave three phase resonance inverter for operation of renewable energy systemsR .... performance in this application [8]. Also it was ... A circuit implementation of the three phase boost dc–ac converter with two switches, two diodes, two.
A SINE-based dichotomous key for primate identification.
Herke, Scott W; Xing, Jinchuan; Ray, David A; Zimmerman, Jacquelyn W; Cordaux, Richard; Batzer, Mark A
2007-04-01
For DNA samples or 'divorced' tissues, identifying the organism from which they were taken generally requires some type of analytical method. The ideal approach would be robust even in the hands of a novice, requiring minimal equipment, time, and effort. Genotyping SINEs (Short INterspersed Elements) is such an approach as it requires only PCR-related equipment, and the analysis consists solely of interpreting fragment sizes in agarose gels. Modern primate genomes are known to contain lineage-specific insertions of Alu elements (a primate-specific SINE); thus, to demonstrate the utility of this approach, we used members of the Alu family to identify DNA samples from evolutionarily divergent primate species. For each node of a combined phylogenetic tree (56 species; n=8 [Hominids]; 11 [New World monkeys]; 21 [Old World monkeys]; 2 [Tarsiformes]; and, 14 [Strepsirrhines]), we tested loci (>400 in total) from prior phylogenetic studies as well as newly identified elements for their ability to amplify in all 56 species. Ultimately, 195 loci were selected for inclusion in this Alu-based key for primate identification. This dichotomous SINE-based key is best used through hierarchical amplification, with the starting point determined by the level of initial uncertainty regarding sample origin. With newly emerging genome databases, finding informative retrotransposon insertions is becoming much more rapid; thus, the general principle of using SINEs to identify organisms is broadly applicable.
Chaos Suppression in a Sine Square Map through Nonlinear Coupling
Eduardo L. Brugnago; Paulo C. Rech
2011-01-01
We study a pair of nonlinearly coupled identical chaotic sine square maps.More specifically,we investigate the chaos suppression associated with the variation of two parameters.Two-dimensional parameter-space regions where the chaotic dynamics of the individual chaotic sine square map is driven towards regular dynamics are delimited.Additionally,the dynamics of the coupled system is numerically characterized as the parameters are changed.In recent years,many efforts have been devoted to chaos suppression in a nonlinear dynamics field.Iglesias et al.[1] reported a chaos suppression method through numerical truncation and rounding errors,with applications in discrete-time systems.Hénon map[2] and the Burgers map[3] were used to illustrate the method.A method of feedback impulsive chaos suppression was introduced by Osipov et al.[4]It is an algorithm of suppressing chaos in continuoustime dissipative systems with an external impulsive force,whose necessary condition is a reduction of the continuous flow to a discrete-time one-dimensional map.%We study a pair of nonlinearly coupled identical chaotic sine square maps. More specifically, we investigate the chaos suppression associated with the variation of two parameters. Two-dimensional parameter-space regions where the chaotic dynamics of the individual chaotic sine square map is driven towards regular dynamics are delimited. Additionally, the dynamics of the coupled system is numerically characterized as the parameters are changed.
Emotional intelligence : Sine qua non of leadership or folderol?
Walter, Frank; Cole, Michael S.; Humphrey, Ronald H.
2011-01-01
Emotional intelligence (EI) is a divisive topic for many individuals interested in the subject of leadership. Whereas practitioner-oriented publications have claimed that EI is the sine qua non of leadership, academics continue to discuss EI's relevance for understanding leadership emergence, behavi
Mariegaard, Jesper Sandvig
We consider a control problem for the wave equation: Given the initial state, find a specific boundary condition, called a control, that steers the system to a desired final state. The Hilbert uniqueness method (HUM) is a mathematical method for the solution of such control problems. It builds...... on the duality between the control system and its adjoint system, and these systems are connected via a so-called controllability operator. In this project, we are concerned with the numerical approximation of HUM control for the one-dimensional wave equation. We study two semi-discretizations of the wave...... equation: a linear finite element method (L-FEM) and a discontinuous Galerkin-FEM (DG-FEM). The controllability operator is discretized with both L-FEM and DG-FEM to obtain a HUM matrix. We show that formulating HUM in a sine basis is beneficial for several reasons: (i) separation of low and high frequency...
A new compound control method for sine-on-random mixed vibration test
Zhang, Buyun; Wang, Ruochen; Zeng, Falin
2017-09-01
Vibration environmental test (VET) is one of the important and effective methods to provide supports for the strength design, reliability and durability test of mechanical products. A new separation control strategy was proposed to apply in multiple-input multiple-output (MIMO) sine on random (SOR) mixed mode vibration test, which is the advanced and intensive test type of VET. As the key problem of the strategy, correlation integral method was applied to separate the mixed signals which included random and sinusoidal components. The feedback control formula of MIMO linear random vibration system was systematically deduced in frequency domain, and Jacobi control algorithm was proposed in view of the elements, such as self-spectrum, coherence, and phase of power spectral density (PSD) matrix. Based on the excessive correction of excitation in sine vibration test, compression factor was introduced to reduce the excitation correction, avoiding the destruction to vibration table or other devices. The two methods were synthesized to be applied in MIMO SOR vibration test system. In the final, verification test system with the vibration of a cantilever beam as the control object was established to verify the reliability and effectiveness of the methods proposed in the paper. The test results show that the exceeding values can be controlled in the tolerance range of references accurately, and the method can supply theory and application supports for mechanical engineering.
Isegawa, Miho; Truhlar, Donald G.
2013-04-01
Time-dependent density functional theory (TDDFT) holds great promise for studying photochemistry because of its affordable cost for large systems and for repeated calculations as required for direct dynamics. The chief obstacle is uncertain accuracy. There have been many validation studies, but there are also many formulations, and there have been few studies where several formulations were applied systematically to the same problems. Another issue, when TDDFT is applied with only a single exchange-correlation functional, is that errors in the functional may mask successes or failures of the formulation. Here, to try to sort out some of the issues, we apply eight formulations of adiabatic TDDFT to the first valence excitations of ten molecules with 18 density functionals of diverse types. The formulations examined are linear response from the ground state (LR-TDDFT), linear response from the ground state with the Tamm-Dancoff approximation (TDDFT-TDA), the original collinear spin-flip approximation with the Tamm-Dancoff (TD) approximation (SF1-TDDFT-TDA), the original noncollinear spin-flip approximation with the TDA approximation (SF1-NC-TDDFT-TDA), combined self-consistent-field (SCF) and collinear spin-flip calculations in the original spin-projected form (SF2-TDDFT-TDA) or non-spin-projected (NSF2-TDDFT-TDA), and combined SCF and noncollinear spin-flip calculations (SF2-NC-TDDFT-TDA and NSF2-NC-TDDFT-TDA). Comparing LR-TDDFT to TDDFT-TDA, we observed that the excitation energy is raised by the TDA; this brings the excitation energies underestimated by full linear response closer to experiment, but sometimes it makes the results worse. For ethylene and butadiene, the excitation energies are underestimated by LR-TDDFT, and the error becomes smaller making the TDA. Neither SF1-TDDFT-TDA nor SF2-TDDFT-TDA provides a lower mean unsigned error than LR-TDDFT or TDDFT-TDA. The comparison between collinear and noncollinear kernels shows that the noncollinear kernel
Method of Running Sines: Modeling Variability in Long-Period Variables
Andronov, Ivan L
2013-01-01
We review one of complementary methods for time series analysis - the method of "Running Sines". "Crash tests" of the method include signals with a large period variation and with a large trend. The method is most effective for "nearly periodic" signals, which exhibit "wavy shape" with a "cycle length" varying within few dozen per cent (i.e. oscillations of low coherence). This is a typical case for brightness variations of long-period pulsating variables and resembles QPO (Quasi-Periodic Oscillations) and TPO (Transient Periodic Oscillations) in interacting binary stars - cataclysmic variables, symbiotic variables, low-mass X-Ray binaries etc. General theory of "running approximations" was described by Andronov (1997A &AS..125..207A), one of realizations of which is the method of "running sines". The method is related to Morlet-type wavelet analysis improved for irregularly spaced data (Andronov, 1998KFNT...14..490A, 1999sss..conf...57A), as well as to a classical "running mean" (="moving average"). The ...
M. I. Popov
2016-01-01
Full Text Available The approximate analytical solution of a problem about nonstationary free convection in the conductive and laminar mode of the Newtonian liquid in square area at the instantaneous change of temperature of a sidewall and lack of heat fluxes is submitted on top and bottom the bases. The equations of free convection in an approximation of Oberbeka-Bussinesk are linearized due to neglect by convective items. For reduction of number of hydrothermal parameters the system is given to the dimensionless look by introduction of scales for effect and explanatory variables. Transition from classical variables to the variables "whirlwind-a flow function" allowed to reduce system to a nonstationary heat conduction equation and a nonstationary nonuniform biharmonic equation, and the first is not dependent on the second. The decision in the form of a flow function is received by application integral a sine - Fourier transforms with terminating limits to a biharmonic equation at first on a variable x, and then on a variable y. The flow function has an appearance of a double series of Fourier on sine with coefficients in an integral form. Coefficients of a row represent integrals from unknown functions. On the basis of a hypothesis of an express type of integrals coefficients are calculated from the linear equation system received from boundary conditions on partial derivatives of function. Dependence of structure of a current on Prandtl's number is investigated. The cards of streamlines and isolines of components of speed describing development of a current from the moment of emergence before transition to a stationary state are received. The schedules of a field of vectors of speeds in various time illustrating dynamics of a current are provided. Reliability of a hypothesis of an express type of integral coefficients is confirmed by adequacy to physical sense and coherence of the received results with the numerical solution of a problem.
Nonlinear Approximation Using Gaussian Kernels
Hangelbroek, Thomas
2009-01-01
It is well-known that non-linear approximation has an advantage over linear schemes in the sense that it provides comparable approximation rates to those of the linear schemes, but to a larger class of approximands. This was established for spline approximations and for wavelet approximations, and more recently for homogeneous radial basis function (surface spline) approximations. However, no such results are known for the Gaussian function. The crux of the difficulty lies in the necessity to vary the tension parameter in the Gaussian function spatially according to local information about the approximand: error analysis of Gaussian approximation schemes with varying tension are, by and large, an elusive target for approximators. We introduce and analyze in this paper a new algorithm for approximating functions using translates of Gaussian functions with varying tension parameters. Our scheme is sophisticated to a degree that it employs even locally Gaussians with varying tensions, and that it resolves local ...
High SINE RNA Expression Correlates with Post-Transcriptional Downregulation of BRCA1
Giovanni Bosco
2013-04-01
Full Text Available Short Interspersed Nuclear Elements (SINEs are non-autonomous retrotransposons that comprise a large fraction of the human genome. SINEs are demethylated in human disease, but whether SINEs become transcriptionally induced and how the resulting transcripts may affect the expression of protein coding genes is unknown. Here, we show that downregulation of the mRNA of the tumor suppressor gene BRCA1 is associated with increased transcription of SINEs and production of sense and antisense SINE small RNAs. We find that BRCA1 mRNA is post-transcriptionally down-regulated in a Dicer and Drosha dependent manner and that expression of a SINE inverted repeat with sequence identity to a BRCA1 intron is sufficient for downregulation of BRCA1 mRNA. These observations suggest that transcriptional activation of SINEs could contribute to a novel mechanism of RNA mediated post-transcriptional silencing of human genes.
Varshney, Dhaval; Vavrova-Anderson, Jana; Oler, Andrew J.; Cowling, Victoria H.; Cairns, Bradley R.; White, Robert J.
2015-01-01
Short interspersed nuclear elements (SINEs), such as Alu, spread by retrotransposition, which requires their transcripts to be copied into DNA and then inserted into new chromosomal sites. This can lead to genetic damage through insertional mutagenesis and chromosomal rearrangements between non-allelic SINEs at distinct loci. SINE DNA is heavily methylated and this was thought to suppress its accessibility and transcription, thereby protecting against retrotransposition. Here we provide several lines of evidence that methylated SINE DNA is occupied by RNA polymerase III, including the use of high-throughput bisulphite sequencing of ChIP DNA. We find that loss of DNA methylation has little effect on accessibility of SINEs to transcription machinery or their expression in vivo. In contrast, a histone methyltransferase inhibitor selectively promotes SINE expression and occupancy by RNA polymerase III. The data suggest that methylation of histones rather than DNA plays a dominant role in suppressing SINE transcription. PMID:25798578
The role of pulse shape in motor cortex transcranial magnetic stimulation using full-sine stimuli
Delvendahl, Igor; Gattinger, Norbert; Berger, Thomas;
2014-01-01
excitation. Preferential excitation of neuronal target cells in the posterior-anterior segment or targeting of different neuronal structures by the two half-segments can explain this result. Thus, our findings help understanding the mechanisms of neural stimulation by full-sine TMS.......A full-sine (biphasic) pulse waveform is most commonly used for repetitive transcranial magnetic stimulation (TMS), but little is known about how variations in duration or amplitude of distinct pulse segments influence the effectiveness of a single TMS pulse to elicit a corticomotor response. Using......) compared monophasic, half-sine, and full-sine pulses, (ii) applied two-segment pulses consisting of two identical half-sines, and (iii) manipulated amplitude, duration, and current direction of the first or second full-sine pulse half-segments. RMT was significantly higher using half-sine or monophasic...
Modal approximations to damped linear systems
Veseli/'c, K
2009-01-01
We consider a finite dimensional damped second order system and obtain spectral inclusion theorems for the related quadratic eigenvalue problem. The inclusion sets are the 'quasi Cassini ovals' which may greatly outperform standard Gershgorin circles. As the unperturbed system we take a modally damped part of the system; this includes the known proportionally damped models, but may give much sharper estimates. These inclusions are then applied to derive some easily calculable sufficient conditions for the overdampedness of a given damped system.
Norton, Andrew H.
1991-01-01
Local spline approximants offer a means for constructing finite difference formulae for numerical solution of PDEs. These formulae seem particularly well suited to situations in which the use of conventional formulae leads to non-linear computational instability of the time integration. This is explained in terms of frequency responses of the FDF.
Use of a genetic algorithm for the analysis of eye movements from the linear vestibulo-ocular reflex
Shelhamer, M.
2001-01-01
It is common in vestibular and oculomotor testing to use a single-frequency (sine) or combination of frequencies [sum-of-sines (SOS)] stimulus for head or target motion. The resulting eye movements typically contain a smooth tracking component, which follows the stimulus, in which are interspersed rapid eye movements (saccades or fast phases). The parameters of the smooth tracking--the amplitude and phase of each component frequency--are of interest; many methods have been devised that attempt to identify and remove the fast eye movements from the smooth. We describe a new approach to this problem, tailored to both single-frequency and sum-of-sines stimulation of the human linear vestibulo-ocular reflex. An approximate derivative is used to identify fast movements, which are then omitted from further analysis. The remaining points form a series of smooth tracking segments. A genetic algorithm is used to fit these segments together to form a smooth (but disconnected) wave form, by iteratively removing biases due to the missing fast phases. A genetic algorithm is an iterative optimization procedure; it provides a basis for extending this approach to more complex stimulus-response situations. In the SOS case, the genetic algorithm estimates the amplitude and phase values of the component frequencies as well as removing biases.
Parametric approximation of airfoil aerodynamic coefficients at high angles of attack
Skrzypinski, Witold Robert; Zahle, Frederik; Bak, Christian
2014-01-01
, and the third method, also utilizing trigonometric functions, was developed with the scope on stall-regulated turbines. The method of the even sine and cosine functions was further developed in the present work by using two independent harmonic approximations in the positive and negative α regions......Three methods for estimating the lift and drag curves in the 360° angle of attack (α) range with harmonic approximation functions were analyzed in the present work. The first method assumes aerodynamic response of a flat plate, the second utilizes even sine and even cosine approximation functions...
毛潭; 冯志彬; 尹宇鹤; 潘博
2015-01-01
This article presents an instability analysis method based on approximate linear elastic theory ,for solving the installing stability issues of solar panels bracket supporting by ground column. Firstly ,we determined the bracket installing angle according to the simulation results of illumination conditions in Beijing area based on shadow ratio method and spherical trigonometry. Secondly,we used static analysis and linear buckling analysis method to anlyze and compare three representative bracket structures by checking their respective force loads ,structural strength and stability. Finally ,we verified the accuracy and reliability of instability analysis method based on approximate linear elastic theory through experiments.%针对地面立柱式太阳能电池板支架安装稳定性问题，引入基于近似线性弹性理论的失稳分析的方法求解。首先基于影子倍率法和球形三角函数法模拟北京光照情况并确定太阳能设备的支架安装角度；其次利用静力学分析法和线性屈曲分析法，通过分析比较三种有代表性的支架系统方案，分别计算出受力载荷、结构强度和稳定性；最后通过实例验证近似线性弹性理论的失稳分析方法的准确性和可靠性。
Multiresonance modes in sine-Gordon brane models
Cruz, W T; Almeida, C A S
2015-01-01
In this work, we study the localization of the vector gauge field in two five-dimensional braneworlds generated by scalar fields coupled to gravity. The sine-Gordon like potentials are employed to produce different thick brane setups. A zero mode localized is obtained, and we show the existence of reverberations with the wave solutions indicating a quasi-localized massive mode. More interesting results are achieved when we propose a double sine-Gordon potential to the scalar field. The resulting thick brane shows a more detailed topology with the presence of an internal structure composed by two kinks. The massive spectrum of the gauge field is revalued on this scenario revealing the existence of various resonant modes
Multiresonance modes in sine-Gordon brane models
Cruz, W. T.; Maluf, R. V.; Dantas, D. M.; Almeida, C. A. S.
2016-12-01
In this work, we study the localization of the vector gauge field in two five-dimensional braneworlds generated by scalar fields coupled to gravity. The sine-Gordon like potentials are employed to produce different thick brane setups. A zero mode localized is obtained, and we show the existence of reverberations with the wave solutions indicating a quasi-localized massive mode. More interesting results are achieved when we propose a double sine-Gordon potential to the scalar field. The resulting thick brane shows a more detailed topology with the presence of an internal structure composed by two kinks. The massive spectrum of the gauge field is revalued on this scenario revealing the existence of various resonant modes. Furthermore, we compute the corrections to Coulomb law coming from these massive KK vector modes in these thick scenarios, which is concluded that the dilaton parameter regulates these corrections.
Approximate Representations and Approximate Homomorphisms
Moore, Cristopher
2010-01-01
Approximate algebraic structures play a defining role in arithmetic combinatorics and have found remarkable applications to basic questions in number theory and pseudorandomness. Here we study approximate representations of finite groups: functions f:G -> U_d such that Pr[f(xy) = f(x) f(y)] is large, or more generally Exp_{x,y} ||f(xy) - f(x)f(y)||^2$ is small, where x and y are uniformly random elements of the group G and U_d denotes the unitary group of degree d. We bound these quantities in terms of the ratio d / d_min where d_min is the dimension of the smallest nontrivial representation of G. As an application, we bound the extent to which a function f : G -> H can be an approximate homomorphism where H is another finite group. We show that if H's representations are significantly smaller than G's, no such f can be much more homomorphic than a random function. We interpret these results as showing that if G is quasirandom, that is, if d_min is large, then G cannot be embedded in a small number of dimensi...
The Quantum Sine-Gordon Model in Perturbative AQFT
Bahns, Dorothea; Rejzner, Kasia
2017-08-01
We study the Sine-Gordon model with Minkowski signature in the framework of perturbative algebraic quantum field theory. We calculate the vertex operator algebra braiding property. We prove that in the finite regime of the model, the expectation value—with respect to the vacuum or a Hadamard state—of the Epstein Glaser S-matrix and the interacting current or the field respectively converge, both given as formal power series.
Breather Dynamics of the Sine-Gordon Equation
Stephen Johnson; Anjan Biswas
2013-01-01
This paper studies the adiabatic dynamics of the breather soliton of the sine-Gordon equation.The integrals of motion are found and then used in soliton perturbation theory to derive the differential equation governing the soliton velocity.Time-dependent functions arise and their properties are studied.These functions are found to be bounded and periodic and affect the soliton velocity.The soliton velocity is numerically plotted against time for different combinations of initial velocities and perturbation terms.
The Quantum Sine Gordon model in perturbative AQFT
Bahns, Dorothea
2016-01-01
We study the Sine Gordon model in the framework of perturbative algebraic quantum field theory, without making use of a representation on Fock space. In particular, we calculate the vertex operator algebra braiding property. We prove that in the finite regime of the model, the vacuum expectation value of the Epstein Glaser $S$-matrix and the interacting current, both given as formal power series, converge in a suitable topology on the space of functionals.
Exact constants in approximation theory
Korneichuk, N
1991-01-01
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base
Kinematic analysis of tandem gait on a sine wave walkway
Kawakami, Shingo; Fujisawa, Hiroyuki; Tomizawa, Yoshiyuki; Murakami, Kenichi
2016-01-01
[Purpose] The purpose of this study was to ascertain the kinematic characteristics on a horizontal plane, including knee joint rotation, when walking with a tandem gait on a sine wave walkway. [Subjects and Methods] Eighteen healthy adults were enrolled as subjects in this study. They walked with a tandem gait on a sine wave walkway. A three-dimensional motion analysis system was used to record data and calculate the trunk, hip joint, and knee joint rotation angles. [Results] The rotation angle ranges for the trunk, hip joint, and knee joint were 23.3°, 53.3°, and 47.3°, respectively. The trunk generally rotated towards the direction of movement, and when turning left using the left leg as the pivot, the hip joint was internally rotated and the knee joint was externally rotated. In contrast, when making a directional change to the right using the left leg as the pivot, the hip joint was externally rotated and the knee joint was internally rotated. [Conclusion] Through tandem gait analysis on a sine wave walkway, knee joint rotation was found to be important in changes of direction. PMID:27799663
Polypteridae (Actinopterygii: Cladistia) and DANA-SINEs insertions.
Morescalchi, Maria Alessandra; Barucca, Marco; Stingo, Vincenzo; Capriglione, Teresa
2010-06-01
SINE sequences are interspersed throughout virtually all eukaryotic genomes and greatly outnumber the other repetitive elements. These sequences are of increasing interest for phylogenetic studies because of their diagnostic power for establishing common ancestry among taxa, once properly characterized. We identified and characterized a peculiar family of composite tRNA-derived short interspersed SINEs, DANA-SINEs, associated with mutational activities in Danio rerio, in a group of species belonging to one of the most basal bony fish families, the Polypteridae, in order to investigate their own inner specific phylogenetic relationships. DANA sequences were identified, sequenced and then localized, by means of fluorescent in situ hybridization (FISH), in six Polypteridae species (Polypterus delhezi, P. ornatipinnis, P. palmas, P. buettikoferi P. senegalus and Erpetoichthys calabaricus) After cloning, the sequences obtained were aligned for phylogenetic analysis, comparing them with three Dipnoan lungfish species (Protopterus annectens, P. aethiopicus, Lepidosiren paradoxa), and Lethenteron reissneri (Petromyzontidae)was used as outgroup. The obtained overlapping MP, ML and NJ tree clustered together the species belonging to the two taxonomically different Osteichthyans groups: the Polypteridae, by one side, and the Protopteridae by the other, with the monotypic genus Erpetoichthys more distantly related to the Polypterus genus comprising three distinct groups: P. palmas and P. buettikoferi, P. delhezi and P. ornatipinnis and P. senegalus. In situ hybridization with DANA probes marked along the whole chromosome arms in the metaphases of all the Polypteridae species examined. Copyright © 2010 Elsevier B.V. All rights reserved.
[Non-LTR retrotransposons: LINEs and SINEs in plant genome].
Cheng, Xu-Dong; Ling, Hong-Qing
2006-06-01
Retrotransposons are one of the drivers of genome evolution. They include LTR (long terminal repeat) retrotransposons, which widespread in Eukaryotagenomes, show structural similarity to retroviruses. Non-LTR retrotransposons were first discovered in animal genomes and then identified as ubiquitous components of nuclear genomes in many species across the plant kingdom. They constitute a large fraction of the repetitive DNA. Non-LTR retrotransposons are divided into LINEs (long interspersed nuclear elements) and SINEs (short interspersed nuclear elements). Transposition of non-LTR retrotransposons is rarely observed in plants indicating that most of them are inactive and/or under regulation of the host genome. Transposition is poorly understood, but experimental evidence from other genetic systems shows that LINEs are able to transpose autonomously while non-autonomous SINEs depend on the reverse transcription machinery of other retrotransposons. Phylogenic analysis shows LINEs are probably the most ancient class of retrotransposons in plant genomes, while the origin of SINEs is unknown. This review sums up the above data and wants to show readers a clear picture of non-LTR retrotransposons.
Sánchez, A; Domínguez-Adame, F; Angel Sanchez; Francisco Dominguez-Adame
1994-01-01
We have examined the dynamical behavior of the kink solutions of the one-dimensional sine-Gordon equation in the presence of a spatially periodic parametric perturbation. Our study clarifies and extends the currently available knowledge on this and related nonlinear problems in four directions. First, we present the results of a numerical simulation program which are not compatible with the existence of a radiative threshold, predicted by earlier calculations. Second, we carry out a perturbative calculation which helps interpret those previous predictions, enabling us to understand in depth our numerical results. Third, we apply the collective coordinate formalism to this system and demonstrate numerically that it accurately reproduces the observed kink dynamics. Fourth, we report on a novel occurrence of length scale competition in this system and show how it can be understood by means of linear stability analysis. Finally, we conclude by summarizing the general physical framework that arises from our study.
The Critical Properties of a Modulated Quantum sine-Gordon Model
WANG ZhiGuo; ZHANG YuMei
2002-01-01
A new procedure of trial variational wave functional is proposed for invostigating the mass reuormalizationand the local structure of the ground state of a one-dimensional quantum sine-Gorrdonm model with linear spatial modu-lation, whose ground state differs from that without modulation. Thc phase diagram obtained in parameters (αA 2,β2)plane shows that the vertical part of the boundary between soliton lattice phase and iucommensurate (IC) phase withvanishing gap sticks at β2 = 4, the IC phase can only appear forβ2 ＞ 47r and thc IC phase regime is enlarged withincreasing spatial modulation in the case of definite parameter αA-2. The transition is of the continuous type on thevertical part of the boundary, while it is of the first order on the boundary forβ2 ＞ 47r.
CERN. Geneva
2015-01-01
Most physics results at the LHC end in a likelihood ratio test. This includes discovery and exclusion for searches as well as mass, cross-section, and coupling measurements. The use of Machine Learning (multivariate) algorithms in HEP is mainly restricted to searches, which can be reduced to classification between two fixed distributions: signal vs. background. I will show how we can extend the use of ML classifiers to distributions parameterized by physical quantities like masses and couplings as well as nuisance parameters associated to systematic uncertainties. This allows for one to approximate the likelihood ratio while still using a high dimensional feature vector for the data. Both the MEM and ABC approaches mentioned above aim to provide inference on model parameters (like cross-sections, masses, couplings, etc.). ABC is fundamentally tied Bayesian inference and focuses on the “likelihood free” setting where only a simulator is available and one cannot directly compute the likelihood for the dat...
The solution of the two-dimensional sine-Gordon equation using the method of lines
Bratsos, A. G.
2007-09-01
The method of lines is used to transform the initial/boundary-value problem associated with the two-dimensional sine-Gordon equation in two space variables into a second-order initial-value problem. The finite-difference methods are developed by replacing the matrix-exponential term in a recurrence relation with rational approximants. The resulting finite-difference methods are analyzed for local truncation error, stability and convergence. To avoid solving the nonlinear system a predictor-corrector scheme using the explicit method as predictor and the implicit as corrector is applied. Numerical solutions for cases involving the most known from the bibliography line and ring solitons are given.
Scenario Based Approach for Multiple Source Tsunami Hazard Assessment for Sines, Portugal
Wronna, Martin; Omira, Rachid; Baptista, Maria Ana
2015-04-01
In this paper, we present a scenario-based approach for tsunami hazard assessment for the city and harbour of Sines, Portugal one the test-sites of project ASTARTE. Sines holds one of the most important deep-water ports which contains oil-bearing, petrochemical, liquid bulk, coal and container terminals. The port and its industrial infrastructures are facing the ocean to the southwest facing the main seismogenic sources. This work considers two different seismic zones: the Southwest Iberian Margin and the Gloria Fault. Within these two regions, a total of five scenarios were selected to assess tsunami impact at the test site. These scenarios correspond to the worst-case credible scenario approach based upon the largest events of the historical and paleo tsunami catalogues. The tsunami simulations from the source area towards the coast is carried out using NSWING a Non-linear Shallow Water Model With Nested Grids. The code solves the non-linear shallow water equations using the discretization and explicit leap-frog finite difference scheme, in a Cartesian or Spherical frame. The initial sea surface displacement is assumed to be equal to the sea bottom deformation that is computed by Okada equations. Both uniform and non-uniform slip conditions are used. The presented results correspond to the models using non-uniform slip conditions. In this study, the static effect of tides is analysed for three different tidal stages MLLW (mean lower low water) MSL (mean sea level) and MHHW (mean higher high water). For each scenario, inundation is described by maximum values of wave height, flow depth, drawdown, run-up and inundation distance. Synthetic waveforms are computed at virtual tide gages at specific locations outside and inside the harbour. The final results consist of Aggregate Scenario Maps presented for the different inundation parameters. This work is funded by ASTARTE - Assessment, Strategy And Risk Reduction for Tsunamis in Europe - FP7-ENV2013 6.4-3, Grant 603839
The Evolution of SINEs and LINEs in the genus Chironomus (Diptera).
Papusheva, Ekaterina; Gruhl, Mary C; Berezikov, Eugene; Groudieva, Tatiana; Scherbik, Svetlana V; Martin, Jon; Blinov, Alexander; Bergtrom, Gerald
2004-03-01
Genomic DNA amplification from 51 species of the family Chironomidae shows that most contain relatives of NLRCth1 LINE and CTRT1 SINE retrotransposons first found in Chironomus thummi. More than 300 cloned PCR products were sequenced. The amplified region of the reverse transcriptase gene in the LINEs is intact and highly conserved, suggesting active elements. The SINEs are less conserved, consistent with minimal/no selection after transposition. A mitochondrial gene phylogeny resolves the Chironomus genus into six lineages (Guryev et al. 2001). LINE and SINE phylogenies resolve five of these lineages, indicating their monophyletic origin and vertical inheritance. However, both the LINE and the SINE tree topologies differ from the species phylogeny, resolving the elements into "clusters I-IV" and "cluster V" families. The data suggest a descent of all LINE and SINE subfamilies from two major families. Based on the species phylogeny, a few LINEs and a larger number of SINEs are cladisitically misplaced. Most misbranch with LINEs or SINEs from species with the same families of elements. From sequence comparisons, cladistically misplaced LINEs and several misplaced SINEs arose by convergent base substitutions. More diverged SINEs result from early transposition and some are derived from multiple source SINEs in the same species. SINEs from two species (C. dorsalis, C. pallidivittatus), expected to belong to the clusters I-IV family, branch instead with cluster V family SINEs; apparently both families predate separation of cluster V from clusters I-IV species. Correlation of the distribution of active SINEs and LINEs, as well as similar 3' sequence motifs in CTRT1 and NLRCth1, suggests coevolving retrotransposon pairs in which CTRT1 transposition depends on enzymes active during NLRCth1 LINE mobility.
Linearly constrained minimax optimization
Madsen, Kaj; Schjær-Jacobsen, Hans
1978-01-01
We present an algorithm for nonlinear minimax optimization subject to linear equality and inequality constraints which requires first order partial derivatives. The algorithm is based on successive linear approximations to the functions defining the problem. The resulting linear subproblems...
The dynamic proliferation of CanSINEs mirrors the complex evolution of Feliforms
2014-01-01
Background Repetitive short interspersed elements (SINEs) are retrotransposons ubiquitous in mammalian genomes and are highly informative markers to identify species and phylogenetic associations. Of these, SINEs unique to the order Carnivora (CanSINEs) yield novel insights on genome evolution in domestic dogs and cats, but less is known about their role in related carnivores. In particular, genome-wide assessment of CanSINE evolution has yet to be completed across the Feliformia (cat-like) suborder of Carnivora. Within Feliformia, the cat family Felidae is composed of 37 species and numerous subspecies organized into eight monophyletic lineages that likely arose 10 million years ago. Using the Felidae family as a reference phylogeny, along with representative taxa from other families of Feliformia, the origin, proliferation and evolution of CanSINEs within the suborder were assessed. Results We identified 93 novel intergenic CanSINE loci in Feliformia. Sequence analyses separated Feliform CanSINEs into two subfamilies, each characterized by distinct RNA polymerase binding motifs and phylogenetic associations. Subfamily I CanSINEs arose early within Feliformia but are no longer under active proliferation. Subfamily II loci are more recent, exclusive to Felidae and show evidence for adaptation to extant RNA polymerase activity. Further, presence/absence distributions of CanSINE loci are largely congruent with taxonomic expectations within Feliformia and the less resolved nodes in the Felidae reference phylogeny present equally ambiguous CanSINE data. SINEs are thought to be nearly impervious to excision from the genome. However, we observed a nearly complete excision of a CanSINEs locus in puma (Puma concolor). In addition, we found that CanSINE proliferation in Felidae frequently targeted existing CanSINE loci for insertion sites, resulting in tandem arrays. Conclusions We demonstrate the existence of at least two SINE families within the Feliformia suborder, one
Genomic distribution of SINEs in Entamoeba histolytica strains: implication for genotyping
2013-01-01
Background The major clinical manifestations of Entamoeba histolytica infection include amebic colitis and liver abscess. However the majority of infections remain asymptomatic. Earlier reports have shown that some E. histolytica isolates are more virulent than others, suggesting that virulence may be linked to genotype. Here we have looked at the genomic distribution of the retrotransposable short interspersed nuclear elements EhSINE1 and EhSINE2. Due to their mobile nature, some EhSINE copies may occupy different genomic locations among isolates of E. histolytica possibly affecting adjacent gene expression; this variability in location can be exploited to differentiate strains. Results We have looked for EhSINE1- and EhSINE2-occupied loci in the genome sequence of Entamoeba histolytica HM-1:IMSS and searched for homologous loci in other strains to determine the insertion status of these elements. A total of 393 EhSINE1 and 119 EhSINE2 loci were analyzed in the available sequenced strains (Rahman, DS4-868, HM1:CA, KU48, KU50, KU27 and MS96-3382. Seventeen loci (13 EhSINE1 and 4 EhSINE2) were identified where a EhSINE1/EhSINE2 sequence was missing from the corresponding locus of other strains. Most of these loci were unoccupied in more than one strain. Some of the loci were analyzed experimentally for SINE occupancy using DNA from strain Rahman. These data helped to correctly assemble the nucleotide sequence at three loci in Rahman. SINE occupancy was also checked at these three loci in 7 other axenically cultivated E. histolytica strains and 16 clinical isolates. Each locus gave a single, specific amplicon with the primer sets used, making this a suitable method for strain typing. Based on presence/absence of SINE and amplification with locus-specific primers, the 23 strains could be divided into eleven genotypes. The results obtained by our method correlated with the data from other typing methods. We also report a bioinformatic analysis of EhSINE2 copies
田铮; 文奇; 金子
2001-01-01
The convergence property of the projection pursuit learning network (PPLN) that is used to approximate to non-linear autoregrcssion is studied in this paper. The authros prove that PPLN can approximate to non-linear autoregression at any given precision in Lk space, where k is integer. The learning strategy and calculative procedures of PPLN's, which are used to establishthe models of non-linear time series {Xt } and forecast the subsequent behavior of {Xt}, are also presented. Using PPLN, the Wolfer sunspont number(1749-1894), Canada lvnx data(1821-1924) and Xi'an data(0-360) are fitted. Furthermore, the predictors for the above three kinds of data are also pre sented, respectively. Finally, we compare the performance the projection pursuit learning network not only with that of backpropagation learning (BPLN) but also with that of the threshold model. It is shown that the projection pursuit learning networks perform well and compare favorably to BPLN and the threshold model.%本文研究非线性自回归模型投影寻踪学习网络逼近的收敛性，证明了在Lk(k为正整数)空间上，投影寻踪学习网络可以以任意精度逼近非线性自回归模型，给出基于投影寻踪学习网络的非线性时间序列模型建模和预报的计算方法和应用实例，对太阳黑子数据、山猫数据及西安数据进行了拟合和预报，将其结果与改进的BP网和门限自回归模型相应的结果进行比较，结果表明基于投影寻踪学习网络的非线性时间序列的建模和预报方法是一类行之有效的方法。
The role of pulse shape in motor cortex transcranial magnetic stimulation using full-sine stimuli.
Igor Delvendahl
Full Text Available A full-sine (biphasic pulse waveform is most commonly used for repetitive transcranial magnetic stimulation (TMS, but little is known about how variations in duration or amplitude of distinct pulse segments influence the effectiveness of a single TMS pulse to elicit a corticomotor response. Using a novel TMS device, we systematically varied the configuration of full-sine pulses to assess the impact of configuration changes on resting motor threshold (RMT as measure of stimulation effectiveness with single-pulse TMS of the non-dominant motor hand area (M1. In young healthy volunteers, we (i compared monophasic, half-sine, and full-sine pulses, (ii applied two-segment pulses consisting of two identical half-sines, and (iii manipulated amplitude, duration, and current direction of the first or second full-sine pulse half-segments. RMT was significantly higher using half-sine or monophasic pulses compared with full-sine. Pulses combining two half-sines of identical polarity and duration were also characterized by higher RMT than full-sine stimuli resulting. For full-sine stimuli, decreasing the amplitude of the half-segment inducing posterior-anterior oriented current in M1 resulted in considerably higher RMT, whereas varying the amplitude of the half-segment inducing anterior-posterior current had a smaller effect. These findings provide direct experimental evidence that the pulse segment inducing a posterior-anterior directed current in M1 contributes most to corticospinal pathway excitation. Preferential excitation of neuronal target cells in the posterior-anterior segment or targeting of different neuronal structures by the two half-segments can explain this result. Thus, our findings help understanding the mechanisms of neural stimulation by full-sine TMS.
Evolutionary history of 7SL RNA-derived SINEs in Supraprimates.
Kriegs, Jan Ole; Churakov, Gennady; Jurka, Jerzy; Brosius, Jürgen; Schmitz, Jürgen
2007-04-01
The evolutionary relationships of 7SL RNA-derived SINEs such as the primate Alu or the rodent B1 elements have hitherto been obscure. We established an unambiguous phylogenetic tree for Supraprimates, and derived intraordinal relationships of the 7SL RNA-derived SINEs. As well as new elements in Tupaia and primates, we also found that the purported ancestral fossil Alu monomer was restricted to Primates, and provide here the first description of a potential chimeric promoter box region in SINEs.
SINE Retrotransposition: Evaluation of Alu Activity and Recovery of De Novo Inserts.
Ade, Catherine; Roy-Engel, Astrid M
2016-01-01
Mobile element activity is of great interest due to its impact on genomes. However, the types of mobile elements that inhabit any given genome are remarkably varied. Among the different varieties of mobile elements, the Short Interspersed Elements (SINEs) populate many genomes, including many mammalian species. Although SINEs are parasites of Long Interspersed Elements (LINEs), SINEs have been highly successful in both the primate and rodent genomes. When comparing copy numbers in mammals, SINEs have been vastly more successful than other nonautonomous elements, such as the retropseudogenes and SVA. Interestingly, in the human genome the copy number of Alu (a primate SINE) outnumbers LINE-1 (L1) copies 2 to 1. Estimates suggest that the retrotransposition rate for Alu is tenfold higher than LINE-1 with about 1 insert in every twenty births. Furthermore, Alu-induced mutagenesis is responsible for the majority of the documented instances of human retroelement insertion-induced disease. However, little is known on what contributes to these observed differences between SINEs and LINEs. The development of an assay to monitor SINE retrotransposition in culture has become an important tool for the elucidation of some of these differences. In this chapter, we present details of the SINE retrotransposition assay and the recovery of de novo inserts. We also focus on the nuances that are unique to the SINE assay.
Matveev, Vitaliy; Nishihara, Hidenori; Okada, Norihiro
2007-01-01
Short interspersed elements (SINEs) constitute a group of retroposons propagating in the genome via a mechanism of reverse transcription, in which they depend on the enzymatic machinery of long retroposons (LINEs...
Sakhel, Asaad R.
2015-01-01
The properties of interacting bosons in a weak, one-dimensional, and bichromatic optical with a rational ratio of the constituting wavelengths $\\lambda_1$ and $\\lambda_2$ are numerically examined along a broad range of the Lieb-Liniger interaction parameter $\\gamma$ passing through the Sine-Gordon transition. It is argued that there should not be much difference in the results between those due to an irrational ratio $\\lambda_1/\\lambda_2$ and due to a rational approximation of the latter. For...
Overlaps after quantum quenches in the sine-Gordon model
Horváth, D. X.; Takács, G.
2017-08-01
We present a numerical computation of overlaps in mass quenches in sine-Gordon quantum field theory using truncated conformal space approach (TCSA). To improve the cut-off dependence of the method, we use a novel running coupling definition which has a general applicability in free boson TCSA. The numerical results for the first breather overlaps are compared with the analytic continuation of a previously proposed analytical Ansatz for the initial state in a related sinh-Gordon quench, and good agreement is found between the numerical data and the analytical prediction in a large energy range.
Takasaki, N.; Yamaki, T.; Hamada, M.; Park, L; Okada, N
1997-01-01
The genomes of chum salmon and pink salmon contain a family of short interspersed repetitive elements (SINEs), designated the salmon SmaI family. It is restricted to these two species, a distribution that suggests that this SINE family might have been generated in their common ancestor. When insertions of the SmaI SINEs at 10 orthologous loci of these species were analyzed, however, it was found that there were no shared insertion sites between chum and pink salmon. Furthermore, at six loci w...
Alu SINE analyses of 3,000-year-old human skeletal remains: a pilot study.
Kothe, Maximilian; Seidenberg, Verena; Hummel, Susanne; Piskurek, Oliver
2016-01-01
As Short Interspersed Elements (SINEs), human-specific Alu elements can be used for population genetic studies. Very recent inserts are polymorphic within and between human populations. In a sample of 30 elements originating from three different Alu subfamilies, we investigated whether they are preserved in prehistorical skeletal human remains from the Bronze Age Lichtenstein cave in Lower Saxony, Germany. In the present study, we examined a prehistoric triad of father, mother and daughter. For 26 of the 30 Alu loci investigated, definite results were obtained. We were able to demonstrate that presence/absence analyses of Alu elements can be conducted on individuals who lived 3,000 years ago. The preservation of the ancient DNA (aDNA) is good enough in two out of three ancient individuals to routinely allow the amplification of 500 bp fragments. The third individual revealed less well-preserved DNA, which results in allelic dropout or complete amplification failures. We here present an alternative molecular approach to deal with these degradation phenomena by using internal Alu subfamily specific primers producing short fragments of approximately 150 bp. Our data clearly show the possibility of presence/absence analyses of Alu elements in individuals from the Lichtenstein cave. Thus, we demonstrate that our method is reliably applicable for aDNA samples with good or moderate DNA preservation. This method will be very useful for further investigations with more Alu loci and larger datasets. Human population genetic studies and other large-scale investigations would provide insight into Alu SINE-based microevolutionary processes in humans during the last few thousand years and help us comprehend the evolutionary dynamics of our genome.
Efficient Derivation and Approximations of Cepstral Coefficients for Speech Coding
1992-12-01
A new formulation is presented for the calculation of cepstral coefficients directly from measured sine wave amplitudes and frequencies of speech waveforms. Approximations to these cepstral coefficients are shown to be suitable for operation in a real-time speech coding environment. These results were encoded in the C programming language and then evaluated through experiments that were conducted on the McAulay-Quatieri Sinusoidal Transform Coder (STC).... Speech coding, Cepstral processing.
Borodulina, Olga R; Golubchikova, Julia S; Ustyantsev, Ilia G; Kramerov, Dmitri A
2016-02-01
It is generally accepted that only transcripts synthesized by RNA polymerase II (e.g., mRNA) were subject to AAUAAA-dependent polyadenylation. However, we previously showed that RNA transcribed by RNA polymerase III (pol III) from mouse B2 SINE could be polyadenylated in an AAUAAA-dependent manner. Many species of mammalian SINEs end with the pol III transcriptional terminator (TTTTT) and contain hexamers AATAAA in their A-rich tail. Such SINEs were united into Class T(+), whereas SINEs lacking the terminator and AATAAA sequences were classified as T(-). Here we studied the structural features of SINE pol III transcripts that are necessary for their polyadenylation. Eight and six SINE families from classes T(+) and T(-), respectively, were analyzed. The replacement of AATAAA with AACAAA in T(+) SINEs abolished the RNA polyadenylation. Interestingly, insertion of the polyadenylation signal (AATAAA) and pol III transcription terminator in T(-) SINEs did not result in polyadenylation. The detailed analysis of three T(+) SINEs (B2, DIP, and VES) revealed areas important for the polyadenylation of their pol III transcripts: the polyadenylation signal and terminator in A-rich tail, β region positioned immediately downstream of the box B of pol III promoter, and τ region located upstream of the tail. In DIP and VES (but not in B2), the τ region is a polypyrimidine motif which is also characteristic of many other T(+) SINEs. Most likely, SINEs of different mammals acquired these structural features independently as a result of parallel evolution. Copyright © 2015 Elsevier B.V. All rights reserved.
Golden Sine Algorithm: A Novel Math-Inspired Algorithm
TANYILDIZI, E.
2017-05-01
Full Text Available In this study, Golden Sine Algorithm (Gold-SA is presented as a new metaheuristic method for solving optimization problems. Gold-SA has been developed as a new search algorithm based on population. This math-based algorithm is inspired by sine that is a trigonometric function. In the algorithm, random individuals are created as many as the number of search agents with uniform distribution for each dimension. The Gold-SA operator searches to achieve a better solution in each iteration by trying to bring the current situation closer to the target value. The solution space is narrowed by the golden section so that the areas that are supposed to give only good results are scanned instead of the whole solution space scan. In the tests performed, it is seen that Gold-SA has better results than other population based methods. In addition, Gold-SA has fewer algorithm-dependent parameters and operators than other metaheuristic methods, increasing the importance of this method by providing faster convergence of this new method.
Construction Of 3phase Sine Waves Using Digital Technique
S.Madhavi
2012-11-01
Full Text Available All the real world parameters such as temperature, pressure etc., are analog in nature, In order to control these physical parameters using computers, which are digital in nature, high speed signal processing board is used. This mainly consists of devices such as analog to digital converter, digital to analog converters and timer which perform the interfacing function between analog and digital are known as data converters. By using Digital methods accuracy and precision of the equipment will be very high compared to analog method of sine wave generation. It provides highly stable and accurate Voltages, Currents and frequency of the 3 phase signals because it is having feedback mechanism. This work consists of DAC 8822[7], 8254 [6] Programmable Timer. This timer is programmed to generate an interrupt of 56µs time period which is fed to IRQ10 pin of PC 104 bus based single board computer [3]. A Device driver is written in Linux which is inserted into the Kernel. Then the processor communicates with 16- bit high speed DAC[7]which outputs the sine samples of 50Hz frequency.
Circularly polarized few-optical-cycle solitons in the short-wave-approximation regime
Leblond, Herve [Laboratoire de Photonique d' Angers, EA 4464, Universite d' Angers, 2 Boulevard Lavoisier, F-49045 Angers Cedex 01 (France); Triki, Houria [Radiation Physics Laboratory, Department of Physics, Faculty of Sciences, Badji Mokhtar University, Post Office Box 12, 23000 Annaba (Algeria); Mihalache, Dumitru [Laboratoire de Photonique d' Angers, EA 4464, Universite d' Angers, 2 Boulevard Lavoisier, F-49045 Angers Cedex 01 (France); Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), 407 Atomistilor, RO-077125 Magurele-Bucharest (Romania); Academy of Romanian Scientists, 54 Splaiul Independentei, RO-050094 Bucharest (Romania)
2011-08-15
We consider the propagation of few-cycle pulses (FCPs) beyond the slowly varying envelope approximation in media in which the dynamics of constituent atoms is described by a two-level Hamiltonian by taking into account the wave polarization. We consider the short-wave approximation, assuming that the resonance frequency of the two-level atoms is well below the inverse of the characteristic duration of the optical pulse. By using the reductive perturbation method (multiscale analysis), we derive from the Maxwell-Bloch-Heisenberg equations the governing evolution equations for the two polarization components of the electric field in the first order of the perturbation approach. We show that propagation of circularly polarized (CP) few-optical-cycle solitons is described by a system of coupled nonlinear equations, which reduces in the scalar case to the standard sine Gordon equation describing the dynamics of linearly polarized FCPs in the short-wave-approximation regime. By direct numerical simulations, we calculate the lifetime of CP FCPs, and we study the transition to two orthogonally polarized single-humped pulses as a generic route of their instability.
Mobile Element Evolution Playing Jigsaw—SINEs in Gastropod and Bivalve Mollusks
Matetovici, Irina; Sajgo, Szilard; Ianc, Bianca; Ochis, Cornelia; Bulzu, Paul; Popescu, Octavian; Damert, Annette
2016-01-01
SINEs (Short INterspersed Elements) are widely distributed among eukaryotes. Some SINE families are organized in superfamilies characterized by a shared central domain. These central domains are conserved across species, classes, and even phyla. Here we report the identification of two novel such superfamilies in the genomes of gastropod and bivalve mollusks. The central conserved domain of the first superfamily is present in SINEs in Caenogastropoda and Vetigastropoda as well as in all four subclasses of Bivalvia. We designated the domain MESC (Romanian for MElc—snail and SCoica—mussel) because it appears to be restricted to snails and mussels. The second superfamily is restricted to Caenogastropoda. Its central conserved domain—Snail—is related to the Nin-DC domain. Furthermore, we provide evidence that a 40-bp subdomain of the SINE V-domain is conserved in SINEs in mollusks and arthropods. It is predicted to form a stable stem-loop structure that is preserved in the context of the overall SINE RNA secondary structure in invertebrates. Our analysis also recovered short retrotransposons with a Long INterspersed Element (LINE)-derived 5′ end. These share the body and/or the tail with transfer RNA (tRNA)-derived SINEs within and across species. Finally, we identified CORE SINEs in gastropods and bivalves—extending the distribution range of this superfamily. PMID:26739168
Novel SINEs families in Medicago truncatula and Lotus japonicus: bioinformatic analysis.
Gadzalski, Marek; Sakowicz, Tomasz
2011-07-01
Although short interspersed elements (SINEs) were discovered nearly 30 years ago, the studies of these genomic repeats were mostly limited to animal genomes. Very little is known about SINEs in legumes--one of the most important plant families. Here we report identification, genomic distribution and molecular features of six novel SINE elements in Lotus japonicus (named LJ_SINE-1, -2, -3) and Medicago truncatula (MT_SINE-1, -2, -3), model species of legume. They possess all the structural features commonly found in short interspersed elements including RNA polymerase III promoter, polyA tail and flanking repeats. SINEs described here are present in low to moderate copy numbers from 150 to 3000. Bioinformatic analyses were used to searched public databases, we have shown that three of new SINE elements from M. truncatula seem to be characteristic of Medicago and Trifolium genera. Two SINE families have been found in L. japonicus and one is present in both M. truncatula and L. japonicus. In addition, we are discussing potential activities of the described elements. Copyright © 2011 Elsevier B.V. All rights reserved.
Inverse PCR-based method for isolating novel SINEs from genome.
Han, Yawei; Chen, Liping; Guan, Lihong; He, Shunping
2014-04-01
Short interspersed elements (SINEs) are moderately repetitive DNA sequences in eukaryotic genomes. Although eukaryotic genomes contain numerous SINEs copy, it is very difficult and laborious to isolate and identify them by the reported methods. In this study, the inverse PCR was successfully applied to isolate SINEs from Opsariichthys bidens genome in Eastern Asian Cyprinid. A group of SINEs derived from tRNA(Ala) molecular had been identified, which were named Opsar according to Opsariichthys. SINEs characteristics were exhibited in Opsar, which contained a tRNA(Ala)-derived region at the 5' end, a tRNA-unrelated region, and AT-rich region at the 3' end. The tRNA-derived region of Opsar shared 76 % sequence similarity with tRNA(Ala) gene. This result indicated that Opsar could derive from the inactive or pseudogene of tRNA(Ala). The reliability of method was tested by obtaining C-SINE, Ct-SINE, and M-SINEs from Ctenopharyngodon idellus, Megalobrama amblycephala, and Cyprinus carpio genomes. This method is simpler than the previously reported, which successfully omitted many steps, such as preparation of probes, construction of genomic libraries, and hybridization.
Mobile Element Evolution Playing Jigsaw - SINEs in Gastropod and Bivalve Mollusks.
Matetovici, Irina; Sajgo, Szilard; Ianc, Bianca; Ochis, Cornelia; Bulzu, Paul; Popescu, Octavian; Damert, Annette
2016-01-06
SINEs (Short INterspersed Elements) are widely distributed among eukaryotes. Some SINE families are organized in superfamilies characterized by a shared central domain. These central domains are conserved across species, classes, and even phyla. Here we report the identification of two novel such superfamilies in the genomes of gastropod and bivalve mollusks. The central conserved domain of the first superfamily is present in SINEs in Caenogastropoda and Vetigastropoda as well as in all four subclasses of Bivalvia. We designated the domain MESC (Romanian for MElc-snail and SCoica-mussel) because it appears to be restricted to snails and mussels. The second superfamily is restricted to Caenogastropoda. Its central conserved domain-Snail-is related to the Nin-DC domain. Furthermore, we provide evidence that a 40-bp subdomain of the SINE V-domain is conserved in SINEs in mollusks and arthropods. It is predicted to form a stable stem-loop structure that is preserved in the context of the overall SINE RNA secondary structure in invertebrates. Our analysis also recovered short retrotransposons with a Long INterspersed Element (LINE)-derived 5' end. These share the body and/or the tail with transfer RNA (tRNA)-derived SINEs within and across species. Finally, we identified CORE SINEs in gastropods and bivalves-extending the distribution range of this superfamily. © The Author(s) 2016. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution.
Functional Integrals and Free Energy in sine-Gordon-Thirring Model with Impurity Coupling
无
2007-01-01
The free energy at low temperature in ID sine-Gordon-Thirring model with impurity coupling is studied by means of functional integrals method. For massive free sine-Gordon-Thirring model, free energy is obtained from perturbation expansion of functional determinant. Moreover, the free energy of massive model is calculated by use of an auxiliary Bose Geld method.
Friedline, Terri; Masa, Rainier D; Chowa, Gina A N
2015-01-01
The natural log and categorical transformations commonly applied to wealth for meeting the statistical assumptions of research may not always be appropriate for adjusting for skewness given wealth's unique properties. Finding and applying appropriate transformations is becoming increasingly important as researchers consider wealth as a predictor of well-being. We present an alternative transformation-the inverse hyperbolic sine (IHS)-for simultaneously dealing with skewness and accounting for wealth's unique properties. Using the relationship between household wealth and youth's math achievement as an example, we apply the IHS transformation to wealth data from US and Ghanaian households. We also explore non-linearity and accumulation thresholds by combining IHS transformed wealth with splines. IHS transformed wealth relates to youth's math achievement similarly when compared to categorical and natural log transformations, indicating that it is a viable alternative to other transformations commonly used in research. Non-linear relationships and accumulation thresholds emerge that predict youth's math achievement when splines are incorporated. In US households, accumulating debt relates to decreases in math achievement whereas accumulating assets relates to increases in math achievement. In Ghanaian households, accumulating assets between the 25th and 50th percentiles relates to increases in youth's math achievement. Copyright © 2014 Elsevier Inc. All rights reserved.
Rytov approximation in electron scattering
Krehl, Jonas; Lubk, Axel
2017-06-01
In this work we introduce the Rytov approximation in the scope of high-energy electron scattering with the motivation of developing better linear models for electron scattering. Such linear models play an important role in tomography and similar reconstruction techniques. Conventional linear models, such as the phase grating approximation, have reached their limits in current and foreseeable applications, most importantly in achieving three-dimensional atomic resolution using electron holographic tomography. The Rytov approximation incorporates propagation effects which are the most pressing limitation of conventional models. While predominately used in the weak-scattering regime of light microscopy, we show that the Rytov approximation can give reasonable results in the inherently strong-scattering regime of transmission electron microscopy.
Evolutionary modes of emergence of short interspersed nuclear element (SINE) families in grasses.
Kögler, Anja; Schmidt, Thomas; Wenke, Torsten
2017-08-30
Short interspersed nuclear elements (SINEs) are non-autonomous transposable elements which are propagated by retrotransposition and constitute an inherent part of the genome of most eukaryotic species. Knowledge of heterogeneous and highly abundant SINEs is crucial for de novo (or improvement of) annotation of whole genome sequences. We scanned Poaceae genome sequences of six important cereals (Oryza sativa, Triticum aestivum, Hordeum vulgare, Panicum virgatum, Sorghum bicolor, Zea mays) and Brachypodium distachyon to examine the diversity and evolution of SINE populations. We comparatively analyzed the structural features, distribution, evolutionary relation and abundance of 32 SINE families and subfamilies within grasses, comprising 11 052 individual copies. The investigation of activity profiles within the Poaceae provides insights into their species-specific diversification and amplification. We found that Poaceae SINEs (PoaS) fall into two length categories: simple SINEs of up to 180 bp and dimeric SINEs larger than 240 bp. Detailed analysis at the nucleotide level revealed that multimerization of related and unrelated SINE copies is an important evolutionary mechanism of SINE formation. We conclude that PoaS families diversify by massive reshuffling between SINE families, likely caused by insertion of truncated copies, and provide a model for this evolutionary scenario. Twenty-eight of 32 PoaS families and subfamilies show significant conservation, in particular either in the 5' or 3' regions, across Poaceae species and share large sequence stretches with one or more other PoaS families. © 2017 The Authors The Plant Journal © 2017 John Wiley & Sons Ltd.
邓晓平; 申建平; 桑会平; 马路娟
2015-01-01
Turbo 均衡将 Turbo 码的迭代译码思想扩展到信道均衡领域，通过迭代的方式在信道均衡器和解码器之间进行数次软信息交互，从而能够达到比传统均衡处理更优的抗多径干扰性能。针对 Turbo 均衡在实际应用中的复杂度过高的问题，给出了一种基于近似线性 MMSE 的频域 Turbo 均衡算法。该算法通过快速傅里叶变换将基于 MMSE 准则信道均衡处理转换到频域进行，从而避免了复杂的矩阵求逆运算。仿真结果表明，相对于时域的近似线性 Turbo 均衡算法，该算法在时不变多径信道下能够以相对较低的复杂度实现更好的抗多径干扰性能。%Turbo equalization extends the idea of iterative decoding in Turbo code to channel equalization,which can achieve bet⁃ter anti⁃multipath performance than traditional equalization process through iterative exchange of soft information between channel equal⁃izer and decoder. To overcome the high complexity of Turbo equalization in practice, a Turbo equalization algorithm based on approximate linear MMSE is introduced. This algorithm avoids highly complicated matrix inversion process by transforming channel equalization based on MMSE criterion to frequency domain using FFT.The results of simulation indicate that,as compared with linear Turbo equalization,this algorithm can achieve better anti⁃multipath performance with lower complexity in time⁃invariant multipath chan⁃nels.
SINEs of progress: Mobile element applications to molecular ecology.
Ray, David A
2007-01-01
Mobile elements represent a unique and under-utilized set of tools for molecular ecologists. They are essentially homoplasy-free characters with the ability to be genotyped in a simple and efficient manner. Interpretation of the data generated using mobile elements can be simple compared to other genetic markers. They exist in a wide variety of taxa and are useful over a wide selection of temporal ranges within those taxa. Furthermore, their mode of evolution instills them with another advantage over other types of multilocus genotype data: the ability to determine loci applicable to a range of time spans in the history of a taxon. In this review, I discuss the application of mobile element markers, especially short interspersed elements (SINEs), to phylogenetic and population data, with an emphasis on potential applications to molecular ecology.
Massless Boundary Sine-Gordon Model Coupled to External Fields
Kogetsu, H
2005-01-01
We investigate a generalization of the massless boundary sine-Gordon model with conformal invariance, which has been used to describe an array of D-branes (or rolling tachyon). We consider a similar action whose couplings are replaced with external fields depending on the boundary coordinate. Even in the presence of the external fields, this model is still solvable, though it does not maintain the whole conformal symmetry. We obtain, to all orders in perturbation theory in terms of the external fields, a simpler expression of the boundary state and the disc partition function. As a by-product, we fix the relation between the bare couplings and the renormalized couplings which has been appeared in papers on tachyon lump and rolling tachyon.
The nullum crimen sine iure principle in contemporary International Law
Hector Olásolo Alonso
2014-03-01
Full Text Available This paper deals with the evolution and current content of the nullum crimen sine iure principle in international law. It analyses the development of the nullum crimen principle from its definition as a principle of justice at the end of Second World War, to its current definition as an individual right imposing a limitation upon States’ sovereignty. The article also explains that, nowadays, the nullum cri- men principle requires for the relevant conduct to be a crime at the time of its com- mission, according to any of the sources of criminal law in the relevant national or international legal system. No written law is necessarily required. As a result, accessibility and foreseability are the main elements of the nullum crimen principle in current international law.
Approximately liner phase IIR digital filter banks
J. D. Ćertić; M. D. Lutovac; L. D. Milić
2013-01-01
In this paper, uniform and nonuniform digital filter banks based on approximately linear phase IIR filters and frequency response masking technique (FRM) are presented. Both filter banks are realized as a connection of an interpolated half-band approximately linear phase IIR filter as a first stage of the FRM design and an appropriate number of masking filters. The masking filters are half-band IIR filters with an approximately linear phase. The resulting IIR filter banks are compared with li...
Characterization of Three Novel SINE Families with Unusual Features in Helicoverpa armigera
Wang, Jianjun; Wang, Aina; Han, Zhaojun; Zhang, Zan; Li, Fei; Li, Xianchun
2012-01-01
Although more than 120 families of short interspersed nuclear elements (SINEs) have been isolated from the eukaryotic genomes, little is known about SINEs in insects. Here, we characterize three novel SINEs from the cotton bollworm, Helicoverpa armigera. Two of them, HaSE1 and HaSE2, share similar 5′ -structure including a tRNA-related region immediately followed by conserved central domain. The 3′ -tail of HaSE1 is significantly similar to that of one LINE retrotransposon element, HaRTE1.1, in H. armigera genome. The 3′ -region of HaSE2 showed high identity with one mariner-like element in H. armigera. The third family, termed HaSE3, is a 5S rRNA-derived SINE and shares both body part and 3′-tail with HaSE1, thus may represent the first example of a chimera generated by recombination between 5S rRNA and tRNA-derived SINE in insect species. Further database searches revealed the presence of these SINEs in several other related insect species, but not in the silkworm, Bombyx mori, indicating a relatively narrow distribution of these SINEs in Lepidopterans. Apart from above, we found a copy of HaSE2 in the GenBank EST entry for the cotton aphid, Aphis gossypii, suggesting the occurrence of horizontal transfer. PMID:22319625
Greally, John M
2002-01-08
To test whether regions undergoing genomic imprinting have unique genomic characteristics, imprinted and nonimprinted human loci were compared for nucleotide and retroelement composition. Maternally and paternally expressed subgroups of imprinted genes were found to differ in terms of guanine and cytosine, CpG, and retroelement content, indicating a segregation into distinct genomic compartments. Imprinted regions have been normally permissive to L1 long interspersed transposable element retroposition during mammalian evolution but universally and significantly lack short interspersed transposable elements (SINEs). The primate-specific Alu SINEs, as well as the more ancient mammalian-wide interspersed repeat SINEs, are found at significantly low densities in imprinted regions. The latter paleogenomic signature indicates that the sequence characteristics of currently imprinted regions existed before the mammalian radiation. Transitions from imprinted to nonimprinted genomic regions in cis are characterized by a sharp inflection in SINE content, demonstrating that this genomic characteristic can help predict the presence and extent of regions undergoing imprinting. During primate evolution, SINE accumulation in imprinted regions occurred at a decreased rate compared with control loci. The constraint on SINE accumulation in imprinted regions may be mediated by an active selection process. This selection could be because of SINEs attracting and spreading methylation, as has been found at other loci. Methylation-induced silencing could lead to deleterious consequences at imprinted loci, where inactivation of one allele is already established, and expression is often essential for embryonic growth and survival.
Characterization of three novel SINE families with unusual features in Helicoverpa armigera.
Jianjun Wang
Full Text Available Although more than 120 families of short interspersed nuclear elements (SINEs have been isolated from the eukaryotic genomes, little is known about SINEs in insects. Here, we characterize three novel SINEs from the cotton bollworm, Helicoverpa armigera. Two of them, HaSE1 and HaSE2, share similar 5' -structure including a tRNA-related region immediately followed by conserved central domain. The 3' -tail of HaSE1 is significantly similar to that of one LINE retrotransposon element, HaRTE1.1, in H. armigera genome. The 3' -region of HaSE2 showed high identity with one mariner-like element in H. armigera. The third family, termed HaSE3, is a 5S rRNA-derived SINE and shares both body part and 3'-tail with HaSE1, thus may represent the first example of a chimera generated by recombination between 5S rRNA and tRNA-derived SINE in insect species. Further database searches revealed the presence of these SINEs in several other related insect species, but not in the silkworm, Bombyx mori, indicating a relatively narrow distribution of these SINEs in Lepidopterans. Apart from above, we found a copy of HaSE2 in the GenBank EST entry for the cotton aphid, Aphis gossypii, suggesting the occurrence of horizontal transfer.
Ichiyanagi, Kenji
2013-01-01
Short interspersed elements (SINEs) are a class of retrotransposons, which amplify their copy numbers in their host genomes by retrotransposition. More than a million copies of SINEs are present in a mammalian genome, constituting over 10% of the total genomic sequence. In contrast to the other two classes of retrotransposons, long interspersed elements (LINEs) and long terminal repeat (LTR) elements, SINEs are transcribed by RNA polymerase III. However, like LINEs and LTR elements, the SINE transcription is likely regulated by epigenetic mechanisms such as DNA methylation, at least for human Alu and mouse B1. Whereas SINEs and other transposable elements have long been thought as selfish or junk DNA, recent studies have revealed that they play functional roles at their genomic locations, for example, as distal enhancers, chromatin boundaries and binding sites of many transcription factors. These activities imply that SINE retrotransposition has shaped the regulatory network and chromatin landscape of their hosts. Whereas it is thought that the epigenetic mechanisms were originated as a host defense system against proliferation of parasitic elements, this review discusses a possibility that the same mechanisms are also used to regulate the SINE-derived functions.
Kink propagation and trapping in a two dimensional curved sine-Gordon system
Sørensen, Mads Peter
The sine-Gordon equation is one of the three classical nonlinear partial differential equations possessing soliton solutions in the case of one spatial dimension. Extending the sine-Gordon equation to two spatial dimensions is relevant for applications to the dynamics of large area Josephson...... to investigate how kink shaped solitons of the sine-Gordon equation propagate through the bent section. We have found that the region with finite curvature acts as a potential barrier whose height and width depends on the radius of curvature of the waveguide. The kink transmission, reflection and trapping...
Kink propagation and trapping in a two dimensional curved sine-Gordon system
Sørensen, Mads Peter
The sine-Gordon equation is one of the three classical nonlinear partial differential equations possessing soliton solutions in the case of one spatial dimension. Extending the sine-Gordon equation to two spatial dimensions is relevant for applications to the dynamics of large area Josephson...... to investigate how kink shaped solitons of the sine-Gordon equation propagate through the bent section. We have found that the region with finite curvature acts as a potential barrier whose height and width depends on the radius of curvature of the waveguide. The kink transmission, reflection and trapping...
Schröder, Christiane; Bleidorn, Christoph; Hartmann, Stefanie; Tiedemann, Ralph
2009-12-15
Investigating the dog genome we found 178965 introns with a moderate length of 200-1000 bp. A screening of these sequences against 23 different repeat libraries to find insertions of short interspersed elements (SINEs) detected 45276 SINEs. Virtually all of these SINEs (98%) belong to the tRNA-derived Can-SINE family. Can-SINEs arose about 55 million years ago before Carnivora split into two basal groups, the Caniformia (dog-like carnivores) and the Feliformia (cat-like carnivores). Genome comparisons of dog and cat recovered 506 putatively informative SINE loci for caniformian phylogeny. In this study we show how to use such genome information of model organisms to research the phylogeny of related non-model species of interest. Investigating a dataset including representatives of all major caniformian lineages, we analysed 24 randomly chosen loci for 22 taxa. All loci were amplifiable and revealed 17 parsimony-informative SINE insertions. The screening for informative SINE insertions yields a large amount of sequence information, in particular of introns, which contain reliable phylogenetic information as well. A phylogenetic analysis of intron- and SINE sequence data provided a statistically robust phylogeny which is congruent with the absence/presence pattern of our SINE markers. This phylogeny strongly supports a sistergroup relationship of Musteloidea and Pinnipedia. Within Pinnipedia, we see strong support from bootstrapping and the presence of a SINE insertion for a sistergroup relationship of the walrus with the Otariidae.
Sine-Gordon modulation solutions: Application to macroscopic non-lubricant friction
Gershenzon, Naum I.; Bambakidis, Gust; Skinner, Thomas E.
2016-10-01
The Frenkel-Kontorova (FK) model and its continuum approximation, the sine-Gordon (SG) equation, are widely used to model a variety of important nonlinear physical systems. Many practical applications require the wave-train solution, which includes many solitons. In such cases, an important and relevant extension of these models applies Whitham's averaging procedure to the SG equation. The resulting SG modulation equations describe the behavior of important measurable system parameters that are the average of the small-scale solutions given by the SG equation. A fundamental problem of modern physics that is the topic of this paper is the description of the transitional process from a static to a dynamic frictional regime. We have shown that the SG modulation equations are a suitable apparatus for describing this transition. The model provides relations between kinematic (rupture and slip velocities) and dynamic (shear and normal stresses) parameters of the transition process. A particular advantage of the model is its ability to describe frictional processes over a wide range of rupture and slip velocities covering seismic events ranging from regular earthquakes, with rupture velocities on the order of a few km/s, to slow slip events, with rupture velocities on the order of a few km/day.
HEXIM1蛋白与Alu SINE RNA相互作用的研究%Study of the interaction between HEXIM1 protein and Alu SINE RNA
田平平; 吴传芳; 欧阳劲; 秦岭
2014-01-01
为了探讨Alu SINE RNA和HEXIM1蛋白之间是否存在相互作用.本实验构建了带有FLAG标签的HEXIM1真核表达载体,转染人胚肾293(HEK293)细胞,做anti FLAG 的RNA免疫共沉淀(RIP)后运用免疫印记和逆转录PCR (reverse transcription PCR,RT PCR)等方法检测.证明了Alu SINE RNA和HEXIM1蛋白之间存在相互作用,表明AluSINE RNA和HEXIM1蛋白共同影响基因转录调控,以及细胞在应对外界刺激时能及时在基因水平做出有效反应的可能.
Traveling Wave Solutions of ZK-BBM Equation Sine-Cosine Method
Sadaf Bibi
2014-03-01
Full Text Available Travelling wave solutions are obtained by using a relatively new technique which is called sine-cosine method for ZK-BBM equations. Solution procedure and obtained results re-confirm the efficiency of the proposed scheme.
Perish, then publish: Thomas Harriot and the sine law of refraction.
Fishman, R S
2000-03-01
A talented young scientist, Thomas Harriot, wrote the first English account of the New World, "A Briefe and True Report of the New Found Land of Virginia," distinguished by its serious effort to describe and understand the American Indian. Harriot went on to make innovations in mathematics and was one of the first astronomers to use the telescope. His largely unappreciated contribution to the history of ophthalmology was the first formulation of the sine law of refraction of light, found in his unpublished papers long after his death in 1621. Willebrord Snell discovered the sine law in Holland in 1621 but also died without formally publishing it. Rene Descartes first published the sine law in 1637. The sine law of refraction became not only the prime law of all lens systems but ushered in a new world of physical laws.
Sine-Gordon solitons in networks: Scattering and transmission at vertices
Sobirov, Zarif; Babajanov, Doniyor; Matrasulov, Davron; Nakamura, Katsuhiro; Uecker, Hannes
2016-09-01
We consider the sine-Gordon equation on metric graphs with simple topologies and derive vertex boundary conditions from the fundamental conservation laws together with successive space-derivatives of sine-Gordon equation. We analytically obtain traveling-wave solutions in the form of standard sine-Gordon solitons such as kinks and antikinks for star and tree graphs. We show that for this case the sine-Gordon equation becomes completely integrable just as in case of a simple 1D chain. This simple analysis provides a cornerstone for the numerical solution of the general case, including a quantification of the vertex scattering. Applications of the obtained results to Josephson junction networks and DNA double helix are discussed.
SINE polymorphism reveals distinct strains of Entamoeba histolytica from North India.
Sharma, Shraddha; Banyal, Neha; Singh, Mukul; Mandal, A K; Bhattacharya, Sudha; Paul, Jaishree
2017-04-01
Entamoeba histolytica is an intestinal parasite causing significant morbidity and mortality in the developing world. More tools are needed to understand the epidemiology and molecular pathogenesis of amebiasis. Virulence pattern of E. histolytica could be linked with the genotype of a strain. Several loci showing insertion polymorphism of retrotransposable short interspersed nuclear elements EhSINE1 and EhSINE2 have been reported among laboratory strains of E. histolytica. The present study was undertaken to validate this observation in clinical isolates from north India. Our results indicate that the Indian samples show a different propensity of SINE retention or loss at two of the polymorphic loci compared with non-Indian samples. Statistical analysis of different loci revealed Locus 17 of EhSINE1as a potential geographical marker for distinguishing Indian isolates from non Indian isolates. Copyright © 2017 Elsevier Inc. All rights reserved.
Sine Rotation Vector Method for Attitude Estimation of an Underwater Robot.
Ko, Nak Yong; Jeong, Seokki; Bae, Youngchul
2016-01-01
This paper describes a method for estimating the attitude of an underwater robot. The method employs a new concept of sine rotation vector and uses both an attitude heading and reference system (AHRS) and a Doppler velocity log (DVL) for the purpose of measurement. First, the acceleration and magnetic-field measurements are transformed into sine rotation vectors and combined. The combined sine rotation vector is then transformed into the differences between the Euler angles of the measured attitude and the predicted attitude; the differences are used to correct the predicted attitude. The method was evaluated according to field-test data and simulation data and compared to existing methods that calculate angular differences directly without a preceding sine rotation vector transformation. The comparison verifies that the proposed method improves the attitude estimation performance.
THE DYNAMICS OF SINE-GORDON SYSTEM WITH DIRICHLET BOUNDARY CONDITION
Liu Yingdong; Li Zhengyuan
2000-01-01
We prove the existence of the global attractor of Sine-Gordon system with Dirichlet boundary condition and show the attractor is the unique steady state when the damping constant and the diffusion constant are sufficiently large.
Selective activation of primary afferent fibers evaluated by sine-wave electrical stimulation
Katafuchi Toshihiko; Takaki Atsushi; Rashid Md Harunor; Furue Hidemasa; Koga Kohei; Yoshimura Megumu
2005-01-01
Abstract Transcutaneous sine-wave stimuli at frequencies of 2000, 250 and 5 Hz (Neurometer) are thought to selectively activate Aβ, Aδ and C afferent fibers, respectively. However, there are few reports to test the selectivity of these stimuli at the cellular level. In the present study, we analyzed action potentials (APs) generated by sine-wave stimuli applied to the dorsal root in acutely isolated rat dorsal root ganglion (DRG) preparations using intracellular recordings. We also measured e...
Pi-kinks in a parametrically driven sine-Gordon chain
Kivshar, Yuri S.; Grønbech-Jensen, Niels; Samuelsen, Mogens Rugholm
1992-01-01
We consider the sine-Gordon chain driven by a high-frequency parametric force in the presence of loss. Using an analytical approach based on the method of averaging in fast oscillations, we predict that such a parametric force may support propagation of π kinks, which are unstable in the standard...... sine-Gordon model. The steady-state velocity of the π kinks is calculated, and the analytical results are in good agreement with direct numerical simulations....
Davidson, A.; Pedersen, Niels Falsig; Dueholm, B.
1985-01-01
We show some experimental results which suggest that total damping, including surface loss, plays a fundamental role in limiting the stability of high-velocity sine-Gordon solitons in real Josephson tunnel junctions.......We show some experimental results which suggest that total damping, including surface loss, plays a fundamental role in limiting the stability of high-velocity sine-Gordon solitons in real Josephson tunnel junctions....
Implementing the Law of Sines to solve SAS triangles
Zelator, Konstantine
2010-01-01
By "solving a triangle", one refers to determining the three sidelengths and the three angles, based on given information.Depending on the specific information, one or more triangles may satisfy the requirements of the given information.In the SAS case, two of sidelengths are given, as well as the angle contained by the two sides.According to Euclidean Geometry, such a triangle must be unique. In reference [1], and pretty much in standard trigonometry and precalculus texts,the Law of Cosines is employed in solving a SAS triangle. In this work we use an alternative approach by using the Law of Cosines.In Section 2, we list some basic trigonometric identities and in Section 3 we prove a lemma which is used in Section4. In Section4, we demonstrate the use of the Law of Sines in solving an SAS triangle. In Section 5 we offer three examples in detail; the last one being more general in nature.
LINE-1 ORF1 protein enhances Alu SINE retrotransposition.
Wallace, Nicholas; Wagstaff, Bradley J; Deininger, Prescott L; Roy-Engel, Astrid M
2008-08-01
Retroelements have contributed over one third of the human genome mass. The currently active LINE-1 (L1) codes for two proteins (ORF1p and ORF2p), both strictly required for retrotransposition. In contrast, the non-coding parasitic SINE (Alu) only appears to need the L1 ORF2p for its own amplification. This requirement was previously determined using a tissue culture assay system in human cells (HeLa). Because HeLa are likely to express functional L1 proteins, it is possible that low levels of endogenous ORF1p are necessary for the observed tagged Alu mobilization. By individually expressing ORF1 and ORF2 proteins from both human (L1RP and LRE3) and rodent (L1A102 and L1spa) L1 sources, we demonstrate that increasing amounts of ORF1 expressing vector enhances tagged Alu mobilization in HeLa cells. In addition, using chicken fibroblast cells as an alternate cell culture source, we confirmed that ORF1p is not strictly required for Alu mobilization in our assay. Supporting our observations in HeLa cells, we find that tagged Alu retrotransposition is improved by supplementation of ORF1p in the cultured chicken cells. We postulate that L1 ORF1p plays either a direct or indirect role in enhancing the interaction between the Alu RNA and the required factors needed for its retrotransposition.
Spectral Target-Detecting System Using Sine-Wave Modulation
DENG Wei; ZHAO Chun-jiang; ZHANG Lu-da; CHENG Li-ping; Andrew Landers
2011-01-01
Target detection is one of the key technology of precision chemical application.Previously the digital coding modulation technique was commonly used to emit and receive the optical signal in the target detection systems previously in China.It was difficult to adjust the output power,and the anti-interference ability was weak in these systems.In order to resolve these problems,the target detection method based on analog sinewave modulation was studied.The spectral detecting system was set up in the aspects of working principle,electric circuit,and optical path.Lab testing was performed.The results showed that the reflected signal from the target varied inversely with detection distances.It indicated that it was feasible to establish the target detection system using analog sine-wave modulation technology.Furthermore,quantitative measurement of the reflected optical signal for near-infrared and visible light could be achieved by using this system.The research laid the foundation for the future development of the corresponding instrument.
Analysis of exact linearization and aproximate feedback linearization techniques
Schnitman, Leizer; Cardoso, Gildeberto de Souza
2011-01-01
p. 1-17 This paper presents a study of linear control systems based on exact feedback linearization and approximate feedback linearization. As exact feedback linearization is applied, a linear controller can perform the control objectives. The approximate feedback linearization is required when a nonlinear system presents a noninvolutive property. It uses a Taylor series expansion in order to compute a nonlinear transformation of coordinates to satisfy the involutivity conditions.
Analysis of Exact Linearization and Aproximate Feedback Linearization Techniques
Cardoso, Gildeberto S.; Leizer Schnitman
2011-01-01
This paper presents a study of linear control systems based on exact feedback linearization and approximate feedback linearization. As exact feedback linearization is applied, a linear controller can perform the control objectives. The approximate feedback linearization is required when a nonlinear system presents a noninvolutive property. It uses a Taylor series expansion in order to compute a nonlinear transformation of coordinates to satisfy the involutivity conditions.
Identification of a Recently Active Mammalian SINE Derived from Ribosomal RNA
Longo, Mark S.; Brown, Judy D.; Zhang, Chu; O’Neill, Michael J.; O’Neill, Rachel J.
2015-01-01
Complex eukaryotic genomes are riddled with repeated sequences whose derivation does not coincide with phylogenetic history and thus is often unknown. Among such sequences, the capacity for transcriptional activity coupled with the adaptive use of reverse transcription can lead to a diverse group of genomic elements across taxa, otherwise known as selfish elements or mobile elements. Short interspersed nuclear elements (SINEs) are nonautonomous mobile elements found in eukaryotic genomes, typically derived from cellular RNAs such as tRNAs, 7SL or 5S rRNA. Here, we identify and characterize a previously unknown SINE derived from the 3′-end of the large ribosomal subunit (LSU or 28S rDNA) and transcribed via RNA polymerase III. This new element, SINE28, is represented in low-copy numbers in the human reference genome assembly, wherein we have identified 27 discrete loci. Phylogenetic analysis indicates these elements have been transpositionally active within primate lineages as recently as 6 MYA while modern humans still carry transcriptionally active copies. Moreover, we have identified SINE28s in all currently available assembled mammalian genome sequences. Phylogenetic comparisons indicate that these elements are frequently rederived from the highly conserved LSU rRNA sequences in a lineage-specific manner. We propose that this element has not been previously recognized as a SINE given its high identity to the canonical LSU, and that SINE28 likely represents one of possibly many unidentified, active transposable elements within mammalian genomes. PMID:25637222
A New Class of SINEs with snRNA Gene-Derived Heads.
Kojima, Kenji K
2015-05-27
Eukaryotic genomes are colonized by various transposons including short interspersed elements (SINEs). The 5' region (head) of the majority of SINEs is derived from one of the three types of RNA genes--7SL RNA, transfer RNA (tRNA), or 5S ribosomal RNA (rRNA)--and the internal promoter inside the head promotes the transcription of the entire SINEs. Here I report a new group of SINEs whose heads originate from either the U1 or U2 small nuclear RNA gene. These SINEs, named SINEU, are distributed among crocodilians and classified into three families. The structures of the SINEU-1 subfamilies indicate the recurrent addition of a U1- or U2-derived sequence onto the 5' end of SINEU-1 elements. SINEU-1 and SINEU-3 are ancient and shared among alligators, crocodiles, and gharials, while SINEU-2 is absent in the alligator genome. SINEU-2 is the only SINE family that was active after the split of crocodiles and gharials. All SINEU families, especially SINEU-3, are preferentially inserted into a family of Mariner DNA transposon, Mariner-N4_AMi. A group of Tx1 non-long terminal repeat retrotransposons designated Tx1-Mar also show target preference for Mariner-N4_AMi, indicating that SINEU was mobilized by Tx1-Mar. © The Author(s) 2015. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution.
Terai, Yohey; Takezaki, Naoko; Mayer, Werner E; Tichy, Herbert; Takahata, Naoyuki; Klein, Jan; Okada, Norihiro
2004-01-01
Genomic DNA libraries were prepared from two endemic species of Lake Victoria haplochromine (cichlid) fish and used to isolate and characterize a set of short interspersed elements (SINEs). The distribution and sequences of the SINEs were used to infer phylogenetic relationships among East African haplochromines. The SINE-based classification divides the fish into four groups, which, in order of their divergence from a stem lineage, are the endemic Lake Tanganyika flock (group 1); fish of the nonendemic, monotypic, widely distributed genus Astatoreochromis (group 2); the endemic Lake Malawi flock (group 3); and group 4, which contains fish from widely dispersed East African localities including Lakes Victoria, Edward, George, Albert, and Rukwa, as well as many rivers. The group 4 haplochromines are characterized by a subset of polymorphic SINEs, each of which is present in some individuals and absent in others of the same population at a given locality, the same morphologically defined species, and the same mtDNA-defined haplogroup. SINE-defined group 4 contains six of the seven previously described mtDNA haplogroups. One of the polymorphic SINEs appears to be fixed in the endemic Lake Victoria flock; four others display the presence-or-absence polymorphism within the species of this flock. These findings have implications for the origin of Lake Victoria cichlids and for their founding population sizes.
RNA-Mediated Gene Duplication and Retroposons: Retrogenes, LINEs, SINEs, and Sequence Specificity
2013-01-01
A substantial number of “retrogenes” that are derived from the mRNA of various intron-containing genes have been reported. A class of mammalian retroposons, long interspersed element-1 (LINE1, L1), has been shown to be involved in the reverse transcription of retrogenes (or processed pseudogenes) and non-autonomous short interspersed elements (SINEs). The 3′-end sequences of various SINEs originated from a corresponding LINE. As the 3′-untranslated regions of several LINEs are essential for retroposition, these LINEs presumably require “stringent” recognition of the 3′-end sequence of the RNA template. However, the 3′-ends of mammalian L1s do not exhibit any similarity to SINEs, except for the presence of 3′-poly(A) repeats. Since the 3′-poly(A) repeats of L1 and Alu SINE are critical for their retroposition, L1 probably recognizes the poly(A) repeats, thereby mobilizing not only Alu SINE but also cytosolic mRNA. Many flowering plants only harbor L1-clade LINEs and a significant number of SINEs with poly(A) repeats, but no homology to the LINEs. Moreover, processed pseudogenes have also been found in flowering plants. I propose that the ancestral L1-clade LINE in the common ancestor of green plants may have recognized a specific RNA template, with stringent recognition then becoming relaxed during the course of plant evolution. PMID:23984183
RNA-Mediated Gene Duplication and Retroposons: Retrogenes, LINEs, SINEs, and Sequence Specificity
Kazuhiko Ohshima
2013-01-01
Full Text Available A substantial number of “retrogenes” that are derived from the mRNA of various intron-containing genes have been reported. A class of mammalian retroposons, long interspersed element-1 (LINE1, L1, has been shown to be involved in the reverse transcription of retrogenes (or processed pseudogenes and non-autonomous short interspersed elements (SINEs. The -end sequences of various SINEs originated from a corresponding LINE. As the -untranslated regions of several LINEs are essential for retroposition, these LINEs presumably require “stringent” recognition of the -end sequence of the RNA template. However, the -ends of mammalian L1s do not exhibit any similarity to SINEs, except for the presence of -poly(A repeats. Since the -poly(A repeats of L1 and Alu SINE are critical for their retroposition, L1 probably recognizes the poly(A repeats, thereby mobilizing not only Alu SINE but also cytosolic mRNA. Many flowering plants only harbor L1-clade LINEs and a significant number of SINEs with poly(A repeats, but no homology to the LINEs. Moreover, processed pseudogenes have also been found in flowering plants. I propose that the ancestral L1-clade LINE in the common ancestor of green plants may have recognized a specific RNA template, with stringent recognition then becoming relaxed during the course of plant evolution.
Comparative study of two linearization methods for time intervals generation of SVPWM technique
Khaled N. Faris
2016-12-01
In this paper a comparative study for two linearization methods are carried out for generating the time intervals of SVPWM technique. The proposed linearization methods achieve a minimum computational time rather than the trigonometric sine function which is considered the base for the time interval calculations of the SVPWM technique. The first linearization method is based on the first order equation, and the second method is the (Takagi–Sugeno fuzzy modeling system. The comparative study includes the accuracy of the two models, also a simulation model is carried out for current THD estimation using the two proposed methods compared with the current THD generated by SVPWM based on the trigonometric sine function.
Genome-wide mapping of infection-induced SINE RNAs reveals a role in selective mRNA export.
Karijolich, John; Zhao, Yang; Alla, Ravi; Glaunsinger, Britt
2017-06-02
Short interspersed nuclear elements (SINEs) are retrotransposons evolutionarily derived from endogenous RNA Polymerase III RNAs. Though SINE elements have undergone exaptation into gene regulatory elements, how transcribed SINE RNA impacts transcriptional and post-transcriptional regulation is largely unknown. This is partly due to a lack of information regarding which of the loci have transcriptional potential. Here, we present an approach (short interspersed nuclear element sequencing, SINE-seq), which selectively profiles RNA Polymerase III-derived SINE RNA, thereby identifying transcriptionally active SINE loci. Applying SINE-seq to monitor murine B2 SINE expression during a gammaherpesvirus infection revealed transcription from 28 270 SINE loci, with ∼50% of active SINE elements residing within annotated RNA Polymerase II loci. Furthermore, B2 RNA can form intermolecular RNA-RNA interactions with complementary mRNAs, leading to nuclear retention of the targeted mRNA via a mechanism involving p54nrb. These findings illuminate a pathway for the selective regulation of mRNA export during stress via retrotransposon activation. © The Author(s) 2017. Published by Oxford University Press on behalf of Nucleic Acids Research.
Ecoutin, J. M.; Simier, M.; Albaret, J. J.; Laë, R.; Tito de Morais, L.
2010-04-01
To investigate the changes in the fish assemblage of the Sine Saloum estuary (Senegal) over a 10-year period, it was surveyed during a complete hydrological cycle (three principal hydro-climatic seasons) first in 1992 and then in 2002-2003. The sampling protocol for the two surveys was identical, using the same sampling technique, the same collection periods, and the same sampling stations. The Sine Saloum is an inverse estuary in terms of its salinity gradient. It is affected by the intense drought that has occurred in this biogeographic region for more than 50 years. The estuary is also subjected to high fishing pressure. The second data-collection period followed a few years of higher recorded rainfall (approximately 35% higher than in 1992) and was characterized by increased fishing pressure (over 50% higher than in 1992). For the two study periods, the same set of indicators were calculated, including fishing indicators (catches, density, yields), size-based indicators (size structures, mean length, maximum observed length, size spectra), ecological indicators (richness, species diversity, K-dominance models, ABC curves, ecological categories) and trophic indicators (mean trophic level, trophic composition of catches). Overall, the main changes in the estuary's fish assemblage between 1992 and 2002 were (1) a loss in total biomass (40% less) for an equivalent species richness (approximately 55 species); (2) a decrease in the maximum observed lengths for many species (mean decrease of 17%); and (3) a decrease in the mean trophic level (more than 0.11 units). Analysis by bio-ecological and trophic category showed that the main species concerned were benthophagous species and, to a lesser degree, generalist predator species from marine origin that inhabit the estuary more or less permanently.
Razavi, M.; Mollai, M.; Khorshid, P. [Department of Physics, Islamic Azad University, Mashhad Branch, Mashhad 91735-413 (Iran, Islamic Republic of); Nedzelskiy, I. [Instituto de Plasma e Fusao Nuclear, Lisboa 1049-001 (Portugal); Ghoranneviss, M. [Plasma Physics Research Center, Islamic Azad University, Tehran 14665-678 (Iran, Islamic Republic of)
2010-05-15
The modified Rogowski sine-coil (MRSC) has been designed and implemented for the plasma column horizontal displacement measurements on small IR-T1 tokamak. MRSC operation has been examined on test assembly and tokamak. Obtained results show high sensitivity to the plasma column horizontal displacement and negligible sensitivity to the vertical displacement; linearity in wide, {+-}0.1 m, range of the displacements; and excellent, 1.5%, agreement with the results of numerical solution of Biot-Savart and magnetic flux equations.
Nullum Crimen sine Lege in the International Criminal Court
Venus GHAREH BAGHI
2010-10-01
Full Text Available The Principles of legality in crimes and punishments refer to the fact that an act is not considered a crime and deserves no punishment, until the legislator determines and announces thecriminal title and its penalty. In Iranian legal system, before the Islamic Revolution and also after it, the Constitution and ordinary laws have explicitly emphasized the observance of the mentionedprinciple. When there is no text or in the case of the silence or lack of law, the criminal judge is bound to issue the verdict of innocence. According to the Rome statute the court shall exercisejurisdiction over the crime of aggressions once a provision is adopted. And, according to the article 121 and 123 defending the crime and setting out, the condition under which the Court shall exercise jurisdiction with respect to crimes such as provision shall be consisted of the head of the general principle the relevant provision of the charter of the United Nations. The principle of legality is set out in article 22 to 24 of the ICC statute. These norms are derived from the customary law and the national law. Article 15, International Covenant on Civil and Political rights, states that no one shall be found guilty of any criminal offence based on an act or omission which did not constitute a criminal offence under national or international laws at the time when it was committed. Yet, in the context of prosecuting mass atrocities, genocide, crimes against humanity, and war crimes, international criminal law appears to be resigned to such a principle, if not openly including it. fact, that it may be considered the poor cousin of nullum crimen sine lege (no crime without law which has attracted far greater consideration in scholarship and jurisprudence.
Analyses of carnivore microsatellites and their intimate association with tRNA-derived SINEs
Bosch Montserrat
2006-10-01
Full Text Available Abstract Background The popularity of microsatellites has greatly increased in the last decade on account of their many applications. However, little is currently understood about the factors that influence their genesis and distribution among and within species genomes. In this work, we analyzed carnivore microsatellite clones from GenBank to study their association with interspersed repeats and elucidate the role of the latter in microsatellite genesis and distribution. Results We constructed a comprehensive carnivore microsatellite database comprising 1236 clones from GenBank. Thirty-three species of 11 out of 12 carnivore families were represented, although two distantly related species, the domestic dog and cat, were clearly overrepresented. Of these clones, 330 contained tRNALys-derived SINEs and 357 contained other interspersed repeats. Our rough estimates of tRNA SINE copies per haploid genome were much higher than published ones. Our results also revealed a distinct juxtaposition of AG and A-rich repeats and tRNALys-derived SINEs suggesting their coevolution. Both microsatellites arose repeatedly in two regions of the insterspersed repeat. Moreover, microsatellites associated with tRNALys-derived SINEs showed the highest complexity and less potential instability. Conclusion Our results suggest that tRNALys-derived SINEs are a significant source for microsatellite generation in carnivores, especially for AG and A-rich repeat motifs. These observations indicate two modes of microsatellite generation: the expansion and variation of pre-existing tandem repeats and the conversion of sequences with high cryptic simplicity into a repeat array; mechanisms which are not specific to tRNALys-derived SINEs. Microsatellite and interspersed repeat coevolution could also explain different distribution of repeat types among and within species genomes. Finally, due to their higher complexity and lower potential informative content of microsatellites
Analyses of carnivore microsatellites and their intimate association with tRNA-derived SINEs.
López-Giráldez, Francesc; Andrés, Olga; Domingo-Roura, Xavier; Bosch, Montserrat
2006-10-23
The popularity of microsatellites has greatly increased in the last decade on account of their many applications. However, little is currently understood about the factors that influence their genesis and distribution among and within species genomes. In this work, we analyzed carnivore microsatellite clones from GenBank to study their association with interspersed repeats and elucidate the role of the latter in microsatellite genesis and distribution. We constructed a comprehensive carnivore microsatellite database comprising 1236 clones from GenBank. Thirty-three species of 11 out of 12 carnivore families were represented, although two distantly related species, the domestic dog and cat, were clearly overrepresented. Of these clones, 330 contained tRNALys-derived SINEs and 357 contained other interspersed repeats. Our rough estimates of tRNA SINE copies per haploid genome were much higher than published ones. Our results also revealed a distinct juxtaposition of AG and A-rich repeats and tRNALys-derived SINEs suggesting their coevolution. Both microsatellites arose repeatedly in two regions of the interspersed repeat. Moreover, microsatellites associated with tRNALys-derived SINEs showed the highest complexity and less potential instability. Our results suggest that tRNALys-derived SINEs are a significant source for microsatellite generation in carnivores, especially for AG and A-rich repeat motifs. These observations indicate two modes of microsatellite generation: the expansion and variation of pre-existing tandem repeats and the conversion of sequences with high cryptic simplicity into a repeat array; mechanisms which are not specific to tRNALys-derived SINEs. Microsatellite and interspersed repeat coevolution could also explain different distribution of repeat types among and within species genomes.Finally, due to their higher complexity and lower potential informative content of microsatellites associated with tRNALys-derived SINEs, we recommend avoiding
Grechko, Vernata V; Kosushkin, Sergei A; Borodulina, Olga R; Butaeva, Fatima G; Darevsky, Ilya S
2011-05-15
Short interspersed elements (SINEs) are important nuclear molecular markers of the evolution of many eukaryotes. However, the SINEs of squamate reptile genomes have been little studied. We first identified two families of SINEs, termed Squam1 and Squam2, in the DNA of meadow lizard Darevskia praticola (Lacertidae) by performing DNA hybridization and PCR. Later, the same families of retrotransposons were found using the same methods in members of another 25 lizard families (from Iguania, Scincomorpha, Gekkota, Varanoidea, and Diploglossa infraorders) and two snake families, but their abundances in these taxa varied greatly. Both SINEs were Squamata-specific and were absent from mammals, birds, crocodiles, turtles, amphibians, and fish. Squam1 possessed some characteristics common to tRNA-related SINEs from fish and mammals, while Squam2 belonged to the tRNA(Ala) group of SINEs and had a more unusual and divergent structure. Squam2-related sequences were found in several unannotated GenBank sequences of squamate reptiles. Squam1 abundance in the Polychrotidae, Agamidae, Leiolepididae, Chamaeleonidae, Scincidae, Lacertidae, Gekkonidae, Varanidae, Helodermatidae, and two snake families were 10(2) -10(4) times higher than those in other taxa (Corytophanidae, Iguanidae, Anguidae, Cordylidae, Gerrhosauridae, Pygopodidae, and Eublepharidae). A less dramatic degree of copy number variation was observed for Squam2 in different taxa. Several Squam1 copies from Lacertidae, Chamaeleonidae, Gekkonidae, Varanidae, and Colubridae were sequenced and found to have evident orthologous features, as well as taxa-specific autapomorphies. Squam1 from Lacertidae and Chamaeleonidae could be divided into several subgroups based on sequence differences. Possible applications of these SINEs as Squamata phylogeny markers are discussed. Copyright © 2010 Wiley-Liss, Inc., A Wiley Company.
Tajaddod, Mansoureh; Tanzer, Andrea; Licht, Konstantin; Wolfinger, Michael T; Badelt, Stefan; Huber, Florian; Pusch, Oliver; Schopoff, Sandy; Janisiw, Michael; Hofacker, Ivo; Jantsch, Michael F
2016-10-25
Short interspersed elements (SINEs) represent the most abundant group of non-long-terminal repeat transposable elements in mammalian genomes. In primates, Alu elements are the most prominent and homogenous representatives of SINEs. Due to their frequent insertion within or close to coding regions, SINEs have been suggested to play a crucial role during genome evolution. Moreover, Alu elements within mRNAs have also been reported to control gene expression at different levels. Here, we undertake a genome-wide analysis of insertion patterns of human Alus within transcribed portions of the genome. Multiple, nearby insertions of SINEs within one transcript are more abundant in tandem orientation than in inverted orientation. Indeed, analysis of transcriptome-wide expression levels of 15 ENCODE cell lines suggests a cis-repressive effect of inverted Alu elements on gene expression. Using reporter assays, we show that the negative effect of inverted SINEs on gene expression is independent of known sensors of double-stranded RNAs. Instead, transcriptional elongation seems impaired, leading to reduced mRNA levels. Our study suggests that there is a bias against multiple SINE insertions that can promote intramolecular base pairing within a transcript. Moreover, at a genome-wide level, mRNAs harboring inverted SINEs are less expressed than mRNAs harboring single or tandemly arranged SINEs. Finally, we demonstrate a novel mechanism by which inverted SINEs can impact on gene expression by interfering with RNA polymerase II.
Nonlinear approximation with redundant dictionaries
Borup, Lasse; Nielsen, M.; Gribonval, R.
2005-01-01
In this paper we study nonlinear approximation and data representation with redundant function dictionaries. In particular, approximation with redundant wavelet bi-frame systems is studied in detail. Several results for orthonormal wavelets are generalized to the redundant case. In general......, for a wavelet bi-frame system the approximation properties are limited by the number of vanishing moments of the system. In some cases this can be overcome by oversampling, but at a price of replacing the canonical expansion by another linear expansion. Moreover, for special non-oversampled wavelet bi-frames we...... can obtain good approximation properties not restricted by the number of vanishing moments, but again without using the canonical expansion....
CORE-SINEs: eukaryotic short interspersed retroposing elements with common sequence motifs.
Gilbert, N; Labuda, D
1999-03-16
A 65-bp "core" sequence is dispersed in hundreds of thousands copies in the human genome. This sequence was found to constitute the central segment of a group of short interspersed elements (SINEs), referred to as mammalian-wide interspersed repeats, that proliferated before the radiation of placental mammals. Here, we propose that the core identifies an ancient tRNA-like SINE element, which survived in different lineages such as mammals, reptiles, birds, and fish, as well as mollusks, presumably for >550 million years. This element gave rise to a number of sequence families (CORE-SINEs), including mammalian-wide interspersed repeats, whose distinct 3' ends are shared with different families of long interspersed elements (LINEs). The evolutionary success of the generic CORE-SINE element can be related to the recruitment of the internal promoter from highly transcribed host RNA as well as to its capacity to adapt to changing retropositional opportunities by sequence exchange with actively amplifying LINEs. It reinforces the notion that the very existence of SINEs depends on the cohabitation with both LINEs and the host genome.
Halder, G; Callaerts, P; Flister, S; Walldorf, U; Kloter, U; Gehring, W J
1998-06-01
The Drosophila Pax-6 gene eyeless acts high up in the genetic hierarchy involved in compound eye development and can direct the formation of extra eyes in ectopic locations. Here we identify sine oculis and eyes absent as two mediators of the eye-inducing activity of eyeless. We show that eyeless induces and requires the expression of both genes independently during extra eye development. During normal eye development, eyeless is expressed earlier than and is required for the expression of sine oculis and eyes absent, but not vice versa. Based on the results presented here and those of others, we propose a model in which eyeless induces the initial expression of both sine oculis and eyes absent in the eye disc. sine oculis and eyes absent then appear to participate in a positive feedback loop that regulates the expression of all three genes. In contrast to the regulatory interactions that occur in the developing eye disc, we also show that in the embryonic head, sine oculis acts in parallel to eyeless and twin of eyeless, a second Pax-6 gene from Drosophila. Recent studies in vertebrate systems indicate that the epistatic relationships among the corresponding vertebrate homologs are very similar to those observed in Drosophila.
Diophantine approximation and badly approximable sets
Kristensen, S.; Thorn, R.; Velani, S.
2006-01-01
Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X. The clas......Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X....... The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...
Non-minimally coupled bulk scalar fields in sine-Gordon braneworld models
Moazzen, Masoumeh; Ghalenovi, Zahra
2017-10-01
In this paper, we investigate localization of bulk scalar fields in two types of five-dimensional braneworld models given by sine-Gordon potentials (SG). The sine-Gordon and Double sine-Gordon (DSG) branes are employed to produce different thick brane setups. In both scenarios, we include the bulk mass and non-minimally coupled terms in the global action and obtain some implications on the volcano-like potentials of the Kaluza-Klein modes associated to the corresponding Schrödinger-like equations. Also, we find that minimally and non-minimally coupled massive bulk scalar fields can be localized on SG and DSG branes if their bulk mass obeys an upper bound. Furthermore, it is shown that at the critical value of the non-minimal coupling constant the bulk scalar field cannot be localized on the branes.
Cross-Correlation-Function-Based Multipath Mitigation Method for Sine-BOC Signals
H. H. Chen
2012-06-01
Full Text Available Global Navigation Satellite Systems (GNSS positioning accuracy indoor and urban canyons environments are greatly affected by multipath due to distortions in its autocorrelation function. In this paper, a cross-correlation function between the received sine phased Binary Offset Carrier (sine-BOC modulation signal and the local signal is studied firstly, and a new multipath mitigation method based on cross-correlation function for sine-BOC signal is proposed. This method is implemented to create a cross-correlation function by designing the modulated symbols of the local signal. The theoretical analysis and simulation results indicate that the proposed method exhibits better multipath mitigation performance compared with the traditional Double Delta Correlator (DDC techniques, especially the medium/long delay multipath signals, and it is also convenient and flexible to implement by using only one correlator, which is the case of low-cost mass-market receivers.
APPROXIMATE SAMPLING THEOREM FOR BIVARIATE CONTINUOUS FUNCTION
杨守志; 程正兴; 唐远炎
2003-01-01
An approximate solution of the refinement equation was given by its mask, and the approximate sampling theorem for bivariate continuous function was proved by applying the approximate solution. The approximate sampling function defined uniquely by the mask of the refinement equation is the approximate solution of the equation, a piece-wise linear function, and posseses an explicit computation formula. Therefore the mask of the refinement equation is selected according to one' s requirement, so that one may controll the decay speed of the approximate sampling function.
Bernstein-type approximations of smooth functions
Andrea Pallini
2007-10-01
Full Text Available The Bernstein-type approximation for smooth functions is proposed and studied. We propose the Bernstein-type approximation with definitions that directly apply the binomial distribution and the multivariate binomial distribution. The Bernstein-type approximations generalize the corresponding Bernstein polynomials, by considering definitions that depend on a convenient approximation coefficient in linear kernels. In the Bernstein-type approximations, we study the uniform convergence and the degree of approximation. The Bernstein-type estimators of smooth functions of population means are also proposed and studied.
Upper Bounds on Numerical Approximation Errors
Raahauge, Peter
2004-01-01
This paper suggests a method for determining rigorous upper bounds on approximationerrors of numerical solutions to infinite horizon dynamic programming models.Bounds are provided for approximations of the value function and the policyfunction as well as the derivatives of the value function....... The bounds apply to moregeneral problems than existing bounding methods do. For instance, since strict concavityis not required, linear models and piecewise linear approximations can bedealt with. Despite the generality, the bounds perform well in comparison with existingmethods even when applied...... to approximations of a standard (strictly concave)growth model.KEYWORDS: Numerical approximation errors, Bellman contractions, Error bounds...
Arbitrarily large numbers of kink internal modes in inhomogeneous sine-Gordon equations
González, J.A., E-mail: jalbertgonz@yahoo.es [Department of Physics, Florida International University, Miami, FL 33199 (United States); Department of Natural Sciences, Miami Dade College, 627 SW 27th Ave., Miami, FL 33135 (United States); Bellorín, A., E-mail: alberto.bellorin@ucv.ve [Escuela de Física, Facultad de Ciencias, Universidad Central de Venezuela, Apartado Postal 47586, Caracas 1041-A (Venezuela, Bolivarian Republic of); García-Ñustes, M.A., E-mail: monica.garcia@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059 (Chile); Guerrero, L.E., E-mail: lguerre@usb.ve [Departamento de Física, Universidad Simón Bolívar, Apartado Postal 89000, Caracas 1080-A (Venezuela, Bolivarian Republic of); Jiménez, S., E-mail: s.jimenez@upm.es [Departamento de Matemática Aplicada a las TT.II., E.T.S.I. Telecomunicación, Universidad Politécnica de Madrid, 28040-Madrid (Spain); Vázquez, L., E-mail: lvazquez@fdi.ucm.es [Departamento de Matemática Aplicada, Facultad de Informática, Universidad Complutense de Madrid, 28040-Madrid (Spain)
2017-06-28
We prove analytically the existence of an infinite number of internal (shape) modes of sine-Gordon solitons in the presence of some inhomogeneous long-range forces, provided some conditions are satisfied. - Highlights: • We have found exact kink solutions to the perturbed sine-Gordon equation. • We have been able to study analytically the kink stability problem. • A kink equilibrated by an exponentially-localized perturbation has a finite number of oscillation modes. • A sufficiently broad equilibrating perturbation supports an infinite number of soliton internal modes.
Thermal sine-Gordon system in the presence of different types of dissipation
Salerno, M.; Samuelsen, Mogens Rugholm; Svensmark, Henrik
1988-01-01
The effects of thermal fluctuations on solitons and phonons of the sine-Gordon system are investigated in the presence of a αφt-βφxxt dissipation. The analysis requires the assumption of a more general autocorrelation function for the noise than the one used in previous works. We verify that this......The effects of thermal fluctuations on solitons and phonons of the sine-Gordon system are investigated in the presence of a αφt-βφxxt dissipation. The analysis requires the assumption of a more general autocorrelation function for the noise than the one used in previous works. We verify...
Development of a sine-dwell ground vibration test (GVT) system
Van Zyl, Lourens H
2006-02-27
Full Text Available stream_source_info VanZyl_2006.pdf.txt stream_content_type text/plain stream_size 9765 Content-Encoding UTF-8 stream_name VanZyl_2006.pdf.txt Content-Type text/plain; charset=UTF-8 Development of a Sine-Dwell Ground... vibration testing? • Basics of sine-dwell testing Getting the structure to vibrate in phase, and what then? • Excitation hardware Exciters are similar to speakers • Measurement system Force and response as complex numbers • Excitation control...
Usmanova, N M; Kazakov, V I; Tomilin, N V
2008-01-01
Using computer-based methods we determined the global distribution of short interspersed nuclear elements (SINEs) in the human and mouse X chromosomes. It has been shown that this distributions is similar to the distributions of CpG islands and genes but is different from the distribution of LINE1 elements. Since SINEs (human Alu and mouse B2) may have binding sites for Polycomb protein YY1, we suggest that these repeats can serve as additional signals ("boosters") in Polycomb-dependent silencing of gene rich segments during X inactivation.
Characterization of short interspersed elements (SINEs) in a red alga, Porphyra yezoensis.
Zhang, Wenbo; Lin, Xiaofei; Peddigari, Suresh; Takechi, Katsuaki; Takano, Hiroyoshi; Takio, Susumu
2007-02-01
Short interspersed element (SINE)-like sequences referred to as PySN1 and PySN2 were identified in a red alga, Porphyra yezoensis. Both elements contained an internal promoter with motifs (A box and B box) recognized by RNA polymerase III, and target site duplications at both ends. Genomic Southern blot analysis revealed that both elements were widely and abundantly distributed on the genome. 3' and 5' RACE suggested that PySN1 was expressed as a chimera transcript with flanking SINE-unrelated sequences and possessed the poly-A tail at the same position near the 3' end of PySN1.
Intermittent Switching between Soliton Dynamic States in a Perturbed Sine-Gordon Model
Sørensen, Mads Peter; Arley, N.; Christiansen, Peter Leth
1983-01-01
Chaotic intermittency between soliton dynamic states has been found in a perturbed sine-Gordon system in the absence of an external ac driving term. The system is a model of a long Josephson oscillator with constant loss and bias current in an external magnetic field. The results predict the exis......Chaotic intermittency between soliton dynamic states has been found in a perturbed sine-Gordon system in the absence of an external ac driving term. The system is a model of a long Josephson oscillator with constant loss and bias current in an external magnetic field. The results predict...
Nonabelian sine-Gordon theory and its application to nonlinear optics
Park, Q H; Park, Q Han
1996-01-01
Using a field theory generalization of the spinning top motion, we construct nonabelian generalizations of the sine-Gordon theory according to each symmetric spaces. A Lagrangian formulation of these generalized sine-Gordon theories is given in terms of a deformed gauged Wess-Zumino-Witten action which also accounts for integrably perturbed coset conformal field theories. As for physical applications, we show that they become precisely the effective field theories of self-induced transparency in nonlinear optics. This provides a dictionary between field theory and nonlinear optics.
Leike, Reimar H
2016-01-01
In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a ranking function that quantifies how "embarrassing" it is to communicate a given approximation. We show that there is only one ranking under the requirements that (1) the best ranked approximation is the non-approximated belief and (2) that the ranking judges approximations only by their predictions for actual outcomes. We find that this ranking is equivalent to the Kullback-Leibler divergence that is frequently used in the literature. However, there seems to be confusion about the correct order in which its functional arguments, the approximated and non-approximated beliefs, should be used. We hope that our elementary derivation settles the apparent confusion. We show for example that when approximating beliefs with Gaussian distributions the optimal approximation is given by moment matching. This is in contrast to many su...
Kalmykov, M Yu
2004-01-01
Generalized log-sine functions appear in higher order epsilon-expansion of different Feynman diagrams. We present an algorithm for numerical evaluation of these functions of real argument. This algorithm is implemented as C++ library with arbitrary-precision arithmetics for integer 0 1. Some new relations and representations for the generalized log-sine functions are given.
Rašin, Andrija
1994-01-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
On Element SDD Approximability
Avron, Haim; Toledo, Sivan
2009-01-01
This short communication shows that in some cases scalar elliptic finite element matrices cannot be approximated well by an SDD matrix. We also give a theoretical analysis of a simple heuristic method for approximating an element by an SDD matrix.
Piecewise linear models for the quasiperiodic transition to chaos
Campbell, D K; Tresser, C; Uherka, D J; Campbell, David K; Galeeva, Roza; Tresser, Charles; Uherka, David J
1995-01-01
We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking and the quasi-periodic transition to chaos. For instance, for these families, we obtain complete solutions to several questions still largely unanswered for families of smooth circle maps. Our main results describe (1) the sets of maps in these families having some prescribed rotation interval; (2) the boundaries between zero and positive topological entropy and between zero length and non-zero length rotation interval; and (3) the structure and bifurcations of the attractors in one of these families. We discuss the interpretation of these maps as low-order spline approximations to the classic ``sine-circle'' map and examine more generally the implications of our results for the case of smooth circle maps. We also mention a possible connection to recent experiments on mode...
Approximate iterative algorithms
Almudevar, Anthony Louis
2014-01-01
Iterative algorithms often rely on approximate evaluation techniques, which may include statistical estimation, computer simulation or functional approximation. This volume presents methods for the study of approximate iterative algorithms, providing tools for the derivation of error bounds and convergence rates, and for the optimal design of such algorithms. Techniques of functional analysis are used to derive analytical relationships between approximation methods and convergence properties for general classes of algorithms. This work provides the necessary background in functional analysis a
V. Bacsó
2015-12-01
Full Text Available In this paper we study the c-function of the sine-Gordon model taking explicitly into account the periodicity of the interaction potential. The integration of the c-function along trajectories of the non-perturbative renormalization group flow gives access to the central charges of the model in the fixed points. The results at vanishing frequency β2, where the periodicity does not play a role, are retrieved and the independence on the cutoff regulator for small frequencies is discussed. Our findings show that the central charge obtained integrating the trajectories starting from the repulsive low-frequencies fixed points (β2<8π to the infra-red limit is in good quantitative agreement with the expected Δc=1 result. The behavior of the c-function in the other parts of the flow diagram is also discussed. Finally, we point out that including also higher harmonics in the renormalization group treatment at the level of local potential approximation is not sufficient to give reasonable results, even if the periodicity is taken into account. Rather, incorporating the wave-function renormalization (i.e. going beyond local potential approximation is crucial to get sensible results even when a single frequency is used.
Approximation of distributed delays
Lu, Hao; Eberard, Damien; Simon, Jean-Pierre
2010-01-01
We address in this paper the approximation problem of distributed delays. Such elements are convolution operators with kernel having bounded support, and appear in the control of time-delay systems. From the rich literature on this topic, we propose a general methodology to achieve such an approximation. For this, we enclose the approximation problem in the graph topology, and work with the norm defined over the convolution Banach algebra. The class of rational approximates is described, and a constructive approximation is proposed. Analysis in time and frequency domains is provided. This methodology is illustrated on the stabilization control problem, for which simulations results show the effectiveness of the proposed methodology.
Abundant new travelling wave solutions for the (2 + 1)-dimensional Sine-Gordon equation
Li Zhu [College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000 (China)], E-mail: lizhu1813@163.com; Dong Huanhe [College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266510 (China)
2008-07-15
Abundant new travelling wave solutions of the (2 + 1)-dimensional Sine-Gordon equation are obtained by the generalized Jacobi elliptic function method. The solutions obtained include the kink-shaped solutions, bell-shaped solutions, singular solutions and periodic solutions.
A Classroom Note on Generating Examples for the Laws of Sines and Cosines from Pythagorean Triangles
Sher, Lawrence; Sher, David
2007-01-01
By selecting certain special triangles, students can learn about the laws of sines and cosines without wrestling with long decimal representations or irrational numbers. Since the law of cosines requires only one of the three angles of a triangle, there are many examples of triangles with integral sides and a cosine that can be represented exactly…
Breather kink-antikink-pair conversion in the driven sine-Gordon system
Lomdahl, P. S.; Olsen, O. H.; Samuelsen, Mogens Rugholm
1984-01-01
Breather excitations in the sine-Gordon equation influenced by constant driving forces are investigated—large driving forces cause the breather to split into a kk― (2π kink-2π antikink) pair while for small driving forces the breather excitations enter stationary modes. A perturbation method...
Discovering Trigonometric Relationships Implied by the Law of Sines and the Law of Cosines
Skurnick, Ronald; Javadi, Mohammad
2006-01-01
The Law of Sines and The Law of Cosines are of paramount importance in the field of trigonometry because these two theorems establish relationships satisfied by the three sides and the three angles of any triangle. In this article, the authors use these two laws to discover a host of other trigonometric relationships that exist within any…
Sine-Gordon 2-pi-kink dynamics in the presence of small perturbations
Olsen, O. H.; Samuelsen, Mogens Rugholm
1983-01-01
The influence of external driving forces on the 2π-kink solution to the sine-Gordon equation is examined. The analysis is based on the approach that the solution to the problem can be divided into a 2π-kink part and a background or vacuum part. The behavior of the 2π kink depends strongly...
Internal oscillation frequencies and anharmonic effects for the double sine-Gordon kink
Salerno, M.; Samuelsen, Mogens Rugholm
1989-01-01
A simple derivation of the small oscillation frequency around 4π-kink solutions of the double sine-Gordon equation is presented. Small corrections to these frequencies due to anharmonic effects are also numerically and analytically investigated. The analysis is based on energetic considerations...
Stabilization of breathers in a parametrically driven sine-Gordon system with loss
Grønbech-Jensen, N.; Kivshar, Yu. S.; Samuelsen, Mogens Rugholm
1991-01-01
We demonstrate that in a parametrically driven sine-Gordon system with loss, a breather, if driven, can be maintained in a steady state at half the external frequency. In the small-amplitude limit the system is described by the effective perturbed nonlinear Schrödinger equation. For an arbitrary...
Stress induction of Bm1 RNA in silkworm larvae: SINEs, an unusual class of stress genes
Kimura, Richard H.; Choudary, Prabhakara V.; Stone, Koni K.; Schmid, Carl W.
2001-01-01
This study surveys the induction of RNA polymerase III (Pol III)–directed expression of short interspersed element (SINE) transcripts by various stresses in an animal model, silkworm larvae. Sublethal heat shock and exposure to several toxic compounds increase the level of Bm1 RNA, the silkworm SINE transcript, while also transiently increasing expression of a well-characterized stress-induced transcript, Hsp70 messenger RNA (mRNA). In certain cases, the Bm1 RNA response coincides with that of Hsp70 mRNA, but more often Bm1 RNA responds later in recovery. Baculovirus infection and exposure to certain toxic compounds increase Bm1 RNA but not Hsp70 mRNA, showing that SINE induction is not necessarily coupled to transcription of this particular heat shock gene. SINEs behave as an additional class of stress-inducible genes in living animals but are unusual as stress genes because of their high copy number, genomic dispersion, and Pol III–directed transcription. PMID:11599568
The LINEs and SINEs of Entamoeba histolytica: comparative analysis and genomic distribution.
Bakre, Abhijeet A; Rawal, Kamal; Ramaswamy, Ram; Bhattacharya, Alok; Bhattacharya, Sudha
2005-07-01
Autonomous non-long terminal repeat retrotransposons are commonly referred to as long interspersed elements (LINEs). Short non-autonomous elements that borrow the LINE machinery are called SINES. The Entamoeba histolytica genome contains three classes of LINEs and SINEs. Together the EhLINEs/SINEs account for about 6% of the genome. The recognizable functional domains in all three EhLINEs included reverse transcriptase and endonuclease. A novel feature was the presence of two types of members-some with a single long ORF (less frequent) and some with two ORFs (more frequent) in both EhLINE1 and 2. The two ORFs were generated by conserved changes leading to stop codon. Computational analysis of the immediate flanking sequences for each element showed that they inserted in AT-rich sequences, with a preponderance of Ts in the upstream site. The elements were very frequently located close to protein-coding genes and other EhLINEs/SINEs. The possible influence of these elements on expression of neighboring genes needs to be determined.
Short interspersed CAN SINE elements as prognostic markers in canine mammary neoplasia.
Gelaleti, Gabriela B; Granzotto, Adriana; Leonel, Camila; Jardim, Bruna V; Moschetta, Marina G; Carareto, Claudia M A; Zuccari, Debora Ap P C
2014-01-01
The genome of mammals is characterized by a large number of non-LTR retrotransposons, and among them, the CAN SINEs are characteristics of the canine species. Small amounts of DNA freely circulate in normal blood serum and high amounts are found in human patients with cancer, characterizing it as a candidate tumor-biomarker. The aim of this study was to estimate, through its absolute expression, the number of copies of CAN SINE sequences present in free circulating DNA of female dogs with mammary cancer, in order to correlate with the clinical and pathological characteristics and the follow-up period. The copy number of CAN SINE sequences was estimated by qPCR in 28 female dogs with mammary neoplasia. The univariate analysis showed an increased number of copies in female dogs with mammary tumor in female dogs >10 years old (p=0.02) and tumor time >18 months (pSINE fragments can be good markers for the detection of tumor DNA in blood and may characterize it as a marker of poor prognosis, being related to female dogs with shorter survival times. This estimate can be used as a prognostic marker in non-invasive breast cancer research and is useful in predicting tumor progression and patient monitoring.
Fatigue Damage Spectrum calculation in a Mission Synthesis procedure for Sine-on-Random excitations
Angeli, Andrea; Cornelis, Bram; Troncossi, Marco
2016-09-01
In many real-life environments, certain mechanical and electronic components may be subjected to Sine-on-Random vibrations, i.e. excitations composed of random vibrations superimposed on deterministic (sinusoidal) contributions, in particular sine tones due to some rotating parts of the system (e.g. helicopters, engine-mounted components,...). These components must be designed to withstand the fatigue damage induced by the “composed” vibration environment, and qualification tests are advisable for the most critical ones. In the case of an accelerated qualification test, a proper test tailoring which starts from the real environment (measured vibration signals) and which preserves not only the accumulated fatigue damage but also the “nature” of the excitation (i.e. sinusoidal components plus random process) is important to obtain reliable results. In this paper, the classic time domain approach is taken as a reference for the comparison of different methods for the Fatigue Damage Spectrum (FDS) calculation in case of Sine-on-Random vibration environments. Then, a methodology to compute a Sine-on-Random specification based on a mission FDS is proposed.
Determinant representation for a quantum correlation function of the lattice sine-Gordon model
Essler, F H L; Korepin, V E
1995-01-01
We consider a completely integrable lattice regularization of the sine--Gordon model with discrete space and continuous time. We derive a determinant representation for a correlation function which in the continuum limit turns into the correlation function of local fields.
Meshing Theoretical Study and Simulation on Cylindrical Tri-sine Oscillating Tooth Gear Drive
李瑰贤; 孙瑜; 张欣
2004-01-01
The structure of cylindrical tri-sine oscillating tooth gear drive is presented. Based on the space meshing theory, equations of meshing and tooth profile are established and its meshing theory is studied. Using Pro/E, this system is modeled and simulated,which is compared with the above-established equations.
The spectrum of boundary states in sine-Gordon model with integrable boundary conditions
Bajnok, Z; Takács, G; Tóth, G
2002-01-01
The bound state spectrum and the associated reflection factors are determined for the sine-Gordon model with arbitrary integrable boundary condition by closing the bootstrap. Comparing the symmetries of the bound state spectrum with that of the Lagrangian it is shown how one can "derive" the relationship between the UV and IR parameters conjectured earlier.
Some semi-classical issues in boundary sine-Gordon model
Kormos, M
2002-01-01
The semi-classical quantisation of the two lowest energy static solutions of boundary sine-Gordon model is considered. A relation between the Lagrangian and bootstrap parameters is established by comparing their quantum corrected energy difference and the exact one. This relation is also confirmed by studying the semi-classical limit of soliton reflections on the boundary.
Spectrum of boundary states in N=1 SUSY sine-Gordon theory
Bajnok, Z; Takács, G
2002-01-01
We consider N=1 supersymmetric sine-Gordon theory (SSG) with supersymmetric integrable boundary conditions (boundary SSG = BSSG). We find two possible ways to close the boundary bootstrap for this model, corresponding to two different choices for the boundary supercharge. We argue that these two bootstrap solutions should correspond to the two integrable Lagrangian boundary theories considered recently by Nepomechie.
A generalized exp-function method for multiwave solutions of sine-Gordon equation
Sheng Zhang; Jian Wang; Au-Xue Peng; Bin Cai
2013-11-01
In this paper, the exp-function method is generalized to sine-Gordon (sG) equation and single-, double- and three-wave solutions are obtained. It is shown that the generalized exp-function method combined with appropriate anstaz may provide a straightforward, effective and alternative method for constructing multiwave solutions of some nonlinear partial differential equations.
Quantization of Sine-Gordon solitons on the circle: semiclassical vs. exact results
Pawellek, Michael
2008-01-01
We consider the semiclassical quantization of sine-Gordon solitons on the circle with periodic and anti-periodic boundary conditions. The 1-loop quantum corrections to the mass of the solitons are determined using zeta function regularization in the integral representation. We compare the semiclassical results with exact numerical calculations in the literature and find excellent agreement even outside the plain semiclassical regime.
Emotional Intelligence: The Sine Qua Non for a Clinical Leadership Toolbox
Rao, Paul R.
2006-01-01
Over the past decade, it has become increasingly clear that although IQ and technical skills are important, emotional intelligence is the Sine Qua Non of leadership. According to Goleman [Goleman, D. (1998). What makes a leader? "Harvard Business Review," 93-102] "effective leaders are alike in one crucial way: they all have a high degree of…
Emotional Intelligence: The Sine Qua Non for a Clinical Leadership Toolbox
Rao, Paul R.
2006-01-01
Over the past decade, it has become increasingly clear that although IQ and technical skills are important, emotional intelligence is the Sine Qua Non of leadership. According to Goleman [Goleman, D. (1998). What makes a leader? "Harvard Business Review," 93-102] "effective leaders are alike in one crucial way: they all have a high degree of…
Diophantine approximation and badly approximable sets
Kristensen, S.; Thorn, R.; Velani, S.
2006-01-01
Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X. The clas......Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X...
Sparse approximation with bases
2015-01-01
This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...
Regression with Sparse Approximations of Data
Noorzad, Pardis; Sturm, Bob L.
2012-01-01
We propose sparse approximation weighted regression (SPARROW), a method for local estimation of the regression function that uses sparse approximation with a dictionary of measurements. SPARROW estimates the regression function at a point with a linear combination of a few regressands selected by...
Approximation of the Inverse -Frame Operator
M R Abdollahpour; A Najati
2011-05-01
In this paper, we introduce the concept of (strong) projection method for -frames which works for all conditional -Riesz frames. We also derive a method for approximation of the inverse -frame operator which is efficient for all -frames. We show how the inverse of -frame operator can be approximated as close as we like using finite-dimensional linear algebra.
Kanhayuwa, Lakkhana; Coutts, Robert H A
2016-01-01
Novel families of short interspersed nuclear element (SINE) sequences in the human pathogenic fungus Aspergillus fumigatus, clinical isolate Af293, were identified and categorised into tRNA-related and 5S rRNA-related SINEs. Eight predicted tRNA-related SINE families originating from different tRNAs, and nominated as AfuSINE2 sequences, contained target site duplications of short direct repeat sequences (4-14 bp) flanking the elements, an extended tRNA-unrelated region and typical features of RNA polymerase III promoter sequences. The elements ranged in size from 140-493 bp and were present in low copy number in the genome and five out of eight were actively transcribed. One putative tRNAArg-derived sequence, AfuSINE2-1a possessed a unique feature of repeated trinucleotide ACT residues at its 3'-terminus. This element was similar in sequence to the I-4_AO element found in A. oryzae and an I-1_AF long nuclear interspersed element-like sequence identified in A. fumigatus Af293. Families of 5S rRNA-related SINE sequences, nominated as AfuSINE3, were also identified and their 5'-5S rRNA-related regions show 50-65% and 60-75% similarity to respectively A. fumigatus 5S rRNAs and SINE3-1_AO found in A. oryzae. A. fumigatus Af293 contains five copies of AfuSINE3 sequences ranging in size from 259-343 bp and two out of five AfuSINE3 sequences were actively transcribed. Investigations on AfuSINE distribution in the fungal genome revealed that the elements are enriched in pericentromeric and subtelomeric regions and inserted within gene-rich regions. We also demonstrated that some, but not all, AfuSINE sequences are targeted by host RNA silencing mechanisms. Finally, we demonstrated that infection of the fungus with mycoviruses had no apparent effects on SINE activity.
Expansion of CORE-SINEs in the genome of the Tasmanian devil
Nilsson Maria A
2012-05-01
Full Text Available Abstract Background The genome of the carnivorous marsupial, the Tasmanian devil (Sarcophilus harrisii, Order: Dasyuromorphia, was sequenced in the hopes of finding a cure for or gaining a better understanding of the contagious devil facial tumor disease that is threatening the species’ survival. To better understand the Tasmanian devil genome, we screened it for transposable elements and investigated the dynamics of short interspersed element (SINE retroposons. Results The temporal history of Tasmanian devil SINEs, elucidated using a transposition in transposition analysis, indicates that WSINE1, a CORE-SINE present in around 200,000 copies, is the most recently active element. Moreover, we discovered a new subtype of WSINE1 (WSINE1b that comprises at least 90% of all Tasmanian devil WSINE1s. The frequencies of WSINE1 subtypes differ in the genomes of two of the other Australian marsupial orders. A co-segregation analysis indicated that at least 66 subfamilies of WSINE1 evolved during the evolution of Dasyuromorphia. Using a substitution rate derived from WSINE1 insertions, the ages of the subfamilies were estimated and correlated with a newly established phylogeny of Dasyuromorphia. Phylogenetic analyses and divergence time estimates of mitochondrial genome data indicate a rapid radiation of the Tasmanian devil and the closest relative the quolls (Dasyurus around 14 million years ago. Conclusions The radiation and abundance of CORE-SINEs in marsupial genomes indicates that they may be a major player in the evolution of marsupials. It is evident that the early phases of evolution of the carnivorous marsupial order Dasyuromorphia was characterized by a burst of SINE activity. A correlation between a speciation event and a major burst of retroposon activity is for the first time shown in a marsupial genome.
Expansion of CORE-SINEs in the genome of the Tasmanian devil.
Nilsson, Maria A; Janke, Axel; Murchison, Elizabeth P; Ning, Zemin; Hallström, Björn M
2012-05-06
The genome of the carnivorous marsupial, the Tasmanian devil (Sarcophilus harrisii, Order: Dasyuromorphia), was sequenced in the hopes of finding a cure for or gaining a better understanding of the contagious devil facial tumor disease that is threatening the species' survival. To better understand the Tasmanian devil genome, we screened it for transposable elements and investigated the dynamics of short interspersed element (SINE) retroposons. The temporal history of Tasmanian devil SINEs, elucidated using a transposition in transposition analysis, indicates that WSINE1, a CORE-SINE present in around 200,000 copies, is the most recently active element. Moreover, we discovered a new subtype of WSINE1 (WSINE1b) that comprises at least 90% of all Tasmanian devil WSINE1s. The frequencies of WSINE1 subtypes differ in the genomes of two of the other Australian marsupial orders. A co-segregation analysis indicated that at least 66 subfamilies of WSINE1 evolved during the evolution of Dasyuromorphia. Using a substitution rate derived from WSINE1 insertions, the ages of the subfamilies were estimated and correlated with a newly established phylogeny of Dasyuromorphia. Phylogenetic analyses and divergence time estimates of mitochondrial genome data indicate a rapid radiation of the Tasmanian devil and the closest relative the quolls (Dasyurus) around 14 million years ago. The radiation and abundance of CORE-SINEs in marsupial genomes indicates that they may be a major player in the evolution of marsupials. It is evident that the early phases of evolution of the carnivorous marsupial order Dasyuromorphia was characterized by a burst of SINE activity. A correlation between a speciation event and a major burst of retroposon activity is for the first time shown in a marsupial genome.
A SINE-derived element constitutes a unique modular enhancer for mammalian diencephalic Fgf8.
Akiko Nakanishi
Full Text Available Transposable elements, including short interspersed repetitive elements (SINEs, comprise nearly half the mammalian genome. Moreover, they are a major source of conserved non-coding elements (CNEs, which play important functional roles in regulating development-related genes, such as enhancing and silencing, serving for the diversification of morphological and physiological features among species. We previously reported a novel SINE family, AmnSINE1, as part of mammalian-specific CNEs. One AmnSINE1 locus, named AS071, showed an enhancer property in the developing mouse diencephalon. Indeed, AS071 appears to recapitulate the expression of diencephalic fibroblast growth factor 8 (Fgf8. Here we established three independent lines of AS071-transgenic mice and performed detailed expression profiling of AS071-enhanced lacZ in comparison with that of Fgf8 across embryonic stages. We demonstrate that AS071 is a distal enhancer that directs Fgf8 expression in the developing diencephalon. Furthermore, enhancer assays with constructs encoding partially deleted AS071 sequence revealed a unique modular organization in which AS071 contains at least three functionally distinct sub-elements that cooperatively direct the enhancer activity in three diencephalic domains, namely the dorsal midline and the lateral wall of the diencephalon, and the ventral midline of the hypothalamus. Interestingly, the AmnSINE1-derived sub-element was found to specify the enhancer activity to the ventral midline of the hypothalamus. To our knowledge, this is the first discovery of an enhancer element that could be separated into respective sub-elements that determine regional specificity and/or the core enhancing activity. These results potentiate our understanding of the evolution of retroposon-derived cis-regulatory elements as well as the basis for future studies of the molecular mechanism underlying the determination of domain-specificity of an enhancer.
Nonlinear Dynamics of Globally Coupled Sine-Gordon Equations
2011-05-01
studied too, including a triangular configuration of linearly coupled parallel fiber Bragg gratings [15], coupled triplets of Gross-Pitaevskii...B. Dueholm, O. A. Levring, J. Mygind, N. F. Pedersen , O. H. Soerensen, and M. Cirillo, Phys. Rev. Lett. 46, 1299 (1981); E. Joergensen, V. P...Malomed, Phys. Rev. B 37, 9325 (1988); A. V. Ustinov, H. Kohlstedt, M. Cirillo, N. F. Pedersen , G. Hallmanns, and C. Heiden, ibid. B 48, 10614
MLP based models to predict PM10, O3 concentrations, in Sines industrial area
Durao, R.; Pereira, M. J.
2012-04-01
Sines is an important Portuguese industrial area located southwest cost of Portugal with important nearby protected natural areas. The main economical activities are related with this industrial area, the deep-water port, petrochemical and thermo-electric industry. Nevertheless, tourism is also an important economic activity especially in summer time with potential to grow. The aim of this study is to develop prediction models of pollutant concentration categories (e.g. low concentration and high concentration) in order to provide early warnings to the competent authorities who are responsible for the air quality management. The knowledge in advanced of pollutant high concentrations occurrence will allow the implementation of mitigation actions and the release of precautionary alerts to population. The regional air quality monitoring network consists in three monitoring stations where a set of pollutants' concentrations are registered on a continuous basis. From this set stands out the tropospheric ozone (O3) and particulate matter (PM10) due to the high concentrations occurring in the region and their adverse effects on human health. Moreover, the major industrial plants of the region monitor SO2, NO2 and particles emitted flows at the principal chimneys (point sources), also on a continuous basis,. Therefore Artificial neuronal networks (ANN) were the applied methodology to predict next day pollutant concentrations; due to the ANNs structure they have the ability to capture the non-linear relationships between predictor variables. Hence the first step of this study was to apply multivariate exploratory techniques to select the best predictor variables. The classification trees methodology (CART) was revealed to be the most appropriate in this case.. Results shown that pollutants atmospheric concentrations are mainly dependent on industrial emissions and a complex combination of meteorological factors and the time of the year. In the second step, the Multi
Approximation techniques for engineers
Komzsik, Louis
2006-01-01
Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you''re looking for approximate solutions to engineering problems, everything you need is nestled between the covers of this book. Now you can benefit from Louis Komzsik''s years of industrial experience to gain a working knowledge of a vast array of approximation techniques through this complete and self-contained resource.
Belich, H; Paunov, R R
1999-01-01
By studying the {\\it internal} Riemannian geometry of the surfaces of constant negative scalar curvature, we obtain a natural map between the Liouville, and the sine-Gordon equations. First, considering isometric immersions into the Lobachevskian plane, we obtain an uniform expression for the general (locally defined) solution of both the equations. Second, we prove that there is a Lie-Bäcklund transformation interpolating between Liouville and sine-Gordon. Third, we use isometric immersions into the Lobachevskian plane to describe sine-Gordon N-solitons explicitly.
Finite-dimensional linear algebra
Gockenbach, Mark S
2010-01-01
Some Problems Posed on Vector SpacesLinear equationsBest approximationDiagonalizationSummaryFields and Vector SpacesFields Vector spaces Subspaces Linear combinations and spanning sets Linear independence Basis and dimension Properties of bases Polynomial interpolation and the Lagrange basis Continuous piecewise polynomial functionsLinear OperatorsLinear operatorsMore properties of linear operatorsIsomorphic vector spaces Linear operator equations Existence and uniqueness of solutions The fundamental theorem; inverse operatorsGaussian elimination Newton's method Linear ordinary differential eq
Expectation Consistent Approximate Inference
Opper, Manfred; Winther, Ole
2005-01-01
We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood from replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability dis...
Rational approximation of vertical segments
Salazar Celis, Oliver; Cuyt, Annie; Verdonk, Brigitte
2007-08-01
In many applications, observations are prone to imprecise measurements. When constructing a model based on such data, an approximation rather than an interpolation approach is needed. Very often a least squares approximation is used. Here we follow a different approach. A natural way for dealing with uncertainty in the data is by means of an uncertainty interval. We assume that the uncertainty in the independent variables is negligible and that for each observation an uncertainty interval can be given which contains the (unknown) exact value. To approximate such data we look for functions which intersect all uncertainty intervals. In the past this problem has been studied for polynomials, or more generally for functions which are linear in the unknown coefficients. Here we study the problem for a particular class of functions which are nonlinear in the unknown coefficients, namely rational functions. We show how to reduce the problem to a quadratic programming problem with a strictly convex objective function, yielding a unique rational function which intersects all uncertainty intervals and satisfies some additional properties. Compared to rational least squares approximation which reduces to a nonlinear optimization problem where the objective function may have many local minima, this makes the new approach attractive.
Ordered cones and approximation
Keimel, Klaus
1992-01-01
This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.
Approximate Modified Policy Iteration
Scherrer, Bruno; Ghavamzadeh, Mohammad; Geist, Matthieu
2012-01-01
Modified policy iteration (MPI) is a dynamic programming (DP) algorithm that contains the two celebrated policy and value iteration methods. Despite its generality, MPI has not been thoroughly studied, especially its approximation form which is used when the state and/or action spaces are large or infinite. In this paper, we propose three approximate MPI (AMPI) algorithms that are extensions of the well-known approximate DP algorithms: fitted-value iteration, fitted-Q iteration, and classification-based policy iteration. We provide an error propagation analysis for AMPI that unifies those for approximate policy and value iteration. We also provide a finite-sample analysis for the classification-based implementation of AMPI (CBMPI), which is more general (and somehow contains) than the analysis of the other presented AMPI algorithms. An interesting observation is that the MPI's parameter allows us to control the balance of errors (in value function approximation and in estimating the greedy policy) in the fina...
Tu Zhijian
2008-08-01
Full Text Available Abstract Background SINEs (Short INterspersed Elements are homoplasy-free and co-dominant genetic markers which are considered to represent useful tools for population genetic studies, and could help clarifying the speciation processes ongoing within the major malaria vector in Africa, Anopheles gambiae s.s. Here, we report the results of the analysis of the insertion polymorphism of a nearly 200 bp-long SINE (SINE200 within genome areas of high differentiation (i.e. "speciation islands" of M and S A. gambiae molecular forms. Methods A SINE-PCR approach was carried out on thirteen SINE200 insertions in M and S females collected along the whole range of distribution of A. gambiae s.s. in sub-Saharan Africa. Ten specimens each for Anopheles arabiensis, Anopheles melas, Anopheles quadriannulatus A and 15 M/S hybrids from laboratory crosses were also analysed. Results Eight loci were successfully amplified and were found to be specific for A. gambiae s.s.: 5 on 2L chromosome and one on X chromosome resulted monomorphic, while two loci positioned respectively on 2R (i.e. S200 2R12D and X (i.e. S200 X6.1 chromosomes were found to be polymorphic. S200 2R12D was homozygote for the insertion in most S-form samples, while intermediate levels of polymorphism were shown in M-form, resulting in an overall high degree of genetic differentiation between molecular forms (Fst = 0.46 p S200 X6.1 was found to be fixed in all M- and absent in all S-specimens. This led to develop a novel easy-to-use PCR approach to straightforwardly identify A. gambiae molecular forms. This novel approach allows to overcome the constraints associated with markers on the rDNA region commonly used for M and S identification. In fact, it is based on a single copy and irreversible SINE200 insertion and, thus, is not subjected to peculiar evolutionary patterns affecting rDNA markers, e.g. incomplete homogenization of the arrays through concerted evolution and/or mixtures of M and S IGS
An Approximate Approach to Automatic Kernel Selection.
Ding, Lizhong; Liao, Shizhong
2016-02-02
Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.
A Note on Generalized Approximation Property
Antara Bhar
2013-01-01
Full Text Available We introduce a notion of generalized approximation property, which we refer to as --AP possessed by a Banach space , corresponding to an arbitrary Banach sequence space and a convex subset of , the class of bounded linear operators on . This property includes approximation property studied by Grothendieck, -approximation property considered by Sinha and Karn and Delgado et al., and also approximation property studied by Lissitsin et al. We characterize a Banach space having --AP with the help of -compact operators, -nuclear operators, and quasi--nuclear operators. A particular case for ( has also been characterized.
Approximate calculation of integrals
Krylov, V I
2006-01-01
A systematic introduction to the principal ideas and results of the contemporary theory of approximate integration, this volume approaches its subject from the viewpoint of functional analysis. In addition, it offers a useful reference for practical computations. Its primary focus lies in the problem of approximate integration of functions of a single variable, rather than the more difficult problem of approximate integration of functions of more than one variable.The three-part treatment begins with concepts and theorems encountered in the theory of quadrature. The second part is devoted to t
Approximate and renormgroup symmetries
Ibragimov, Nail H. [Blekinge Institute of Technology, Karlskrona (Sweden). Dept. of Mathematics Science; Kovalev, Vladimir F. [Russian Academy of Sciences, Moscow (Russian Federation). Inst. of Mathematical Modeling
2009-07-01
''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)
Approximating Stationary Statistical Properties
Xiaoming WANG
2009-01-01
It is well-known that physical laws for large chaotic dynamical systems are revealed statistically. Many times these statistical properties of the system must be approximated numerically. The main contribution of this manuscript is to provide simple and natural criterions on numerical methods (temporal and spatial discretization) that are able to capture the stationary statistical properties of the underlying dissipative chaotic dynamical systems asymptotically. The result on temporal approximation is a recent finding of the author, and the result on spatial approximation is a new one. Applications to the infinite Prandtl number model for convection and the barotropic quasi-geostrophic model are also discussed.
Alvarez-Estrada, R.F.
1979-08-01
A comprehensive review of the inverse scattering solution of certain non-linear evolution equations of physical interest in one space dimension is presented. We explain in some detail the interrelated techniques which allow to linearize exactly the following equations: (1) the Korteweg and de Vries equation; (2) the non-linear Schrodinger equation; (3) the modified Korteweg and de Vries equation; (4) the Sine-Gordon equation. We concentrate in discussing the pairs of linear operators which accomplish such an exact linearization and the solution of the associated initial value problem. The application of the method to other non-linear evolution equations is reviewed very briefly.
Approximate Controllability of Abstract Discrete-Time Systems
Cuevas Claudio
2010-01-01
Full Text Available Approximate controllability for semilinear abstract discrete-time systems is considered. Specifically, we consider the semilinear discrete-time system , , where are bounded linear operators acting on a Hilbert space , are -valued bounded linear operators defined on a Hilbert space , and is a nonlinear function. Assuming appropriate conditions, we will show that the approximate controllability of the associated linear system implies the approximate controllability of the semilinear system.
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.
Agarwalla Arun
2001-01-01
Full Text Available Linear psoriasis, inflammatory linear varrucous epidermal naevus (ILVEN. Lichen straitus, linear lichen planus and invasion of epidermal naevi by psoriasis have clinical and histopathological overlap. We report two young male patients of true linear psoriasis without classical lesions elsewhere which were proved histopathologically. Seasonal variation and good response to topical antipsoriatic treatment supported the diagnosis.
Malvina Baica
1985-01-01
Full Text Available The author uses a new modification of Jacobi-Perron Algorithm which holds for complex fields of any degree (abbr. ACF, and defines it as Generalized Euclidean Algorithm (abbr. GEA to approximate irrationals.
Approximations in Inspection Planning
Engelund, S.; Sørensen, John Dalsgaard; Faber, M. H.
2000-01-01
Planning of inspections of civil engineering structures may be performed within the framework of Bayesian decision analysis. The effort involved in a full Bayesian decision analysis is relatively large. Therefore, the actual inspection planning is usually performed using a number of approximations....... One of the more important of these approximations is the assumption that all inspections will reveal no defects. Using this approximation the optimal inspection plan may be determined on the basis of conditional probabilities, i.e. the probability of failure given no defects have been found...... by the inspection. In this paper the quality of this approximation is investigated. The inspection planning is formulated both as a full Bayesian decision problem and on the basis of the assumption that the inspection will reveal no defects....
The Karlqvist approximation revisited
Tannous, C
2015-01-01
The Karlqvist approximation signaling the historical beginning of magnetic recording head theory is reviewed and compared to various approaches progressing from Green, Fourier, Conformal mapping that obeys the Sommerfeld edge condition at angular points and leads to exact results.
Approximations in Inspection Planning
Engelund, S.; Sørensen, John Dalsgaard; Faber, M. H.
2000-01-01
Planning of inspections of civil engineering structures may be performed within the framework of Bayesian decision analysis. The effort involved in a full Bayesian decision analysis is relatively large. Therefore, the actual inspection planning is usually performed using a number of approximations....... One of the more important of these approximations is the assumption that all inspections will reveal no defects. Using this approximation the optimal inspection plan may be determined on the basis of conditional probabilities, i.e. the probability of failure given no defects have been found...... by the inspection. In this paper the quality of this approximation is investigated. The inspection planning is formulated both as a full Bayesian decision problem and on the basis of the assumption that the inspection will reveal no defects....
Smulevich, A B; Dorozhenok, I Iu; Romanov, D V; L'vov, A N
2012-01-01
Hypochondria sine materia is a disorder with physical complains corresponding to no any somatic diagnosis. Hypochondria sine materia is a more complicated psychopathological condition compared to hypochondria cum materia. Hypochondria sine materia could be diagnosed not only in psychiatry, but mainly in general medicine. It is especially prevalent in dermatology. As a result of analysis of hypochondriac disorders involving cutaneous sphere in patients without dermatological diseases, a binary model of psychodermatological syndromes presenting with hypochondria sine materia in dermatology was developed. The binary structure of the psychodermatological syndromes includes secondary psychiatric symptoms based on primary coenesthesiopathic phenomena. The heterogeneous psychodermatological syndromes (cutaneous organ neurosis, impulsive excoriations syndrome, circumscripta hypochondria, coenesthesiopathic paranoia) could be arranged in a continuum of consecutively worsening conditions from neurotic to psychotic severity register. The syndromes differ in clinical and social prognosis requiring different approach to diagnosis and treatment.
Sine wave gating silicon single-photon detectors for multiphoton entanglement experiments
Zhou, Nan; Jiang, Wen-Hao; Chen, Luo-Kan; Fang, Yu-Qiang; Li, Zheng-Da; Liang, Hao; Chen, Yu-Ao; Zhang, Jun; Pan, Jian-Wei
2017-08-01
Silicon single-photon detectors (SPDs) are the key devices for detecting single photons in the visible wavelength range. Here we present high detection efficiency silicon SPDs dedicated to the generation of multiphoton entanglement based on the technique of high-frequency sine wave gating. The silicon single-photon avalanche diode components are acquired by disassembling 6 commercial single-photon counting modules (SPCMs). Using the new quenching electronics, the average detection efficiency of SPDs is increased from 68.6% to 73.1% at a wavelength of 785 nm. These sine wave gating SPDs are then applied in a four-photon entanglement experiment, and the four-fold coincidence count rate is increased by 30% without degrading its visibility compared with the original SPCMs.
The long (LINEs) and the short (SINEs) of it: altered methylation as a precursor to toxicity.
Carnell, Ammie N; Goodman, Jay I
2003-10-01
Although once thought of as "junk" DNA, the importance of interspersed elements in the genome has become increasingly appreciated in recent years. In a broad sense these are collectively referred to as transposable elements, which encompass both transposons and retrotransposons. The latter include long interspersed nuclear elements (LINEs) and short interspersed nuclear elements (SINEs). Expression of these elements leads to genetic instability. Therefore, it is important that they remain transcriptionally silenced, and DNA methylation plays a key role in this regard. A framework for understanding the possible interplay between altered DNA methylation, an epigenetic change, and mutational events is presented. A case is made as to how retrotransposable elements, specifically LINEs and SINEs, are likely to emerge as key players in furthering our understanding of mechanisms underlying a variety of toxicities, including carcinogenesis but not limited to this endpoint.
Novak, Antonin; Simon, Laurent; Lotton, Pierrick
2010-12-01
A new method of identification, based on an input synchronized exponential swept-sine signal, is used to analyze and synthesize nonlinear audio systems like overdrive pedals for guitar. Two different pedals are studied; the first one exhibiting a strong influence of the input signal level on its input/output law and the second one exhibiting a weak influence of this input signal level. The Synchronized Swept Sine method leads to a Generalized Polynomial Hammerstein model equivalent to the pedals under test. The behaviors of both pedals are illustrated through model-based resynthesized signals. Moreover, it is also shown that this method leads to a criterion allowing the classification of the nonlinear systems under test, according to the influence of the input signal levels on their input/output law.
Generation and propagation of a sine-azimuthal wavefront modulated Gaussian beam.
Lao, Guanming; Zhang, Zhaohui; Luo, Meilan; Zhao, Daomu
2016-07-21
We introduce a method for modulating the Gaussian beam by means of sine-azimuthal wavefront and carry out the experimental generation. The analytical propagation formula of such a beam passing through a paraxial ABCD optical system is derived, by which the intensity properties of the sine-azimuthal wavefront modulated Gaussian (SWMG) beam are examined both theoretically and experimentally. Both of the experimental and theoretical results show that the SWMG beam goes through the process from beam splitting to a Gaussian-like profile, which is closely determined by the phase factor and the propagation distance. Appropriate phase factor and short distance are helpful for the splitting of beam. However, in the cases of large phase factor and focal plane, the intensity distributions tend to take a Gaussian form. Such unique features may be of importance in particle trapping and medical applications.
STIMA DE SINE – ELEMENT IMPORTANT ÎN PROIECTAREA CARIEREI
Carolina PLATON
2015-11-01
Full Text Available Savanţii susţin că doar o persoană cu stimă de sine înaltă are şanse să-şi dea seama de propriul potenţial. În procesul de orientare în carieră stima de sine va ajuta persoana să ia decizii corecte, să se autoevalueze şi să acţioneze în sensul aspiraţiilor sale.SELF-ESTEEM – AN IMPORTANT ELEMENT IN THE CAREER PLANNING PROCESSThe scientists support the idea about the awakening that is happening throughout the world to the fact that a human being cannot realize his potential without a healthy self-esteem. A high self-esteem will help a person to make decisions, self-assessment and to act according to his aspirations in the career planning process.
Novak Antonin
2010-01-01
Full Text Available A new method of identification, based on an input synchronized exponential swept-sine signal, is used to analyze and synthesize nonlinear audio systems like overdrive pedals for guitar. Two different pedals are studied; the first one exhibiting a strong influence of the input signal level on its input/output law and the second one exhibiting a weak influence of this input signal level. The Synchronized Swept Sine method leads to a Generalized Polynomial Hammerstein model equivalent to the pedals under test. The behaviors of both pedals are illustrated through model-based resynthesized signals. Moreover, it is also shown that this method leads to a criterion allowing the classification of the nonlinear systems under test, according to the influence of the input signal levels on their input/output law.
Petrache, Horia I
2011-01-01
In classical physics, the familiar sine and cosine functions appear in two forms: (1) geometrical, in the treatment of vectors such as forces and velocities, and (2) differential, as solutions of oscillation and wave equations. These two forms correspond to two different definitions of trigonometric functions, one geometrical using right triangles and unit circles, and the other employing differential equations. Although the two definitions must be equivalent, this equivalence is not demonstrated in textbooks. In this manuscript, the equivalence between the geometrical and the differential definition is presented assuming no a priori knowledge of the properties of sine and cosine functions. We start with the usual length projections on the unit circle and use elementary geometry and elementary calculus to arrive to harmonic differential equations. This more general and abstract treatment not only reveals the equivalence of the two definitions but also provides an instructive perspective on circular and harmon...
Peyret, Nicolas; Dion, Jean-Luc; Chevallier, Gael
2016-10-01
This paper deals with the use of piezoelectric patches for nonlinear dynamic identification. The patches are glued on the structure to identify amplitude-dependent damping and natural frequency; their positions are defined in order to perform the excitation concentrated on the first bending mode. Their locations on the structure allow to perform "stop sines" tests, as, unlike electrodynamic shakers, piezos are embedded on structures and do not modify the studied structure after the excitation signal is switched off. Although, despite the piezo and the stop-sine, the signal is still modulated by other frequency components or polluted by random signals, a post processing with the extended Kalman Filter allows a very good determination of the modal damping and the natural frequency, especially when they depends on the free vibration amplitude.
Research of sine waveguide slow-wave structure for a 220-GHz backward wave oscillator
Xu Xiong; Wei Yan-Yu; Shen Fei; Huang Min-Zhi; Tang Tao; Duan Zhao-Yun; Gong Yu-Bin
2012-01-01
A watt-class backward wave oscillator is proposed,using the concise sine waveguide slow-wave structure combined with a pencil electron beam to operate at 220 GHz.Firstly,the dispersion curve of the sine waveguide is calculated,then,the oscillation frequency and operating voltage of the device are predicted and the circuit transmission loss is calculated.Finally,the particle-in-cell simulation method is used to forecast its radiation performance.The results show that this novel backward wave oscillator can produce over 1-W continuous wave power output in a frequency range from 210 GHz to 230 GHz.Therefore,it will be considered as a very promising high-power millimeter-wave to terahertz-wave radiation source.
Campbell, Joel F; Nehrir, Amin R
2014-01-01
A CW lidar system using sine waves modulated by ML pseudo random noise codes is described, which uses a time shifting approach to separate online and offline wavelength transmitted and received channels and make multiple, simultaneous online/offline differential absorption measurements. Unlike the pure ML sequence, this technique is useful in hardware that is band pass filtered as the IM sine wave carrier shifts the main power band. Both amplitude and Phase Shift Keying (PSK) modulated IM carriers are investigated that exibit optimal autocorrelation properties down to one cycle per code bit with zero off mainlobe values to within numerical precision. In addition, a method is presented to bandwidth limit the ML sequence based on a filter implemented in terms of Jacobi theta functions that does not significantly degrade the resolution or introduce side lobes as a means of reducing aliasing and IM carrier bandwidth.
Gautschi, Walter; Rassias, Themistocles M
2011-01-01
Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovia, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational alg
Approximation Behooves Calibration
da Silva Ribeiro, André Manuel; Poulsen, Rolf
2013-01-01
Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009.......Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009....
Approximate kernel competitive learning.
Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang
2015-03-01
Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches.
Maksim Duškin
2015-11-01
Full Text Available Approximation and supposition This article compares exponents of approximation (expressions like Russian около, примерно, приблизительно, более, свыше and the words expressing supposition (for example Russian скорее всего, наверное, возможно. These words are often confused in research, in particular researchers often mention exponents of supposition in case of exponents of approximation. Such approach arouses some objections. The author intends to demonstrate in this article a notional difference between approximation and supposition, therefore the difference between exponents of these two notions. This difference could be described by specifying different attitude of approximation and supposition to the notion of knowledge. Supposition implies speaker’s ignorance of the exact number, while approximation does not mean such ignorance. The article offers examples proving this point of view.
Explicit, Nearly Optimal, Linear Rational Approximation with Preassigned Poles,
1983-02-01
Henrici , P., "Applied and Computational Complex Analysis ", V. 2., John Wiley, N.Y. (1977). [8] Magnus, W., Oberhettinger, F., and Soni, R. P., "Formulas...U denote the unit disc in the complex plane, let g be in the Hardy space H (U), and let f(z) = (I - z 2)g(z). Let P denote thep n space of polynomials...Fourier series. Let R > 1, and let A denote the annular region in the R A 5 complex plane C, AR = (w e C: R < lwl < R), let F be analytic in AR, and
Distortion Contribution Analysis with the Best Linear Approximation
Cooman, Adam; Bronders, Piet; Peumans, Dries; Vandersteen, Gerd; Rolain, Yves
2016-01-01
A Distortion Contribution Analysis (DCA) obtains the distortion at the output of an analog electronic circuit as a sum of distortion contributions of its sub-circuits. Similar to a noise analysis, a DCA helps a designer to pinpoint the actual source of the distortion. Classically, the DCA uses the Volterra theory to model the circuit and its sub-circuits. This DCA has been proven useful for small circuits or heavily simplified examples. In more complex circuits however, the amount of contribu...
Conformational Asymmetry and Quasicrystal Approximants in Linear Diblock Copolymers
Schulze, Morgan W.; Lewis, Ronald M.; Lettow, James H.; Hickey, Robert J.; Gillard, Timothy M.; Hillmyer, Marc A.; Bates, Frank S.
2017-05-01
Small angle x-ray scattering experiments on three model low molar mass diblock copolymer systems containing minority polylactide and majority hydrocarbon blocks demonstrate that conformational asymmetry stabilizes the Frank-Kasper σ phase. Differences in block flexibility compete with space filling at constant density inducing the formation of polyhedral shaped particles that assemble into this low symmetry ordered state with local tetrahedral coordination. These results confirm predictions from self-consistent field theory that establish the origins of symmetry breaking in the ordering of block polymer melts subjected to compositional and conformational asymmetry.
Gan Xiaoni
2010-04-01
Full Text Available Abstract Background We recently characterized HAmo SINE and its partner LINE in silver carp and bighead carp based on hybridization capture of repetitive elements from digested genomic DNA in solution using a bead-probe 1. To reveal the distribution and evolutionary history of SINEs and LINEs in cyprinid genomes, we performed a multi-species search for HAmo SINE and its partner LINE using the bead-probe capture and internal-primer-SINE polymerase chain reaction (PCR techniques. Results Sixty-seven full-size and 125 internal-SINE sequences (as well as 34 full-size and 9 internal sequences previously reported in bighead carp and silver carp from 17 species of the family Cyprinidae were aligned as well as 14 new isolated HAmoL2 sequences. Four subfamilies (type I, II, III and IV, which were divided based on diagnostic nucleotides in the tRNA-unrelated region, expanded preferentially within a certain lineage or within the whole family of Cyprinidae as multiple active source genes. The copy numbers of HAmo SINEs were estimated to vary from 104 to 106 in cyprinid genomes by quantitative RT-PCR. Over one hundred type IV members were identified and characterized in the primitive cyprinid Danio rerio genome but only tens of sequences were found to be similar with type I, II and III since the type IV was the oldest subfamily and its members dispersed in almost all investigated cyprinid fishes. For determining the taxonomic distribution of HAmo SINE, inter-primer SINE PCR was conducted in other non-cyprinid fishes, the results shows that HAmo SINE- related sequences may disperse in other families of order Cypriniforms but absent in other orders of bony fishes: Siluriformes, Polypteriformes, Lepidosteiformes, Acipenseriformes and Osteoglossiforms. Conclusions Depending on HAmo LINE2, multiple source genes (subfamilies of HAmo SINE actively expanded and underwent retroposition in a certain lineage or within the whole family of Cyprinidae. From this
Exact Travelling Solutions of Discrete sine-Gordon Equation via Extended Tanh-Function Approach
DAI Chao-Qing; ZHANG Jie-Fang
2006-01-01
In this paper, we generalize the extended tanh-function approach, which was used to find new exact travelling wave solutions of nonlinear partial differential equations or coupled nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, two series of exact travelling wave solutions of the discrete sine-Gordon equation are obtained by means of the extended tanh-function approach.
李建平; 唐远炎; 严中洪; 张万萍
2001-01-01
Based on sine and cosine functions, the compactly supported orthogonal wavelet filter coefficients with arbitrary length are constructed for the first time. When/N = 2k- 1 and N = 2k , the unified analytic constructions of orthogonal wavelet filters are put forward,respectively. The famous Daubechies filter and some other well-known wavelet filters are tested by the proposed novel method which is very useful for wavelet theory research and many application areas such as pattern recognition.
Interconnection between static regimes in the LJJs described by the double sine-Gordon equation
Atanasova, P. Kh; Zemlyanaya, E. V.; Shukrinov, Yu M.
2012-11-01
The second harmonic contribution to the current-phase relation changes the properties of the static magnetic flux distributions in the long Josephson junction (LJJ) and inspires new homogenious and fluxon static states. We study stability properties and bifurcations of these static regimes within the frame of a model described by the double sine-Gordon equation. The critical curves behavior and the interconnection between different types of magnetic flux distributions are analyzed.
[Short interspersed repetitive sequences (SINEs) and their use as a phylogenetic tool].
Kramerov, D A; Vasetskiĭ, N S
2009-01-01
The data on one of the most common repetitive elements of eukaryotic genomes, short interspersed elements (SINEs), are reviewed. Their structure, origin, and functioning in the genome are discussed. The variation and abundance of these neutral genomic markers makes them a convenient and reliable tool for phylogenetic analysis. The main methods of such analysis are presented, and the potential and limitations of this approach are discussed using specific examples.
The RNA polymerase dictates ORF1 requirement and timing of LINE and SINE retrotransposition.
Emily N Kroutter
2009-04-01
Full Text Available Mobile elements comprise close to one half of the mass of the human genome. Only LINE-1 (L1, an autonomous non-Long Terminal Repeat (LTR retrotransposon, and its non-autonomous partners-such as the retropseudogenes, SVA, and the SINE, Alu-are currently active human retroelements. Experimental evidence shows that Alu retrotransposition depends on L1 ORF2 protein, which has led to the presumption that LINEs and SINEs share the same basic insertional mechanism. Our data demonstrate clear differences in the time required to generate insertions between marked Alu and L1 elements. In our tissue culture system, the process of L1 insertion requires close to 48 hours. In contrast to the RNA pol II-driven L1, we find that pol III transcribed elements (Alu, the rodent SINE B2, and the 7SL, U6 and hY sequences can generate inserts within 24 hours or less. Our analyses demonstrate that the observed retrotransposition timing does not dictate insertion rate and is independent of the type of reporter cassette utilized. The additional time requirement by L1 cannot be directly attributed to differences in transcription, transcript length, splicing processes, ORF2 protein production, or the ability of functional ORF2p to reach the nucleus. However, the insertion rate of a marked Alu transcript drastically drops when driven by an RNA pol II promoter (CMV and the retrotransposition timing parallels that of L1. Furthermore, the "pol II Alu transcript" behaves like the processed pseudogenes in our retrotransposition assay, requiring supplementation with L1 ORF1p in addition to ORF2p. We postulate that the observed differences in retrotransposition kinetics of these elements are dictated by the type of RNA polymerase generating the transcript. We present a model that highlights the critical differences of LINE and SINE transcripts that likely define their retrotransposition timing.
Jannson, Tomasz; Wang, Wenjian; Hodelin, Juan; Forrester, Thomas; Romanov, Volodymyr; Kostrzewski, Andrew
2016-05-01
In this paper, Bayesian Binary Sensing (BBS) is discussed as an effective tool for Bayesian Inference (BI) evaluation in interdisciplinary areas such as ISR (and, C3I), Homeland Security, QC, medicine, defense, and many others. In particular, Hilbertian Sine (HS) as an absolute measure of BI, is introduced, while avoiding relativity of decision threshold identification, as in the case of traditional measures of BI, related to false positives and false negatives.
Relation between Type-II Discrete Sine Transform and Type -I Discrete Hartley Transform
M.Narayan Murty
2017-06-01
Full Text Available In this paper, a relation for finding type-II discrete sine transform (DST from type-I discrete Hartley transform (DHT has been derived. The transform length N is taken as even. Using this relation, the (N - 1 output components of DST can be realized from DHT. The DHT is one of the transforms used for converting data in time domain into frequency domain using only real values.
A Family of Interesting Exact Solutions of the Sine-Gordon Equation
HUANG De-Bin; LIU Zeng-Rong; WANG Li-Lian
2000-01-01
By using AKNS [Phys. Rev. Lett. 31 (1973) 125] system and introducing the wave function, a family of interesting exact solutions of the sine-Gordon equation are constructed. These solutions seem to be some soliton, kink, and anti-kink ones respectively for the different choice of the spectrum, whereas due to the interaction between two traveling-waves they have some properties different from usual soliton, kink, and anti-kink solutions.
Boundary states and finite size effects in sine-Gordon model with Neumann boundary condition
Bajnok, Z; Takács, G
2001-01-01
The sine-Gordon model with Neumann boundary condition is investigated. Using the bootstrap principle the spectrum of boundary bound states is established. Somewhat surprisingly it is found that Coleman-Thun diagrams and bound state creation may coexist. A framework to describe finite size effects in boundary integrable theories is developed and used together with the truncated conformal space approach to confirm the bound states and reflection factors derived by bootstrap.
GROWTH ESTIMATES FOR SINE-TYPE-FUNCTIONS AND APPLICATIONS TO RIESZ BASES OF EXPONENTIALS
Alexander M. Lindner
2002-01-01
We present explicit estimates for the growth of sine-type-functions as well as for the derivatives at theirzero sets, thus obtaining explicit constants in a result of Levin. The estimates are then used to derive explicitlower bounds for exponential Riesz bases, as they arise in Avdonin's Theorem on 1/4 in the mean or in alower bounds of exponential Riesz bases is desirable.
Noncommutative (generalized) sine-Gordon/massive Thirring correspondence, integrability and solitons
Blas, H
2010-01-01
Some properties of the correspondence between the non-commutative versions of the (generalized) sine-Gordon (NCGSG$_{1,2}$) and the massive Thirring (NCGMT$_{1,2}$) models are studied. Our method relies on the master Lagrangian approach to deal with dual theories. The master Lagrangians turn out to be the NC versions of the so-called affine Toda model coupled to matter fields (NCATM$_{1,2}$), in which the Toda field $g$ belongs to certain subgroups of $ GL(3)$, and the matter fields lie in the higher grading directions of an affine Lie algebra. Depending on the form of $g$ one arrives at two different NC versions of the NCGSG$_{1,2}$/NCGMT$_{1,2}$ correspondence. In the NCGSG$_{1,2}$ sectors, through consistent reduction procedures, we find NC versions of some well-known models, such as the NC sine-Gordon (NCSG$_{1,2}$) (Lechtenfeld et al. and Grisaru-Penati proposals, respectively), NC (bosonized) Bukhvostov-Lipatov (NCbBL$_{1,2}$) and NC double sine-Gordon (NCDSG$_{1,2}$) models. The NCGMT$_{1,2}$ models co...
Solitons, kinks and extended hadron model based on the generalized sine-Gordon theory
Blas, H
2007-01-01
The solitons and kinks of the generalized $sl(3, \\IC)$ sine-Gordon (GSG) model are explicitly obtained through the hybrid of the Hirota and dressing methods in which the {\\sl tau} functions play an important role. The various properties are investigated, such as the potential vacuum structure, the soliton and kink solutions, and the soliton masses formulae. As a reduced submodel we obtain the double sine-Gordon model. Moreover, we provide the algebraic construction of the $sl(3, \\IC)$ affine Toda model coupled to matter (Dirac spinor) (ATM) and through a gauge fixing procedure we obtain the classical version of the generalized $sl(3, \\IC)$ sine-Gordon model (cGSG) which completely decouples from the Dirac spinors. In the spinor sector we are left with Dirac fields coupled to cGSG fields. Based on the equivalence between the U(1) vector and topological currents it is shown the confinement of the spinors inside the solitons and kinks of the cGSG model providing an extended hadron model for "quark" confinement.
Solitons, kinks and extended hadron model based on the generalized sine-Gordon theory
Blas, Harold [Departamentos de Matematica e Fisica - ICET, Universidade Federal de Mato Grosso, Av. Fernando Correa, s/n, Coxipo, 78060-900, Cuiaba - MT (Brazil); Carrion, Hector L. [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970, Sao Paulo, SP (Brazil)
2007-01-15
The solitons and kinks of the generalized sl(3,C) sine-Gordon (GSG) model are explicitly obtained through the hybrid of the Hirota and dressing methods in which the tau functions play an important role. The various properties are investigated, such as the potential vacuum structure, the soliton and kink solutions, and the soliton masses formulae. As a reduced submodel we obtain the double sine-Gordon model. Moreover, we provide the algebraic construction of the sl(3,C) affine Toda model coupled to matter (Dirac spinor) (ATM) and through a gauge fixing procedure we obtain the classical version of the generalized sl(3,C) sine-Gordon model (cGSG) which completely decouples from the Dirac spinors. In the spinor sector we are left with Dirac fields coupled to cGSG fields. Based on the equivalence between the U(1) vector and topological currents it is shown the confinement of the spinors inside the solitons and kinks of the cGSG model providing an extended hadron model for 'quark' confinement.
Acosta, M J; Marchal, J A; Fernández-Espartero, C H; Bullejos, M; Sánchez, A
2008-01-01
The chromosomal distribution of mobile genetic elements is scarcely known in Arvicolinae species, but could be of relevance to understand the origin and complex evolution of the sex chromosome heterochromatin. In this work we cloned two retrotransposon sequences, L1 and SINE-B1, from the genome of Chionomys nivalis and investigated their chromosomal distribution on several arvicoline species. Our results demonstrate first that both retroelements are the most abundant repeated DNA sequences in the genome of these species. L1 elements, in most species, are highly accumulated in the sex chromosomes compared to the autosomes. This favoured L1 insertion could have played an important role in the origin of the enlarged heterochromatic blocks existing in the sex chromosomes of some Microtus species. Also, we propose that L1 accumulation on the X heterochromatin could have been the consequence of different, independent and rapid amplification processes acting in each species. SINE elements, however, were completely lacking from the constitutive heterochromatin, either in autosomes or in the heterochromatic blocks of sex chromosomes. These data could indicate that some SINE elements are incompatible with the formation of heterochromatic complexes and hence are necessarily missing from the constitutive heterochromatin.
L1-mediated retrotransposition of murine B1 and B2 SINEs recapitulated in cultured cells.
Dewannieux, Marie; Heidmann, Thierry
2005-06-03
SINEs are short interspersed nucleotide elements with transpositional activity, present at a high copy number (up to a million) in mammalian genomes. They are 80-400 bp long, non-coding sequences which derive either from the 7SL RNA (e.g. human Alus, murine B1s) or tRNA (e.g. murine B2s) polymerase III-driven genes. We have previously demonstrated that Alus very efficiently divert the enzymatic machinery of the autonomous L1 LINE (long interspersed nucleotide element) retrotransposons to transpose at a high rate. Here we show, using an ex vivo assay for transposition, that both B1 and B2 SINEs can be mobilized by murine LINEs, with the hallmarks of a bona fide retrotransposition process, including target site duplications of varying lengths and integrations into A-rich sequences. Despite different phylogenetic origins, transposition of the tRNA-derived B2 sequences is as efficient as that of the human Alus, whereas that of B1s is 20-100-fold lower despite a similar high copy number of these elements in the mouse genome. We provide evidence, via an appropriate nucleotide substitution within the B1 sequence in a domain essential for its intracellular targeting, that the current B1 SINEs are not optimal for transposition, a feature most probably selected for the host sake in the course of evolution.
A SINE in the genome of the cephalochordate amphioxus is an Alu element
Holland, Linda Z.
2006-01-01
Transposable elements of about 300 bp, termed “short interspersed nucleotide elements or SINEs are common in eukaryotes. However, Alu elements, SINEs containing restriction sites for the AluI enzyme, have been known only from primates. Here I report the first SINE found in the genome of the cephalochordate, amphioxus. It is an Alu element of 375 bp that does not share substantial identity with any genomic sequences in vertebrates. It was identified because it was located in the FoxD regulatory region in a cosmid derived from one individual, but absent from the two FoxD alleles of BACs from a second individual. However, searches of sequences of BACs and genomic traces from this second individual gave an estimate of 50-100 copies in the amphioxus genome. The finding of an Alu element in amphioxus raises the question of whether Alu elements in amphioxus and primates arose by convergent evolution or by inheritance from a common ancestor. Genome-wide analyses of transposable elements in amphioxus and other chordates such as tunicates, agnathans and cartilaginous fishes could well provide the answer. PMID:16733535
A specific family of interspersed repeats (SINEs facilitates meiotic synapsis in mammals
Johnson Matthew E
2013-01-01
Full Text Available Abstract Background Errors during meiosis that affect synapsis and recombination between homologous chromosomes contribute to aneuploidy and infertility in humans. Despite the clinical relevance of these defects, we know very little about the mechanisms by which homologous chromosomes interact with one another during mammalian meiotic prophase. Further, we remain ignorant of the way in which chromosomal DNA complexes with the meiosis-specific structure that tethers homologs, the synaptonemal complex (SC, and whether specific DNA elements are necessary for this interaction. Results In the present study we utilized chromatin immunoprecipitation (ChIP and DNA sequencing to demonstrate that the axial elements of the mammalian SC are markedly enriched for a specific family of interspersed repeats, short interspersed elements (SINEs. Further, we refine the role of the repeats to specific sub-families of SINEs, B1 in mouse and AluY in old world monkey (Macaca mulatta. Conclusions Because B1 and AluY elements are the most actively retrotransposing SINEs in mice and rhesus monkeys, respectively, our observations imply that they may serve a dual function in axial element binding; i.e., as the anchoring point for the SC but possibly also as a suppressor/regulator of retrotransposition.
Baart, Martijn; Bortfeld, Heather; Vroomen, Jean
2015-01-01
The correspondence between auditory speech and lip-read information can be detected based on a combination of temporal and phonetic cross-modal cues. Here, we determined the point in developmental time at which children start to effectively use phonetic information to match a speech sound with one of two articulating faces. We presented 4- to 11-year-olds (N=77) with three-syllabic sine-wave speech replicas of two pseudo-words that were perceived as non-speech and asked them to match the sounds with the corresponding lip-read video. At first, children had no phonetic knowledge about the sounds, and matching was thus based on the temporal cues that are fully retained in sine-wave speech. Next, we trained all children to perceive the phonetic identity of the sine-wave speech and repeated the audiovisual (AV) matching task. Only at around 6.5 years of age did the benefit of having phonetic knowledge about the stimuli become apparent, thereby indicating that AV matching based on phonetic cues presumably develops more slowly than AV matching based on temporal cues. Copyright © 2014 Elsevier Inc. All rights reserved.
Covariant approximation averaging
Shintani, Eigo; Blum, Thomas; Izubuchi, Taku; Jung, Chulwoo; Lehner, Christoph
2014-01-01
We present a new class of statistical error reduction techniques for Monte-Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in $N_f=2+1$ lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte-Carlo calculations over conventional methods for the same cost.
Diophantine approximations on fractals
Einsiedler, Manfred; Shapira, Uri
2009-01-01
We exploit dynamical properties of diagonal actions to derive results in Diophantine approximations. In particular, we prove that the continued fraction expansion of almost any point on the middle third Cantor set (with respect to the natural measure) contains all finite patterns (hence is well approximable). Similarly, we show that for a variety of fractals in [0,1]^2, possessing some symmetry, almost any point is not Dirichlet improvable (hence is well approximable) and has property C (after Cassels). We then settle by similar methods a conjecture of M. Boshernitzan saying that there are no irrational numbers x in the unit interval such that the continued fraction expansions of {nx mod1 : n is a natural number} are uniformly eventually bounded.
Monotone Boolean approximation
Hulme, B.L.
1982-12-01
This report presents a theory of approximation of arbitrary Boolean functions by simpler, monotone functions. Monotone increasing functions can be expressed without the use of complements. Nonconstant monotone increasing functions are important in their own right since they model a special class of systems known as coherent systems. It is shown here that when Boolean expressions for noncoherent systems become too large to treat exactly, then monotone approximations are easily defined. The algorithms proposed here not only provide simpler formulas but also produce best possible upper and lower monotone bounds for any Boolean function. This theory has practical application for the analysis of noncoherent fault trees and event tree sequences.
Prestack wavefield approximations
Alkhalifah, Tariq
2013-09-01
The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
Approximation by Cylinder Surfaces
Randrup, Thomas
1997-01-01
We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...
Analytical approximations for spiral waves
Löber, Jakob, E-mail: jakob@physik.tu-berlin.de; Engel, Harald [Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, EW 7-1, 10623 Berlin (Germany)
2013-12-15
We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency Ω and core radius R{sub 0}. For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent Ω(R{sub +}) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R{sub +} with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium.
Mathematical analysis, approximation theory and their applications
Gupta, Vijay
2016-01-01
Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.
Regression with Sparse Approximations of Data
Noorzad, Pardis; Sturm, Bob L.
2012-01-01
We propose sparse approximation weighted regression (SPARROW), a method for local estimation of the regression function that uses sparse approximation with a dictionary of measurements. SPARROW estimates the regression function at a point with a linear combination of a few regressands selected...... by a sparse approximation of the point in terms of the regressors. We show SPARROW can be considered a variant of \\(k\\)-nearest neighbors regression (\\(k\\)-NNR), and more generally, local polynomial kernel regression. Unlike \\(k\\)-NNR, however, SPARROW can adapt the number of regressors to use based...
Topology, calculus and approximation
Komornik, Vilmos
2017-01-01
Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2011-01-01
Most prestack traveltime relations we tend work with are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multi-focusing or double square-root (DSR) and the common reflection stack (CRS) equations. Using the DSR equation, I analyze the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I derive expansion based solutions of this eikonal based on polynomial expansions in terms of the reflection and dip angles in a generally inhomogenous background medium. These approximate solutions are free of singularities and can be used to estimate travetimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. A Marmousi example demonstrates the usefulness of the approach. © 2011 Society of Exploration Geophysicists.
Optimization and approximation
Pedregal, Pablo
2017-01-01
This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.
Topics in Metric Approximation
Leeb, William Edward
This thesis develops effective approximations of certain metrics that occur frequently in pure and applied mathematics. We show that distances that often arise in applications, such as the Earth Mover's Distance between two probability measures, can be approximated by easily computed formulas for a wide variety of ground distances. We develop simple and easily computed characterizations both of norms measuring a function's regularity -- such as the Lipschitz norm -- and of their duals. We are particularly concerned with the tensor product of metric spaces, where the natural notion of regularity is not the Lipschitz condition but the mixed Lipschitz condition. A theme that runs throughout this thesis is that snowflake metrics (metrics raised to a power less than 1) are often better-behaved than ordinary metrics. For example, we show that snowflake metrics on finite spaces can be approximated by the average of tree metrics with a distortion bounded by intrinsic geometric characteristics of the space and not the number of points. Many of the metrics for which we characterize the Lipschitz space and its dual are snowflake metrics. We also present applications of the characterization of certain regularity norms to the problem of recovering a matrix that has been corrupted by noise. We are able to achieve an optimal rate of recovery for certain families of matrices by exploiting the relationship between mixed-variable regularity conditions and the decay of a function's coefficients in a certain orthonormal basis.
Rational approximations to fluid properties
Kincaid, J. M.
1990-05-01
The purpose of this report is to summarize some results that were presented at the Spring AIChE meeting in Orlando, Florida (20 March 1990). We report on recent attempts to develop a systematic method, based on the technique of rational approximation, for creating mathematical models of real-fluid equations of state and related properties. Equation-of-state models for real fluids are usually created by selecting a function tilde p(T,rho) that contains a set of parameters (gamma sub i); the (gamma sub i) is chosen such that tilde p(T,rho) provides a good fit to the experimental data. (Here p is the pressure, T the temperature and rho is the density). In most cases, a nonlinear least-squares numerical method is used to determine (gamma sub i). There are several drawbacks to this method: one has essentially to guess what tilde p(T,rho) should be; the critical region is seldom fit very well and nonlinear numerical methods are time consuming and sometimes not very stable. The rational approximation approach we describe may eliminate all of these drawbacks. In particular, it lets the data choose the function tilde p(T,rho) and its numerical implementation involves only linear algorithms.