Approximation of N(k)(infinity)-functions II : Convergence of Models
Dijksma, Aad; Luger, Annemarie; Shondin, Yuri; Behrndt, J; Forster, KH; Trunk, C
2010-01-01
This paper is a continuation of Part I, [9] in the list of references, where models for N(k)(infinity)-functions have been studied in detail. In the present paper we investigate the convergence of the corresponding models as a singular N(k)(infinity)-functionis approximated by regular N(k)(infinity)
Montoya-Castillo, Andrés
2016-01-01
The ability to efficiently and accurately calculate equilibrium time correlation functions of many-body condensed phase quantum systems is one of the outstanding problems in theoretical chemistry. The Nakajima-Zwanzig-Mori formalism coupled to the self-consistent solution of the memory kernel has recently proven to be highly successful for the computation of nonequilibrium dynamical averages. Here, we extend this formalism to treat symmetrized equilibrium time correlation functions for the spin-boson model. Following the first paper in this series [A. Montoya-Castillo and D. R. Reichman, J. Chem. Phys. $\\bf{144}$, 184104 (2016)], we use a Dyson-type expansion of the projected propagator to obtain a self-consistent solution for the memory kernel that requires only the calculation of normally evolved auxiliary kernels. We employ the approximate mean-field Ehrenfest method to demonstrate the feasibility of this approach. Via comparison with numerically exact results for the correlation function $\\mathcal{C}_{zz}...
Energy Technology Data Exchange (ETDEWEB)
Novaes, Marcel [Instituto de Física, Universidade Federal de Uberlândia, Av. João Naves de Ávila, 2121, Uberlândia, MG 38408-100 (Brazil)
2015-06-15
We consider S-matrix correlation functions for a chaotic cavity having M open channels, in the absence of time-reversal invariance. Relying on a semiclassical approximation, we compute the average over E of the quantities Tr[S{sup †}(E − ϵ) S(E + ϵ)]{sup n}, for general positive integer n. Our result is an infinite series in ϵ, whose coefficients are rational functions of M. From this, we extract moments of the time delay matrix Q = − iħS{sup †}dS/dE and check that the first 8 of them agree with the random matrix theory prediction from our previous paper [M. Novaes, J. Math. Phys. 56, 062110 (2015)].
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.
Montoya-Castillo, Andrés; Reichman, David R.
2017-02-01
The ability to efficiently and accurately calculate equilibrium time correlation functions of many-body condensed phase quantum systems is one of the outstanding problems in theoretical chemistry. The Nakajima-Zwanzig-Mori formalism coupled to the self-consistent solution of the memory kernel has recently proven to be highly successful for the computation of nonequilibrium dynamical averages. Here, we extend this formalism to treat symmetrized equilibrium time correlation functions for the spin-boson model. Following the first paper in this series [A. Montoya-Castillo and D. R. Reichman, J. Chem. Phys. 144, 184104 (2016)], we use a Dyson-type expansion of the projected propagator to obtain a self-consistent solution for the memory kernel that requires only the calculation of normally evolved auxiliary kernels. We employ the approximate mean-field Ehrenfest method to demonstrate the feasibility of this approach. Via comparison with numerically exact results for the correlation function Cz z(t ) =Re ⟨σz(0 ) σz(t ) ⟩ , we show that the current scheme affords remarkable boosts in accuracy and efficiency over bare Ehrenfest dynamics. We further explore the sensitivity of the resulting dynamics to the choice of kernel closures and the accuracy of the initial canonical density operator.
Montoya-Castillo, Andrés; Reichman, David R
2017-02-28
The ability to efficiently and accurately calculate equilibrium time correlation functions of many-body condensed phase quantum systems is one of the outstanding problems in theoretical chemistry. The Nakajima-Zwanzig-Mori formalism coupled to the self-consistent solution of the memory kernel has recently proven to be highly successful for the computation of nonequilibrium dynamical averages. Here, we extend this formalism to treat symmetrized equilibrium time correlation functions for the spin-boson model. Following the first paper in this series [A. Montoya-Castillo and D. R. Reichman, J. Chem. Phys. 144, 184104 (2016)], we use a Dyson-type expansion of the projected propagator to obtain a self-consistent solution for the memory kernel that requires only the calculation of normally evolved auxiliary kernels. We employ the approximate mean-field Ehrenfest method to demonstrate the feasibility of this approach. Via comparison with numerically exact results for the correlation function Czz(t)=Re⟨σz(0)σz(t)⟩, we show that the current scheme affords remarkable boosts in accuracy and efficiency over bare Ehrenfest dynamics. We further explore the sensitivity of the resulting dynamics to the choice of kernel closures and the accuracy of the initial canonical density operator.
Global approximation of convex functions
Azagra, D
2011-01-01
We show that for every (not necessarily bounded) open convex subset $U$ of $\\R^n$, every (not necessarily Lipschitz or strongly) convex function $f:U\\to\\R$ can be approximated by real analytic convex functions, uniformly on all of $U$. In doing so we provide a technique which transfers results on uniform approximation on bounded sets to results on uniform approximation on unbounded sets, in such a way that not only convexity and $C^k$ smoothness, but also local Lipschitz constants, minimizers, order, and strict or strong convexity, are preserved. This transfer method is quite general and it can also be used to obtain new results on approximation of convex functions defined on Riemannian manifolds or Banach spaces. We also provide a characterization of the class of convex functions which can be uniformly approximated on $\\R^n$ by strongly convex functions.
APPROXIMATE SAMPLING THEOREM FOR BIVARIATE CONTINUOUS FUNCTION
Institute of Scientific and Technical Information of China (English)
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.
Approximation of continuously differentiable functions
Llavona, JG
1986-01-01
This self-contained book brings together the important results of a rapidly growing area.As a starting point it presents the classic results of the theory. The book covers such results as: the extension of Wells'' theorem and Aron''s theorem for the fine topology of order m; extension of Bernstein''s and Weierstrass'' theorems for infinite dimensional Banach spaces; extension of Nachbin''s and Whitney''s theorem for infinite dimensional Banach spaces; automatic continuity of homomorphisms in algebras of continuously differentiable functions, etc.
Computing Functions by Approximating the Input
Goldberg, Mayer
2012-01-01
In computing real-valued functions, it is ordinarily assumed that the input to the function is known, and it is the output that we need to approximate. In this work, we take the opposite approach: we show how to compute the values of some transcendental functions by approximating the input to these functions, and obtaining exact answers for their…
Bernstein-type approximations of smooth functions
Directory of Open Access Journals (Sweden)
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.
Nonlinear approximation with dictionaries,.. II: Inverse estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
In this paper we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for separated decomposable dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal mutually...
Nonlinear approximation with dictionaries. II. Inverse Estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
2006-01-01
In this paper, which is the sequel to [16], we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for blockwise incoherent dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal...
Trigonometric Approximations for Some Bessel Functions
Muhammad Taher Abuelma'atti
1999-01-01
Formulas are obtained for approximating the tabulated Bessel functions Jn(x), n = 0–9 in terms of trigonometric functions. These formulas can be easily integrated and differentiated and are convenient for personal computers and pocket calculators.
Function Approximation Using Probabilistic Fuzzy Systems
J.H. van den Berg (Jan); U. Kaymak (Uzay); R.J. Almeida e Santos Nogueira (Rui Jorge)
2011-01-01
textabstractWe consider function approximation by fuzzy systems. Fuzzy systems are typically used for approximating deterministic functions, in which the stochastic uncertainty is ignored. We propose probabilistic fuzzy systems in which the probabilistic nature of uncertainty is taken into account.
Frankenstein's Glue: Transition functions for approximate solutions
Yunes, N
2006-01-01
Approximations are commonly employed to find approximate solutions to the Einstein equations. These solutions, however, are usually only valid in some specific spacetime region. A global solution can be constructed by gluing approximate solutions together, but this procedure is difficult because discontinuities can arise, leading to large violations of the Einstein equations. In this paper, we provide an attempt to formalize this gluing scheme by studying transition functions that join approximate solutions together. In particular, we propose certain sufficient conditions on these functions and proof that these conditions guarantee that the joined solution still satisfies the Einstein equations to the same order as the approximate ones. An example is also provided for a binary system of non-spinning black holes, where the approximate solutions are taken to be given by a post-Newtonian expansion and a perturbed Schwarzschild solution. For this specific case, we show that if the transition functions satisfy the...
Intelligent comparisons II inequalities and approximations
Anastassiou, George A
2017-01-01
This compact book focuses on self-adjoint operators’ well-known named inequalities and Korovkin approximation theory, both in a Hilbert space environment. It is the first book to study these aspects, and all chapters are self-contained and can be read independently. Further, each chapter includes an extensive list of references for further reading. The book’s results are expected to find applications in many areas of pure and applied mathematics. Given its concise format, it is especially suitable for use in related graduate classes and research projects. As such, the book offers a valuable resource for researchers and graduate students alike, as well as a key addition to all science and engineering libraries.
Frankenstein's glue: transition functions for approximate solutions
Yunes, Nicolás
2007-09-01
Approximations are commonly employed to find approximate solutions to the Einstein equations. These solutions, however, are usually only valid in some specific spacetime region. A global solution can be constructed by gluing approximate solutions together, but this procedure is difficult because discontinuities can arise, leading to large violations of the Einstein equations. In this paper, we provide an attempt to formalize this gluing scheme by studying transition functions that join approximate analytic solutions together. In particular, we propose certain sufficient conditions on these functions and prove that these conditions guarantee that the joined solution still satisfies the Einstein equations analytically to the same order as the approximate ones. An example is also provided for a binary system of non-spinning black holes, where the approximate solutions are taken to be given by a post-Newtonian expansion and a perturbed Schwarzschild solution. For this specific case, we show that if the transition functions satisfy the proposed conditions, then the joined solution does not contain any violations to the Einstein equations larger than those already inherent in the approximations. We further show that if these functions violate the proposed conditions, then the matter content of the spacetime is modified by the introduction of a matter shell, whose stress energy tensor depends on derivatives of these functions.
Polynomial approximation of functions in Sobolev spaces
Dupont, T.; Scott, R.
1980-01-01
Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces.
Approximations for the Erlang Loss Function
DEFF Research Database (Denmark)
Mejlbro, Leif
1998-01-01
Theoretically, at least three formulae are needed for arbitrarily good approximates of the Erlang Loss Function. In the paper, for convenience five formulae are presented guaranteeing a relative error <1E-2, and methods are indicated for improving this bound.......Theoretically, at least three formulae are needed for arbitrarily good approximates of the Erlang Loss Function. In the paper, for convenience five formulae are presented guaranteeing a relative error
Approximation of Bivariate Functions via Smooth Extensions
Zhang, Zhihua
2014-01-01
For a smooth bivariate function defined on a general domain with arbitrary shape, it is difficult to do Fourier approximation or wavelet approximation. In order to solve these problems, in this paper, we give an extension of the bivariate function on a general domain with arbitrary shape to a smooth, periodic function in the whole space or to a smooth, compactly supported function in the whole space. These smooth extensions have simple and clear representations which are determined by this bivariate function and some polynomials. After that, we expand the smooth, periodic function into a Fourier series or a periodic wavelet series or we expand the smooth, compactly supported function into a wavelet series. Since our extensions are smooth, the obtained Fourier coefficients or wavelet coefficients decay very fast. Since our extension tools are polynomials, the moment theorem shows that a lot of wavelet coefficients vanish. From this, with the help of well-known approximation theorems, using our extension methods, the Fourier approximation and the wavelet approximation of the bivariate function on the general domain with small error are obtained. PMID:24683316
Kravchuk functions for the finite oscillator approximation
Atakishiyev, Natig M.; Wolf, Kurt Bernardo
1995-01-01
Kravchuk orthogonal functions - Kravchuk polynomials multiplied by the square root of the weight function - simplify the inversion algorithm for the analysis of discrete, finite signals in harmonic oscillator components. They can be regarded as the best approximation set. As the number of sampling points increases, the Kravchuk expansion becomes the standard oscillator expansion.
APPROXIMATION MULTIDIMENSION FUCTION WITH FUNCTIONAL NETWORK
Institute of Scientific and Technical Information of China (English)
Li Weibin; Liu Fang; Jiao Licheng; Zhang Shuling; Li Zongling
2006-01-01
The functional network was introduced by E.Catillo, which extended the neural network. Not only can it solve the problems solved, but also it can formulate the ones that cannot be solved by traditional network.This paper applies functional network to approximate the multidimension function under the ridgelet theory.The method performs more stable and faster than the traditional neural network. The numerical examples demonstrate the performance.
The Numerical Approximation of Functional Differential Equations
Venturi, Daniele
2016-01-01
The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional equations), quantum field theory (Schwinger-Dyson equations) and statistical physics (equations for generating functionals and effective action methods). However, no effective numerical method has yet been developed to compute their solution. The purpose of this manuscript is to fill this gap, and provide a new perspective on the problem of numerical approximation of nonlinear functionals and functional differential equations. The proposed methods will be described and demonstrated in various examples.
Approximate Bayesian computation with functional statistics.
Soubeyrand, Samuel; Carpentier, Florence; Guiton, François; Klein, Etienne K
2013-03-26
Functional statistics are commonly used to characterize spatial patterns in general and spatial genetic structures in population genetics in particular. Such functional statistics also enable the estimation of parameters of spatially explicit (and genetic) models. Recently, Approximate Bayesian Computation (ABC) has been proposed to estimate model parameters from functional statistics. However, applying ABC with functional statistics may be cumbersome because of the high dimension of the set of statistics and the dependences among them. To tackle this difficulty, we propose an ABC procedure which relies on an optimized weighted distance between observed and simulated functional statistics. We applied this procedure to a simple step model, a spatial point process characterized by its pair correlation function and a pollen dispersal model characterized by genetic differentiation as a function of distance. These applications showed how the optimized weighted distance improved estimation accuracy. In the discussion, we consider the application of the proposed ABC procedure to functional statistics characterizing non-spatial processes.
Eignets for function approximation on manifolds
Mhaskar, H N
2009-01-01
Let $\\XX$ be a compact, smooth, connected, Riemannian manifold without boundary, $G:\\XX\\times\\XX\\to \\RR$ be a kernel. Analogous to a radial basis function network, an eignet is an expression of the form $\\sum_{j=1}^M a_jG(\\circ,y_j)$, where $a_j\\in\\RR$, $y_j\\in\\XX$, $1\\le j\\le M$. We describe a deterministic, universal algorithm for constructing an eignet for approximating functions in $L^p(\\mu;\\XX)$ for a general class of measures $\\mu$ and kernels $G$. Our algorithm yields linear operators. Using the minimal separation amongst the centers $y_j$ as the cost of approximation, we give modulus of smoothness estimates for the degree of approximation by our eignets, and show by means of a converse theorem that these are the best possible for every \\emph{individual function}. We also give estimates on the coefficients $a_j$ in terms of the norm of the eignet. Finally, we demonstrate that if any sequence of eignets satisfies the optimal estimates for the degree of approximation of a smooth function, measured in ter...
Development of New Density Functional Approximations
Su, Neil Qiang; Xu, Xin
2017-05-01
Kohn-Sham density functional theory has become the leading electronic structure method for atoms, molecules, and extended systems. It is in principle exact, but any practical application must rely on density functional approximations (DFAs) for the exchange-correlation energy. Here we emphasize four aspects of the subject: (a) philosophies and strategies for developing DFAs; (b) classification of DFAs; (c) major sources of error in existing DFAs; and (d) some recent developments and future directions.
Function approximation using adaptive and overlapping intervals
Energy Technology Data Exchange (ETDEWEB)
Patil, R.B.
1995-05-01
A problem common to many disciplines is to approximate a function given only the values of the function at various points in input variable space. A method is proposed for approximating a function of several to one variable. The model takes the form of weighted averaging of overlapping basis functions defined over intervals. The number of such basis functions and their parameters (widths and centers) are automatically determined using given training data and a learning algorithm. The proposed algorithm can be seen as placing a nonuniform multidimensional grid in the input domain with overlapping cells. The non-uniformity and overlap of the cells is achieved by a learning algorithm to optimize a given objective function. This approach is motivated by the fuzzy modeling approach and a learning algorithms used for clustering and classification in pattern recognition. The basics of why and how the approach works are given. Few examples of nonlinear regression and classification are modeled. The relationship between the proposed technique, radial basis neural networks, kernel regression, probabilistic neural networks, and fuzzy modeling is explained. Finally advantages and disadvantages are discussed.
On approximation of functions by product operators
Directory of Open Access Journals (Sweden)
Hare Krishna Nigam
2013-12-01
Full Text Available In the present paper, two quite new reults on the degree of approximation of a function f belonging to the class Lip(α,r, 1≤ r <∞ and the weighted class W(Lr,ξ(t, 1≤ r <∞ by (C,2(E,1 product operators have been obtained. The results obtained in the present paper generalize various known results on single operators.
Semiclassical approximations to quantum time correlation functions
Egorov, S. A.; Skinner, J. L.
1998-09-01
Over the last 40 years several ad hoc semiclassical approaches have been developed in order to obtain approximate quantum time correlation functions, using as input only the corresponding classical time correlation functions. The accuracy of these approaches has been tested for several exactly solvable gas-phase models. In this paper we test the accuracy of these approaches by comparing to an exactly solvable many-body condensed-phase model. We show that in the frequency domain the Egelstaff approach is the most accurate, especially at high frequencies, while in the time domain one of the other approaches is more accurate.
Optimal Approximation of Quadratic Interval Functions
Koshelev, Misha; Taillibert, Patrick
1997-01-01
Measurements are never absolutely accurate, as a result, after each measurement, we do not get the exact value of the measured quantity; at best, we get an interval of its possible values, For dynamically changing quantities x, the additional problem is that we cannot measure them continuously; we can only measure them at certain discrete moments of time t(sub 1), t(sub 2), ... If we know that the value x(t(sub j)) at a moment t(sub j) of the last measurement was in the interval [x-(t(sub j)), x + (t(sub j))], and if we know the upper bound D on the rate with which x changes, then, for any given moment of time t, we can conclude that x(t) belongs to the interval [x-(t(sub j)) - D (t - t(sub j)), x + (t(sub j)) + D (t - t(sub j))]. This interval changes linearly with time, an is, therefore, called a linear interval function. When we process these intervals, we get an expression that is quadratic and higher order w.r.t. time t, Such "quadratic" intervals are difficult to process and therefore, it is necessary to approximate them by linear ones. In this paper, we describe an algorithm that gives the optimal approximation of quadratic interval functions by linear ones.
Discovery of functional and approximate functional dependencies in relational databases
Directory of Open Access Journals (Sweden)
Ronald S. King
2003-01-01
Full Text Available This study develops the foundation for a simple, yet efficient method for uncovering functional and approximate functional dependencies in relational databases. The technique is based upon the mathematical theory of partitions defined over a relation's row identifiers. Using a levelwise algorithm the minimal non-trivial functional dependencies can be found using computations conducted on integers. Therefore, the required operations on partitions are both simple and fast. Additionally, the row identifiers provide the added advantage of nominally identifying the exceptions to approximate functional dependencies, which can be used effectively in practical data mining applications.
Approximation of Analytic Functions by Bessel's Functions of Fractional Order
Directory of Open Access Journals (Sweden)
Soon-Mo Jung
2011-01-01
Full Text Available We will solve the inhomogeneous Bessel's differential equation x2y″(x+xy′(x+(x2-ν2y(x=∑m=0∞amxm, where ν is a positive nonintegral number and apply this result for approximating analytic functions of a special type by the Bessel functions of fractional order.
Ji, Fei-Yu; Zhang, Shun-Li
2013-11-01
In this paper, the generalized diffusion equation with perturbation ut = A(u;ux)uII+eB(u;ux) is studied in terms of the approximate functional variable separation approach. A complete classification of these perturbed equations which admit approximate functional separable solutions is presented. Some approximate solutions to the resulting perturbed equations are obtained by examples.
Approximating Smooth Step Functions Using Partial Fourier Series Sums
2012-09-01
interp1(xt(ii), smoothstepbez( t(ii), min(t(ii)), max(t(ii)), ’y’), t(ii), ’linear’, ’ extrap ’); ii = find( abs(t - tau/2) <= epi ); iii = t(ii...interp1( xt(ii), smoothstepbez( rt, min(rt), max(rt), ’y’), t(ii), ’linear’, ’ extrap ’ ); % stepm(ii) = 1 - interp1(xt(ii), smoothstepbez( t(ii...min(t(ii)), max(t(ii)), ’y’), t(ii), ’linear’, ’ extrap ’); In this case, because x is also defined as a function of the independent parameter
Approximations of Two-Attribute Utility Functions
1976-09-01
Introduction to Approximation Theory, McGraw-Hill, New York, 1966. Faber, G., Uber die interpolatorische Darstellung stetiger Funktionen, Deutsche...Management Review 14 (1972b) 37-50. Keeney, R. L., A decision analysis with multiple objectives: the Mexico City airport, Bell Journal of Economics
New Approach to Fractal Approximation of Vector-Functions
Directory of Open Access Journals (Sweden)
Konstantin Igudesman
2015-01-01
Full Text Available This paper introduces new approach to approximation of continuous vector-functions and vector sequences by fractal interpolation vector-functions which are multidimensional generalization of fractal interpolation functions. Best values of fractal interpolation vector-functions parameters are found. We give schemes of approximation of some sets of data and consider examples of approximation of smooth curves with different conditions.
A partition function approximation using elementary symmetric functions.
Directory of Open Access Journals (Sweden)
Ramu Anandakrishnan
Full Text Available In statistical mechanics, the canonical partition function [Formula: see text] can be used to compute equilibrium properties of a physical system. Calculating [Formula: see text] however, is in general computationally intractable, since the computation scales exponentially with the number of particles [Formula: see text] in the system. A commonly used method for approximating equilibrium properties, is the Monte Carlo (MC method. For some problems the MC method converges slowly, requiring a very large number of MC steps. For such problems the computational cost of the Monte Carlo method can be prohibitive. Presented here is a deterministic algorithm - the direct interaction algorithm (DIA - for approximating the canonical partition function [Formula: see text] in [Formula: see text] operations. The DIA approximates the partition function as a combinatorial sum of products known as elementary symmetric functions (ESFs, which can be computed in [Formula: see text] operations. The DIA was used to compute equilibrium properties for the isotropic 2D Ising model, and the accuracy of the DIA was compared to that of the basic Metropolis Monte Carlo method. Our results show that the DIA may be a practical alternative for some problems where the Monte Carlo method converge slowly, and computational speed is a critical constraint, such as for very large systems or web-based applications.
Function approximation for learning control : a key sample based approach
Kruif, de Bastiaan Johannes
2004-01-01
Two function approximators are introduced in this thesis for use in learning control. These function approximators identify a relation between input and output based on samples. Two different, but closely related function approximators are introduced: the key sample machine and the recursive key sam
Function approximation for learning control : a key sample based approach
2004-01-01
Two function approximators are introduced in this thesis for use in learning control. These function approximators identify a relation between input and output based on samples. Two different, but closely related function approximators are introduced: the key sample machine and the recursive key sample machine.
Triebel, Hans
1992-01-01
Theory of Function Spaces II deals with the theory of function spaces of type Bspq and Fspq as it stands at the present. These two scales of spaces cover many well-known function spaces such as Hölder-Zygmund spaces, (fractional) Sobolev spaces, Besov spaces, inhomogeneous Hardy spaces, spaces of BMO-type and local approximation spaces which are closely connected with Morrey-Campanato spaces. Theory of Function Spaces II is self-contained, although it may be considered an update of the author’s earlier book of the same title. The book’s 7 chapters start with a historical survey of the subject, and then analyze the theory of function spaces in Rn and in domains, applications to (exotic) pseudo-differential operators, and function spaces on Riemannian manifolds. ------ Reviews The first chapter deserves special attention. This chapter is both an outstanding historical survey of function spaces treated in the book and a remarkable survey of rather different techniques developed in the last 50 years. It is s...
Directory of Open Access Journals (Sweden)
Mohamed Mahmoud Mohamed
2016-09-01
Full Text Available In this paper we develop approximate Bayes estimators of the parameters,reliability, and hazard rate functions of the Logistic distribution by using Lindley’sapproximation, based on progressively type-II censoring samples. Noninformativeprior distributions are used for the parameters. Quadratic, linexand general Entropy loss functions are used. The statistical performances of theBayes estimates relative to quadratic, linex and general entropy loss functionsare compared to those of the maximum likelihood based on simulation study.
Subdifferentials of Distance Functions, Approximations and Enlargements
Institute of Scientific and Technical Information of China (English)
Jean-Paul PENOT; Robert RATSIMAHALO
2007-01-01
In this work, we study some subdifferentials of the distance function to a nonempty non-convex closed subset of a general Banach space. We relate them to the normal cone of the enlargements of the set which can be considered as regularizations of the set.
SOME NONLINEAR APPROXIMATIONS FOR MATRIX-VALUED FUNCTIONS
Institute of Scientific and Technical Information of China (English)
Guo-liang Xu
2003-01-01
Some nonlinear approximants, i.e., exponential-sum interpolation with equal distance or at origin, (0,1)-type, (0,2)-type and (1,2)-type fraction-sum approximations, for matrixvalued functions are introduced. All these approximation problems lead to a same form system of nonlinear equations. Solving methods for the nonlinear system are discussed.Conclusions on uniqueness and convergence of the approximants for certain class of functions are given.
Institute of Scientific and Technical Information of China (English)
Zhou Shi-Qi
2007-01-01
A universal theoretical approach is proposed which enables all hard sphere density functional approximations(DFAs) applicable to van der Waals fluids. The resultant DFA obtained by combining the universal theoretical approach with any hard sphere DFAs only needs as input a second-order direct correlation function (DCF) of a coexistence bulk fluid, and is applicable in both supercritical and subcritical temperature regions. The associated effective hard sphere density can be specified by a hard wall sum rule. It is indicated that the value of the effective hard sphere density so determined can be universal, i.e. can be applied to any external potentials different from the single hard wall. As an illustrating example, the universal theoretical approach is combined with a hard sphere bridge DFA to predict the density profile of a hard core attractive Yukawa model fluid influenced by diverse external fields; agreement between the present formalism's predictions and the corresponding simulation data is good or at least comparable to several previous DFT approaches. The primary advantage of the present theoretical approach combined with other hard sphere DFAs is discussed.
Finding the Best Quadratic Approximation of a Function
Yang, Yajun; Gordon, Sheldon P.
2011-01-01
This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact…
Approximate Augmented Lagrangian Functions and Nonlinear Semidefinite Programs
Institute of Scientific and Technical Information of China (English)
X. X. HUANG; K. L. TEO; X. Q. YANG
2006-01-01
In this paper, an approximate augmented Lagrangian function for nonlinear semidefinite programs is introduced. Some basic properties of the approximate augmented Lagrange function such as monotonicity and convexity are discussed. Necessary and sufficient conditions for approximate strong duality results are derived. Conditions for an approximate exact penalty representation in the framework of augmented Lagrangian are given. Under certain conditions, it is shown that any limit point of a sequence of stationary points of approximate augmented Lagrangian problems is a KKT point of the original semidefinite program and that a sequence of optimal solutions to augmented Lagrangian problems converges to a solution of the original semidefinite program.
Approximating the partition function of the ferromagnetic Potts model
Goldberg, Leslie Ann
2010-01-01
We provide evidence that it is computationally difficult to approximate the partition function of the ferromagnetic q-state Potts model when q>2. Specifically we show that the partition function is hard for the complexity class #RHPi_1 under approximation-preserving reducibility. Thus, it is as hard to approximate the partition function as it is to find approximate solutions to a wide range of counting problems, including that of determining the number of independent sets in a bipartite graph. Our proof exploits the second order phase transition of the "random cluster" model, which is a probability distribution on graphs that is closely related to the q-state Potts
Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation
Gordon, Sheldon P.; Yang, Yajun
2017-01-01
This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…
Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation
Gordon, Sheldon P.; Yang, Yajun
2017-01-01
This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…
Function approximation using combined unsupervised and supervised learning.
Andras, Peter
2014-03-01
Function approximation is one of the core tasks that are solved using neural networks in the context of many engineering problems. However, good approximation results need good sampling of the data space, which usually requires exponentially increasing volume of data as the dimensionality of the data increases. At the same time, often the high-dimensional data is arranged around a much lower dimensional manifold. Here we propose the breaking of the function approximation task for high-dimensional data into two steps: (1) the mapping of the high-dimensional data onto a lower dimensional space corresponding to the manifold on which the data resides and (2) the approximation of the function using the mapped lower dimensional data. We use over-complete self-organizing maps (SOMs) for the mapping through unsupervised learning, and single hidden layer neural networks for the function approximation through supervised learning. We also extend the two-step procedure by considering support vector machines and Bayesian SOMs for the determination of the best parameters for the nonlinear neurons in the hidden layer of the neural networks used for the function approximation. We compare the approximation performance of the proposed neural networks using a set of functions and show that indeed the neural networks using combined unsupervised and supervised learning outperform in most cases the neural networks that learn the function approximation using the original high-dimensional data.
Sparse tensor product wavelet approximation of singular functions
Dauge, M.; Stevenson, R.
2010-01-01
On product domains, sparse-grid approximation yields optimal, dimension-independent convergence rates when the function that is approximated has L-2-bounded mixed derivatives of a sufficiently high order. We show that the solution of Poisson's equation on the n-dimensional hypercube with Dirichlet
Democracy functions and optimal embeddings for approximation spaces
Garrigós, Gustavo; de Natividade, Maria
2009-01-01
We prove optimal embeddings for nonlinear approximation spaces in terms of weighted Lorentz sequence spaces, with the weights depending on the democracy functions of the basis. As applications we recover known embeddings for $N$-term wavelet approximation in Lebesgue, Orlicz, and Lorentz norms. We also study the "greedy classes" introduced by Gribonval and Nielsen.
Frankenstein's glue: transition functions for approximate solutions
Energy Technology Data Exchange (ETDEWEB)
Yunes, Nicolas [Center for Gravitational Wave Physics, Institute for Gravitational Physics and Geometry, Department of Physics, Pennsylvania State University, University Park, PA 16802-6300 (United States)
2007-09-07
Approximations are commonly employed to find approximate solutions to the Einstein equations. These solutions, however, are usually only valid in some specific spacetime region. A global solution can be constructed by gluing approximate solutions together, but this procedure is difficult because discontinuities can arise, leading to large violations of the Einstein equations. In this paper, we provide an attempt to formalize this gluing scheme by studying transition functions that join approximate analytic solutions together. In particular, we propose certain sufficient conditions on these functions and prove that these conditions guarantee that the joined solution still satisfies the Einstein equations analytically to the same order as the approximate ones. An example is also provided for a binary system of non-spinning black holes, where the approximate solutions are taken to be given by a post-Newtonian expansion and a perturbed Schwarzschild solution. For this specific case, we show that if the transition functions satisfy the proposed conditions, then the joined solution does not contain any violations to the Einstein equations larger than those already inherent in the approximations. We further show that if these functions violate the proposed conditions, then the matter content of the spacetime is modified by the introduction of a matter shell, whose stress-energy tensor depends on derivatives of these functions.
Approximate controllability of neutral functional differential system with unbounded delay
Directory of Open Access Journals (Sweden)
Jong Yeoul Park
2001-01-01
Full Text Available We consider a class of control systems governed by the neutral functional differential equation with unbounded delay and study the approximate controllability of the system. An example is given to illustrate the result.
Universal approximation by radial basis function networks of Delsarte translates.
Arteaga, Cristian; Marrero, Isabel
2013-10-01
We prove that, under certain mild conditions on the kernel function (or activation function), the family of radial basis function neural networks obtained by replacing the usual translation with the Delsarte one, and taking the same smoothing factor in all kernel nodes, has the universal approximation property.
2-D NONSEPARABLE SCALING FUNCTION INTERPOLATION AND APPROXIMATION
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The authors introduce nonseparable scaling function interpolation and show that its approximation can provide similar convergence properties as scalar wavelet system.Several equivalent statements of accuracy of nonseparable scaling function are also given.In the numerical experiments, it appears that nonseparable scaling function interpolation has better convergence results than scalar wavelet systems in some cases.
Intelligent systems II complete approximation by neural network operators
Anastassiou, George A
2016-01-01
This monograph is the continuation and completion of the monograph, “Intelligent Systems: Approximation by Artificial Neural Networks” written by the same author and published 2011 by Springer. The book you hold in hand presents the complete recent and original work of the author in approximation by neural networks. Chapters are written in a self-contained style and can be read independently. Advanced courses and seminars can be taught out of this brief book. All necessary background and motivations are given per chapter. A related list of references is given also per chapter. The book’s results are expected to find applications in many areas of applied mathematics, computer science and engineering. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also for all science and engineering libraries. .
Interpolation and approximation by rational functions in the complex domain
Walsh, J L
1935-01-01
The present work is restricted to the representation of functions in the complex domain, particularly analytic functions, by sequences of polynomials or of more general rational functions whose poles are preassigned, the sequences being defined either by interpolation or by extremal properties (i.e. best approximation). Taylor's series plays a central role in this entire study, for it has properties of both interpolation and best approximation, and serves as a guide throughout the whole treatise. Indeed, almost every result given on the representation of functions is concerned with a generaliz
Disorder and size effects in the envelope-function approximation
Dargam, T. G.; Capaz, R. B.; Koiller, Belita
1997-10-01
We investigate the validity and limitations of the envelope-function approximation (EFA), widely accepted for the description of the electronic states of semiconductor heterostructures. We consider narrow quantum wells of GaAs confined by AlxGa1-xAs barriers. Calculations performed within the tight-binding approximation using ensembles of supercells are compared to the EFA results. Results for miniband widths in superlattices obtained in different approximations are also discussed. The main source of discrepancy for narrow wells is the treatment of alloy disorder within the virtual crystal approximation. We also test the two key assumptions of the EFA: (a) that the electronic wave functions have Bloch symmetry with well-defined k--> in the alloy region; (b) that the periodic parts of the Bloch functions are the same throughout the heterostructure. We show that inaccuracies are mainly due to the former assumption.
Interpolation function for approximating knee joint behavior in human gait
Toth-Taşcǎu, Mirela; Pater, Flavius; Stoia, Dan Ioan
2013-10-01
Starting from the importance of analyzing the kinematic data of the lower limb in gait movement, especially the angular variation of the knee joint, the paper propose an approximation function that can be used for processing the correlation among a multitude of knee cycles. The approximation of the raw knee data was done by Lagrange polynomial interpolation on a signal acquired using Zebris Gait Analysis System. The signal used in approximation belongs to a typical subject extracted from a lot of ten investigated subjects, but the function domain of definition belongs to the entire group. The study of the knee joint kinematics plays an important role in understanding the kinematics of the gait, this articulation having the largest range of motion in whole joints, in gait. The study does not propose to find an approximation function for the adduction-abduction movement of the knee, this being considered a residual movement comparing to the flexion-extension.
Decomposition and Approximation of Multivariate Functions on the Cube
Institute of Scientific and Technical Information of China (English)
Zhi Hua ZHANG
2013-01-01
In this paper,we present a decomposition method of multivariate functions.This method shows that any multivariate function f on [0,1]d is a finite sum of the form ∑j φjΨj,where each φj can be extended to a smooth periodic function,each Ψj is an algebraic polynomial,and each φjΨj is a product of separated variable type and its smoothness is same as f.Since any smooth periodic function can be approximated well by trigonometric polynomials,using our decomposition method,we find that any smooth multivariate function on [0,1]d can be approximated well by a combination of algebraic polynomials and trigonometric polynomials.Meanwhile,we give a precise estimate of the approximation error.
Total variation approximation for quasi-equilibrium distributions, II
Barbour, A D
2011-01-01
Quasi-stationary distributions, as discussed by Darroch & Seneta (1965), have been used in biology to describe the steady state behaviour of population models which, while eventually certain to become extinct, nevertheless maintain an apparent stochastic equilibrium for long periods. These distributions have some drawbacks: they need not exist, nor be unique, and their calculation can present problems. In an earlier paper, we gave biologically plausible conditions under which the quasi-stationary distribution is unique, and can be closely approximated by distributions that are simple to compute. In this paper, we consider conditions under which the quasi-stationary distribution, if it exists, need not be unique, but an apparent stochastic equilibrium can nonetheless be identified and computed; we call such a distribution a quasi-equilibrium distribution.
Generalized Order and Best Approximation of Entire Function in -Norm
Directory of Open Access Journals (Sweden)
Mohammed Harfaoui
2010-01-01
Full Text Available The aim of this paper is the characterization of the generalized growth of entire functions of several complex variables by means of the best polynomial approximation and interpolation on a compact with respect to the set Ω={∈;exp(≤}, where =sup{(1/ln||,polynomialofdegree≤,‖‖≤1} is the Siciak extremal function of a -regular compact .
The Chen-Fliess approximation for diffusion functionals
Litterer, Christian
2011-01-01
We show that a large class of functionals of a stochastic differential equation can be approximated by a Chen-Fliess series of iterated stochastic integrals and give a L^{2} error estimate, thus generalizing the standard stochastic Taylor expansion. The coefficients in this series are given a very intuitive meaning by using functional derivatives, recently introduced by B. Dupire.
Pole-Based Approximation of the Fermi-Dirac Function
Institute of Scientific and Technical Information of China (English)
Lin LIN; Jianfeng LU; Lexing YING; Weinan E
2009-01-01
Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed: one uses the contour integral representation and conformal map-ping, and the other is based on a version of the multipole representation of the Fermi-Dirac function that uses only simple poles. Both representations have logarithmic computational complexity. They are of great interest for electronic structure calculations.
An optimized semiclassical approximation for vibrational response functions
Gerace, Mallory; Loring, Roger F.
2013-03-01
The observables of multidimensional infrared spectroscopy may be calculated from nonlinear vibrational response functions. Fully quantum dynamical calculations of vibrational response functions are generally impractical, while completely classical calculations are qualitatively incorrect at long times. These challenges motivate the development of semiclassical approximations to quantum mechanics, which use classical mechanical information to reconstruct quantum effects. The mean-trajectory (MT) approximation is a semiclassical approach to quantum vibrational response functions employing classical trajectories linked by deterministic transitions representing the effects of the radiation-matter interaction. Previous application of the MT approximation to the third-order response function R(3)(t3, t2, t1) demonstrated that the method quantitatively describes the coherence dynamics of the t3 and t1 evolution times, but is qualitatively incorrect for the waiting-time t2 period. Here we develop an optimized version of the MT approximation by elucidating the connection between this semiclassical approach and the double-sided Feynman diagrams (2FD) that represent the quantum response. Establishing the direct connection between 2FD and semiclassical paths motivates a systematic derivation of an optimized MT approximation (OMT). The OMT uses classical mechanical inputs to accurately reproduce quantum dynamics associated with all three propagation times of the third-order vibrational response function.
QUASI-INTERPOLATION AND APPROXIMATION VIA NONSEPARABLE SCALING FUNCTION
Institute of Scientific and Technical Information of China (English)
Enbing Lin; Ling Yi
2002-01-01
Quasi-interpolation has been audied in many papers, e.g. , [5]. Here we introduce nonseparable scal-ing function quasi-interpolation and show that its approximation can provide similar convergence propertiesas scalar wavelet system. Several equivalent statements of accuracy of nonseparable scaling function are alsogien. In the numerical experiments, it appears that nonseparable scaling function interpolation has betterconvergonce results than scalar wavelet systems in some cases.
Greedy feature replacement for online value function approximation
Institute of Scientific and Technical Information of China (English)
Feng-fei ZHAO; Zheng QIN; Zhuo SHAO; Jun FANG; Bo-yan REN
2014-01-01
Reinforcement learning (RL) in real-world problems requires function approximations that depend on selecting the appropriate feature representations. Representational expansion techniques can make linear approximators represent value functions more effectively;however, most of these techniques function well only for low dimensional problems. In this paper, we present the greedy feature replacement (GFR), a novel online expansion technique, for value-based RL algorithms that use binary features. Given a simple initial representation, the feature representation is expanded incrementally. New feature dependencies are added automatically to the current representation and conjunctive features are used to replace current features greedily. The virtual temporal difference (TD) error is recorded for each conjunctive feature to judge whether the replacement can improve the approximation. Correctness guarantees and computational complexity analysis are provided for GFR. Experimental results in two domains show that GFR achieves much faster learning and has the capability to handle large-scale problems.
Quantal Density Functional Theory II
Sahni, Viraht
2009-01-01
Discusses approximation methods and applications of Quantal Density Functional Theory (QDFT), a local effective-potential-energy theory of electronic structure. This book describes approximations methods based on the incorporation of different electron correlations, as well as a many-body perturbation theory within the context of QDFT
Delta-function Approximation SSC Model in 3C 273
Indian Academy of Sciences (India)
S. J. Kang; Y. G. Zheng; Q. Wu
2014-09-01
We obtain an approximate analytical solution using approximate calculation on the traditional one-zone synchrotron self-Compton (SSC) model. In this model, we describe the electron energy distribution by a broken power-law function with a sharp cut-off, and non-thermal photons are produced by both synchrotron and inverse Compton scattering of synchrotron photons. We calculate the radiation energy spectrum of electrons by the function. We apply this model to the multi-wavelength Spectral Energy Distributions (SED) of the 3C 273 in different states, and obtain excellent fits to the observed spectra of this source.
On Approximate Solutions of Functional Equations in Vector Lattices
Directory of Open Access Journals (Sweden)
Bogdan Batko
2014-01-01
Full Text Available We provide a method of approximation of approximate solutions of functional equations in the class of functions acting into a Riesz space (algebra. The main aim of the paper is to provide a general theorem that can act as a tool applicable to a possibly wide class of functional equations. The idea is based on the use of the Spectral Representation Theory for Riesz spaces. The main result will be applied to prove the stability of an alternative Cauchy functional equation F(x+y+F(x+F(y≠0⇒F(x+y=F(x+F(y in Riesz spaces, the Cauchy equation with squares F(x+y2=(F(x+F(y2 in f-algebras, and the quadratic functional equation F(x+y+F(x-y=2F(x+2F(y in Riesz spaces.
GREEN‘S FUNCTION APPROACH IN APPROXIMATE CONTROLLABILITY PROBLEMS
Directory of Open Access Journals (Sweden)
Avetisyan A. S.
2016-06-01
Full Text Available A mathematical approach based on Green‘s function approach allowing to construct controls providing approximate controllability is suggested in the present paper. Representing the solution of governing system via Green’s formula and substituting it in prescribed terminal conditions, we obtain control functions providing approximate controllability of the system under study in explicit form. Choosing appropriate controls, we can provide required accuracy of approximation for prescribed conditions. Examples illustrating the procedure are described. Particularly, infinite string, controlled by a concentrated force, semi-infinite rod heated by a point heat source, finite rod heated from its boundary and parameter optimization for electrical circuit are considered. Results of computsations are brought.
Animating Nested Taylor Polynomials to Approximate a Function
Mazzone, Eric F.; Piper, Bruce R.
2010-01-01
The way that Taylor polynomials approximate functions can be demonstrated by moving the center point while keeping the degree fixed. These animations are particularly nice when the Taylor polynomials do not intersect and form a nested family. We prove a result that shows when this nesting occurs. The animations can be shown in class or…
Approximation solutions for indifference pricing under general utility functions
Chen, An; Pelsser, Antoon; Vellekoop, M.H.
2008-01-01
With the aid of Taylor-based approximations, this paper presents results for pricing insurance contracts by using indifference pricing under general utility functions. We discuss the connection between the resulting "theoretical" indifference prices and the pricing rule-of-thumb that practitioners u
Approximation solutions for indifference pricing under general utility functions
Chen, An; Pelsser, Antoon; Vellekoop, M.H.
2008-01-01
With the aid of Taylor-based approximations, this paper presents results for pricing insurance contracts by using indifference pricing under general utility functions. We discuss the connection between the resulting "theoretical" indifference prices and the pricing rule-of-thumb that practitioners
Approximation solutions for indifference pricing under general utility functions
Chen, An; Pelsser, Antoon; Vellekoop, Michel
2008-01-01
With the aid of Taylor-based approximations, this paper presents results for pricing insurance contracts by using indifference pricing under general utility functions. We discuss the connection between the resulting "theoretical" indifference prices and the pricing rule-of-thumb that practitioners u
The Fractional Differential Polynomial Neural Network for Approximation of Functions
Directory of Open Access Journals (Sweden)
Rabha W. Ibrahim
2013-09-01
Full Text Available In this work, we introduce a generalization of the differential polynomial neural network utilizing fractional calculus. Fractional calculus is taken in the sense of the Caputo differential operator. It approximates a multi-parametric function with particular polynomials characterizing its functional output as a generalization of input patterns. This method can be employed on data to describe modelling of complex systems. Furthermore, the total information is calculated by using the fractional Poisson process.
Multiple functions of photosystem II
Rensen, van J.J.S.; Curwiel, V.B.
2000-01-01
The most important function of photosystem II (PSII) is its action as a water-plastoquinone oxido-reductase. At the expense of light energy, water is split, and oxygen and plastoquinol are formed. In addition to this most important activity, PSII has additional functions, especially in the
Strong semiclassical approximation of Wigner functions for the Hartree dynamics
Athanassoulis, Agissilaos
2011-01-01
We consider the Wigner equation corresponding to a nonlinear Schrödinger evolution of the Hartree type in the semiclassical limit h → 0. Under appropriate assumptions on the initial data and the interaction potential, we show that the Wigner function is close in L 2 to its weak limit, the solution of the corresponding Vlasov equation. The strong approximation allows the construction of semiclassical operator-valued observables, approximating their quantum counterparts in Hilbert-Schmidt topology. The proof makes use of a pointwise-positivity manipulation, which seems necessary in working with the L 2 norm and the precise form of the nonlinearity. We employ the Husimi function as a pivot between the classical probability density and the Wigner function, which - as it is well known - is not pointwise positive in general.
Approximation methods for the partition functions of anharmonic systems
Energy Technology Data Exchange (ETDEWEB)
Lew, P.; Ishida, T.
1979-07-01
The analytical approximations for the classical, quantum mechanical and reduced partition functions of the diatomic molecule oscillating internally under the influence of the Morse potential have been derived and their convergences have been tested numerically. This successful analytical method is used in the treatment of anharmonic systems. Using Schwinger perturbation method in the framework of second quantization formulism, the reduced partition function of polyatomic systems can be put into an expression which consists separately of contributions from the harmonic terms, Morse potential correction terms and interaction terms due to the off-diagonal potential coefficients. The calculated results of the reduced partition function from the approximation method on the 2-D and 3-D model systems agree well with the numerical exact calculations.
Numerical approximations of difference functional equations and applications
Directory of Open Access Journals (Sweden)
Zdzisław Kamont
2005-01-01
Full Text Available We give a theorem on the error estimate of approximate solutions for difference functional equations of the Volterra type. We apply this general result in the investigation of the stability of difference schemes generated by nonlinear first order partial differential functional equations and by parabolic problems. We show that all known results on difference methods for initial or initial boundary value problems can be obtained as particular cases of this general and simple result. We assume that the right hand sides of equations satisfy nonlinear estimates of the Perron type with respect to functional variables.
Mean Spherical Approximation-Based Partitioned Density Functional Theory
Institute of Scientific and Technical Information of China (English)
ZHOU Shi-Qi
2003-01-01
Previous literature claims that the density functional theory for non-uniform non-hard sphere interaction potential fluid can be improved on by treating the tail part by the third order functional perturbation expansion approximation (FPEA) with the symmetrical and intuitive consideration-based simple function C0(3)(r1, r2, r3) =ζ∫ dr4a(r4 - r1)a(r4 - r2)a(r4 - r3) as the uniform third order direct correlation function (DCF) for the tail part,here kernel function a(r) = (6/πσ3)Heaviside(σ/2 - r). The present contribution concludes that for the mean spherical approximation-based second order DCF, the terms higher than second order in the FPEA of the tail part of the non-uniform first order DCF are exactly zero. The reason for the partial success of the previous a kernel function-based third order FPEA for the tail part is due to the adjustable parameter ζ and the short range of the a kernel function.Improvement over the previous theories is proposed and tested.
Mean Spherical Approximation-Based Partitioned Density Functional Theory
Institute of Scientific and Technical Information of China (English)
ZHOUShi-Qi
2003-01-01
Previous literature claims that the density functional theory for non-uniform non-hard sphere interaction potential fluid can be improved on by treating the tail part by the third order functional perturbation expansion approximation (FPEA) with the symmetrical and intuitive consideration-based simple function C0(3)(r1, r2, r3) =(∫dr4a(r4-r1)a(r4-r2)a(r4-r3) as the uniform third order direct correlation function (DCF) for the tail part,here kernel function a(r) = (6/πσ3)Heaviside(σ/2 - r). The present contribution concludes that for the mean spherical approximation-based second order DCF, the terms higher than second order in the FPEA of the tail part of the non-uniform first order DCF are exactly zero. The reason for the partial success of the previous a kernel function-based third order FPEA for the tail part is due to the adjustable parameter ξ and the short range of the a kernel function.Improvement over the previous theories is proposed and tested.
Construction and use of numerical-analytical approximating functions
Serazutdinov, M. N.
2016-11-01
The article goes over the methodology of constructing numerical-analytical approximating functions, satisfying the given boundary conditions for the function of its derivatives in the circuit areas of various shapes. The methodology is based on presenting the unknown function as a series in a complete set of functions that do not satisfy the given boundary conditions on the contour of the area, but additionally numerically defined near the contour to satisfy the boundary conditions. The additional definition of the functions near the area contour is performed numerically based on finite-difference relations. The main advantage of the stated method is the ability to build a relatively simple approximating functions satisfying the given boundary conditions on the boundary of complex shaped areas. The examples of applying the described method for solving the boundary value problem of a plate of different shapes. The possibility of using numerical-analytical functions for solving boundary value problems that contain higher derivatives up to fourth order is shown.
Constrained Parmeterization of Reduced Density Approximation of Kinetic Energy Functionals
Chakraborty, Debajit; Trickey, Samuel; Karasiev, Valentin
2014-03-01
Evaluation of forces in ab initio MD is greatly accelerated by orbital-free DFT, especially at finite temperature. The recent achievement of a fully non-empirical constraint-based generalized gradient (GGA) functional for the Kohn-Sham KE Ts [ n ] brings to light the inherent limitations of GGAs. This motivates inclusion of higher-order derivatives in the form of reduced derivative approximation (RDA) functionals. That, in turn, requires new functional forms and design criteria. RDA functionals are constrained further to produce a positive-definite, non-singular Pauli potential. We focus on designing a non-empirical constraint-based meta-GGA functional with certain combinations of higher-order derivatives which avoid nuclear-site singularities to a specified order of gradient expansion. Here we report progress on this agenda. Work supported by U.S. Dept. of Energy, grant DE-SC0002139.
Corrected Fourier series and its application to function approximation
Directory of Open Access Journals (Sweden)
Qing-Hua Zhang
2005-01-01
Full Text Available Any quasismooth function f(x in a finite interval [0,x0], which has only a finite number of finite discontinuities and has only a finite number of extremes, can be approximated by a uniformly convergent Fourier series and a correction function. The correction function consists of algebraic polynomials and Heaviside step functions and is required by the aperiodicity at the endpoints (i.e., f(0≠f(x0 and the finite discontinuities in between. The uniformly convergent Fourier series and the correction function are collectively referred to as the corrected Fourier series. We prove that in order for the mth derivative of the Fourier series to be uniformly convergent, the order of the polynomial need not exceed (m+1. In other words, including the no-more-than-(m+1 polynomial has eliminated the Gibbs phenomenon of the Fourier series until its mth derivative. The corrected Fourier series is then applied to function approximation; the procedures to determine the coefficients of the corrected Fourier series are illustrated in detail using examples.
PGO models in the envelope function and effective mass approximations
Paulescu, M.; Tulcan-Paulescu, E.; Gravila, P.
2011-03-01
A recipe to design quantum devices that exhibit the theoretical pseudo-Gaussian oscillator electronic states properties is given. The algorithm is described en detail and is illustrated by the computation of a Mn x Cd1- x Te ternary alloy pseudo-Gaussian heterostructure. The numerical procedure reaches beyond of pseudo-Gaussian models and can be used for designing epitaxial growth devices with desired electronic states structure. The calculations are carried out in the envelope function and effective mass approximations.
Neural networks for function approximation in nonlinear control
Linse, Dennis J.; Stengel, Robert F.
1990-01-01
Two neural network architectures are compared with a classical spline interpolation technique for the approximation of functions useful in a nonlinear control system. A standard back-propagation feedforward neural network and a cerebellar model articulation controller (CMAC) neural network are presented, and their results are compared with a B-spline interpolation procedure that is updated using recursive least-squares parameter identification. Each method is able to accurately represent a one-dimensional test function. Tradeoffs between size requirements, speed of operation, and speed of learning indicate that neural networks may be practical for identification and adaptation in a nonlinear control environment.
Ito, K.
1984-01-01
The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A charactristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.
Ito, K.
1985-01-01
The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A characteristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.
Machine-learned approximations to Density Functional Theory Hamiltonians
Hegde, Ganesh; Bowen, R. Chris
2017-01-01
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest. PMID:28198471
Machine-learned approximations to Density Functional Theory Hamiltonians
Hegde, Ganesh; Bowen, R. Chris
2017-02-01
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest.
Optimal and Approximate Q-value Functions for Decentralized POMDPs
Oliehoek, Frans A; Vlassis, Nikos; 10.1613/jair.2447
2011-01-01
Decision-theoretic planning is a popular approach to sequential decision making problems, because it treats uncertainty in sensing and acting in a principled way. In single-agent frameworks like MDPs and POMDPs, planning can be carried out by resorting to Q-value functions: an optimal Q-value function Q* is computed in a recursive manner by dynamic programming, and then an optimal policy is extracted from Q*. In this paper we study whether similar Q-value functions can be defined for decentralized POMDP models (Dec-POMDPs), and how policies can be extracted from such value functions. We define two forms of the optimal Q-value function for Dec-POMDPs: one that gives a normative description as the Q-value function of an optimal pure joint policy and another one that is sequentially rational and thus gives a recipe for computation. This computation, however, is infeasible for all but the smallest problems. Therefore, we analyze various approximate Q-value functions that allow for efficient computation. We descri...
Approximated Function Based Spectral Gradient Algorithm for Sparse Signal Recovery
Directory of Open Access Journals (Sweden)
Weifeng Wang
2014-02-01
Full Text Available Numerical algorithms for the l0-norm regularized non-smooth non-convex minimization problems have recently became a topic of great interest within signal processing, compressive sensing, statistics, and machine learning. Nevertheless, the l0-norm makes the problem combinatorial and generally computationally intractable. In this paper, we construct a new surrogate function to approximate l0-norm regularization, and subsequently make the discrete optimization problem continuous and smooth. Then we use the well-known spectral gradient algorithm to solve the resulting smooth optimization problem. Experiments are provided which illustrate this method is very promising.
Nonlinear programming extensions to rational function approximations of unsteady aerodynamics
Tiffany, Sherwood H.; Adams, William M., Jr.
1987-01-01
This paper deals with approximating unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft. Two methods of formulating these approximations are extended to include both the same flexibility in constraining them and the same methodology in optimizing nonlinear parameters as another currently used 'extended least-squares' method. Optimal selection of 'nonlinear' parameters is made in each of the three methods by use of the same nonlinear (nongradient) optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is of lower order than that required when no optimization of the nonlinear terms is performed. The free 'linear' parameters are determined using least-squares matrix techniques on a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from the different approaches are described, and results are presented which show comparative evaluations from application of each of the extended methods to a numerical example. The results obtained for the example problem show a significant (up to 63 percent) reduction in the number of differential equations used to represent the unsteady aerodynamic forces in linear time-invariant equations of motion as compared to a conventional method in which nonlinear terms are not optimized.
Institute of Scientific and Technical Information of China (English)
李中夫; 刘应明
1994-01-01
This paper discusses the problem of simple representation of multi-place functions from the viewpoint of "simple approximation". We prove that a class of associative functions, which have a wide range of applications, can be approximately represented by a monotone 1-place function and addition.
Neural network design for J function approximation in dynamic programming
Pang, X
1998-01-01
This paper shows that a new type of artificial neural network (ANN) -- the Simultaneous Recurrent Network (SRN) -- can, if properly trained, solve a difficult function approximation problem which conventional ANNs -- either feedforward or Hebbian -- cannot. This problem, the problem of generalized maze navigation, is typical of problems which arise in building true intelligent control systems using neural networks. (Such systems are discussed in the chapter by Werbos in K.Pribram, Brain and Values, Erlbaum 1998.) The paper provides a general review of other types of recurrent networks and alternative training techniques, including a flowchart of the Error Critic training design, arguable the only plausible approach to explain how the brain adapts time-lagged recurrent systems in real-time. The C code of the test is appended. As in the first tests of backprop, the training here was slow, but there are ways to do better after more experience using this type of network.
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.
Longitudinal functional principal component modelling via Stochastic Approximation Monte Carlo
Martinez, Josue G.
2010-06-01
The authors consider the analysis of hierarchical longitudinal functional data based upon a functional principal components approach. In contrast to standard frequentist approaches to selecting the number of principal components, the authors do model averaging using a Bayesian formulation. A relatively straightforward reversible jump Markov Chain Monte Carlo formulation has poor mixing properties and in simulated data often becomes trapped at the wrong number of principal components. In order to overcome this, the authors show how to apply Stochastic Approximation Monte Carlo (SAMC) to this problem, a method that has the potential to explore the entire space and does not become trapped in local extrema. The combination of reversible jump methods and SAMC in hierarchical longitudinal functional data is simplified by a polar coordinate representation of the principal components. The approach is easy to implement and does well in simulated data in determining the distribution of the number of principal components, and in terms of its frequentist estimation properties. Empirical applications are also presented.
Efficient Density Functional Approximation for Electronic Properties of Conjugated Systems
Caldas, Marília J.; Pinheiro, José Maximiano, Jr.; Blum, Volker; Rinke, Patrick
2014-03-01
There is on-going discussion about reliable prediction of electronic properties of conjugated oligomers and polymers, such as ionization potential IP and energy gap. Several exchange-correlation (XC) functionals are being used by the density functional theory community, with different success for different properties. In this work we follow a recent proposal: a fraction α of exact exchange is added to the semi-local PBE XC aiming consistency, for a given property, with the results obtained by many-body perturbation theory within the G0W0 approximation. We focus the IP, taken as the negative of the highest occupied molecular orbital energy. We choose α from a study of the prototype family trans-acetylene, and apply this same α to a set of oligomers for which there is experimental data available (acenes, phenylenes and others). Our results indicate we can have excellent estimates, within 0,2eV mean ave. dev. from the experimental values, better than through complete EN - 1 -EN calculations from the starting PBE functional. We also obtain good estimates for the electrical gap and orbital energies close to the band edge. Work supported by FAPESP, CNPq, and CAPES, Brazil, and DAAD, Germany.
Functional hand proportion is approximated by the Fibonacci series.
Choo, K W-Q; Quah, W-K; Chang, G-H; Chan, J Y
2012-08-01
The debatable relationship of functional human hand proportion with the Fibonacci series has remained an obscure scientific enigma short of clinical interest. The main difficulty of proving such a relationship lies in defining what should constitute true functional proportion. In this study, we re-evaluate this unique relationship using hand flexion creases as anatomical surrogates for the functional axes of joint rotation. Standardised desktop photocopies of palmar views of both hands in full digital extension and abduction were obtained from 100 healthy male volunteers of Chinese ethnicity. The functional axes were represented by the distal digital crease (distal interphalangeal joint, DIPJ), proximal digital crease (proximal interphalangeal joint, PIPJ), as well as the midpoint between the palmar digital and transverse palmar creases (metacarpophalangeal joint, MCPJ). The ratio of DIPJ-Fingertip:PIPJ-DIPJ:MCPJ-PIPJ (p3:p2:p1) was measured by two independent observers and represented as standard deviation about the mean, and then compared to the theoretical ratio of 1:1:2. Our results showed that, for the 2nd to 5th digits, the p2:p3 ratios were 0.97 ± ± 0.09, 1.10 ± 0.10, 1.04 ± 0.12, and 0.80 ± 0.08, respectively; whilst the p1:p2 ratios were 1.91 ± 0.17, 1.98 ± 0.14, 1.89 ± 0.16, and 2.09 ± 0.24, respectively. When the data were analysed for all digits, they showed a combined p3:p2:p1 ratio of 1:0.98:2.01. In conclusion, our results suggest that functional human hand proportion, as defined by flexion creases, is approximated by the Fibonacci series.
Polymer quantization and the saddle point approximation of partition functions
Morales-Técotl, Hugo A.; Orozco-Borunda, Daniel H.; Rastgoo, Saeed
2015-11-01
The saddle point approximation of the path integral partition functions is an important way of deriving the thermodynamical properties of black holes. However, there are certain black hole models and some mathematically analog mechanical models for which this method cannot be applied directly. This is due to the fact that their action evaluated on a classical solution is not finite and its first variation does not vanish for all consistent boundary conditions. These problems can be dealt with by adding a counterterm to the classical action, which is a solution of the corresponding Hamilton-Jacobi equation. In this work we study the effects of polymer quantization on a mechanical model presenting the aforementioned difficulties and contrast it with the above counterterm method. This type of quantization for mechanical models is motivated by the loop quantization of gravity, which is known to play a role in the thermodynamics of black hole systems. The model we consider is a nonrelativistic particle in an inverse square potential, and we analyze two polarizations of the polymer quantization in which either the position or the momentum is discrete. In the former case, Thiemann's regularization is applied to represent the inverse power potential, but we still need to incorporate the Hamilton-Jacobi counterterm, which is now modified by polymer corrections. In the latter, momentum discrete case, however, such regularization could not be implemented. Yet, remarkably, owing to the fact that the position is bounded, we do not need a Hamilton-Jacobi counterterm in order to have a well-defined saddle point approximation. Further developments and extensions are commented upon in the discussion.
Polymer quantization and the saddle point approximation of partition functions
Técotl, Hugo A Morales; Rastgoo, Saeed
2015-01-01
The saddle point approximation of the path integral partition functions is an important way of deriving the thermodynamical properties of black holes. However, there are certain black hole models and some mathematically analog mechanical models for which this method can not be applied directly. This is due to the fact that their action evaluated on a classical solution is not finite and its first variation does not vanish for all consistent boundary conditions. These problems can be dealt with by adding a counter-term to the classical action, which is a solution of the corresponding Hamilton-Jacobi equation. In this work we study the effects of polymer quantization on a mechanical model presenting the aforementioned difficulties and contrast it with the above counter-term method. This type of quantization for mechanical models is motivated by the loop quantization of gravity which is known to play a role in the thermodynamics of black holes systems. The model we consider is a non relativistic particle in an i...
Energy Technology Data Exchange (ETDEWEB)
Liu, Jian; Miller, William H.
2006-09-06
The thermal Gaussian approximation (TGA) recently developed by Mandelshtam et al has been demonstrated to be a practical way for approximating the Boltzmann operator exp(-{beta}H) for multidimensional systems. In this paper the TGA is combined with semiclassical (SC) initial value representations (IVRs) for thermal time correlation functions. Specifically, it is used with the linearized SC-IVR (LSC-IVR, equivalent to the classical Wigner model), and the 'forward-backward semiclassical dynamics' (FBSD) approximation developed by Makri et al. Use of the TGA with both of these approximate SC-IVRs allows the oscillatory part of the IVR to be integrated out explicitly, providing an extremely simple result that is readily applicable to large molecular systems. Calculation of the force-force autocorrelation for a strongly anharmonic oscillator demonstrates its accuracy, and of the velocity autocorrelation function (and thus the diffusion coefficient) of liquid neon demonstrates its applicability.
Algorithms for spline and other approximations to functions and data
Phillips, G. M.; Taylor, P. J.
1992-12-01
A succinct introduction to splines, explaining how and why B-splines are used as a basis and how cubic and quadratic splines may be constructed, is followed by brief account of Hermite interpolation and Padé approximations.
Approximation of several dimensional functions by trigonometric polynomials
Institute of Scientific and Technical Information of China (English)
CHENG Minde; CHEN Yonghe
2006-01-01
Let f(x,y) be a periodic function defined on the region D 0≤x≤2π, 0≤y≤2πwith period 2π for each variable.If f(x,y) ∈ CP(D),i.e.,f(x,y) has continuous partial derivatives of order p on D,then we denote by ωα,β(ρ) the modulus of continuity of the function(a)pf(x,y)/(a)xα(a)yβ (α,β≥0,α+β=p)and writeωp(ρ)=max ωα,β(ρ) α,β≥0,α+β=pFor p=0,we write simply C(D) and ω(p) instead of C0(D) and ω0(ρ).Let T(x,y) be a trigonometrical polynomial written in the complex form T(x,y) = ΣCm,nei(mx+ny).We consider R=max(m2+n2)1/2 as the degree of T(x,y),and write TR(x,y)for the trigonometrical polynomial of degree≤R.Our main purpose is to find the trigonometrical polynomial TR(x,y) for a given f(x,y) of a certain class of functions such that max xy|f(x,y)-TR(x,y)|attains the same order of accuracy as the best approximation of f(x,y).Let the Fourier series of f(x,y)∈C(D) be f(x,y)～∞Σ-∞ Cm,n ei(mx+ny),and let Av(x,y)=Σm2+n2=v Cm,n ei(mx+ny).Our results are as follows:Theorem 1 Let f(x,y)∈CP(D) (p=0,1) andSδR(x,y;f)=Σv=R2 (1-v/R2)δAv(x,y) (δ＞1/2).ThenSδR(x,y;f)-f(x,y)=0[1/Rp ωp(1/R)](p=0,1)holds uniformly on D.If we consider the circular mean of the Riesz sum SδR(x,y)≡SδR(x,y;f):μt[SδR(x,y)]=1/2π∫2π0 SδR(x+t cosθ,y+t sinθ)dθ,then we have the following:Theorem 2 If f(x,y)∈CP(D) andωp(ρ)=O(pα) (0＜α≤1;p=0,1),thenμλ0/R[SδR(x,y)-f(x,y)=O(1/Rp+α) (p=0,1;δ≥0)holds uniformly on D,where λ0 is a positive root of the Bessel function Jo(x).It should be noted that eitherSδR(x,y;f)-f(x,y)=o(1/R2)orμλ0/R[SδR(x,y)]-f(x,y)=o(1/R2)implies that f (x,y)≡const.Now we consider the following trigonometrical polynomialSκR(x,y;f)=Σ(1-νk/2/Rk)δAν(x,y)(k ∈Z+).Then we haveTheorem 3 If f(x,y)∈CP(D),then uniformly on D,S(k)R(x,y;f)-f(x,y)={O[1/Rpωp(1/R)],p=0,1,...,k-1 for k even,O[1/Rpωp(1/R)InR],p=k-1 for k odd.Theorems 1 and 2 include the results of Chandrasekharan and Minakshisundaram,and Theorem 3 is a
Polynomial Approximation of Functions: Historical Perspective and New Tools
Kidron, Ivy
2003-01-01
This paper examines the effect of applying symbolic computation and graphics to enhance students' ability to move from a visual interpretation of mathematical concepts to formal reasoning. The mathematics topics involved, Approximation and Interpolation, were taught according to their historical development, and the students tried to follow the…
Directory of Open Access Journals (Sweden)
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.
Strong Convergence of Stochastic Approximation Without Lyapunov Functions
1995-01-01
We prove convergence with probability one of a multivariate Markov stochastic approximation procedure of the Robbins-Monro type with several roots. The argument exploits convergence of the corresponding system of ordinary differential equations to its stationary points. If the points are either linearly stable or linearly unstable, we prove convergence with probability 1 of the procedure to a random vector whose distribution concentrates on the set of stable stationary points. This generalize...
Multi-level methods and approximating distribution functions
Wilson, D.; Baker, R. E.
2016-07-01
Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via simulation techniques. There is a well documented class of simulation techniques known as exact stochastic simulation algorithms, an example of which is Gillespie's direct method. These algorithms often come with high computational costs, therefore approximate stochastic simulation algorithms such as the tau-leap method are used. However, in order to minimise the bias in the estimates generated using them, a relatively small value of tau is needed, rendering the computational costs comparable to Gillespie's direct method. The multi-level Monte Carlo method (Anderson and Higham, Multiscale Model. Simul. 10:146-179, 2012) provides a reduction in computational costs whilst minimising or even eliminating the bias in the estimates of system statistics. This is achieved by first crudely approximating required statistics with many sample paths of low accuracy. Then correction terms are added until a required level of accuracy is reached. Recent literature has primarily focussed on implementing the multi-level method efficiently to estimate a single system statistic. However, it is clearly also of interest to be able to approximate entire probability distributions of species counts. We present two novel methods that combine known techniques for distribution reconstruction with the multi-level method. We demonstrate the potential of our methods using a number of examples.
Approximate inference for spatial functional data on massively parallel processors
DEFF Research Database (Denmark)
Raket, Lars Lau; Markussen, Bo
2014-01-01
With continually increasing data sizes, the relevance of the big n problem of classical likelihood approaches is greater than ever. The functional mixed-effects model is a well established class of models for analyzing functional data. Spatial functional data in a mixed-effects setting...... in linear time. An extremely efficient GPU implementation is presented, and the proposed methods are illustrated by conducting a classical statistical analysis of 2D chromatography data consisting of more than 140 million spatially correlated observation points....
Specification of Density Functional Approximation by Radial Distribution Function of Bulk Fluid
Institute of Scientific and Technical Information of China (English)
ZHOU Shi-Qi
2002-01-01
A systematic methodology is proposed to deal with the weighted density approximation version of clas-sical density functional theory by employing the knowledge of radial distribution function of bulk fluid. The presentmethodology results from the concept of universality of the free energy density functional combined with the test particlemethod. It is shown that the new method is very accurate for the predictions of density distribution ofa hard sphere fluidat different confining geometries. The physical foundation of the present methodology is also applied to the quantumdensity functional theory.
Specification of Density Functional Approximation by Radial Distribution Function of Bulk Fluid
Institute of Scientific and Technical Information of China (English)
ZHOUShi－Qi
2002-01-01
A systematic methodology is proposed to deal with the weighted density approximation version of classical density functional theory by employing the knowledge of radial distribution function of bulk fluid.The present methodology results from the concept of universality of the free energy density functional combined with the test particle method.It is shown that the new method is very accurate for the predictions of density distribution of a hard sphere fluid at different confining geometries.The physical foundation of the present methodology is also applied to the quantum density functional theory.
On approximating the modified Bessel function of the second kind.
Yang, Zhen-Hang; Chu, Yu-Ming
2017-01-01
In the article, we prove that the double inequalities [Formula: see text] hold for all [Formula: see text] if and only if [Formula: see text] and [Formula: see text] if [Formula: see text], where [Formula: see text] is the modified Bessel function of the second kind. As applications, we provide bounds for [Formula: see text] with [Formula: see text] and present the necessary and sufficient condition such that the function [Formula: see text] is strictly increasing (decreasing) on [Formula: see text].
Papillary muscle approximation to septum for functional tricuspid regurgitation.
Lohchab, Shamsher Singh; Chahal, Ashok Kumar; Agrawal, Nilesh
2015-07-01
Current techniques for repair of functional tricuspid regurgitation are associated with a significant degree of residual or recurrent regurgitation. We describe a technique of anterior papillary muscle attachment to the septum to correct residual tricuspid regurgitation persisting after annuloplasty. In our early experience in 15 patients (6 men and 9 women) with a mean age of 32 ± 11 years, who underwent annuloplasty for severe functional tricuspid regurgitation secondary to rheumatic mitral valve disease, this technique effectively eliminated residual tricuspid regurgitation.
Approximation to Continuous Functions by a Kind of Interpolation Polynomials
Institute of Scientific and Technical Information of China (English)
Yuan Xue-gang; Wang De-hui
2001-01-01
In this paper, an interpolation polynomial operator Fn (f; l, x ) is constructed based on the zeros of a kind of Jacobi polynomials as the interpolation nodes. For any continuous function f(x)∈ Cb[1,1] (0≤b≤l) Fn(f; l,x) converges to f(x) uniformly, where l is an odd number.
Optimal and approximate Q-value functions for decentralized POMDPs
F.A. Oliehoek; M.T.J. Spaan; N. Vlassis
2008-01-01
Decision-theoretic planning is a popular approach to sequential decision making problems, because it treats uncertainty in sensing and acting in a principled way. In single-agent frameworks like MDPs and POMDPs, planning can be carried out by resorting to Q-value functions: an optimal Q-value functi
H$_4$: A Challenging System For Natural Orbital Functional Approximations
Ramos-Cordoba, Eloy; Piris, Mario; Matito, Eduard
2015-01-01
The correct description of nondynamic correlation by electronic structure methods not belonging to the multireference family is a challenging issue. The transition of $D_{2h}$ to $D_{4h}$ symmetry in H$_4$ molecule is among the most simple archetypal examples to illustrate the consequences of missing nondynamic correlation effects. The resurge of interest in density matrix functional methods has brought several new methods including the family of Piris Natural Orbital Functionals (PNOF). In this work we compare PNOF5 and PNOF6, which include nondynamic electron correlation effects to some extent, with other standard ab initio methods in the H$_4$ $D_{4h}/D_{2h}$ potential energy surface. Thus far, the wrongful behavior of single-reference methods at the $D_{2h}-D_{4h}$ transition of H$_4$ has been attributed to wrong account of nondynamic correlation effects, whereas in geminal-based approaches it has been assigned to a wrong coupling of spins and the localized nature of the orbitals. We will show that actual...
Leading corrections to local approximations. II. The case with turning points
Ribeiro, Raphael F.; Burke, Kieron
2017-03-01
Quantum corrections to Thomas-Fermi (TF) theory are investigated for noninteracting one-dimensional fermions with known uniform semiclassical approximations to the density and kinetic energy. Their structure is analyzed, and contributions from distinct phase space regions (classically-allowed versus forbidden at the Fermi energy) are derived analytically. Universal formulas are derived for both particle numbers and energy components in each region. For example, in the semiclassical limit, exactly (6π √{3 }) -1 of a particle leaks into the evanescent region beyond a turning point. The correct normalization of semiclassical densities is proven analytically in the semiclassical limit. Energies and densities are tested numerically in a variety of one-dimensional potentials, especially in the limit where TF theory becomes exact. The subtle relation between the pointwise accuracy of the semiclassical approximation and integrated expectation values is explored. The limitations of the semiclassical formulas are also investigated when the potential varies too rapidly. The approximations are shown to work for multiple wells, except right at the mid-phase point of the evanescent regions. The implications for density functional approximations are discussed.
Casadei, D.
2014-10-01
The objective Bayesian treatment of a model representing two independent Poisson processes, labelled as ``signal'' and ``background'' and both contributing additively to the total number of counted events, is considered. It is shown that the reference prior for the parameter of interest (the signal intensity) can be well approximated by the widely (ab)used flat prior only when the expected background is very high. On the other hand, a very simple approximation (the limiting form of the reference prior for perfect prior background knowledge) can be safely used over a large portion of the background parameters space. The resulting approximate reference posterior is a Gamma density whose parameters are related to the observed counts. This limiting form is simpler than the result obtained with a flat prior, with the additional advantage of representing a much closer approximation to the reference posterior in all cases. Hence such limiting prior should be considered a better default or conventional prior than the uniform prior. On the computing side, it is shown that a 2-parameter fitting function is able to reproduce extremely well the reference prior for any background prior. Thus, it can be useful in applications requiring the evaluation of the reference prior for a very large number of times.
Manos, P.; Turner, L. R.
1972-01-01
Approximations which can be evaluated with precision using floating-point arithmetic are presented. The particular set of approximations thus far developed are for the function TAN and the functions of USASI FORTRAN excepting SQRT and EXPONENTIATION. These approximations are, furthermore, specialized to particular forms which are especially suited to a computer with a small memory, in that all of the approximations can share one general purpose subroutine for the evaluation of a polynomial in the square of the working argument.
Casadei, Diego
2014-01-01
The objective Bayesian treatment of a model representing two independent Poisson processes, labelled as "signal" and "background" and both contributing additively to the total number of counted events, is considered. It is shown that the reference prior for the parameter of interest (the signal intensity) is well approximated by the widely (ab)used flat prior only when the expected background is very high. For a large portion of the background parameters space, a very simple approximation (the asymptotic form of the reference prior for the limit of perfect prior background knowledge) can be safely used. In all cases, this approximation outperforms the uniform prior. When the asymptotic prior is not good enough, a simple 1-parameter fitting function is often sufficient to obtain an objective Bayesian solution. Otherwise, it is shown that a 2-parameters fitting function is able to reproduce the reference prior in all other cases. The latter is also useful to speed-up the computing time, which can be useful in a...
An approximation for zero-balanced Appell function $F_1$ near $(1,1)$
Karp, D.
2007-01-01
We suggest an approximation for the zero-balanced Appell hypergeometric function $F_1$ near the singular point $(1,1)$. Our approximation can be viewed as a generalization of Ramanujan's approximation for zero-balanced ${_2F_1}$ and is expressed in terms of ${_3F_2}$. We find an error bound and prove some basic properties of the suggested approximation which reproduce the similar properties of the Appell function. Our approximation reduces to the approximation of Carlson-Gustafson when the Ap...
Inductance and hypergeometric functions. II
DEFF Research Database (Denmark)
Karlsson, Per W.
2000-01-01
A previously obtained integral for the self-inductance of a solenoid is further transformed. The resulting formula involves double Kampé de Fériet functions which are analytic continuations rather than power series.......A previously obtained integral for the self-inductance of a solenoid is further transformed. The resulting formula involves double Kampé de Fériet functions which are analytic continuations rather than power series....
Sahu, Subrata K.; Acharya, D.; Nayak, P. C.; Misra, U. K.
2016-06-01
Trigonometric Fourier approximation and Lipchitz class of function had been introduced by Zygmund and McFadden respectively. Dealing with degree of approximation of conjugate series of a Fourier series of a function of Lipchitz class Misra et al. have established certain theorems. Extending their results, in this paper a theorem on trigonometric approximation of conjugate series of Fourier series of a function f ∈ W(Lp, ξ(t)) by product summability (E, s)(N, pn, qn) has been established.
High-Dimensional Function Approximation With Neural Networks for Large Volumes of Data.
Andras, Peter
2017-01-25
Approximation of high-dimensional functions is a challenge for neural networks due to the curse of dimensionality. Often the data for which the approximated function is defined resides on a low-dimensional manifold and in principle the approximation of the function over this manifold should improve the approximation performance. It has been show that projecting the data manifold into a lower dimensional space, followed by the neural network approximation of the function over this space, provides a more precise approximation of the function than the approximation of the function with neural networks in the original data space. However, if the data volume is very large, the projection into the low-dimensional space has to be based on a limited sample of the data. Here, we investigate the nature of the approximation error of neural networks trained over the projection space. We show that such neural networks should have better approximation performance than neural networks trained on high-dimensional data even if the projection is based on a relatively sparse sample of the data manifold. We also find that it is preferable to use a uniformly distributed sparse sample of the data for the purpose of the generation of the low-dimensional projection. We illustrate these results considering the practical neural network approximation of a set of functions defined on high-dimensional data including real world data as well.
Limit theory of restricted range approximations of complex-valued continuous functions
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This paper is concerned with the problem of the best restricted range approximations of complex-valued continuous functions. Several properties for the approximating set PΩ such that the classical characterization results and/or the uniqueness results of the best approximations hold are introduced. Under the very mild conditions, we prove that these properties are equivalent that P is a Haar subspce.
Yang, Weitao; Mori-Sánchez, Paula; Cohen, Aron J
2013-09-14
The exact conditions for density functionals and density matrix functionals in terms of fractional charges and fractional spins are known, and their violation in commonly used functionals has been shown to be the root of many major failures in practical applications. However, approximate functionals are designed for physical systems with integer charges and spins, not in terms of the fractional variables. Here we develop a general framework for extending approximate density functionals and many-electron theory to fractional-charge and fractional-spin systems. Our development allows for the fractional extension of any approximate theory that is a functional of G(0), the one-electron Green's function of the non-interacting reference system. The extension to fractional charge and fractional spin systems is based on the ensemble average of the basic variable, G(0). We demonstrate the fractional extension for the following theories: (1) any explicit functional of the one-electron density, such as the local density approximation and generalized gradient approximations; (2) any explicit functional of the one-electron density matrix of the non-interacting reference system, such as the exact exchange functional (or Hartree-Fock theory) and hybrid functionals; (3) many-body perturbation theory; and (4) random-phase approximations. A general rule for such an extension has also been derived through scaling the orbitals and should be useful for functionals where the link to the Green's function is not obvious. The development thus enables the examination of approximate theories against known exact conditions on the fractional variables and the analysis of their failures in chemical and physical applications in terms of violations of exact conditions of the energy functionals. The present work should facilitate the calculation of chemical potentials and fundamental bandgaps with approximate functionals and many-electron theories through the energy derivatives with respect to the
A. Beléndez; ALVAREZ, M. L.; Francés, J.; S. Bleda; Beléndez, T.; Nájera, A.; Arribas, E.
2012-01-01
Accurate approximate closed-form solutions for the cubic-quintic Duffing oscillator are obtained in terms of elementary functions. To do this, we use the previous results obtained using a cubication method in which the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a cubic Duffing equation. Explicit approximate solutions are then expressed as a function of the complete elliptic integral of the first kind and the Jacobi ...
Multi-point quasi-rational approximants for the modified Bessel function I1(x)
Martin, P.; Olivares, J.; Cortés-Vega, L.; Sotomayor, A.
2016-08-01
Approximants for the modified Bessel function I1(x) has been found using the multi-point quasi-rational technique. The approximations here determined has good accuracy for any positive value of the variable, and it seems to be adequate for most of the works where this function are used. Furthermore, the approximants are simple to calculate numerically in a direct way or using any usual MAPLE or MATLAB software.
APPROXIMATION OF CONVEX TYPE FUNCTION BY PARTIAL SUMS OF FOURIER SERIES
Institute of Scientific and Technical Information of China (English)
YuGuohua
2004-01-01
The concept of convex type function is introduced in this paper,from which a kind of convex-decomposition approach is proposed. As one of applications of this approach, the approximation of the convex type function by the partial sum of its Fourier series is investigated. Moreover,the order of approximation is described with the 2th continuous modulus.
UNIFORM APPROXIMATION OF ENTIRE FUNCTIONS OF SLOW GROWTH ON COMPACT SETS
Institute of Scientific and Technical Information of China (English)
G.S.Srivastava; S.Kumar
2012-01-01
In the present paper,we study the polynomial approximation of entire functions of several complex variables.The characterizations of generalized order and generalized type of entire functions of slow growth are obtained in terms of approximation and interpolation errors.
On the Rational Approximation of Analytic Functions Having Generalized Types of Rate of Growth
Directory of Open Access Journals (Sweden)
Devendra Kumar
2012-01-01
Full Text Available The present paper is concerned with the rational approximation of functions holomorphic on a domain G⊂C, having generalized types of rates of growth. Moreover, we obtain the characterization of the rate of decay of product of the best approximation errors for functions f having fast and slow rates of growth of the maximum modulus.
Institute of Scientific and Technical Information of China (English)
Fang Gensun; Ye Peixin
2005-01-01
The order of computational complexity of all bounded linear functional approximation problem is determined for the generalized Sobolev class Wp∧(Id), Nikolskii class Hk∞(Id) in the worst (deterministic), stochastic and average case setting, from which it is concluded that the bounded linear functional approximation problem for the classes stochastic and average case setting.
An Approximate Proximal Bundle Method to Minimize a Class of Maximum Eigenvalue Functions
Directory of Open Access Journals (Sweden)
Wei Wang
2014-01-01
Full Text Available We present an approximate nonsmooth algorithm to solve a minimization problem, in which the objective function is the sum of a maximum eigenvalue function of matrices and a convex function. The essential idea to solve the optimization problem in this paper is similar to the thought of proximal bundle method, but the difference is that we choose approximate subgradient and function value to construct approximate cutting-plane model to solve the above mentioned problem. An important advantage of the approximate cutting-plane model for objective function is that it is more stable than cutting-plane model. In addition, the approximate proximal bundle method algorithm can be given. Furthermore, the sequences generated by the algorithm converge to the optimal solution of the original problem.
Akhtar, T.; Shoemaker, C. A.
2009-12-01
Water Resources design decisions frequently entail trade-offs between conflicting objectives, for instance cost minimization and contaminant(s) concentration minimization. Multi-objective optimization methods (including those based on evolutionary methods) typically require a very large number of simulations to find a solution. Many groundwater remediation problems are modeled by computationally intensive systems of Partial Differential Equations and simulations. Hence it is desirable that these models are calibrated via algorithms that require less number of simulations. A new strategy called Gap Optimized Multi-Objective Optimization using Response Surfaces (GOMORS) is proposed for multi-objective optimization of computationally expensive problems. A multi-objective management framework is devised to analyze the trade-offs between conflicting objectives. We will present applications to test functions and to a groundwater contamination problem. The pumping rates at different well locations and management periods are the decision variables, and cost and contaminant concentration are the objectives to be minimized. The optimization strategy is iterative and makes use of Radial Basic Functions to develop response surfaces as an approximation of the computationally expensive objectives. A novel method called the Gap Optimization method is introduced. The gap optimization method incorporates use of a multi-objective evolutionary optimization (MOEA) method that is applied to select the next point for expensive evaluation and consequent improvement of the surrogate model. In order to provide sound alternatives to the decision makers, the evaluation point selection procedure strives to ensure that the final trade-off curve generated from the algorithm is close to the true Pareto front and includes a diverse set of solutions. After the final iteration, a set of candidate solutions is selected via the iterative Gap Optimization procedure and the last MOEA iteration, and
APPROXIMATE FUNCTION FOR UNSTEADY AERODYNAMIC KERNEL FUNCTION OF AEROELASTIC LIFTING SURFACES
Directory of Open Access Journals (Sweden)
Erwin Sulaeman
2014-05-01
Full Text Available Normal 0 false false false EN-US X-NONE X-NONE ABSTRACT: Prediction of unsteady aerodynamic loads is still the most challenging task in flutter aeroelastic analysis. Generally the numerical estimation of steady and unsteady aerodynamic of thin lifting surface is conducted based on an integral equation relating aerodynamic pressure and normal wash velocity. The present work attempts to increase the accuracy of the prediction by using an approximate approach to evaluate kernel function occurring in the integral equation in the form of cylindrical function. Following previous approximation approach by other researchers to solve the cylindrical function for planar lifting surfaces, in the present work such approach is extended to non planar lifting surfaces. To increase the accuracy of the method, the integration region of the kernel function is divided into two parts namely near and far regions, where a nonlinear regression curve fitting technique is adapted to approximate the denominator part of the cylindrical function of each region.ABSTRAK: Penelahan daya aerodinamik tidak stabil merupakan satu tugas yang mencabar dalam menganalisis getaran aeroanjalan. Umumnya, anggaran berangka untuk daya aerodinamik stabil dan tidak stabil pada permukaan mengangkat yang nipis, adalah berdasarkan kepada persamaan kamiran di antara tekanan aerodinamik dan halaju aliran udara pada garis normal yang terhasil di bawah sayap pesawat. Kajian ini adalah bertujuan untuk menghasilkan penelahan daya aerodinamik yang lebih tepat dengan menggunakan pendekatan kira hampir untuk menilai fungsi Kernel yang terdapat dalam persamaan kamiran dalam bentuk fungsi silinder. Dengan menggunakan pendekatan kira hampir yang digunakan oleh penyelidik sebelumnya untuk menyelesaikan fungsi silinder pada permukaan mengangkat satah, kajian ini mengembangkan pendekatan tersebut kepada permukaan mengangkat tak sesatah. Untuk meningkatkan lagi ketepatan penelahan, kawasan pengamiran
Sparse Signal Reconstruction Based on Multiparameter Approximation Function with Smoothed l0 Norm
Directory of Open Access Journals (Sweden)
Xiao-Feng Fang
2014-01-01
Full Text Available The smoothed l0 norm algorithm is a reconstruction algorithm in compressive sensing based on approximate smoothed l0 norm. It introduces a sequence of smoothed functions to approximate the l0 norm and approaches the solution using the specific iteration process with the steepest method. In order to choose an appropriate sequence of smoothed function and solve the optimization problem effectively, we employ approximate hyperbolic tangent multiparameter function as the approximation to the big “steep nature” in l0 norm. Simultaneously, we propose an algorithm based on minimizing a reweighted approximate l0 norm in the null space of the measurement matrix. The unconstrained optimization involved is performed by using a modified quasi-Newton algorithm. The numerical simulation results show that the proposed algorithms yield improved signal reconstruction quality and performance.
Padé approximants for inverse trigonometric functions and their applications.
Wu, Shanhe; Bercu, Gabriel
2017-01-01
The Padé approximation is a useful method for creating new inequalities and improving certain inequalities. In this paper we use the Padé approximant to give the refinements of some remarkable inequalities involving inverse trigonometric functions, it is shown that the new inequalities presented in this paper are more refined than that obtained in earlier papers.
Directory of Open Access Journals (Sweden)
W. Łenski
2015-01-01
Full Text Available The results generalizing some theorems on N, pnE, γ summability are shown. The same degrees of pointwise approximation as in earlier papers by weaker assumptions on considered functions and examined summability methods are obtained. From presented pointwise results, the estimation on norm approximation is derived. Some special cases as corollaries are also formulated.
Aarts, Ronald M; Janssen, Augustus J E M
2016-12-01
The Struve functions Hn(z), n=0, 1, ... are approximated in a simple, accurate form that is valid for all z≥0. The authors previously treated the case n = 1 that arises in impedance calculations for the rigid-piston circular radiator mounted in an infinite planar baffle [Aarts and Janssen, J. Acoust. Soc. Am. 113, 2635-2637 (2003)]. The more general Struve functions occur when other acoustical quantities and/or non-rigid pistons are considered. The key step in the paper just cited is to express H1(z) as (2/π)-J0(z)+(2/π) I(z), where J0 is the Bessel function of order zero and the first kind and I(z) is the Fourier cosine transform of [(1-t)/(1+t)](1/2), 0≤t≤1. The square-root function is optimally approximated by a linear function ĉt+d̂, 0≤t≤1, and the resulting approximated Fourier integral is readily computed explicitly in terms of sin z/z and (1-cos z)/z(2). The same approach has been used by Maurel, Pagneux, Barra, and Lund [Phys. Rev. B 75, 224112 (2007)] to approximate H0(z) for all z≥0. In the present paper, the square-root function is optimally approximated by a piecewise linear function consisting of two linear functions supported by [0,t̂0] and [t̂0,1] with t̂0 the optimal take-over point. It is shown that the optimal two-piece linear function is actually continuous at the take-over point, causing a reduction of the additional complexity in the resulting approximations of H0 and H1. Furthermore, this allows analytic computation of the optimal two-piece linear function. By using the two-piece instead of the one-piece linear approximation, the root mean square approximation error is reduced by roughly a factor of 3 while the maximum approximation error is reduced by a factor of 4.5 for H0 and of 2.6 for H1. Recursion relations satisfied by Struve functions, initialized with the approximations of H0 and H1, yield approximations for higher order Struve functions.
Directory of Open Access Journals (Sweden)
A. Beléndez
2012-01-01
Full Text Available Accurate approximate closed-form solutions for the cubic-quintic Duffing oscillator are obtained in terms of elementary functions. To do this, we use the previous results obtained using a cubication method in which the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a cubic Duffing equation. Explicit approximate solutions are then expressed as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function cn. Then we obtain other approximate expressions for these solutions, which are expressed in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean is used and the rational harmonic balance method is applied to obtain the periodic solution of the original nonlinear oscillator.
Discrete Least-norm Approximation by Nonnegative (Trigonomtric) Polynomials and Rational Functions
Siem, A.Y.D.; de Klerk, E.; den Hertog, D.
2005-01-01
Polynomials, trigonometric polynomials, and rational functions are widely used for the discrete approximation of functions or simulation models.Often, it is known beforehand, that the underlying unknown function has certain properties, e.g. nonnegative or increasing on a certain region.However, the
Discrete Least-norm Approximation by Nonnegative (Trigonomtric) Polynomials and Rational Functions
Siem, A.Y.D.; de Klerk, E.; den Hertog, D.
2005-01-01
Polynomials, trigonometric polynomials, and rational functions are widely used for the discrete approximation of functions or simulation models.Often, it is known beforehand, that the underlying unknown function has certain properties, e.g. nonnegative or increasing on a certain region.However, the
Optimal approximation method to characterize the resource trade-off functions for media servers
Chang, Ray-I.
1999-08-01
We have proposed an algorithm to smooth the transmission of the pre-recorded VBR media stream. It takes O(n) time complexity, where n is large, this algorithm is not suitable for online resource management and admission control in media servers. To resolve this drawback, we have explored the optimal tradeoff among resources by an O(nlogn) algorithm. Based on the pre-computed resource tradeoff function, the resource management and admission control procedure is as simple as table hashing. However, this approach requires O(n) space to store and maintain the resource tradeoff function. In this paper, while giving some extra resources, a linear-time algorithm is proposed to approximate the resource tradeoff function by piecewise line segments. We can prove that the number of line segments in the obtained approximation function is minimized for the given extra resources. The proposed algorithm has been applied to approximate the bandwidth-buffer-tradeoff function of the real-world Star War movie. While an extra 0.1 Mbps bandwidth is given, the storage space required for the approximation function is over 2000 times smaller than that required for the original function. While an extra 10 KB buffer is given, the storage space for the approximation function is over 2200 over times smaller than that required for the original function. The proposed algorithm is really useful for resource management and admission control in real-world media servers.
The exact order of approximation to periodic functions by Bernstein-Stechkin polynomials
Energy Technology Data Exchange (ETDEWEB)
Trigub, R M [Donetsk National University, Donetsk (Ukraine)
2013-12-31
The paper concerns the approximation properties of the Bernstein-Stechkin summability method for trigonometric Fourier series. The Jackson-Stechkin theorem is refined. Moreover, for any continuous periodic function not only is the exact upper estimate for approximation found, a lower estimate of the same order is also put forward. To do this special moduli of smoothness and the K-functional are introduced. Bibliography: 16 titles.
An analytical approximation of the growth function in Friedmann-Lema\\^itre universes
Kasai, Masumi
2010-01-01
We present an analytical approximation formula for the growth function in a spatially flat cosmology with dust and a cosmological constant. Our approximate formula is written simply in terms of a rational function. We also show the approximate formula in a dust cosmology without a cosmological constant, directly as a function of the scale factor in terms of a rational function. The single rational function applies for all, open, closed and flat universes. Our results involve no elliptic functions, and have very small relative error of less than 0.2 per cent over the range of the scale factor $1/1000 \\la a \\lid 1$ and the density parameter $0.2 \\la \\Omega_{\\rmn{m}} \\lid 1$ for a flat cosmology, and less than $0.4$ per cent over the range $0.2 \\la \\Omega_{\\rmn{m}} \\la 4$ for a cosmology without a cosmological constant.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Zhenyue [Zhejiang Univ., Hangzhou (People' s Republic of China); Zha, Hongyuan [Pennsylvania State Univ., University Park, PA (United States); Simon, Horst [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2006-07-31
In this paper, we developed numerical algorithms for computing sparse low-rank approximations of matrices, and we also provided a detailed error analysis of the proposed algorithms together with some numerical experiments. The low-rank approximations are constructed in a certain factored form with the degree of sparsity of the factors controlled by some user-specified parameters. In this paper, we cast the sparse low-rank approximation problem in the framework of penalized optimization problems. We discuss various approximation schemes for the penalized optimization problem which are more amenable to numerical computations. We also include some analysis to show the relations between the original optimization problem and the reduced one. We then develop a globally convergent discrete Newton-like iterative method for solving the approximate penalized optimization problems. We also compare the reconstruction errors of the sparse low-rank approximations computed by our new methods with those obtained using the methods in the earlier paper and several other existing methods for computing sparse low-rank approximations. Numerical examples show that the penalized methods are more robust and produce approximations with factors which have fewer columns and are sparser.
The Cosmic Linear Anisotropy Solving System (CLASS). Part II: Approximation schemes
Energy Technology Data Exchange (ETDEWEB)
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.
U(1 )×SU (2 ) gauge invariance made simple for density functional approximations
Pittalis, S.; Vignale, G.; Eich, F. G.
2017-07-01
A semirelativistic density-functional theory that includes spin-orbit couplings and Zeeman fields on equal footing with the electromagnetic potentials, is an appealing framework to develop a unified first-principles computational approach for noncollinear magnetism, spintronics, orbitronics, and topological states. The basic variables of this theory include the paramagnetic current and the spin-current density, besides the particle and the spin density, and the corresponding exchange-correlation (xc) energy functional is invariant under local U (1 )×SU (2 ) gauge transformations. The xc-energy functional must be approximated to enable practical applications, but, contrary to the case of the standard density functional theory, finding simple approximations suited to deal with realistic atomistic inhomogeneities has been a long-standing challenge. Here we propose a way out of this impasse by showing that approximate gauge-invariant functionals can be easily generated from existing approximate functionals of ordinary density-functional theory by applying a simple minimal substitution on the kinetic energy density, which controls the short-range behavior of the exchange hole. Our proposal opens the way to the construction of approximate, yet nonempirical functionals, which do not assume weak inhomogeneity and therefore may have a wide range of applicability in atomic, molecular, and condensed matter physics.
Approximation of Functions of Two Variables by Certain Linear Positive Operators
Indian Academy of Sciences (India)
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.
Isgur–Wise function in a QCD-inspired potential model with WKB approximation
Indian Academy of Sciences (India)
BHASKAR JYOTI HAZARIKA; D K CHOUDHURY
2017-03-01
We use Wentzel–Kramers–Brillouin (WKB) approximation for calculating the slope and curvature of Isgur–Wise function in a QCD-inspired potential model. This work is an extension of the approximation methods to the QCD-inspired potential model. The approach hints at an effective range of distance for calculating the slope and curvature of Isgur–Wise function. Comparison is also made with those of Dalgarno method and variationallyimproved perturbation theory (VIPT) as well as other models to show the advantages of using WKB approximation.
Isgur-Wise function in a QCD-inspired potential model with WKB approximation
Hazarika, Bhaskar Jyoti; Choudhury, D. K.
2017-03-01
We use Wentzel-Kramers-Brillouin (WKB) approximation for calculating the slope and curvature of Isgur-Wise function in a QCD-inspired potential model. This work is an extension of the approximation methods to the QCD-inspired potential model. The approach hints at an effective range of distance for calculating the slope and curvature of Isgur-Wise function. Comparison is also made with those of Dalgarno method and variationally improved perturbation theory (VIPT) as well as other models to show the advantages of using WKB approximation.
Kushwaha, Jitendra Kumar
2013-01-01
Approximation theory is a very important field which has various applications in pure and applied mathematics. The present study deals with a new theorem on the approximation of functions of Lipschitz class by using Euler's mean of conjugate series of Fourier series. In this paper, the degree of approximation by using Euler's means of conjugate of functions belonging to Lip (ξ(t), p) class has been obtained. Lipα and Lip (α, p) classes are the particular cases of Lip (ξ(t), p) class. The main result of this paper generalizes some well-known results in this direction.
Monotone Approximations of Minimum and Maximum Functions and Multi-objective Problems
Energy Technology Data Exchange (ETDEWEB)
Stipanovic, Dusan M., E-mail: dusan@illinois.edu [University of Illinois at Urbana-Champaign, Coordinated Science Laboratory, Department of Industrial and Enterprise Systems Engineering (United States); Tomlin, Claire J., E-mail: tomlin@eecs.berkeley.edu [University of California at Berkeley, Department of Electrical Engineering and Computer Science (United States); Leitmann, George, E-mail: gleit@berkeley.edu [University of California at Berkeley, College of Engineering (United States)
2012-12-15
In this paper the problem of accomplishing multiple objectives by a number of agents represented as dynamic systems is considered. Each agent is assumed to have a goal which is to accomplish one or more objectives where each objective is mathematically formulated using an appropriate objective function. Sufficient conditions for accomplishing objectives are derived using particular convergent approximations of minimum and maximum functions depending on the formulation of the goals and objectives. These approximations are differentiable functions and they monotonically converge to the corresponding minimum or maximum function. Finally, an illustrative pursuit-evasion game example with two evaders and two pursuers is provided.
Toulouse, Julien; Angyan, Janos G; Savin, Andreas
2010-01-01
Using Green-function many-body theory, we present the details of a formally exact adiabatic-connection fluctuation-dissipation density-functional theory based on range separation, which was sketched in Toulouse, Gerber, Jansen, Savin and Angyan, Phys. Rev. Lett. 102, 096404 (2009). Range-separated density-functional theory approaches combining short-range density functional approximations with long-range random phase approximations (RPA) are then obtained as well-identified approximations on the long-range Green-function self-energy. Range-separated RPA-type schemes with or without long-range Hartree-Fock exchange response kernel are assessed on rare-gas and alkaline-earth dimers, and compared to range-separated second-order perturbation theory and range-separated coupled-cluster theory.
Adiabatic approximation of time-dependent density matrix functional response theory.
Pernal, Katarzyna; Giesbertz, Klaas; Gritsenko, Oleg; Baerends, Evert Jan
2007-12-07
Time-dependent density matrix functional theory can be formulated in terms of coupled-perturbed response equations, in which a coupling matrix K(omega) features, analogous to the well-known time-dependent density functional theory (TDDFT) case. An adiabatic approximation is needed to solve these equations, but the adiabatic approximation is much more critical since there is not a good "zero order" as in TDDFT, in which the virtual-occupied Kohn-Sham orbital energy differences serve this purpose. We discuss a simple approximation proposed earlier which uses only results from static calculations, called the static approximation (SA), and show that it is deficient, since it leads to zero response of the natural orbital occupation numbers. This leads to wrong behavior in the omega-->0 limit. An improved adiabatic approximation (AA) is formulated. The two-electron system affords a derivation of exact coupled-perturbed equations for the density matrix response, permitting analytical comparison of the adiabatic approximation with the exact equations. For the two-electron system also, the exact density matrix functional (2-matrix in terms of 1-matrix) is known, enabling testing of the static and adiabatic approximations unobscured by approximations in the functional. The two-electron HeH(+) molecule shows that at the equilibrium distance, SA consistently underestimates the frequency-dependent polarizability alpha(omega), the adiabatic TDDFT overestimates alpha(omega), while AA improves upon SA and, indeed, AA produces the correct alpha(0). For stretched HeH(+), adiabatic density matrix functional theory corrects the too low first excitation energy and overpolarization of adiabatic TDDFT methods and exhibits excellent agreement with high-quality CCSD ("exact") results over a large omega range.
Lavrentiev's approximation theorem with nonvanishing polynomials and universality of zeta-functions
Andersson, Johan
2010-01-01
We prove a variant of the Lavrentiev's approximation theorem that allows us to approximate a continuous function on a compact set K in C without interior points and with connected complement, with polynomial functions that are nonvanishing on K. We use this result to obtain a version of the Voronin universality theorem for compact sets K, without interior points and with connected complement where it is sufficient that the function is continuous on K and the condition that it is nonvanishing can be removed. This implies a special case of a criterion of Bagchi, which in the general case has been proven to be equivalent to the Riemann hypothesis.
Approximating the Influence of a monotone Boolean function in O(\\sqrt{n}) query complexity
Ron, Dana; Rubinfeld, Ronitt; Safra, Muli; Weinstein, Omri
2011-01-01
The {\\em Total Influence} ({\\em Average Sensitivity) of a discrete function is one of its fundamental measures. We study the problem of approximating the total influence of a monotone Boolean function \\ifnum\\plusminus=1 $f: \\{\\pm1\\}^n \\longrightarrow \\{\\pm1\\}$, \\else $f: \\bitset^n \\to \\bitset$, \\fi which we denote by $I[f]$. We present a randomized algorithm that approximates the influence of such functions to within a multiplicative factor of $(1\\pm \\eps)$ by performing $O(\\frac{\\sqrt{n}\\log...
On the Method of Multiplier-enlargement and Approximation of Unbounded Continuous Functions
Institute of Scientific and Technical Information of China (English)
ZHENG Cheng-De; WANG Ren-Hong
2001-01-01
By combining the classical appropriate functions “1, x, x2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite-Fejéinterpolation polynomial operators are analysed and studied, and a general conclusion is obtained.
ON THE CONVERGENCE OF AN APPROXIMATE PROXIMAL METHOD FOR DC FUNCTIONS
Institute of Scientific and Technical Information of China (English)
A. Moudafi; P-E. Maingé
2006-01-01
In this paper we prove the convergence of the approximate proximal method for DC functions proposed by Sun et al [6]. Our analysis also permits to treat the exact method.We then propose an interesting result in the case where the second component of the DC function is differentiable and provide some computational experiences which proved the efficiency of our method.
Energy Technology Data Exchange (ETDEWEB)
Trigub, R M [Donetsk National University, Donetsk (Ukraine)
2009-08-31
We prove a general direct theorem on the simultaneous pointwise approximation of smooth periodic functions and their derivatives by trigonometric polynomials and their derivatives with Hermitian interpolation. We study the order of approximation by polynomials whose graphs lie above or below the graph of the function on certain intervals. We prove several inequalities for Hermitian interpolation with absolute constants (for any system of nodes). For the first time we get a theorem on the best-order approximation of functions by polynomials with interpolation at a given system of nodes. We also provide a construction of Hermitian interpolating trigonometric polynomials for periodic functions (in the case of one node, these are trigonometric Taylor polynomials)
DEFF Research Database (Denmark)
Dohn, Asmus Ougaard; Møller, Klaus Braagaard; Sauer, Stephan P. A.
2013-01-01
The geometry of tetracyanoplatinate(II) (TCP) has been optimized with density functional theory (DFT) calculations in order to compare different computational strategies. Two approximate scalar relativistic methods, i.e. the scalar zeroth-order regular approximation (ZORA) and non-relativistic ca...
Matrix Product Approximations to Multipoint Functions in Two-Dimensional Conformal Field Theory
König, Robert; Scholz, Volkher B.
2016-09-01
Matrix product states (MPSs) illustrate the suitability of tensor networks for the description of interacting many-body systems: ground states of gapped 1D systems are approximable by MPSs, as shown by Hastings [M. B. Hastings, J. Stat. Mech. (2007) P08024]. By contrast, whether MPSs and more general tensor networks can accurately reproduce correlations in critical quantum systems or quantum field theories has not been established rigorously. Ample evidence exists: entropic considerations provide restrictions on the form of suitable ansatz states, and numerical studies show that certain tensor networks can indeed approximate the associated correlation functions. Here, we provide a complete positive answer to this question in the case of MPSs and 2D conformal field theory: we give quantitative estimates for the approximation error when approximating correlation functions by MPSs. Our work is constructive and yields an explicit MPS, thus providing both suitable initial values and a rigorous justification of variational methods.
Elfwing, Stefan; Uchibe, Eiji; Doya, Kenji
2016-12-01
Free-energy based reinforcement learning (FERL) was proposed for learning in high-dimensional state and action spaces. However, the FERL method does only really work well with binary, or close to binary, state input, where the number of active states is fewer than the number of non-active states. In the FERL method, the value function is approximated by the negative free energy of a restricted Boltzmann machine (RBM). In our earlier study, we demonstrated that the performance and the robustness of the FERL method can be improved by scaling the free energy by a constant that is related to the size of network. In this study, we propose that RBM function approximation can be further improved by approximating the value function by the negative expected energy (EERL), instead of the negative free energy, as well as being able to handle continuous state input. We validate our proposed method by demonstrating that EERL: (1) outperforms FERL, as well as standard neural network and linear function approximation, for three versions of a gridworld task with high-dimensional image state input; (2) achieves new state-of-the-art results in stochastic SZ-Tetris in both model-free and model-based learning settings; and (3) significantly outperforms FERL and standard neural network function approximation for a robot navigation task with raw and noisy RGB images as state input and a large number of actions.
Energy Technology Data Exchange (ETDEWEB)
Krasilnikov, M. B., E-mail: mihail.krasilnikov@gmail.com; Kudryavtsev, A. A. [St. Petersburg State University, St. Petersburg 198504 (Russian Federation); Kapustin, K. D. [St. Petersburg University ITMO, St. Petersburg 197101 (Russian Federation)
2014-12-15
It is shown that the local approximation for computing the electron distribution function depends both on the ratio between the energy relaxation length and a characteristic plasma length and on the ratio between heating and ambipolar electric fields. In particular, the local approximation is not valid at the discharge periphery even at high pressure due to the fact that the ambipolar electric field practically always is larger than the heating electric field.
The Chebyshev-polynomials-based unified model neural networks for function approximation.
Lee, T T; Jeng, J T
1998-01-01
In this paper, we propose the approximate transformable technique, which includes the direct transformation and indirect transformation, to obtain a Chebyshev-Polynomials-Based (CPB) unified model neural networks for feedforward/recurrent neural networks via Chebyshev polynomials approximation. Based on this approximate transformable technique, we have derived the relationship between the single-layer neural networks and multilayer perceptron neural networks. It is shown that the CPB unified model neural networks can be represented as a functional link networks that are based on Chebyshev polynomials, and those networks use the recursive least square method with forgetting factor as learning algorithm. It turns out that the CPB unified model neural networks not only has the same capability of universal approximator, but also has faster learning speed than conventional feedforward/recurrent neural networks. Furthermore, we have also derived the condition such that the unified model generating by Chebyshev polynomials is optimal in the sense of error least square approximation in the single variable ease. Computer simulations show that the proposed method does have the capability of universal approximator in some functional approximation with considerable reduction in learning time.
Barber, Michael N.
1980-03-01
An algorithm for determining the sequence of variational parameters in a variational approximation to a real-space renormalization group is developed. Using this procedure, the Kadanoff one-hypercube approximation for the two-dimensional Ising model is investigated in some detail. We conclude that the apparent success of this method is somewhat fortuitous; a consistent and completely optimized treatment yielding considerably poorer estimates of the specific heat exponents. In addition, the variational parameter is found to be non-analytic at the fixed point. The nature of singularity agrees with the predictions of van Saarloos, van Leeuwen, and Pruisken.
Parameter selection of support vector machine for function approximation based on chaos optimization
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The support vector machine (SVM) is a novel machine learning method,which has the ability to approximate nonlinear functions with arbitrary accuracy.Setting parameters well is very crucial for SVM learning results and generalization ability,and now there is no systematic,general method for parameter selection.In this article,the SVM parameter selection for function approximation is regarded as a compound optimization problem and a mutative scale chaos optimization algorithm is employed to search for optimal parameter values.The chaos optimization algorithm is an effective way for global optimal and the mutative scale chaos algorithm could improve the search efficiency and accuracy.Several simulation examples show the sensitivity of the SVM parameters and demonstrate the superiority of this proposed method for nonlinear function approximation.
Directory of Open Access Journals (Sweden)
Cristinel Mortici
2015-01-01
Full Text Available In this survey we present our recent results on analysis of gamma function and related functions. The results obtained are in the theory of asymptotic analysis, approximation of gamma and polygamma functions, or in the theory of completely monotonic functions. The motivation of this first part is the work of C. Mortici [Product Approximations via Asymptotic Integration Amer. Math. Monthly 117 (2010 434-441] where a simple strategy for constructing asymptotic series is presented. The classical asymptotic series associated to Stirling, Wallis, Glaisher-Kinkelin are rediscovered. In the second section we discuss some new inequalities related to Landau constants and we establish some asymptotic formulas.
Trigonometric polynomial approximation, K-functionals and generalized moduli of smoothness
Runovskii, K. V.
2017-02-01
Best approximation and approximation by families of linear polynomial operators (FLPO) in the spaces L_p, 0, are investigated for periodic functions of an arbitrary number of variables in terms of the generalized modulus of smoothness generated by a periodic generator which, near the origin, is assumed to be close in a certain sense to some homogeneous function of positive order. Direct and inverse theorems (Jackson- and Bernstein-type estimates) are proved; conditions on the generators are obtained under which the approximation error by an FLPO is equivalent to an appropriate modulus of smoothness. These problems are solved by going over from the modulus to an equivalent K-functional. The general results obtained are applied to classical objects in the theory of approximation and smoothness. In particular, they are applied to the methods of approximation generated by Fejér, Riesz and Bochner-Riesz kernels, and also to the moduli of smoothness and K-functionals corresponding to the conventional, Weyl and Riesz derivatives and to the Laplace operator. Bibliography: 24 titles.
Bridge density functional approximation for non-uniform hard core repulsive Yukawa fluid
Institute of Scientific and Technical Information of China (English)
Zhou Shi-Qi
2008-01-01
In this work,a bridge density functional approximation(BDFA)(J.Chem.Phys.112,8079(2000))for a non-uniform hard-sphere fluid is extended to a non-uniform hard-core repulsive Yukawa(HCRY)fluid.It is found that the choice of a bulk bridge functional approximation is crucial for both a uniform HCRY fluid and a non-uniform HCRY fluid.A new bridge functional approximation is proposed,which can accurately predict the radial distribution function of the bulk HCRY fluid.With the new bridge functional approximation and its associated bulk second order direct correlation function as input,the BDFA can be used to well calculate the density profile of the HCRY fluid subjected to the influence of varying external fields,and the theoretical predictions are in good agreement with the corresponding simulation data.The calculated results indicate that the present BDFA captures quantitatively the phenomena such as the coexistence of solid-like high density phase and low density gas phase,and the adsorption properties of the HCRY fluid,which qualitatively differ from those of the fluids combining both hard-core repulsion and an attractive tail.
On the approximations of the distribution function of fusion alpha particles
Energy Technology Data Exchange (ETDEWEB)
Bilato, R., E-mail: roberto.bilato@ipp.mpg.de; Brambilla, M.; Poli, E. [Max Planck Institute for Plasma Physics, EURATOM Association, Boltzmannstr. 2, 85748 Garching (Germany)
2014-10-15
The solution of the drift-kinetic equation for fusion-born alpha particles is derived in the limit of dominant parallel streaming, and it is related to the usual slowing-down distribution function. The typical approximations of the fast tail of fusion-born alpha particles are briefly compared and discussed. In particular, approximating the distribution function of fast-alpha particles with an “equivalent” Maxwellian is inaccurate to describe absorption of radio-frequency waves in the ion-cyclotron range of frequencies.
Slow Growth and Optimal Approximation of Pseudoanalytic Functions on the Disk
Directory of Open Access Journals (Sweden)
Devendra Kumar
2013-07-01
Full Text Available Pseudoanalytic functions (PAF are constructed as complex combination of real-valued analytic solutions to the Stokes-Betrami System. These solutions include the generalized biaxisymmetric potentials. McCoy [10] considered the approximation of pseudoanalytic functions on the disk. Kumar et al. [9] studied the generalized order and generalized type of PAF in terms of the Fourier coefficients occurring in its local expansion and optimal approximation errors in Bernstein sense on the disk. The aim of this paper is to improve the results of McCoy [10] and Kumar et al. [9]. Our results apply satisfactorily for slow growth.
Kocifaj, Miroslav
2011-06-10
The approximate bulk-scattering phase function of a polydisperse system of dust particles is derived in an analytical form. In the theoretical solution, the particle size distribution is modeled by a modified gamma function that can satisfy various media differing in modal radii. Unlike the frequently applied power law, the modified gamma distribution shows no singularity when the particle radius approaches zero. The approximate scattering phase function is related to the parameters of the size distribution function. This is an important advantage compared to the empirical Henyey-Greenstein (HG) approximation, which is a simple function of the average cosine. However, any optimized value of average cosine of the HG function cannot provide the information on particle microphysical characteristics, such as the size distribution function. In this paper, the mapping between average cosine and the parameters of size distribution function is given by a semianalytical expression that is applicable in rapid numerical simulations on various dust populations. In particular, the modal radius and half-width can be quickly estimated using the presented formulas.
A full scale approximation of covariance functions for large spatial data sets
Sang, Huiyan
2011-10-10
Gaussian process models have been widely used in spatial statistics but face tremendous computational challenges for very large data sets. The model fitting and spatial prediction of such models typically require O(n 3) operations for a data set of size n. Various approximations of the covariance functions have been introduced to reduce the computational cost. However, most existing approximations cannot simultaneously capture both the large- and the small-scale spatial dependence. A new approximation scheme is developed to provide a high quality approximation to the covariance function at both the large and the small spatial scales. The new approximation is the summation of two parts: a reduced rank covariance and a compactly supported covariance obtained by tapering the covariance of the residual of the reduced rank approximation. Whereas the former part mainly captures the large-scale spatial variation, the latter part captures the small-scale, local variation that is unexplained by the former part. By combining the reduced rank representation and sparse matrix techniques, our approach allows for efficient computation for maximum likelihood estimation, spatial prediction and Bayesian inference. We illustrate the new approach with simulated and real data sets. © 2011 Royal Statistical Society.
Mean-field approximation for spacing distribution functions in classical systems
González, Diego Luis; Pimpinelli, Alberto; Einstein, T. L.
2012-01-01
We propose a mean-field method to calculate approximately the spacing distribution functions p(n)(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p(n)(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.
Higher accurate approximate solutions for the simple pendulum in terms of elementary functions
Energy Technology Data Exchange (ETDEWEB)
Belendez, Augusto; Frances, Jorge; Ortuno, Manuel; Gallego, Sergi; Guillermo Bernabeu, Jose, E-mail: a.belendez@ua.e [Departamento de Fisica, IngenierIa de Sistemas y TeorIa de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2010-05-15
A closed-form approximate expression for the solution of a simple pendulum in terms of elementary functions is obtained. To do this, the exact expression for the maximum tension of the string of the pendulum is first considered and a trial approximate solution depending on some parameters is used, which is substituted in the tension equation. We obtain the parameters for the approximate by means of a term-by-term comparison of the power series expansion for the approximate maximum tension with the corresponding series for the exact one. We believe that this letter may be a suitable and fruitful exercise for teaching and better understanding nonlinear oscillations of a simple pendulum in undergraduate courses on classical mechanics. (letters and comments)
Feil, T. M.; Homeier, H. H. H.
2004-04-01
We present programs for the calculation and evaluation of special type Hermite-Padé-approximations. They allow the user to either numerically approximate multi-valued functions represented by a formal series expansion or to compute explicit approximants for them. The approximation scheme is based on Hermite-Padé polynomials and includes both Padé and algebraic approximants as limiting cases. The algorithm for the computation of the Hermite-Padé polynomials is based on a set of recursive equations which were derived from a generalization of continued fractions. The approximations retain their validity even on the cuts of the complex Riemann surface which allows for example the calculation of resonances in quantum mechanical problems. The programs also allow for the construction of multi-series approximations which can be more powerful than most summation methods. Program summaryTitle of program: hp.sr Catalogue identifier: ADSO Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSO Program obtainable from: CPC Program Library, Queen's University Belfast, Northern Ireland Licensing provisions: Persons requesting the program must sign the standard CPC non-profit use license Computer: Sun Ultra 10 Installation: Computing Center, University of Regensburg, Germany Operating System: Sun Solaris 7.0 Program language used: MapleV.5 Distribution format: tar gzip file Memory required to execute with typical data: 32 MB; the program itself needs only about 20 kB Number of bits in a word: 32 No. of processors used: 1 Has the code been vectorized?: no No. of bytes in distributed program, including test data etc.: 38194 No. of lines in distributed program, including test data, etc.: 4258 Nature of physical problem: Many physical and chemical quantum systems lead to the problem of evaluating a function for which only a limited series expansion is known. These functions can be numerically approximated by summation methods even if the corresponding series is only asymptotic
Nth-order flat approximation of the signum function by a polynomial
Hosenthien, H. H.
1972-01-01
In the interval studied, the signum function, sgn x, was demonstrated to be uniquely approximated by an odd polynomial f sub n (x) of order 2n-1, for which the approximation is nth order flat with respect to the points (1,1) and (-1,-1). A theorem was proved which states that for even integers n or = 2, the approximating polynomial has a pair of nonzero real roots + or - x sub n such that the x sub n form a monotonically decreasing sequence which converges to the root of 2 as n approaches infinity. For odd n i, f sub n (x) represents a strictly increasing monotonic function for all real x. As n tends to infinity, f sub n (x) converges to sgn x uniformly in two interval ranges.
Sparse Approximation of Images Inspired from the Functional Architecture of the Primary Visual Areas
Directory of Open Access Journals (Sweden)
Laurent Perrinet
2007-01-01
Full Text Available Several drawbacks of critically sampled wavelets can be solved by overcomplete multiresolution transforms and sparse approximation algorithms. Facing the difficulty to optimize such nonorthogonal and nonlinear transforms, we implement a sparse approximation scheme inspired from the functional architecture of the primary visual cortex. The scheme models simple and complex cell receptive fields through log-Gabor wavelets. The model also incorporates inhibition and facilitation interactions between neighboring cells. Functionally these interactions allow to extract edges and ridges, providing an edge-based approximation of the visual information. The edge coefficients are shown sufficient for closely reconstructing the images, while contour representations by means of chains of edges reduce the information redundancy for approaching image compression. Additionally, the ability to segregate the edges from the noise is employed for image restoration.
Robust Validation Of Approximate 1-Matrix Functionals With Few-Electron Harmonium Atoms
Cioslowski, Jerzy; Matito, Eduard
2015-01-01
A simple comparison between the exact and approximate correlation components U of the electron-electron repulsion energy of several states of few-electron harmonium atoms with varying confinement strengths provides a superior validation tool for 1-matrix functionals. The robustness of this tool is clearly demonstrated in a survey of 14 known functionals, which reveals their substandard performance within different electron correlation regimes. Unlike spot-testing that employs dissociation curves of diatomic molecules or more extensive benchmarking against experimental atomization energies of molecules comprising one of standard sets, the present approach not only uncovers the flaws and patent failures of the functionals but, even more importantly, allows for pinpointing their root causes. Since the approximate values of U are computed at exact 1-densities, the testing requires minimal programming, and thus is particularly useful in quick screening of new functionals.
Two-component hybrid time-dependent density functional theory within the Tamm-Dancoff approximation
Energy Technology Data Exchange (ETDEWEB)
Kühn, Michael [Institut für Physikalische Chemie, Karlsruher Institut für Technologie, Kaiserstraße 12, 76131 Karlsruhe (Germany); Weigend, Florian, E-mail: florian.weigend@kit.edu [Institut für Physikalische Chemie, Karlsruher Institut für Technologie, Kaiserstraße 12, 76131 Karlsruhe (Germany); Institut für Nanotechnologie, Karlsruher Institut für Technologie, Postfach 3640, 76021 Karlsruhe (Germany)
2015-01-21
We report the implementation of a two-component variant of time-dependent density functional theory (TDDFT) for hybrid functionals that accounts for spin-orbit effects within the Tamm-Dancoff approximation (TDA) for closed-shell systems. The influence of the admixture of Hartree-Fock exchange on excitation energies is investigated for several atoms and diatomic molecules by comparison to numbers for pure density functionals obtained previously [M. Kühn and F. Weigend, J. Chem. Theory Comput. 9, 5341 (2013)]. It is further related to changes upon switching to the local density approximation or using the full TDDFT formalism instead of TDA. Efficiency is demonstrated for a comparably large system, Ir(ppy){sub 3} (61 atoms, 1501 basis functions, lowest 10 excited states), which is a prototype molecule for organic light-emitting diodes, due to its “spin-forbidden” triplet-singlet transition.
Irregular sampling, Toeplitz matrices, and the approximation of entire functions of exponential type
Gröchenig, Karlheinz
In many applications one seeks to recover an entire function of exponential type from its non-uniformly spaced samples. Whereas the mathematical theory usually addresses the question of when such a function in L^2(R) can be recovered, numerical methods operate with a finite-dimensional model. The numerical reconstruction or approximation of the original function amounts to the solution of a large linear system. We show that the solutions of a particularly efficient discrete model in which the data are fit by trigonometric polynomials converge to the solution of the original infinite-dimensional reconstruction problem. This legitimatizes the numerical computations and explains why the algorithms employed produce reasonable results. The main mathematical result is a new type of approximation theorem for entire functions of exponential type from a finite number of values. From another point of view our approach provides a new method for proving sampling theorems.
A viscous-convective instability in laminar Keplerian thin discs. II. Anelastic approximation
Shakura, N
2015-01-01
Using the anelastic approximation of linearised hydrodynamic equations, we investigate the development of axially symmetric small perturbations in thin Keplerian discs. The sixth-order dispersion equation is derived and numerically solved for different values of relevant physical parameters (viscosity, heat conductivity, disc semi-thickness and vertical structure). The analysis reveals the appearance of two overstable modes which split out from the classical Rayleigh inertial modes in a wide range of the parameters in both ionized and neutral gases. These modes have a viscous-convective nature and can serve as a seed for turbulence in astrophysical discs even in the absence of magnetic fields.
Yurkin, Maxim A; Hoekstra, Alfons G
2006-01-01
We propose an extrapolation technique that allows accuracy improvement of the discrete dipole approximation computations. The performance of this technique was studied empirically based on extensive simulations for 5 test cases using many different discretizations. The quality of the extrapolation improves with refining discretization reaching extraordinary performance especially for cubically shaped particles. A two order of magnitude decrease of error was demonstrated. We also propose estimates of the extrapolation error, which were proven to be reliable. Finally we propose a simple method to directly separate shape and discretization errors and illustrated this for one test case.
Institute of Scientific and Technical Information of China (English)
ZHANG Juliang; ZHANG Xiangsun
2002-01-01
A robust SQP method, which is analogous to Facchinei's algorithm, is intro duced. The algorithm is globally convergent. It uses automatic rules for choosing penalty parameter, and can efficiently cope with the possible inconsistency of the quadratic search subproblem. In addition, the algorithm employs a differentiable approximate exact penalty function as a merit function. Unlike the merit function in Facchinei's algorithm, which is quite complicated and is not easy to be implemented in practice, this new merit function is very simple. As a result, we can use the Facchinei's idea to construct an algorithm which is easy to be implemented in practice.
Approximation of functions in Besov space by deferred Cesàro mean
Directory of Open Access Journals (Sweden)
Mradul Veer Singh
2016-04-01
Full Text Available Abstract In this paper we study the degree of approximation of functions (signals in a Besov space by trigonometric polynomials using deferred Cesàro mean. We also deduce a few corollaries of our main result and compare them with the existing results.
On Approximation of Function Classes in Lorentz Spaces with Anisotropic Norm
Institute of Scientific and Technical Information of China (English)
G.Akishev
2013-01-01
In this paper, Lorentz space of functions of several variables and Besov’s class are considered. We establish an exact approximation order of Besov’s class by partial sums of Fourier ’s series for multiple trigonometric system.
Ayral, Thomas; Parcollet, Olivier
2016-08-01
We discuss a generalization of the dynamical mean field theory (DMFT) for strongly correlated systems close to a Mott transition based on a systematic approximation of the fully irreducible four-point vertex. It is an atomic-limit approximation of a functional of the one- and two-particle Green functions, built with the second Legendre transform of the free energy with respect to the two-particle Green function. This functional is represented diagrammatically by four-particle irreducible (4PI) diagrams. Like the dynamical vertex approximation (D Γ A ), the fully irreducible vertex is computed from a quantum impurity model whose bath is self-consistently determined by solving the parquet equations. However, in contrast with D Γ A and DMFT, the interaction term of the impurity model is also self-consistently determined. The method interpolates between the parquet approximation at weak coupling and the atomic limit, where it is exact. It is applicable to systems with short-range and long-range interactions.
Sum Rule Constraints and the Quality of Approximate Kubo-Transformed Correlation Functions.
Hernández de la Peña, Lisandro
2016-02-11
In this work, a general protocol for evaluating the quality of approximate Kubo correlation functions of nontrivial systems in many dimensions is discussed. We first note that the generalized deconvolution of the Kubo transformed correlation function onto a time correlation function at a given value τ in imaginary time, such that 0 function and whose iterative extension allows us to link derivatives of different order in the corresponding correlation functions. We focus on the case when τ = βℏ/2, for which all deconvolution kernels become real valued functions and their asymptotic behavior at long times exhibits a polynomial divergence. It is then shown that thermally symmetrized static averages, and the averages of the corresponding time derivatives, are ideally suited to investigate the quality of approximate Kubo correlation functions at successively larger (and up to arbitrarily long) times. This overall strategy is illustrated analytically for a harmonic system and numerically for a multidimensional double-well potential and a Lennard-Jones fluid. The analysis includes an assessment of RPMD position autocorrelation results as a function of the number of dimensions in a double-well potential and of the RPMD velocity autocorrelation function of liquid neon at 30 K.
Heng, Kevin; Lee, Jaemin
2014-01-01
We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and solutions describing two-stream radiative transfer (which approximates the passage of radiation as a pair of outgoing and incoming fluxes), flux-limited diffusion (which describes radiative transfer in the deep interior) and solutions for the temperature-pressure profiles. Generally, the problem is mathematically under-determined unless a set of closures (Eddington coefficients) is specified. We demonstrate that the hemispheric (or hemi-isotropic) closure naturally derives from the radiative transfer equation if energy conservation is obeyed, while the Eddington closure produces spurious enhancements of both reflected light and thermal emission. We further demonstrate that traditional non-isothermal treatments of each atmospheric layer lead to unphysical contributions to the ...
Radial distribution function for hard spheres in fractal dimensions. A heuristic approximation
Santos, Andrés
2016-01-01
Analytic approximations for the radial distribution function, the structure factor, and the equation of state of hard-core fluids in fractal dimension $d$ ($1 \\leq d \\leq 3$) are developed as heuristic interpolations from the knowledge of the exact and Percus-Yevick results for the hard-rod and hard-sphere fluids, respectively. In order to assess their value, such approximate results are compared with those of recent Monte Carlo simulations and numerical solutions of the Percus-Yevick equation for fractal dimension [M. Heinen et al., Phys. Rev. Lett. \\textbf{115}, 097801 (2015)], a good agreement being observed.
ON THE UNIFORM STRONG APPROXIMATION OF MARCINKIEWICZ TYPE FOR MULTIVARIABLE CONTINUOUS FUNCTIONS
Institute of Scientific and Technical Information of China (English)
Yujun Zhang; Xiaoyuan He
2005-01-01
The rate of uniform strong approximation of Marcinkiewicz type for multivariable continuous func-tions is obtained in this paper as follows:‖1/k+1 k∑j=0|Sj(f)- f|q‖≤C/k +1 k∑j=0 Eqj(f),where Sj (f) denotes the square partial Fourier sum of f and Ej (f) denotes the square best approximation of f by trigonometric polynomials of degree (j, j, … ,j),j = 0,1, 2,….
The Approximation Theorem of Convolution Operator in △p Set-valued Function Space
Institute of Scientific and Technical Information of China (English)
Pei-xin Ye
2002-01-01
The paper is a contribution to the problem of approximating random set with values in a separable Banach space. This class of set-valued function is widely used in many areas.We investigate the properties of p-bounded integrable random set. Based on this we endow it with △p metric which can be viewed as a integral type hausdorff metric and present some approximation theorem of a class of convolution operators with respect to △p metric. Moreover we also can establish analogous theorem for other integral type operator in △p space,
Gorban, A N; Mirkes, E M; Zinovyev, A
2016-12-01
Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited properties of non-quadratic error functionals based on L1 norm or even sub-linear potentials corresponding to quasinorms Lp (0basic universal data approximation algorithms (k-means, principal components, principal manifolds and graphs, regularized and sparse regression), based on piece-wise quadratic error potentials of subquadratic growth (PQSQ potentials). We develop a new and universal framework to minimize arbitrary sub-quadratic error potentials using an algorithm with guaranteed fast convergence to the local or global error minimum. The theory of PQSQ potentials is based on the notion of the cone of minorant functions, and represents a natural approximation formalism based on the application of min-plus algebra. The approach can be applied in most of existing machine learning methods, including methods of data approximation and regularized and sparse regression, leading to the improvement in the computational cost/accuracy trade-off. We demonstrate that on synthetic and real-life datasets PQSQ-based machine learning methods achieve orders of magnitude faster computational performance than the corresponding state-of-the-art methods, having similar or better approximation accuracy. Copyright © 2016 Elsevier Ltd. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Kraisler, Eli; Kronik, Leeor [Department of Materials and Interfaces, Weizmann Institute of Science, Rehovoth 76100 (Israel)
2014-05-14
The fundamental gap is a central quantity in the electronic structure of matter. Unfortunately, the fundamental gap is not generally equal to the Kohn-Sham gap of density functional theory (DFT), even in principle. The two gaps differ precisely by the derivative discontinuity, namely, an abrupt change in slope of the exchange-correlation energy as a function of electron number, expected across an integer-electron point. Popular approximate functionals are thought to be devoid of a derivative discontinuity, strongly compromising their performance for prediction of spectroscopic properties. Here we show that, in fact, all exchange-correlation functionals possess a derivative discontinuity, which arises naturally from the application of ensemble considerations within DFT, without any empiricism. This derivative discontinuity can be expressed in closed form using only quantities obtained in the course of a standard DFT calculation of the neutral system. For small, finite systems, addition of this derivative discontinuity indeed results in a greatly improved prediction for the fundamental gap, even when based on the most simple approximate exchange-correlation density functional – the local density approximation (LDA). For solids, the same scheme is exact in principle, but when applied to LDA it results in a vanishing derivative discontinuity correction. This failure is shown to be directly related to the failure of LDA in predicting fundamental gaps from total energy differences in extended systems.
A(α)-ACCEPTABILITY OF RATIONAL APPROXIMATIONS TO FUNCTION exp(z)
Institute of Scientific and Technical Information of China (English)
Yang Fengjian; Chen Xinming
2001-01-01
In this paper, two necessary and sufficient conditions, and asufficient condition of A (a)-acceptability for (n,m) rational approximation to function exp(z) are given, where a∈ (0, π/2). A necessary and sufficient condition of A-acceptability for (n,m) rational approximation to exp(z) of order p is obtained, where n≤m≤p.CLC Number：O17 Document ID：AReferences：[1]Ralston,A. ,A first Course in Numerical Analysis,Mc Graw-Hill,1965.[2]Saff,E. B. and Varga,R.S. ,On the Zeros and Poles of Padé Approximations to exp(x),Numer. Math. ,25(1975),1,1-4.[3]Wanner,G. ,Hairer,E. and Nqrsett,P. ,Order Stars and Stability Theorems,BIT,18(1978),4,475-489.[4]Yang Fengjian and Chen Xinming,A (a)-acceptability of Padé Approximations to Function exp (q). Approx. Thory & its Appl.,15 (1999)3,92- 99.[5]Liniger,W. and Willoughby,R. A.,Efficient Integration Methods for Stiff Systems of Ordinary Differential Equations,SIAM J. Numer. Anal. ,7(1970),1,47- 66.[6]Li Shoufu and Yang Fengjian,Acceptability of Rational Approximations to the Function exp (q) (in Chinese),Math,Numer Sinica,14 (1992),4,480- 488.[7]Yang Fengjian,The necessary and Sufficient Conditions of A-Acceptability of n parameters (n,n) Rational Approximations to the Function exp (q) (in Chinese). Math Numer Sinica,18(1996),4,397-404.[8]Zhong Y. Q.,Complex Analysis (in Chinese),Higher Education Press,Beijing,1979.[9]Nrsett,S. P. ,C-Polynomials for Rational Approximation to the Exponential Function,Numer. Math. ,25(1975),1,39-56.Manuscript Received：1999年9月14日Manuscript Revised：2000年12月2日Published：2001年9月1日
Approximate computation of the Green's function of transverse vibration of the composite rods
Faydaoglu, Serife; Yakhno, Valery G.
2016-10-01
The present paper describes the approximate computation of the time-dependent Green's function for the equation of the transverse vibration of a two-step rod with a piecewise constant varying cross-section. This computation is based on generalization of the Fourier series expansion method. The time-dependent Green's function is derived in the form of the Fourier series with a finite number of terms. The basic functions of this series are eigenfunctions of an ordinary differential equation of four order with boundary and interface conditions.
How Low Can Approximate Degree and Quantum Query Complexity be for Total Boolean Functions?
Ambainis, Andris
2012-01-01
It has long been known that any Boolean function that depends on n input variables has both degree and exact quantum query complexity of Omega(log n), and that this bound is achieved for some functions. In this paper we study the case of approximate degree and bounded-error quantum query complexity. We show that for these measures the correct lower bound is Omega(log n / log log n), and we exhibit quantum algorithms for two functions where this bound is achieved.
Approximation-Exact Penalty Function Method for Solving a Class of Stochastic Programming
Institute of Scientific and Technical Information of China (English)
Wang Guang-min; Wan Zhong-ping
2003-01-01
We present an approximation-exact penalty function method for solving the single stage stochastic programming problem with continuous random variable. The original problem is transformed into a determinate nonlinear programming problem with a discrete random variable sequence, which is obtained by some discrete method. We construct an exact penalty function and obtain an unconstrained optimization. It avoids the difficulty in solution by the rapid growing of the number of constraints for discrete precision. Under lenient conditions, we prove the equivalence of the minimum solution of penalty function and the solution of the determinate programming, and prove that the solution sequences of the discrete problem converge to a solution to the original problem.
The Approximation Theory for the P-Version of the Finite Element Method. II.
1984-04-01
elasticity problems in domains with edges and corners. DDI ’ JAn 73 1473 EDI TIO OF I Nov a is omsoLETz S/N 0102- LP.014. 6601 SECURITY CLASSIFICATION OF THIS...University, St. Louis, 1977. U 8. Bazant , Z.P., Three-dimensional harmonic functions near termination or intersection of gradient singularity lines: a
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.
Approximation of the Duffing oscillator frequency response function using the FPK equation
Energy Technology Data Exchange (ETDEWEB)
Cross, E J; Worden, K, E-mail: k.worden@sheffield.ac.u [Department of Mechanical Engineering, University of Sheffield, Mappin St Sheffield S1 3JD (United Kingdom)
2009-08-01
Although a great deal of work has been carried out on structural dynamic systems under random excitation, there has been a comparatively small amount of this work concentrating on the calculation of the quantities commonly measured in structural dynamic tests. Perhaps the most fundamental of these quantities is the Frequency Response Function (FRF). A number of years ago, Yar and Hammond took an interesting approach to estimating the FRF of a Duffing oscillator system which was based on an approximate solution of the Fokker-Planck-Kolmogorow equation. Despite reproducing the general features of the statistical linearization estimate, the approximation failed to show the presence of the poles at odd multiples of the primary resonance which are known to occur experimentally. The current paper simply extends the work of Yar and Hammond to a higher order of approximation and is thus able to show the existence of a third 'harmonic' in the FRF.
A method for the accurate and smooth approximation of standard thermodynamic functions
Coufal, O.
2013-01-01
A method is proposed for the calculation of approximations of standard thermodynamic functions. The method is consistent with the physical properties of standard thermodynamic functions. This means that the approximation functions are, in contrast to the hitherto used approximations, continuous and smooth in every temperature interval in which no phase transformations take place. The calculation algorithm was implemented by the SmoothSTF program in the C++ language which is part of this paper. Program summaryProgram title:SmoothSTF Catalogue identifier: AENH_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3807 No. of bytes in distributed program, including test data, etc.: 131965 Distribution format: tar.gz Programming language: C++. Computer: Any computer with gcc version 4.3.2 compiler. Operating system: Debian GNU Linux 6.0. The program can be run in operating systems in which the gcc compiler can be installed, see http://gcc.gnu.org/install/specific.html. RAM: 256 MB are sufficient for the table of standard thermodynamic functions with 500 lines Classification: 4.9. Nature of problem: Standard thermodynamic functions (STF) of individual substances are given by thermal capacity at constant pressure, entropy and enthalpy. STF are continuous and smooth in every temperature interval in which no phase transformations take place. The temperature dependence of STF as expressed by the table of its values is for further application approximated by temperature functions. In the paper, a method is proposed for calculating approximation functions which, in contrast to the hitherto used approximations, are continuous and smooth in every temperature interval. Solution method: The approximation functions are
Directory of Open Access Journals (Sweden)
Onursal Çetin
2015-06-01
Full Text Available Objective: Implementation of multilayer neural network (MLNN with sigmoid activation function for the diagnosis of hepatitis disease. Methods: Artificial neural networks (ANNs are efficient tools currently in common use for medical diagnosis. In hardware based architectures activation functions play an important role in ANN behavior. Sigmoid function is the most frequently used activation function because of its smooth response. Thus, sigmoid function and its close approximations were implemented as activation function. The dataset is taken from the UCI machine learning database. Results: For the diagnosis of hepatitis disease, MLNN structure was implemented and Levenberg Morquardt (LM algorithm was used for learning. Our method of classifying hepatitis disease produced an accuracy of 91.9% to 93.8% via 10 fold cross validation. Conclusion: When compared to previous work that diagnosed hepatitis disease using artificial neural networks and the identical data set, our results are promising in order to reduce the size and cost of neural network based hardware. Thus, hardware based diagnosis systems can be developed effectively by using approximations of sigmoid function.
DEFF Research Database (Denmark)
Øjelund, Henrik; Sadegh, Payman
2000-01-01
, constraints are introduced to ensure the conformity of the estimates to a gien global structure. Hierarchical models are then utilized as a tool to ccomodate global model uncertainties via parametric variabilities within the structure. The global parameters and their associated uncertainties are estimated...... simultaneously with the (local estimates of) function values. The approach is applied to modelling of a linear time variant dynamic system under prior linear time invariant structure where local regression fails as a result of high dimensionality.......Local function approximations concern fitting low order models to weighted data in neighbourhoods of the points where the approximations are desired. Despite their generality and convenience of use, local models typically suffer, among others, from difficulties arising in physical interpretation...
Van Raemdonck, Mario; Alcoba, Diego R; Poelmans, Ward; De Baerdemacker, Stijn; Torre, Alicia; Lain, Luis; Massaccesi, Gustavo E; Van Neck, Dimitri; Bultinck, Patrick
2015-09-14
A class of polynomial scaling methods that approximate Doubly Occupied Configuration Interaction (DOCI) wave functions and improve the description of dynamic correlation is introduced. The accuracy of the resulting wave functions is analysed by comparing energies and studying the overlap between the newly developed methods and full configuration interaction wave functions, showing that a low energy does not necessarily entail a good approximation of the exact wave function. Due to the dependence of DOCI wave functions on the single-particle basis chosen, several orbital optimisation algorithms are introduced. An energy-based algorithm using the simulated annealing method is used as a benchmark. As a computationally more affordable alternative, a seniority number minimising algorithm is developed and compared to the energy based one revealing that the seniority minimising orbital set performs well. Given a well-chosen orbital basis, it is shown that the newly developed DOCI based wave functions are especially suitable for the computationally efficient description of static correlation and to lesser extent dynamic correlation.
Korovkin type approximation theorem for functions of two variables via statistical summability (C, 1
Directory of Open Access Journals (Sweden)
Mohammad Mursaleen
2015-05-01
Full Text Available The concept of statistical summability (C, 1 has recently been introduced by Moricz (2002. In this paper, we use this notion of summability to prove the Korovkin type approximation theorem for functions of two variables. Finally we construct an example by Bleimann, Butzer and Hahn operators to show that our result is stronger than those of previously proved by other authors for ordinary convergence and statistical convergence.
Correlation functions of just renormalizable tensorial group field theory: The melonic approximation
Samary, Dine Ousmane; Vignes-Tourneret, Fabien; Wulkenhaar, Raimar
2014-01-01
The $D$-colored version of tensor models has been shown to admit a large $N$-limit expansion. The leading contributions result from so-called melonic graphs which are dual to the $D$-sphere. This is a note about the Schwinger-Dyson equations of the tensorial $\\varphi^{4}_{5}$-model (with propagator $1/{\\bf p}^{2}$) and their melonic approximation. We derive the master equations for two- and four-point correlation functions and discuss their solution.
Directory of Open Access Journals (Sweden)
Laura Angeloni
2016-01-01
Full Text Available We present a review on recent approximation results in the space of functions of bounded variation for some classes of integral operators in the multidimensional setting. In particular, we present estimates and convergence in variation results for both convolution and Mellin integral operators with respect to the Tonelli variation. Results with respect to a multidimensional concept of φ-variation in the sense of Tonelli are also presented.
Vuković, Najdan; Miljković, Zoran
2013-10-01
Radial basis function (RBF) neural network is constructed of certain number of RBF neurons, and these networks are among the most used neural networks for modeling of various nonlinear problems in engineering. Conventional RBF neuron is usually based on Gaussian type of activation function with single width for each activation function. This feature restricts neuron performance for modeling the complex nonlinear problems. To accommodate limitation of a single scale, this paper presents neural network with similar but yet different activation function-hyper basis function (HBF). The HBF allows different scaling of input dimensions to provide better generalization property when dealing with complex nonlinear problems in engineering practice. The HBF is based on generalization of Gaussian type of neuron that applies Mahalanobis-like distance as a distance metrics between input training sample and prototype vector. Compared to the RBF, the HBF neuron has more parameters to optimize, but HBF neural network needs less number of HBF neurons to memorize relationship between input and output sets in order to achieve good generalization property. However, recent research results of HBF neural network performance have shown that optimal way of constructing this type of neural network is needed; this paper addresses this issue and modifies sequential learning algorithm for HBF neural network that exploits the concept of neuron's significance and allows growing and pruning of HBF neuron during learning process. Extensive experimental study shows that HBF neural network, trained with developed learning algorithm, achieves lower prediction error and more compact neural network. Copyright © 2013 Elsevier Ltd. All rights reserved.
ON COEFFICIENT POLYNOMIALS OF CUBIC HERMITE-PAD(E) APPROXIMATIONS TO THE EXPONENTIAL FUNCTION
Institute of Scientific and Technical Information of China (English)
Cheng-de Zheng; Guo-can Wang; Zhi-bin Li
2005-01-01
The polynomials related with cubic Hermite-Pade approximation to the exponential function are investigated which have degrees at most n, m, s respectively. A connection is given between the coefficients of each of the polynomials and certain hypergeometric functions, which leads to a simple expression for a polynomial in a special case. Contour integral representations of the polynomials are given. By using of the saddle point method the exact asymptotics of the polynomials are derived as n, m, s tend to infinity through certain ray sequence. Some further uniform asymptotic aspects of the polynomials are also discussed.
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi; LIN Jing-Xian
2001-01-01
In dealing with the square lattice model,we replace the traditionally needed Born-Von Karmann periodic boundary condition with additional Hamiltonian terms to make up a ring lattice.In doing so,the lattice Green's function of an infinite square lattice in the second nearest-neighbour interaction approximation can be derived by means of the matrix Green's function method.It is shown that the density of states may change when the second nearest-neighbour interaction is turned on.``
Indian Academy of Sciences (India)
Pravin K Gupta; Sri Niwas; Neeta Chaudhary
2006-06-01
The computation of electromagnetic (EM)ﬁelds,for 1-D layered earth model,requires evaluation of Hankel Transform (HT)of the EM kernel function.The digital ﬁltering is the most widely used technique to evaluate HT integrals.However,it has some obvious shortcomings.We present an alternative scheme,based on an orthonormal exponential approximation of the kernel function, for evaluating HT integrals.This approximation of the kernel function was chosen because the analytical solution of HT of an exponential function is readily available in literature.This expansion reduces the integral to a simple algebraic sum.The implementation of such a scheme requires that the weights and the exponents of the exponential function be estimated.The exponents were estimated through a guided search algorithm while the weights were obtained using Marquardt matrix inversion method.The algorithm was tested on analytical HT pairs available in literature. The results are compared with those obtained using the digital ﬁltering technique with Anderson ﬁlters.The ﬁeld curves for four types (A-,K-,H-and Q-type)of 3-layer earth models are generated using the present scheme and compared with the corresponding curves obtained using the Anderson scheme.It is concluded that the present scheme is more accurate than the Anderson scheme.
Mark, W. D.
1979-01-01
The second part of a theory for predicting the vibratory excitation of gear systems from fundamental descriptions of gear tooth elastic properties and deviations of tooth faces from perfect involute surfaces is presented. The first part of the theory provides expressions for the Fourier-series coefficients of the vibratory excitation, and this paper gives expressions for these Fourier-series coefficients in terms of easily interpreted gear tooth metrics that are readily evaluated from tooth-face measurements. Results are given for rectangular tooth-face contact regions using two-dimensional Legendre polynomial expansions of local tooth-pair stiffnesses and stiffness-weighted deviations of tooth faces from perfect involute surfaces. A rigorous transfer function approach is developed that permits separation of the effects of gear tooth errors and gear design parameters; the theory is applicable to helical and spur gears and is illustrated with measurements of tooth-spacing errors and tooth profiles obtained from a pair of spur gears.
CSIR Research Space (South Africa)
Kok, S
2012-07-01
Full Text Available is considered in this paper, but the main result of Zimmermann [2] is disproved. 2 Kriging fundamentals A response y(x) is considered to consist of a deterministic contribution f(x) and a stochastic component Z(x), i.e. y(x) = f(x) + Z(x). (1...) and is symmetric by definition. In computer experiment applications, the Gaussian correlation function is particularly popular. In this case, R is given by R(xi, xj) = m? k=1 e??k|x i k?x j k|2 , (4) where m is the number of design variables (i.e...
Tiffany, Sherwood H.; Adams, William M., Jr.
1988-01-01
The approximation of unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft are discussed. Two methods of formulating these approximations are extended to include the same flexibility in constraining the approximations and the same methodology in optimizing nonlinear parameters as another currently used extended least-squares method. Optimal selection of nonlinear parameters is made in each of the three methods by use of the same nonlinear, nongradient optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is lower order than that required when no optimization of the nonlinear terms is performed. The free linear parameters are determined using the least-squares matrix techniques of a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from different approaches are described and results are presented that show comparative evaluations from application of each of the extended methods to a numerical example.
Giese, Timothy J; York, Darrin M
2010-12-28
We extend the Kohn-Sham potential energy expansion (VE) to include variations of the kinetic energy density and use the VE formulation with a 6-31G* basis to perform a "Jacob's ladder" comparison of small molecule properties using density functionals classified as being either LDA, GGA, or meta-GGA. We show that the VE reproduces standard Kohn-Sham DFT results well if all integrals are performed without further approximation, and there is no substantial improvement in using meta-GGA functionals relative to GGA functionals. The advantages of using GGA versus LDA functionals becomes apparent when modeling hydrogen bonds. We furthermore examine the effect of using integral approximations to compute the zeroth-order energy and first-order matrix elements, and the results suggest that the origin of the short-range repulsive potential within self-consistent charge density-functional tight-binding methods mainly arises from the approximations made to the first-order matrix elements.
A semiclassical initial value approximation for the trace of Green's function
Energy Technology Data Exchange (ETDEWEB)
Kay, Kenneth G, E-mail: Kenneth.Kay@biu.ac.il [Department of Chemistry, Bar-Ilan University, Ramat-Gan 52900 (Israel)
2011-05-20
A semiclassical initial value approximation for the trace of Green's function is derived. In contrast to the well-known formula of Gutzwiller, applicability of the present expression does not require knowledge of the system's periodic orbits but constructs the trace from classical trajectories originating from all points on a Poincare surface. A given trajectory provides a contribution to the trace each time it returns to the surface with a weight based, in part, on the inner product (on this surface) of coherent states associated with the initial and returning points. The treatment is generalized to obtain a version of the initial value formula that is useful for systems having discrete symmetries. The initial value trace expression is shown to be semiclassically valid for chaotic systems by a stationary phase treatment that demonstrates its reduction to Gutzwiller's formula in the classical limit. Numerical calculations of energy eigenvalues verify the applicability of the approximation not only to chaotic systems but to integrable systems and systems with mixed phase space. The approximation presented here has numerical advantages over methods for determining the trace based on initial value treatments of the time-dependent propagator, especially for systems with homogeneous potential energy functions.
Energy Technology Data Exchange (ETDEWEB)
Carmona-Espíndola, Javier, E-mail: jcarmona-26@yahoo.com.mx [Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, México D. F. 09340, México (Mexico); Gázquez, José L., E-mail: jlgm@xanum.uam.mx [Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, México D. F. 09340, México (Mexico); Departamento de Química, Centro de Investigación y de Estudios Avanzados, Av. Instituto Politécnico Nacional 2508, México D. F. 07360, México (Mexico); Vela, Alberto [Departamento de Química, Centro de Investigación y de Estudios Avanzados, Av. Instituto Politécnico Nacional 2508, México D. F. 07360, México (Mexico); Trickey, S. B. [Quantum Theory Project, Department of Physics and Department of Chemistry, University of Florida, P.O. Box 118435, Gainesville, Florida 32611-8435 (United States)
2015-02-07
A new non-empirical exchange energy functional of the generalized gradient approximation (GGA) type, which gives an exchange potential with the correct asymptotic behavior, is developed and explored. In combination with the Perdew-Burke-Ernzerhof (PBE) correlation energy functional, the new CAP-PBE (CAP stands for correct asymptotic potential) exchange-correlation functional gives heats of formation, ionization potentials, electron affinities, proton affinities, binding energies of weakly interacting systems, barrier heights for hydrogen and non-hydrogen transfer reactions, bond distances, and harmonic frequencies on standard test sets that are fully competitive with those obtained from other GGA-type functionals that do not have the correct asymptotic exchange potential behavior. Distinct from them, the new functional provides important improvements in quantities dependent upon response functions, e.g., static and dynamic polarizabilities and hyperpolarizabilities. CAP combined with the Lee-Yang-Parr correlation functional gives roughly equivalent results. Consideration of the computed dynamical polarizabilities in the context of the broad spectrum of other properties considered tips the balance to the non-empirical CAP-PBE combination. Intriguingly, these improvements arise primarily from improvements in the highest occupied and lowest unoccupied molecular orbitals, and not from shifts in the associated eigenvalues. Those eigenvalues do not change dramatically with respect to eigenvalues from other GGA-type functionals that do not provide the correct asymptotic behavior of the potential. Unexpected behavior of the potential at intermediate distances from the nucleus explains this unexpected result and indicates a clear route for improvement.
HyperANF: Approximating the Neighbourhood Function of Very Large Graphs on a Budget
Boldi, Paolo; Vigna, Sebastiano
2010-01-01
The neighbourhood function N(t) of a graph G gives, for each t, the number of pairs of nodes such that y is reachable from x in less that t hops. The neighbourhood function provides a wealth of information about the graph (e.g., it easily allows one to compute its diameter), but it is very expensive to compute it exactly. Recently, the ANF algorithm (approximate neighbourhood function) has been proposed with the purpose of approximating NG(t) on large graphs. We describe a breakthrough improvement over ANF in terms of speed and scalability. Our algorithm, called HyperANF, uses the new HyperLogLog counters and combines them efficiently through broadword programming; our implementation uses overdecomposition to exploit multi-core parallelism. With HyperANF, for the first time we can compute in a few hours the neighbourhood function of graphs with billions of nodes with a small error and good confidence using a standard workstation. Then, we turn to the study of the distribution of the shortest paths between re...
Away from generalized gradient approximation: orbital-dependent exchange-correlation functionals.
Baerends, E J; Gritsenko, O V
2005-08-08
The local-density approximation of density functional theory (DFT) is remarkably accurate, for instance, for geometries and frequencies, and the generalized gradient approximations have also made bond energies quite reliable. Sometimes, however, one meets with failure in individual cases. One of the possible routes towards better functionals would be the incorporation of orbital dependence (which is an implicit density dependency) in the functionals. We discuss this approach both for energies and for response properties. One possibility is the use of the Hartree-Fock-type exchange energy expression as orbital-dependent functional. We will argue that in spite of the increasing popularity of this approach, it does not offer any advantage over Hartree-Fock for energies. We will advocate not to apply the separation of exchange and correlation, which is so ingrained in quantum chemistry, but to model both simultaneously. For response properties the energies and shapes of the virtual orbitals are crucial. We will discuss the benefits that Kohn-Sham potentials can offer which are derived from either an orbital-dependent energy functional, including the exact-exchange functional, or which can be obtained directly as orbital-dependent functional. We highlight the similarity of the Hartree-Fock and Kohn-Sham occupied orbitals and orbital energies, and the essentially different meanings the virtual orbitals and orbital energies have in these two models. We will show that these differences are beneficial for DFT in the case of localized excitations (in a small molecule or in a fragment), but are detrimental for charge-transfer excitations. Again, orbital dependency, in this case in the exchange-correlation kernel, offers a solution.
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.
Approximation of functions on the Sobolev space with a Gaussian measure
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
We discuss the best approximation of periodic functions by trigonometric polynomials and the approximation by Fourier partial summation operators, Valle-Poussin operators, Ces`aro operators, Abel opera-tors, and Jackson operators, respectively, on the Sobolev space with a Gaussian measure and obtain the average error estimations. We show that, in the average case setting, the trigonometric polynomial subspaces are the asymptotically optimal subspaces in the L q space for 1≤q < ∞, and the Fourier partial summation operators and the Valle-Poussin operators are the asymptotically optimal linear operators and are as good as optimal nonlinear operators in the L q space for 1≤q < ∞.
Approximation-Exact Penalty Function Method for Solving a Class of Stochastic Programming
Institute of Scientific and Technical Information of China (English)
WangGuang-min; WanZhong-ping
2003-01-01
We present an approximation-exact penalty function method for solving the single stage stochastic programming problem with continuous random variable. The original problem is transformed into a determinate nonlinear programming problem with a discrete random variable sequence, which is obtained by some discrete method. We construct an exact penalty function and obtain an unconstrained optimization. It avoids the difficulty in solution by the rapid growing of the number of constraints for discrete precision.Under lenient conditions, we prove the equivalence of the minimum solution of penalty function and the solution of the determinate programming, and prove that the solution sequences of the discrete problem converge to a solution to the original problem.
Indian Academy of Sciences (India)
V K Dhar; A K Tickoo; R Koul; B P Dubey
2010-02-01
We report an inter-comparison of some popular algorithms within the artificial neural network domain (viz., local search algorithms, global search algorithms, higher-order algorithms and the hybrid algorithms) by applying them to the standard benchmarking problems like the IRIS data, XOR/N-bit parity and two-spiral problems. Apart from giving a brief description of these algorithms, the results obtained for the above benchmark problems are presented in the paper. The results suggest that while Levenberg–Marquardt algorithm yields the lowest RMS error for the N-bit parity and the two-spiral problems, higher-order neuron algorithm gives the best results for the IRIS data problem. The best results for the XOR problem are obtained with the neuro-fuzzy algo- rithm. The above algorithms were also applied for solving several regression problems such as cos() and a few special functions like the gamma function, the complimentary error function and the upper tail cumulative 2-distribution function. The results of these regression problems indicate that, among all the ANN algorithms used in the present study, Levenberg–Marquardt algorithm yields the best results. Keeping in view the highly non-linear behaviour and the wide dynamic range of these functions, it is suggested that these functions can also be considered as standard benchmark problems for function approximation using artificial neural networks.
Versatile van der Waals Density Functional Based on a Meta-Generalized Gradient Approximation
Directory of Open Access Journals (Sweden)
Haowei Peng
2016-10-01
Full Text Available A “best-of-both-worlds” van der Waals (vdW density functional is constructed, seamlessly supplementing the strongly constrained and appropriately normed (SCAN meta-generalized gradient approximation for short- and intermediate-range interactions with the long-range vdW interaction from rVV10, the revised Vydrov–van Voorhis nonlocal correlation functional. The resultant SCAN+rVV10 is the only vdW density functional to date that yields excellent interlayer binding energies and spacings, as well as intralayer lattice constants in 28 layered materials. Its versatility for various kinds of bonding is further demonstrated by its good performance for 22 interactions between molecules; the cohesive energies and lattice constants of 50 solids; the adsorption energy and distance of a benzene molecule on coinage-metal surfaces; the binding energy curves for graphene on Cu(111, Ni(111, and Co(0001 surfaces; and the rare-gas solids. We argue that a good semilocal approximation should (as SCAN does capture the intermediate-range vdW through its exchange term. We have found an effective range of the vdW interaction between 8 and 16 Å for systems considered here, suggesting that this interaction is negligibly small at the larger distances where it reaches its asymptotic power-law decay.
Versatile van der Waals Density Functional Based on a Meta-Generalized Gradient Approximation
Peng, Haowei; Yang, Zeng-Hui; Perdew, John P.; Sun, Jianwei
2016-10-01
A "best-of-both-worlds" van der Waals (vdW) density functional is constructed, seamlessly supplementing the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation for short- and intermediate-range interactions with the long-range vdW interaction from r VV 10 , the revised Vydrov-van Voorhis nonlocal correlation functional. The resultant SCAN +r VV 10 is the only vdW density functional to date that yields excellent interlayer binding energies and spacings, as well as intralayer lattice constants in 28 layered materials. Its versatility for various kinds of bonding is further demonstrated by its good performance for 22 interactions between molecules; the cohesive energies and lattice constants of 50 solids; the adsorption energy and distance of a benzene molecule on coinage-metal surfaces; the binding energy curves for graphene on Cu(111), Ni(111), and Co(0001) surfaces; and the rare-gas solids. We argue that a good semilocal approximation should (as SCAN does) capture the intermediate-range vdW through its exchange term. We have found an effective range of the vdW interaction between 8 and 16 Å for systems considered here, suggesting that this interaction is negligibly small at the larger distances where it reaches its asymptotic power-law decay.
Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes
DEFF Research Database (Denmark)
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....
Energy Technology Data Exchange (ETDEWEB)
Druskin, V.; Lee, Ping [Schlumberger-Doll Research, Ridgefield, CT (United States); Knizhnerman, L. [Central Geophysical Expedition, Moscow (Russian Federation)
1996-12-31
There is now a growing interest in the area of using Krylov subspace approximations to compute the actions of matrix functions. The main application of this approach is the solution of ODE systems, obtained after discretization of partial differential equations by method of lines. In the event that the cost of computing the matrix inverse is relatively inexpensive, it is sometimes attractive to solve the ODE using the extended Krylov subspaces, originated by actions of both positive and negative matrix powers. Examples of such problems can be found frequently in computational electromagnetics.
Optimal approximation of head-related transfer function's pole-zero model based on genetic algorithm
Institute of Scientific and Technical Information of China (English)
ZHANG Jie; MA Hao; WU Zhen-yang
2006-01-01
In the research on spatial hearing and virtual auditory space,it is important to effectively model the head-related transfer functions (HRTFs).Based on the analysis of the HRTFs' spectrum and some perspectives of psychoacoustics,this paper applied multiple demes' parallel and real-valued coding genetic algorithm (GA) to approximate the HRTFs' zero-pole model.Using the logarithmic magnitude's error criterion for the human auditory sense,the results show that the performance of the GA is on the average 39% better than that of the traditional Prony method,and 46% better than that of the Yule-Walker algorithm.
随机逼近中的Lyapunov函数%On Lyapunov Functions inStochastic Approximation
Institute of Scientific and Technical Information of China (English)
张俊华
2001-01-01
本文研究了随机逼近中满足某种条件的Lyapunov函数的存在性及如何构造Lyapunov函数的问题,讨论了算法收敛性与相应常微分方程系统的渐近稳定性之间的关系.%In this paper, we investigate existence and construction of certain Lyapunov functions instochastic approximation (SA) and discuss the relation between convergence of SA algorithms andasymptotic stability of the corresponding ordinary differential equation systems.
Wang, Zheng; Liu, Xiaoping; Liu, Kefu; Li, Shuai; Wang, Huanqing
2017-10-01
In this paper, backstepping for a class of block strict-feedback nonlinear systems is considered. Since the input function could be zero for each backstepping step, the backstepping technique cannot be applied directly. Based on the assumption that nonlinear systems are polynomials, for each backstepping step, Lypunov function can be constructed in a polynomial form by sum of square (SOS) technique. The virtual control can be obtained by the Sontag feedback formula, which is equivalent to an optimal control-the solution of a Hamilton-Jacobi-Bellman equation. Thus, approximate dynamic programming (ADP) could be used to estimate value functions (Lyapunov functions) instead of SOS. Through backstepping technique, the control Lyapunov function (CLF) of the full system is constructed finally making use of the strict-feedback structure and a stabilizable controller can be obtained through the constructed CLF. The contributions of the proposed method are twofold. On one hand, introducing ADP into backstepping can broaden the application of the backstepping technique. A class of block strict-feedback systems can be dealt by the proposed method and the requirement of nonzero input function for each backstepping step can be relaxed. On the other hand, backstepping with surface dynamic control actually reduces the computation complexity of ADP through constructing one part of the CLF by solving semidefinite programming using SOS. Simulation results verify contributions of the proposed method.
Conserving approximations for response functions of the Fermi gas in a random potential
Janiš, Václav; Kolorenč, Jindřich
2016-07-01
One- and two-electron Green functions are simultaneously needed to determine the response functions of the electron gas in a random potential. Reliable approximations must retain consistency between the two types of Green functions expressed via Ward identities so that their output is compliant with macroscopic symmetries and conservation laws. Such a consistency is not directly guaranteed when summing nonlocal corrections to the local (dynamical) mean field. We analyze the reasons for this failure and show how the full Ward identity can generically be implemented in the diagrammatic approach to the vertex functions without breaking the analytic properties of the self-energy. We use the low-energy asymptotics of the conserving two-particle vertex determining the singular part of response and correlation functions to derive an exact representation of the diffusion constant in terms of Green functions of the perturbation theory. We then calculate explicitly the leading vertex corrections to the mean-field diffusion constant due to maximally-crossed diagrams.
Impaired neural networks for approximate calculation in dyscalculic children: a functional MRI study
Directory of Open Access Journals (Sweden)
Dosch Mengia
2006-09-01
Full Text Available Abstract Background Developmental dyscalculia (DD is a specific learning disability affecting the acquisition of mathematical skills in children with otherwise normal general intelligence. The goal of the present study was to examine cerebral mechanisms underlying DD. Methods Eighteen children with DD aged 11.2 ± 1.3 years and twenty age-matched typically achieving schoolchildren were investigated using functional magnetic resonance imaging (fMRI during trials testing approximate and exact mathematical calculation, as well as magnitude comparison. Results Children with DD showed greater inter-individual variability and had weaker activation in almost the entire neuronal network for approximate calculation including the intraparietal sulcus, and the middle and inferior frontal gyrus of both hemispheres. In particular, the left intraparietal sulcus, the left inferior frontal gyrus and the right middle frontal gyrus seem to play crucial roles in correct approximate calculation, since brain activation correlated with accuracy rate in these regions. In contrast, no differences between groups could be found for exact calculation and magnitude comparison. In general, fMRI revealed similar parietal and prefrontal activation patterns in DD children compared to controls for all conditions. Conclusion In conclusion, there is evidence for a deficient recruitment of neural resources in children with DD when processing analog magnitudes of numbers.
Hallo, M.; Gallovič, F.
2016-11-01
Green functions (GFs) are an essential ingredient in waveform-based earthquake source inversions. Hence, the error due to imprecise knowledge of a crustal velocity model is one of the major sources of uncertainty of the inferred earthquake source parameters. Recent strategies in Bayesian waveform inversions rely on statistical description of the GF uncertainty by means of a Gaussian distribution characterized by a covariance matrix. Here we use Monte-Carlo approach to estimate the GF covariance considering randomly perturbed velocity models. We analyse the dependence of the covariance on various parameters (strength of velocity model perturbations, GF frequency content, source-station distance, etc.). Recognizing that the major source of the GF uncertainty is related to the random time shifts of the signal, we propose a simplified approach to obtain approximate covariances, bypassing the numerically expensive Monte-Carlo simulations. The resulting closed-form formulae for the approximate auto-covariances and cross-covariances between stations and components can be easily implemented in existing inversion techniques. We demonstrate that the approximate covariances exhibit very good agreement with the Monte-Carlo estimates, providing realistic variations of the GF waveforms. Furthermore, we show examples of implementation of the covariance matrix in a Bayesian moment tensor inversion using both synthetic and real data sets. We demonstrate that taking the GF uncertainty into account leads to improved estimates of the moment tensor parameters and their uncertainty.
Székely, Balázs; Kania, Adam; Varga, Katalin; Heilmeier, Hermann
2017-04-01
Lacunarity, a measure of the spatial distribution of the empty space is found to be a useful descriptive quantity of the forest structure. Its calculation, based on laser-scanned point clouds, results in a four-dimensional data set. The evaluation of results needs sophisticated tools and visualization techniques. To simplify the evaluation, it is straightforward to use approximation functions fitted to the results. The lacunarity function L(r), being a measure of scale-independent structural properties, has a power-law character. Previous studies showed that log(log(L(r))) transformation is suitable for analysis of spatial patterns. Accordingly, transformed lacunarity functions can be approximated by appropriate functions either in the original or in the transformed domain. As input data we have used a number of laser-scanned point clouds of various forests. The lacunarity distribution has been calculated along a regular horizontal grid at various (relative) elevations. The lacunarity data cube then has been logarithm-transformed and the resulting values became the input of parameter estimation at each point (point of interest, POI). This way at each POI a parameter set is generated that is suitable for spatial analysis. The expectation is that the horizontal variation and vertical layering of the vegetation can be characterized by this procedure. The results show that the transformed L(r) functions can be typically approximated by exponentials individually, and the residual values remain low in most cases. However, (1) in most cases the residuals may vary considerably, and (2) neighbouring POIs often give rather differing estimates both in horizontal and in vertical directions, of them the vertical variation seems to be more characteristic. In the vertical sense, the distribution of estimates shows abrupt changes at places, presumably related to the vertical structure of the forest. In low relief areas horizontal similarity is more typical, in higher relief areas
Aft-body loading function for penetrators based on the spherical cavity-expansion approximation.
Energy Technology Data Exchange (ETDEWEB)
Longcope, Donald B., Jr.; Warren, Thomas Lynn; Duong, Henry
2009-12-01
In this paper we develop an aft-body loading function for penetration simulations that is based on the spherical cavity-expansion approximation. This loading function assumes that there is a preexisting cavity of radius a{sub o} before the expansion occurs. This causes the radial stress on the cavity surface to be less than what is obtained if the cavity is opened from a zero initial radius. This in turn causes less resistance on the aft body as it penetrates the target which allows for greater rotation of the penetrator. Results from simulations are compared with experimental results for oblique penetration into a concrete target with an unconfined compressive strength of 23 MPa.
An approximate solution to the stress and deformation states of functionally graded rotating disks
Sondhi, Lakshman; Sanyal, Shubhashis; Saha, Kashi Nath; Bhowmick, Shubhankar
2016-07-01
The present work employs variational principle to investigate the stress and deformation states and estimate the limit angular speed of functionally graded high-speed rotating annular disks of constant thickness. Assuming a series approximation following Galerkin's principle, the solution of the governing equation is obtained. In the present study, elasticity modulus and density of the disk material are taken as power function of radius with the gradient parameter ranging between 0.0 and 1.0. Results obtained from numerical solutions are validated with benchmark results and are found to be in good agreement. The results are reported in dimensional form and presented graphically. The results provide a substantial insight in understanding the behavior of FGM rotating disks with constant thickness and different gradient parameter. Furthermore, the stress and deformation state of the disk at constant angular speed and limit angular speed is investigated to explain the existence of optimum gradient parameters.
Institute of Scientific and Technical Information of China (English)
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.
Analytic number theory, approximation theory, and special functions in honor of Hari M. Srivastava
Rassias, Michael
2014-01-01
This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality, and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics, and other computational and applied sciences.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The concept of two-direction refinable functions and two-direction wavelets is introduced.We investigate the existence of distributional(or L2-stable) solutions of the two-direction refinement equation: φ(x)=∑p+kφ(mx-k)+∑p-kφ(k-mx) where m ≥ 2 is an integer. Based on the positive mask {pk+} and negative mask {p-k}, the conditions that guarantee the above equation has compactly distributional solutions or L2-stable solutions are established. Furthermore, the condition that the L2-stable solution of the above equation can generate a two-direction MRA is given. The support interval of φ(x) is discussed amply. The definition of orthogonal two-direction refinable function and orthogonal two-direction wavelets is presented, and the orthogonality criteria for two-direction refinable functions are established. An algorithm for constructing orthogonal two-direction refinable functions and their two-direction wavelets is presented. Another construction algorithm for two-direction L2-refinable functions, which have nonnegative symbol masks and possess high approximation order and regularity, is presented. Finally, two construction examples are given.
Stable computations with flat radial basis functions using vector-valued rational approximations
Wright, Grady B.; Fornberg, Bengt
2017-02-01
One commonly finds in applications of smooth radial basis functions (RBFs) that scaling the kernels so they are 'flat' leads to smaller discretization errors. However, the direct numerical approach for computing with flat RBFs (RBF-Direct) is severely ill-conditioned. We present an algorithm for bypassing this ill-conditioning that is based on a new method for rational approximation (RA) of vector-valued analytic functions with the property that all components of the vector share the same singularities. This new algorithm (RBF-RA) is more accurate, robust, and easier to implement than the Contour-Padé method, which is similarly based on vector-valued rational approximation. In contrast to the stable RBF-QR and RBF-GA algorithms, which are based on finding a better conditioned base in the same RBF-space, the new algorithm can be used with any type of smooth radial kernel, and it is also applicable to a wider range of tasks (including calculating Hermite type implicit RBF-FD stencils). We present a series of numerical experiments demonstrating the effectiveness of this new method for computing RBF interpolants in the flat regime. We also demonstrate the flexibility of the method by using it to compute implicit RBF-FD formulas in the flat regime and then using these for solving Poisson's equation in a 3-D spherical shell.
Approximating Gaussian mixture model or radial basis function network with multilayer perceptron.
Patrikar, Ajay M
2013-07-01
Gaussian mixture models (GMMs) and multilayer perceptron (MLP) are both popular pattern classification techniques. This brief shows that a multilayer perceptron with quadratic inputs (MLPQ) can accurately approximate GMMs with diagonal covariance matrices. The mapping equations between the parameters of GMM and the weights of MLPQ are presented. A similar approach is applied to radial basis function networks (RBFNs) to show that RBFNs with Gaussian basis functions and Euclidean norm can be approximated accurately with MLPQ. The mapping equations between RBFN and MLPQ weights are presented. There are well-established training procedures for GMMs, such as the expectation maximization (EM) algorithm. The GMM parameters obtained by the EM algorithm can be used to generate a set of initial weights of MLPQ. Similarly, a trained RBFN can be used to generate a set of initial weights of MLPQ. MLPQ training can be continued further with gradient-descent based methods, which can lead to improvement in performance compared to the GMM or RBFN from which it is initialized. Thus, the MLPQ can always perform as well as or better than the GMM or RBFN.
Galatolo, Stefano; Monge, Maurizio; Nisoli, Isaia
2016-07-01
We study the problem of the rigorous computation of the stationary measure and of the rate of convergence to equilibrium of an iterated function system described by a stochastic mixture of two or more dynamical systems that are either all uniformly expanding on the interval, either all contracting. In the expanding case, the associated transfer operators satisfy a Lasota-Yorke inequality, we show how to compute a rigorous approximations of the stationary measure in the L 1 norm and an estimate for the rate of convergence. The rigorous computation requires a computer-aided proof of the contraction of the transfer operators for the maps, and we show that this property propagates to the transfer operators of the IFS. In the contracting case we perform a rigorous approximation of the stationary measure in the Wasserstein-Kantorovich distance and rate of convergence, using the same functional analytic approach. We show that a finite computation can produce a realistic computation of all contraction rates for the whole parameter space. We conclude with a description of the implementation and numerical experiments. All the authors were partially supported by ICTP and by EU Marie-Curie IRSES Brazilian-European partnership in Dynamical Systems (FP7-PEOPLE-2012-IRSES 318999 BREUDS), SG thanks The Leverhulme Trust for support through Network Grant IN-2014-021.
Institute of Scientific and Technical Information of China (English)
GU Chuan-qing; PAN Bao-zhen; WU Bei-bei
2006-01-01
To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined.By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for padé-type approximation are explicitly given.
The functional performance of the Argus II retinal prosthesis
2013-01-01
Visual prostheses are devices to treat profound vision loss by stimulating secondary nerve cells anywhere along the visual pathway, typically with electrical pulses. The Argus® II implant, developed by Second Sight Medical Products (SSMP, Sylmar, CA, USA), targets the retina and features 60 electrodes that electrically stimulate the surviving retinal neurons. Of the approximately 20 research groups that are actively developing visual prostheses, SSMP has the longest track record. The Argus II...
Energy Technology Data Exchange (ETDEWEB)
Blain, M.A.; Bonnaud, G.; Chiron, A.; Riazuelo, G.
1996-02-01
This report addresses the propagation of an intense laser beam in a unmagnetized plasma, which is relevant for both the inertial confinement fusion (ICF) and the ultra-high intensity (UHI) pulses. The width and the irradiance of the laser pulses are respectively: (0.1-10) nanosecond and (10{sup 13}-10{sup 16}) W/cm{sup 2} for the ICF context and (0.1-1) picosecond and in excess of 10{sup 1}8 W/cm{sup 2} for the UHI context. The nonlinear mechanisms for beam self-focusing and filamentation, induced by both the ponderomotive expelling of charged particles and the relativistic increase of the electron mass, are specified studied. Part I deals with the theoretical aspects and part II is concerned with the results of two-dimensional simulations. The results have been obtained within the framework of the paraxial approximation and the stationary response of the plasma. The large set of scenarios that characterize the behavior of Gaussian beam and a modulated beam is presented; a synthetic overview of the previous theoretical works is also provided. The interplay of two crossing beams is discussed. This report will be a help to improve the uniformity of the laser irradiation in the ICF context and to channel a very intense laser beam over large distance in the UHI context. (authors). 17 refs., 53 figs., 14 tabs.
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.
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.
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 ...
Bisetti, Fabrizio
2012-06-01
Recent trends in hydrocarbon fuel research indicate that the number of species and reactions in chemical kinetic mechanisms is rapidly increasing in an effort to provide predictive capabilities for fuels of practical interest. In order to cope with the computational cost associated with the time integration of stiff, large chemical systems, a novel approach is proposed. The approach combines an exponential integrator and Krylov subspace approximations to the exponential function of the Jacobian matrix. The components of the approach are described in detail and applied to the ignition of stoichiometric methane-air and iso-octane-air mixtures, here described by two widely adopted chemical kinetic mechanisms. The approach is found to be robust even at relatively large time steps and the global error displays a nominal third-order convergence. The performance of the approach is improved by utilising an adaptive algorithm for the selection of the Krylov subspace size, which guarantees an approximation to the matrix exponential within user-defined error tolerance. The Krylov projection of the Jacobian matrix onto a low-dimensional space is interpreted as a local model reduction with a well-defined error control strategy. Finally, the performance of the approach is discussed with regard to the optimal selection of the parameters governing the accuracy of its individual components. © 2012 Copyright Taylor and Francis Group, LLC.
On function classes related pertaining to strong approximation of double Fourier series
Baituyakova, Zhuldyz
2015-09-01
The investigation of embedding of function classes began a long time ago. After Alexits [1], Leindler [2], and Gogoladze[3] investigated estimates of strong approximation by Fourier series in 1965, G. Freud[4] raised the corresponding saturation problem in 1969. The list of the authors dealing with embedding problems partly is also very long. It suffices to mention some names: V. G. Krotov, W. Lenski, S. M. Mazhar, J. Nemeth, E. M. Nikisin, K. I. Oskolkov, G. Sunouchi, J. Szabados, R. Taberski and V. Totik. Study on this topic has since been carried on over a decade, but it seems that most of the results obtained are limited to the case of one dimension. In this paper, embedding results are considered which arise in the strong approximation by double Fourier series. We prove theorem on the interrelation between the classes Wr1,r2HS,M ω and H(λ, p, r1, r2, ω(δ1, δ2)), in the one-dimensional case proved by L. Leindler.
Marelli, Damián; Baumgartner, Robert; Majdak, Piotr
2015-07-01
Head-related transfer functions (HRTFs) describe the acoustic filtering of incoming sounds by the human morphology and are essential for listeners to localize sound sources in virtual auditory displays. Since rendering complex virtual scenes is computationally demanding, we propose four algorithms for efficiently representing HRTFs in subbands, i.e., as an analysis filterbank (FB) followed by a transfer matrix and a synthesis FB. All four algorithms use sparse approximation procedures to minimize the computational complexity while maintaining perceptually relevant HRTF properties. The first two algorithms separately optimize the complexity of the transfer matrix associated to each HRTF for fixed FBs. The other two algorithms jointly optimize the FBs and transfer matrices for complete HRTF sets by two variants. The first variant aims at minimizing the complexity of the transfer matrices, while the second one does it for the FBs. Numerical experiments investigate the latency-complexity trade-off and show that the proposed methods offer significant computational savings when compared with other available approaches. Psychoacoustic localization experiments were modeled and conducted to find a reasonable approximation tolerance so that no significant localization performance degradation was introduced by the subband representation.
Car-Parrinello treatment for an approximate density-functional theory method.
Rapacioli, Mathias; Barthel, Robert; Heine, Thomas; Seifert, Gotthard
2007-03-28
The authors formulate a Car-Parrinello treatment for the density-functional-based tight-binding method with and without self-consistent charge corrections. This method avoids the numerical solution of the secular equations, the principal drawback for large systems if the linear combination of atomic orbital ansatz is used. The formalism is applicable to finite systems and for supercells using periodic boundary conditions within the Gamma-point approximation. They show that the methodology allows the application of modern computational techniques such as sparse matrix storage and massive parallelization in a straightforward way. All present bottlenecks concerning computer time and consumption of memory and memory bandwidth can be removed. They illustrate the performance of the method by direct comparison with Born-Oppenheimer molecular dynamics calculations. Water molecules, benzene, the C(60) fullerene, and liquid water have been selected as benchmark systems.
A revised electronic Hessian for approximate time-dependent density functional theory.
Ziegler, Tom; Seth, Michael; Krykunov, Mykhaylo; Autschbach, Jochen
2008-11-14
Time-dependent density functional theory (TD-DFT) at the generalized gradient level of approximation (GGA) has shown systematic errors in the calculated excitation energies. This is especially the case for energies representing electron transitions between two separated regions of space or between orbitals of different spatial extents. It will be shown that these limitations can be attributed to the electronic ground state Hessian G(GGA). Specifically, we shall demonstrate that the Hessian G(GGA) can be used to describe changes in energy due to small perturbations of the electron density (Deltarho), but it should not be applied to one-electron excitations involving the density rearrangement (Deltarho) of a full electron charge. This is in contrast to Hartree-Fock theory where G(HF) has a trust region that is accurate for both small perturbations and one-electron excitations. The large trust radius of G(HF) can be traced back to the complete cancellation of Coulomb and exchange terms in Hartree-Fock (HF) theory representing self-interaction (complete self-interaction cancellation, CSIC). On the other hand, it is shown that the small trust radius for G(GGA) can be attributed to the fact that CSIC is assumed for GGA in the derivation of G(GGA) although GGA (and many other approximate DFT schemes) exhibits incomplete self-interaction cancellation (ISIC). It is further shown that one can derive a new matrix G(R-DFT) with the same trust region as G(HF) by taking terms due to ISIC properly into account. Further, with TD-DFT based on G(R-DFT), energies for state-to-state transitions represented by a one-electron excitation (psi(i)-->psi(a)) are approximately calculated as DeltaE(ai). Here DeltaE(ai) is the energy difference between the ground state Kohn-Sham Slater determinant and the energy of a Kohn-Sham Slater determinant where psi(i) has been replaced by psi(a). We make use of the new Hessian in two numerical applications involving charge-transfer excitations. It is
Fragile Nucleosomes Influence Pol II Promoter Function.
Pradhan, Suman K; Xue, Yong; Carey, Michael F
2015-11-05
In this issue of Molecular Cell, Kubik et al. (2015) describe how the RSC chromatin remodeling complex collaborates with two DNA sequence motifs and sequence-specific general regulatory factors to assemble fragile nucleosomes at highly transcribed yeast Pol II promoters, and they distinguish these from promoters bearing stable nucleosomes.
Energy Technology Data Exchange (ETDEWEB)
Diez, Reinaldo Pis [CEQUINOR, Centro de Quimica Inorganica (CONICET, UNLP), Departamento de Quimica, Facultad de Ciencias Exactas, UNLP CC 962, B1900AVV La Plata (Argentina); Karasiev, Valentin V [Centro de Qimica, Instituto Venezolano de Investigaciones Cientificas, IVIC, Apartado 21827, Caracas 1020-A (Venezuela)
2003-07-14
A relationship between the auxiliary density, {rho}(r), defined within the framework of the weighted density approximation and the kinetic energy modulating factor, A{sub N}([{rho}(r)]; r), which appears in the local-scaling transformation version of density functional theory is presented. This relationship imposes the condition of positiveness on the kinetic energy modulating factor and this, in turn, leads to an important mathematical condition on any approximate kinetic energy density functional. It is shown that two well-known approximate kinetic energy density functionals do not satisfy the above relationship at distances very close to the nucleus. By forcing a given approximate kinetic energy density functional to obey the above condition, both the kinetic and exchange energies can be obtained within a framework similar to that of the weighted density approximation. Results on some closed-shell atomic systems provide support for those ideas.
An Optimized Approach for Extracting Approximate Functional Dependencies in XML Documents
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, the definition of approximate XFDs based on value equality is proposed. Two metrics, support and strength, are presented for measuring the degree of approximate XFD. A basic algorithm is designed for extracting minimal set of approximate XFDs, and then two optimized strategies are proposed to improve the performance. Finally, the experimental results show that the optimized algorithms are correct and effective.
Towards the Accuracy of Cybernetic Strategy Planning Models: Causal Proof and Function Approximation
Directory of Open Access Journals (Sweden)
Christian A. Hillbrand
2003-04-01
Full Text Available All kind of strategic tasks within an enterprise require a deep understanding of its critical key success factors and their interrelations as well as an in-depth analysis of relevant environmental influences. Due to the openness of the underlying system, there seems to be an indefinite number of unknown variables influencing strategic goals. Cybernetic or systemic planning techniques try to overcome this intricacy by modeling the most important cause-and-effect relations within such a system. Although it seems to be obvious that there are specific influences between business variables, it is mostly impossible to identify the functional dependencies underlying such relations. Hence simulation or evaluation techniques based on such hypothetically assumed models deliver inaccurate results or fail completely. This paper addresses the need for accurate strategy planning models and proposes an approach to prove their cause-andeffect relations by empirical evidence. Based on this foundation an approach for the approximation of the underlying cause-andeffect function by the means of Artificial Neural Networks is developed.
Differential analysis of matrix convex functions II
DEFF Research Database (Denmark)
Hansen, Frank; Tomiyama, Jun
2009-01-01
We continue the analysis in [F. Hansen, and J. Tomiyama, Differential analysis of matrix convex functions. Linear Algebra Appl., 420:102--116, 2007] of matrix convex functions of a fixed order defined in a real interval by differential methods as opposed to the characterization in terms of divide...
Nakayama, Hiromasa
2006-01-01
We give an algorithm to compute the local $b$ function. In this algorithm, we use the Mora division algorithm in the ring of differential operators and an approximate division algorithm in the ring of differential operators with power series coefficient.
Badillo-Olvera, A.; Begovich, O.; Peréz-González, A.
2017-01-01
The present paper is motivated by the purpose of detection and isolation of a single leak considering the Fault Model Approach (FMA) focused on pipelines with changes in their geometry. These changes generate a different pressure drop that those produced by the friction, this phenomenon is a common scenario in real pipeline systems. The problem arises, since the dynamical model of the fluid in a pipeline only considers straight geometries without fittings. In order to address this situation, several papers work with a virtual model of a pipeline that generates a equivalent straight length, thus, friction produced by the fittings is taking into account. However, when this method is applied, the leak is isolated in a virtual length, which for practical reasons does not represent a complete solution. This research proposes as a solution to the problem of leak isolation in a virtual length, the use of a polynomial interpolation function in order to approximate the conversion of the virtual position to a real-coordinates value. Experimental results in a real prototype are shown, concluding that the proposed methodology has a good performance.
Institute of Scientific and Technical Information of China (English)
Yansu LIU; Yanzhu FAN; Fei XUE; Xizi YUE; Steven E BRAUTH; Yezhong TANG; Guangzhan FANG
2016-01-01
Brain systems engage in what are generally considered to be among the most complex forms of information processing. In the present study, we investigated the functional complexity of anuran auditory processing using the approximate entropy (ApEn) protocol for electroencephalogram (EEG) recordings from the forebrain and midbrain while male and female music frogs (Babina daunchina) listened to acoustic stimuli whose biological significance varied. The stimuli used were synthesized white noise (reflecting a novel signal), conspecific male advertisement calls with either high or low sexual attractiveness (relfecting sexual selection) and silence (relfecting a baseline). The results showed that 1) ApEn evoked by conspeciifc calls exceeded ApEn evoked by synthesized white noise in the left mesencephalon indicating this structure plays a critical role in processing acoustic signals with biological signiifcance;2) ApEn in the mesencephalon was significantly higher than for the telencephalon, consistent with the fact that the anuran midbrain contains a large well-organized auditory nucleus (torus semicircularis) while the forebrain does not; 3) for females ApEn in the mesencephalon was signiifcantly different than that of males, suggesting that males and females process biological stimuli related to mate choice differently.
Zhou, Chenyi; Guo, Hong
2017-01-01
We report a diagrammatic method to solve the general problem of calculating configurationally averaged Green's function correlators that appear in quantum transport theory for nanostructures containing disorder. The theory treats both equilibrium and nonequilibrium quantum statistics on an equal footing. Since random impurity scattering is a problem that cannot be solved exactly in a perturbative approach, we combine our diagrammatic method with the coherent potential approximation (CPA) so that a reliable closed-form solution can be obtained. Our theory not only ensures the internal consistency of the diagrams derived at different levels of the correlators but also satisfies a set of Ward-like identities that corroborate the conserving consistency of transport calculations within the formalism. The theory is applied to calculate the quantum transport properties such as average ac conductance and transmission moments of a disordered tight-binding model, and results are numerically verified to high precision by comparing to the exact solutions obtained from enumerating all possible disorder configurations. Our formalism can be employed to predict transport properties of a wide variety of physical systems where disorder scattering is important.
The functional performance of the Argus II retinal prosthesis.
Stronks, H Christiaan; Dagnelie, Gislin
2014-01-01
Visual prostheses are devices to treat profound vision loss by stimulating nerve cells anywhere along the visual pathway, typically with electrical pulses. The Argus II implant, developed by Second Sight Medical Products (SSMP, Sylmar, CA, USA), targets the retina and features 60 electrodes that electrically stimulate the surviving retinal neurons. Of the approximately 20 research groups that are actively developing visual prostheses, SSMP has the longest track record. The Argus II was the first visual prosthesis to become commercially available: it received the European conformity mark in 2011 and FDA approval was granted in early 2013 for humanitarian use in the USA. Meanwhile, the Argus II safety/benefit study has been extended for research purposes, and is still ongoing. In this review, we will discuss the performance of the Argus II in restoring sight to the blind, and we will shed light on its expected developments in the coming years.
Luminosity function of optically-selected type II QSOs
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
For a sample of 411 type II QSOs with redshifts less then 0.3,we use the Balmer decrements to do the reddening correction of the [O III] luminosities and then derive the intrinsic [O III] luminosity function.We find that the host reddening correction of the [O III] 5007 luminosity for type II QSOs cannot be neglected.The median Balmer decrement of Hα/Hβ=4.0 corresponds to an extinction of 0.94 mag for the [O III] 5007 line,which is consistent with the result derived from the median Hβ/Hγ.Comparing the intrinsic luminosity function of type II QSOs with that of type I QSOs,we find that the upper limit of the type II QSO’s fraction in the total QSOs is 80% for type II QSOs with z < 0.3 and 8.6≤log(L[O III]/L)≤9.4.
Tareyeva, E. E.; Ryzhov, V. N.
2016-12-01
We propose an approximation of a direct correlation function corresponding to the linearization with respect to - βϕ( r) of a generalized mean spherical approximation for a hard-core multi-Yukawa system of particles. We use the results to study the behavior of maximums of thermodynamic response functions in the supercritical region of a fluid with a two-term Yukawa potential imitating the Lennard-Jones potential.
Padé approximant related to remarkable inequalities involving trigonometric functions
Directory of Open Access Journals (Sweden)
Gabriel Bercu
2016-03-01
Full Text Available Abstract In this paper we, respectively, give simple proofs of some remarkable trigonometric inequalities, based on the Padé approximation method. We also obtain rational refinements of these inequalities. We are convinced that the Padé approximation method offers a general framework for solving many other similar inequalities.
Chen, Jianhan
2010-09-14
The generalized Born (GB) theory is a prime choice for implicit treatment of solvent that provides a favorable balance between efficiency and accuracy for reliable simulation of protein conformational equilibria. In GB, the dielectric boundary is a key physical property that needs to be properly described. While it is widely accepted that the molecular surface (MS) should provide the most physical description, most existing GB models are based on van der Waals (vdW)-like surfaces for computational simplicity and efficiency. A simple and effective approximation to molecular volume is explored here using atom-centered dielectric functions within the context of a generalized Born model with simple switching (GBSW). The new model, termed GBSW/MS2, is as efficient as the original vdW-like-surface-based GBSW model, but is able to reproduce the Born radii calculated from the "exact" Poisson-Boltzmann theory with a correlation of 0.95. More importantly, examination of the potentials of mean force of hydrogen-bonding and charge-charge interactions demonstrates that GBSW/MS2 correctly captures the first desolvation peaks, a key signature of true MS. Physical parameters including atomic input radii and peptide backbone torsion were subsequently optimized on the basis of solvation free energies of model compounds, potentials of mean force of their interactions, and conformational equilibria of a set of helical and β-hairpin model peptides. The resulting GBSW/MS2 protein force field reasonably recapitulates the structures and stabilities of these model peptides. Several remaining limitations and possible future developments are also discussed.
Institute of Scientific and Technical Information of China (English)
LongShuyao; HuDe'an
2003-01-01
The meshless method is a new numerical technique presented in recent years .It uses the moving least square (MLS) approximation as a shape function . The smoothness of the MLS approximation is determined by that of the basic function and of the weight function, and is mainly determined by that of the weight function. Therefore, the weight function greatly affects the accuracy of results obtained. Different kinds of weight functions, such as the spline function, the Gauss function and so on, are proposed recently by many researchers. In the present work, the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation method. The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed. Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and a in Gauss and exponential weight functions are in the range of reasonable values, respectively, and the higher the smoothness of the weight function, the better the features of the solutions.
Dratman, Ezequiel
2011-01-01
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, if the absorption is large enough, compared with the flux in the boundary, 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 {\\em linear} in the number of nodes involved in the discretization and the logarithm of the number of digits of approximation required.
Narimani, Mohammand; Lam, H K; Dilmaghani, R; Wolfe, Charles
2011-06-01
Relaxed linear-matrix-inequality-based stability conditions for fuzzy-model-based control systems with imperfect premise matching are proposed. First, the derivative of the Lyapunov function, containing the product terms of the fuzzy model and fuzzy controller membership functions, is derived. Then, in the partitioned operating domain of the membership functions, the relations between the state variables and the mentioned product terms are represented by approximated polynomials in each subregion. Next, the stability conditions containing the information of all subsystems and the approximated polynomials are derived. In addition, the concept of the S-procedure is utilized to release the conservativeness caused by considering the whole operating region for approximated polynomials. It is shown that the well-known stability conditions can be special cases of the proposed stability conditions. Simulation examples are given to illustrate the validity of the proposed approach.
Energy Technology Data Exchange (ETDEWEB)
Urbanski, P. [Institute of Nuclear Chemistry and Technology, Warsaw (Poland)
1996-12-31
Principles of the polynomial regression splines as well as algorithms and programs for their computation are presented. The programs prepared using software package MATLAB are generally intended for approximation of the X-ray spectra and can be applied in the multivariate calibration of radiometric gauges. (author).
Zero and pole distribution of diagonal Padé approximants to the exponential function
K.A. Driver (Kathy); N.M. Temme (Nico)
1997-01-01
textabstractThe polynomials $P_n$ and $Q_m$ having degrees $n$ and $m$ respectively, with $P_n$ monic, that solve the approximation problem $$P_n(z)e^{-z+Q_m(z)={cal O left(z^{n+m+1right)$$ will be investigated for their asymptotic behaviour, in particular in connection with the distribution of
Mora, P J; Woodard, R P
2013-01-01
We use the Hartree approximation to the Einstein equation on de Sitter background to solve for the one loop correction to the graviton mode function. This should give a reasonable approximation to how the ensemble of inflationary gravitons affects a single external graviton. At late times we find that the one loop correction to the plane wave mode function $u(\\eta,k)$ goes like $G H^2 \\ln(a)/a^2$, where $a$ is the inflationary scale factor. One consequence is that the one loop corrections to the "electric" components of the linearized Weyl tensor grow compared to the tree order result.
Study of u and d quark form factors in light front wave function with N{sup 2}LO approximation
Energy Technology Data Exchange (ETDEWEB)
Reza Shojaei, Mohammad [Shahrood University of Technology, Department of Physics, Shahrood (Iran, Islamic Republic of)
2016-04-15
In this paper, we have calculated the Dirac and Pauli form factors for u and d quark with light front quark model in N{sup 2}LO approximation for MSTW2008 quark function distributions. By using this approximation we found the parameters of Dirac and Pauli form factors, and then we calculated the form factors function as Q{sup 2}. By comparing with experimental data we concluded that F{sub 1}(Q{sup 2}) and F{sub 2}(Q{sup 2}) are in good agreement with the experimental data. (orig.)
Mugunthan, Pradeep; Shoemaker, Christine A.; Regis, Rommel G.
2005-11-01
The performance of function approximation (FA) methods is compared to heuristic and derivative-based nonlinear optimization methods for automatic calibration of biokinetic parameters of a groundwater bioremediation model of chlorinated ethenes on a hypothetical and a real field case. For the hypothetical case, on the basis of 10 trials on two different objective functions, the FA methods had the lowest mean and smaller deviation of the objective function among all algorithms for a combined Nash-Sutcliffe objective and among all but the derivative-based algorithm for a total squared error objective. The best algorithms in the hypothetical case were applied to calibrate eight parameters to data obtained from a site in California. In three trials the FA methods outperformed heuristic and derivative-based methods for both objective functions. This study indicates that function approximation methods could be a more efficient alternative to heuristic and derivative-based methods for automatic calibration of computationally expensive bioremediation models.
Optimal hash functions for approximate closest pairs on the n-cube
Gordon, Daniel M; Ostapenko, Peter
2008-01-01
One way to find closest pairs in large datasets is to use hash functions. In recent years locality-sensitive hash functions for various metrics have been given: projecting an n-cube onto k bits is simple hash function that performs well. In this paper we investigate alternatives to projection. For various parameters hash functions given by complete decoding algorithms for codes work better, and asymptotically random codes perform better than projection.
On polynomials related with Hermite-Padé approximations to the exponential function
Driver, K.A.; Temme, N.M.
1997-01-01
We investigate the polynomials $P_n,,Q_m$ and $R_s$, having degrees $n,,m$ and $s$ respectively, with $P_n$ monic, that solve the approximation problem $$E_{nms(x):=P_n(x)e^{-2x+Q_m(x)e^{-x+R_s(x)=O(x^{n+m+s+2) {quad rm as quad x rightarrow 0. $$ We give a connection between the coefficients of eac
Approximation of Integrable Functions by General Linear Operators of Their Fourier Series
Institute of Scientific and Technical Information of China (English)
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].
Directory of Open Access Journals (Sweden)
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].
The frozen nucleon approximation in two-particle two-hole response functions
Directory of Open Access Journals (Sweden)
I. Ruiz Simo
2017-07-01
Full Text Available We present a fast and efficient method to compute the inclusive two-particle two-hole (2p–2h electroweak responses in the neutrino and electron quasielastic inclusive cross sections. The method is based on two approximations. The first neglects the motion of the two initial nucleons below the Fermi momentum, which are considered to be at rest. This approximation, which is reasonable for high values of the momentum transfer, turns out also to be quite good for moderate values of the momentum transfer q≳kF. The second approximation involves using in the “frozen” meson-exchange currents (MEC an effective Δ-propagator averaged over the Fermi sea. Within the resulting “frozen nucleon approximation”, the inclusive 2p–2h responses are accurately calculated with only a one-dimensional integral over the emission angle of one of the final nucleons, thus drastically simplifying the calculation and reducing the computational time. The latter makes this method especially well-suited for implementation in Monte Carlo neutrino event generators.
Non-local velocity distribution function and one-flight approximation
Energy Technology Data Exchange (ETDEWEB)
Bakunin, O.G. [FOM Instituut voor Plasmafysica ' Rijnhuizen' , Associate Euroatom-FOM, 3430 BE Nieuwegein (Netherlands) and Russian Research Center ' Kurchatov Institute' , Nuclear Fusion Institute, sq. Kurchatova 1, 123182 Moscow (Russian Federation)]. E-mail: oleg_bakunin@yahoo.com
2004-09-13
The functional equation describing the collisionless particle velocity distribution function f(V) is considered in the framework of probabilistic approach. The key element of the collisionless particles description is using the waiting time distribution {psi}(t). The solution of the considered functional is obtained for several model functions {psi}(t) and it leads to the power form tails of the velocity distribution f(V). It is possible to adopt considered functional to the Laplace transformation form that allows us to accord 'collision' and 'collisionless' description. This Laplace form of the functional yields the Levy-Smirnov velocity distribution function with the characteristic exponent aL=1/2.
Calculus of Elementary Functions, Part II. Student Text. Revised Edition.
Herriot, Sarah T.; And Others
This course is intended for students who have a thorough knowledge of college preparatory mathematics, including algebra, axiomatic geometry, trigonometry, and analytic geometry. This text, Part II, contains material designed to follow Part I. Chapters included in this text are: (6) Derivatives of Exponential and Related Functions; (7) Area and…
Approximate reconstruction of bandlimited functions for the integrate and fire sampler
Feichtinger, Hans G; Romero, José Luis; Alvarado, Alexander Singh; Velasco, Gino Angelo
2009-01-01
In this paper we study the reconstruction of a bandlimited signal from samples generated by the integrate and fire model. This sampler allows us to trade complexity in the reconstruction algorithms for simple hardware implementations, and is specially convenient in situations where the sampling device is limited in terms of power, area and bandwidth. Although perfect reconstruction for this sampler is impossible, we give a general approximate reconstruction procedure and bound the corresponding error. We also show the performance of the proposed algorithm through numerical simulations.
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.
Directory of Open Access Journals (Sweden)
Fernando Racimo
2014-11-01
Full Text Available Quantifying the proportion of polymorphic mutations that are deleterious or neutral is of fundamental importance to our understanding of evolution, disease genetics and the maintenance of variation genome-wide. Here, we develop an approximation to the distribution of fitness effects (DFE of segregating single-nucleotide mutations in humans. Unlike previous methods, we do not assume that synonymous mutations are neutral or not strongly selected, and we do not rely on fitting the DFE of all new nonsynonymous mutations to a single probability distribution, which is poorly motivated on a biological level. We rely on a previously developed method that utilizes a variety of published annotations (including conservation scores, protein deleteriousness estimates and regulatory data to score all mutations in the human genome based on how likely they are to be affected by negative selection, controlling for mutation rate. We map this and other conservation scores to a scale of fitness coefficients via maximum likelihood using diffusion theory and a Poisson random field model on SNP data. Our method serves to approximate the deleterious DFE of mutations that are segregating, regardless of their genomic consequence. We can then compare the proportion of mutations that are negatively selected or neutral across various categories, including different types of regulatory sites. We observe that the distribution of intergenic polymorphisms is highly peaked at neutrality, while the distribution of nonsynonymous polymorphisms has a second peak at [Formula: see text]. Other types of polymorphisms have shapes that fall roughly in between these two. We find that transcriptional start sites, strong CTCF-enriched elements and enhancers are the regulatory categories with the largest proportion of deleterious polymorphisms.
Yan, Zidan; Perdew, John P.; Kurth, Stefan
2000-03-01
Within a density functional context, the random phase approximation (RPA) for the correlation emergy makes a short-range error which is well-suited for correction by a local spin density or generalized gradient approximation (GGA). Here we construct a GGA for the short-range correction, following the same reliable procedure used earlier to construct the GGA for the whole exchange-correlation energy: real-space cutoff of the spurious long-range contribution to the gradient expansion of the hole around an electron. The resulting density functional is nearly local, and predicts a substantial correction to the RPA correlation energy of an atom but \\underlinevery small corrections to the RPA atomization energy of a molecule, which may by itself come close to "chemical accuracy", and to the RPA surface energy of a metal. A by-product of this work is a density functional for the system-averaged correlation hole within RPA.
Energy Technology Data Exchange (ETDEWEB)
Nakano, Masayoshi, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Minami, Takuya, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Fukui, Hitoshi, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Yoneda, Kyohei, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Shigeta, Yasuteru, E-mail: mnaka@cheng.es.osaka-u.ac.jp; Kishi, Ryohei, E-mail: mnaka@cheng.es.osaka-u.ac.jp [Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531 (Japan); Champagne, Benoît; Botek, Edith [Laboratoire de Chimie Théorique, Facultés Universitaires Notre-Dame de la Paix (FUNDP), rue de Bruxelles, 61, 5000 Namur (Belgium)
2015-01-22
We develop a novel method for the calculation and the analysis of the one-electron reduced densities in open-shell molecular systems using the natural orbitals and approximate spin projected occupation numbers obtained from broken symmetry (BS), i.e., spin-unrestricted (U), density functional theory (DFT) calculations. The performance of this approximate spin projection (ASP) scheme is examined for the diradical character dependence of the second hyperpolarizability (γ) using several exchange-correlation functionals, i.e., hybrid and long-range corrected UDFT schemes. It is found that the ASP-LC-UBLYP method with a range separating parameter μ = 0.47 reproduces semi-quantitatively the strongly-correlated [UCCSD(T)] result for p-quinodimethane, i.e., the γ variation as a function of the diradical character.
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...
Functional orthopedic magnetic appliance (FOMA) II--modus operandi.
Vardimon, A D; Stutzmann, J J; Graber, T M; Voss, L R; Petrovic, A G
1989-05-01
A new functional appliance (FA) to correct Class II dentoskeletal malocclusions is introduced. The functional orthopedic magnetic appliance (FOMA) II uses upper and lower attracting magnetic means (Nd2Fe14B) to constrain the lower jaw in an advanced sagittal posture. In vitro, a special gauge transducer measured the magnetic attractive path and forces. In vivo, 13 prepubertal female Macaca fascicularis monkeys received facial implants and were treated for 4 months with the following appliances: conventional FA (four subjects), FOMA II (five subjects), a combined FOMA II + FA (two subjects), and sham (control) appliance (two subjects). The in vitro results showed the following: vertico-sagitally displaced upper and lower magnets attracted ultimately along an oblique line with a terminal horizonal slide to become fully superimposed; the functional performance improved when the magnetic interface acted as a magnetic inclined plane; and the magnetic force was able to guide and constrain the mandible toward the constructive protrusive closure position (CPCP) (1.2 mm, F = 570 gm) from levels below the habitual rest position (3 mm, F = 219 gm) and the electromyographic (EMG) relaxed position (8.5 mm, F = 45 gm). The in vivo results demonstrated the following: functional performance increased in FOMA II (22%) and in the combined FOMA II + FA (28%) over the conventional FA; mandibular length increased significantly in the treated animals (means = 2.83 +/- 0.70 mm) over the control animals (means = 0.43 +/- 0.08 mm); incisor proclination was lower in magnetic appliances (means = 4.57 +/- 1.76 degrees) than in the conventional FA (means = 8.75 +/- 1.85 degrees); mandibular elongation and condylar posterior inclination resulted from posterosuperior endochondral growth (increased cell proliferation and/or hyperplasia of functional chondroblasts) and by bony remodeling of the condylar neck (apposition posterior border, resorption anterior border), respectively; virtually no
Energy Technology Data Exchange (ETDEWEB)
Mattsson, Ann Elisabet; Modine, Normand Arthur; Desjarlais, Michael Paul; Muller, Richard Partain; Sears, Mark P.; Wright, Alan Francis
2006-11-01
A finite temperature version of 'exact-exchange' density functional theory (EXX) has been implemented in Sandia's Socorro code. The method uses the optimized effective potential (OEP) formalism and an efficient gradient-based iterative minimization of the energy. The derivation of the gradient is based on the density matrix, simplifying the extension to finite temperatures. A stand-alone all-electron exact-exchange capability has been developed for testing exact exchange and compatible correlation functionals on small systems. Calculations of eigenvalues for the helium atom, beryllium atom, and the hydrogen molecule are reported, showing excellent agreement with highly converged quantumMonte Carlo calculations. Several approaches to the generation of pseudopotentials for use in EXX calculations have been examined and are discussed. The difficult problem of finding a correlation functional compatible with EXX has been studied and some initial findings are reported.
Incoherent scatter spectra from plasma of a 13-moment approximation distribution function
Institute of Scientific and Technical Information of China (English)
2008-01-01
The function and physical mechanism of heat flow and the viscous stress in the velocity distribution function expanded by Maxwellian distribution are presented. With the introduction of effective temperature Tf, incoherent scatter spectra from plasma for electromagnetic wave in arbitrary line of sight are given. The effect of asymmetry and anisotropy provided by heat flow and the viscous stress on power spectra is discussed. Radar spectra are calculated for different cases of electric field, direction, collision frequency and temperature. The effect of heat flow and the viscous stress on inversion results is analyzed. With a large electric field, the character of non-Maxwellian must be considered.
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...
二元二次函数逼近的存在性和局部性%The Existence and Local Behavior of the Bivariate Quadratic Function Approximation
Institute of Scientific and Technical Information of China (English)
郑成德
2006-01-01
This paper analysis the local behavior of the bivariate quadratic function approximation to a bivariate function which has a given power series expansion about the origin. It function and that this function is analytic in a neighborhood of the origin.
Electronic structure of ScN and YN:density-functional theory LDA and GW approximation calculations
Institute of Scientific and Technical Information of China (English)
Lü Tie-Yu; Huang Mei-Chun
2007-01-01
The desirable physical properties of hardness, high temperature stability, and conductivity make the early transition metal nitrides important materials for various technological applications. To learn more about the nature of these materials, the local-density approximation(LDA) and GW approximation i.e. combination of the Green function G and the screened Coulomb interaction W, have been performed. This paper investigates the bulk electronic and physical properties of early transition metal mononitrides, ScN and YN in the rocksalt structure. In this paper, the semicore electrons are regarded as valance electrons. ScN appears to be a semimetal, and YN is semiconductor with band gap of0.142 eV within the LDA, but are in fact semiconductors with indirect band gaps of 1.244 and 0.544 eV respectively, as revealed by calculations performed using GW approximation.
Dhar, V K; Dubey, R Koul B P
2009-01-01
We report an inter-comparison of some popular algorithms within the artificial neural network domain (viz., Local search algorithms, global search algorithms, higher order algorithms and the hybrid algorithms) by applying them to the standard benchmarking problems like the IRIS data, XOR/N-Bit parity and Two Spiral. Apart from giving a brief description of these algorithms, the results obtained for the above benchmark problems are presented in the paper. The results suggest that while Levenberg-Marquardt algorithm yields the lowest RMS error for the N-bit Parity and the Two Spiral problems, Higher Order Neurons algorithm gives the best results for the IRIS data problem. The best results for the XOR problem are obtained with the Neuro Fuzzy algorithm. The above algorithms were also applied for solving several regression problems such as cos(x) and a few special functions like the Gamma function, the complimentary Error function and the upper tail cumulative $\\chi^2$-distribution function. The results of these ...
Weighted Approximation of Continuous Functions by Sequences of Linear Positive Operators
Indian Academy of Sciences (India)
Tülin Coşkun
2000-11-01
In this work we obtain, under suitable conditions, theorems of Korovkin type for spaces with different weight, composed of continuous functions defined on unbounded regions. These results can be seen as an extension of theorems by Gadjiev in [4] and [5].
Optimally sparse approximations of 3D functions by compactly supported shearlet frames
DEFF Research Database (Denmark)
Kutyniok, Gitta; Lim, Wang-Q.; Lemvig, Jakob
2012-01-01
We study efficient and reliable methods of capturing and sparsely representing anisotropic structures in 3D data. As a model class for multidimensional data with anisotropic features, we introduce generalized 3D cartoon-like images. This function class will have two smoothness parameters: one par...
Approximation of Mixed-Type Functional Equations in Menger PN-Spaces
Directory of Open Access Journals (Sweden)
M. Eshaghi Gordji
2012-01-01
Full Text Available Let X and Y be vector spaces. We show that a function f:X→Y with f(0=0 satisfies Δf(x1,…,xn=0 for all x1,…,xn∈X, if and only if there exist functions C:X×X×X→Y, B:X×X→Y and A:X→Y such that f(x=C(x,x,x+B(x,x+A(x for all x∈X, where the function C is symmetric for each fixed one variable and is additive for fixed two variables, B is symmetric bi-additive, A is additive and Δf(x1,…,xn=∑k=2n(∑i1=2k∑i2=i1+1k+1⋯∑in-k+1=in-k+1nf(∑i=1,i≠i1,…,in-k+1nxi-∑r=1n-k+1xir+f(∑i=1nxi-2n-2∑i=2n(f(x1+xi+f(x1-xi+2n-1(n-2f(x1 (n∈N, n≥3 for all x1,…,xn∈X. Furthermore, we solve the stability problem for a given function f satisfying Δf(x1,…,xn=0, in the Menger probabilistic normed spaces.
DEFF Research Database (Denmark)
Ruban, Andrei; Simak, S.I.; Korzhavyi, P.A.
2002-01-01
-electron potential and energy. In the case of a random alloy such interactions can be accounted for only by lifting the atomic-sphere and single-site approximations, in order to include the polarization due to local environment effects. Nevertheless, a simple parametrization of the screened Coulomb interactions...... for the ordinary single-site methods, including the generalized perturbation method, is still possible. We obtained such a parametrization for bulk and surface NiPt alloys, which allows one to obtain quantitatively accurate effective interactions in this system....
多元代数函数逼近的存在性与局部性质%The Existence and Local Behavior of Multivariate Algebraic Function Approximations
Institute of Scientific and Technical Information of China (English)
郑成德; 王仁宏
2004-01-01
The existing scheme of rational polynomial approximants, defined by multivariate power series, is extended to define approximants with branch points. The existence theorem is obtained. The basic properties used to define the rational approximants can be preserved almost intactly. Especially, the local behavior of the diagonal bivariate quadratic algebraic function approximation is analysed.
Structural and functional characteristics of plant proteinase inhibitor-II (PI-II) family.
Rehman, Shazia; Aziz, Ejaz; Akhtar, Wasim; Ilyas, Muhammad; Mahmood, Tariq
2017-02-09
Plant proteinase inhibitor-II (PI-II) proteins are one of the promising defensive proteins that helped the plants to resist against different kinds of unfavorable conditions. Different roles for PI-II have been suggested such as regulation of endogenous proteases, modulation of plant growth and developmental processes and mediating stress responses. The basic knowledge on genetic and molecular diversity of these proteins has provided significant insight into their gene structure and evolutionary relationships in various members of this family. Phylogenetic comparisons of these family genes in different plants suggested that the high rate of retention of gene duplication and inhibitory domain multiplication may have resulted in the expansion and functional diversification of these proteins. Currently, a large number of transgenic plants expressing PI-II genes are being developed for enhancing the defensive capabilities against insects, bacteria and pathogenic fungi. Much emphasis is yet to be given to exploit this ever expanding repertoire of genes for improving abiotic stress resistance in transgenic crops. This review presents an overview about the current knowledge on PI-II family genes, their multifunctional role in plant defense and physiology with their potential applications in biotechnology.
Directory of Open Access Journals (Sweden)
Hozejowski Leszek
2012-04-01
Full Text Available The paper is devoted to a computational problem of predicting a local heat transfer coefficient from experimental temperature data. The experimental part refers to boiling flow of a refrigerant in a minichannel. Heat is dissipated from heating alloy to the flowing liquid due to forced convection. The mathematical model of the problem consists of the governing Poisson equation and the proper boundary conditions. For accurate results it is required to smooth the measurements which was obtained by using Trefftz functions. The measurements were approximated with a linear combination of Trefftz functions. Due to the computational procedure in which the measurement errors are known, it was possible to smooth the data and also to reduce the residuals of approximation on the boundaries.
Energy Technology Data Exchange (ETDEWEB)
Birzvalk, Yu.A.
1977-10-01
The peculiarities of averaging of a function with respect to one of its coordinates are studied, resulting in the formulation of two-dimensional MHD problems in the zero-induction approximation. The transition to the two-dimensional approximation is achieved by averaging all of the functions analyzed with respect to one of the coordinates. It is shown that when there is symmetry in the Poisson equation for the potential, components of the scalar product v.rot B appear, as a result of the fact that rot B = O. However, their appearance can also be explained by a clearer, though less strict, method. The importance of consideration of these components must be estimated in each specific problem. An elementary modeling problem is solved allowing the relative significance of the current density component in the direction with respect to which averaging is performed to be estimated. 2 references, 4 figures.
Directory of Open Access Journals (Sweden)
Anne-Mari Moilanen
Full Text Available BACKGROUND: Activation of the renin-angiotensin-system (RAS plays a key pathophysiological role in heart failure in patients with hypertension and myocardial infarction. However, the function of (prorenin receptor ((PRR is not yet solved. We determined here the direct functional and structural effects of (PRR in the heart. METHODOLOGY/PRINCIPAL FINDINGS: (PRR was overexpressed by using adenovirus-mediated gene delivery in normal adult rat hearts up to 2 weeks. (PRR gene delivery into the anterior wall of the left ventricle decreased ejection fraction (P<0.01, fractional shortening (P<0.01, and intraventricular septum diastolic and systolic thickness, associated with approximately 2-fold increase in left ventricular (PRR protein levels at 2 weeks. To test whether the worsening of cardiac function and structure by (PRR gene overexpression was mediated by angiotensin II (Ang II, we infused an AT(1 receptor blocker losartan via osmotic minipumps. Remarkably, cardiac function deteriorated in losartan-treated (PRR overexpressing animals as well. Intramyocardial (PRR gene delivery also resulted in Ang II-independent activation of extracellular-signal-regulated kinase1/2 phosphorylation and myocardial fibrosis, and the expression of transforming growth factor-β1 and connective tissue growth factor genes. In contrast, activation of heat shock protein 27 phosphorylation and apoptotic cell death by (PRR gene delivery was Ang II-dependent. Finally, (PRR overexpression significantly increased direct protein-protein interaction between (PRR and promyelocytic zinc-finger protein. CONCLUSIONS/SIGNIFICANCE: These results indicate for the first time that (PRR triggers distinct Ang II-independent myocardial fibrosis and deterioration of cardiac function in normal adult heart and identify (PRR as a novel therapeutic target to optimize RAS blockade in failing hearts.
On One-Sided Filters for Spectral Fourier Approximations of Discontinuous Functions
1991-03-01
up to the discontinuity from one side. We also use a least square procedure to construct such a filter and test it on several discontinuous functions...thus use a least square procedure, described below, with the objective of obtaining more efficient one-sided filters for a practical range of N...between 8 and 32 (between 16 and 64 grid points for collocation): Least Square Procedure: We make an ansaze { TN ()QykŽ N7 = k (3.1)a k < 0 -k<O where the
B0-B0bar mixing in the static approximation from the Schroedinger Functional and twisted mass QCD
Palombi, F.; Papinutto, M.; Pena., C; Wittig, H.
2005-01-01
We discuss the renormalisation properties of parity-odd Delta B=2 operators with the heavy quark treated in the static approximation. Via twisted mass QCD (tmQCD), these operators provide the matrix elements relevant for the B0-B0bar mixing amplitude. The layout of a non-perturbative renormalisation programme for the operator basis, using Schroedinger Functional techniques, is described. Finally, we report our results for a one-loop perturbative study of various renormalisation schemes with W...
Frolov, Maxim; Chistiakova, Olga
2017-06-01
Paper is devoted to a numerical justification of the recent a posteriori error estimate for Reissner-Mindlin plates. This majorant provides a reliable control of accuracy of any conforming approximate solution of the problem including solutions obtained with commercial software for mechanical engineering. The estimate is developed on the basis of the functional approach and is applicable to several types of boundary conditions. To verify the approach, numerical examples with mesh refinements are provided.
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.
Energy-loss function in the two-pair approximation for the electron liquid
Bachlechner, M. E.; Holas, A.; Böhm, H. M.; Schinner, A.
1996-07-01
The imaginary part of the proper polarizability, Im Π, arising due to excitations of two electron-hole pairs, is studied in detail for electron systems of arbitrary dimensionality, and taking into account arbitrary degeneracy of the electron bands. This allows an application to semiconductors with degenerate valleys, and to ferromagnetic metals. The results obtained not only confirm expressions already known for paramagnetic systems in the high-frequency region, but are also rigorously shown to be valid for all frequencies outside the particle-hole continuum. For a sufficiently high momentum transfer a cutoff frequency (below which Im Π=0) is established for not only two-pair but also any n-pair processes. In contrast, there is no upper cutoff for n>~1. The energy-loss function, including the discussed two-pair contributions, is calculated. The effects of screening are investigated. Numerical results, illustrating various aspects and properties of this function, especially showing finite-width plasmon peaks, are obtained for a two-dimensional electron gas.
Energy Technology Data Exchange (ETDEWEB)
Mardirossian, Narbe [Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720 (United States); Head-Gordon, Martin, E-mail: mhg@cchem.berkeley.edu [Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720 (United States); Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)
2015-02-21
A meta-generalized gradient approximation density functional paired with the VV10 nonlocal correlation functional is presented. The functional form is selected from more than 10{sup 10} choices carved out of a functional space of almost 10{sup 40} possibilities. Raw data come from training a vast number of candidate functional forms on a comprehensive training set of 1095 data points and testing the resulting fits on a comprehensive primary test set of 1153 data points. Functional forms are ranked based on their ability to reproduce the data in both the training and primary test sets with minimum empiricism, and filtered based on a set of physical constraints and an often-overlooked condition of satisfactory numerical precision with medium-sized integration grids. The resulting optimal functional form has 4 linear exchange parameters, 4 linear same-spin correlation parameters, and 4 linear opposite-spin correlation parameters, for a total of 12 fitted parameters. The final density functional, B97M-V, is further assessed on a secondary test set of 212 data points, applied to several large systems including the coronene dimer and water clusters, tested for the accurate prediction of intramolecular and intermolecular geometries, verified to have a readily attainable basis set limit, and checked for grid sensitivity. Compared to existing density functionals, B97M-V is remarkably accurate for non-bonded interactions and very satisfactory for thermochemical quantities such as atomization energies, but inherits the demonstrable limitations of existing local density functionals for barrier heights.
Nuclear angiotensin II type 2 (AT2) receptors are functionally linked to nitric oxide production.
Gwathmey, Tanya M; Shaltout, Hossam A; Pendergrass, Karl D; Pirro, Nancy T; Figueroa, Jorge P; Rose, James C; Diz, Debra I; Chappell, Mark C
2009-06-01
Expression of nuclear angiotensin II type 1 (AT(1)) receptors in rat kidney provides further support for the concept of an intracellular renin-angiotensin system. Thus we examined the cellular distribution of renal ANG II receptors in sheep to determine the existence and functional roles of intracellular ANG receptors in higher order species. Receptor binding was performed using the nonselective ANG II antagonist (125)I-[Sar(1),Thr(8)]-ANG II ((125)I-sarthran) with the AT(1) antagonist losartan (LOS) or the AT(2) antagonist PD123319 (PD) in isolated nuclei (NUC) and plasma membrane (PM) fractions obtained by differential centrifugation or density gradient separation. In both fetal and adult sheep kidney, PD competed for the majority of cortical NUC (> or =70%) and PM (> or =80%) sites while LOS competition predominated in medullary NUC (> or =75%) and PM (> or =70%). Immunodetection with an AT(2) antibody revealed a single approximately 42-kDa band in both NUC and PM extracts, suggesting a mature molecular form of the NUC receptor. Autoradiography for receptor subtypes localized AT(2) in the tubulointerstitium, AT(1) in the medulla and vasa recta, and both AT(1) and AT(2) in glomeruli. Loading of NUC with the fluorescent nitric oxide (NO) detector DAF showed increased NO production with ANG II (1 nM), which was abolished by PD and N-nitro-l-arginine methyl ester, but not LOS. Our studies demonstrate ANG II receptor subtypes are differentially expressed in ovine kidney, while nuclear AT(2) receptors are functionally linked to NO production. These findings provide further evidence of a functional intracellular renin-angiotensin system within the kidney, which may represent a therapeutic target for the regulation of blood pressure.
Approximate Separability of Green’s Function for High Frequency Helmholtz Equations
2014-09-01
ym| ≤ √ 2jh,ynj ∈ Sj , and hence am,nj . ( kjh ) −α = j−αk−αδ. For a fixed α > 0 and take 0 < δ < 1 arbitrary close to 0, we 22 BJÖRN ENGQUIST AND...ynj ∈ Cj , and am,nj . ( kjh )−α = j−αk−αδ. For 0 < δ < 1 arbitrary close to 0, one has the row sum estimate (70) ∑nhk n=1 a 2 mn = 1 + ∑J j=1 ∑ nj∈Cj a 2...ym and its neighbors intersecting X or not, which gives different decorrelation rate of two Green’s functions or different power α in am,nj . ( kjh ) −α
H{sub 4}: A challenging system for natural orbital functional approximations
Energy Technology Data Exchange (ETDEWEB)
Ramos-Cordoba, Eloy, E-mail: eloy.raco@gmail.com, E-mail: ematito@gmail.com; Lopez, Xabier [Faculty of Chemistry, University of the Basque Country UPV/EHU, and Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi (Spain); Piris, Mario; Matito, Eduard, E-mail: eloy.raco@gmail.com, E-mail: ematito@gmail.com [Faculty of Chemistry, University of the Basque Country UPV/EHU, and Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi (Spain); IKERBASQUE, Basque Foundation for Science, 48011 Bilbao (Spain)
2015-10-28
The correct description of nondynamic correlation by electronic structure methods not belonging to the multireference family is a challenging issue. The transition of D{sub 2h} to D{sub 4h} symmetry in H{sub 4} molecule is among the most simple archetypal examples to illustrate the consequences of missing nondynamic correlation effects. The resurgence of interest in density matrix functional methods has brought several new methods including the family of Piris Natural Orbital Functionals (PNOF). In this work, we compare PNOF5 and PNOF6, which include nondynamic electron correlation effects to some extent, with other standard ab initio methods in the H{sub 4} D{sub 4h}/D{sub 2h} potential energy surface (PES). Thus far, the wrongful behavior of single-reference methods at the D{sub 2h}–D{sub 4h} transition of H{sub 4} has been attributed to wrong account of nondynamic correlation effects, whereas in geminal-based approaches, it has been assigned to a wrong coupling of spins and the localized nature of the orbitals. We will show that actually interpair nondynamic correlation is the key to a cusp-free qualitatively correct description of H{sub 4} PES. By introducing interpair nondynamic correlation, PNOF6 is shown to avoid cusps and provide the correct smooth PES features at distances close to the equilibrium, total and local spin properties along with the correct electron delocalization, as reflected by natural orbitals and multicenter delocalization indices.
Directory of Open Access Journals (Sweden)
Montes Vides Luis
2001-08-01
Full Text Available
We present a method to estimate interval velocities, reflector depths and geometries in 3D models consisting of a pile of isotropic and homogeneous layers of any velocities and densities separated by smooth interfaces. The travel time of a ray reflecting on a particular interface and registered in the vicinity of a zero-offset ray is expressed by a function referred to a ray-centered coordinated system, fnnction which is estimated at the uppermost surface of the model. The reflection travel time function associated to each reflecting surface is determined at the superior surface in the neighborhood of the reference ray.
The geometry of the upper limiting surface of a particular layer and the travel time function estimated on this interface allow to calculate the interval velocity of the layer and the geometry of the bottom limiting interface. With the interval velocity and geometry of the two limiting interfaces of the layer, the travel time function of the following reflector is estimated at the bottom interface. This step simulates positioning the sources and detectors on the anterior surface of the next subjacent layer.
The procedure is repeated recursively at deeper layers getting the complete solution without a priori knowledge but the upper determined layers and the estimated travel time functions of each reflecting surface.
Gritsenko, O. V.; Rubio, A.; Balbás, L. C.; Alonso, J. A.
1993-03-01
The model Coulomb pair-correlation functions proposed several years ago by Gritsenko, Bagaturyants, Kazansky, and Zhidomirov are incorporated into the self-consistent local-density approximation (LDA) scheme for electronic systems. Different correlation functions satisfying well-established local boundary conditions and integral conditions have been tested by performing LDA calculations for closed-shell atoms. Those correlation functions contain a single parameter which can be optimized by fitting the atomic correlation energies to empirical data. In this way, a single (universal) value of the parameter is found to give a very good fit for all the atoms studied. The results provide a substantial improvement of calculated correlation energies as compared to the usual LDA functionals and the scheme should be useful for molecular and cluster calculations.
Directory of Open Access Journals (Sweden)
R. Murugadoss
2014-10-01
Full Text Available Neural networks are modeled on the way the human brain. They are capable of learning and can automatically recognize by skillfully training and design complex relationships and hidden dependencies based on historical example patterns and use this information for forecasting. The main difference, and at the same time is biggest advantage of the model of neural networks over statistical techniques seen that the forecaster the exact functional structure between input and Output variables need not be specified, but this by the system with certain Learning algorithms is "learned" using a kind of threshold logic. Goal of the learning procedure is to define the training phase while those parameters of the network, with Help the network has one of those adequate for the problem behavior. Mathematically, the training phase is an iterative, converging towards a minimum error value process. They identify the processors of the network, minimize the "total error". The currently the most popular and most widely for business applications algorithm is the backpropagation algorithm. This paper opens the black box of Backpropagation networks and makes the optimization process in the network over time and locally comprehensible.
Kananenka, Alexei A; Lan, Tran Nguyen; Gull, Emanuel; Zgid, Dominika
2016-01-01
The popular, stable, robust and computationally inexpensive cubic spline interpolation algorithm is adopted and used for finite temperature Green's function calculations of realistic systems. We demonstrate that with appropriate modifications the temperature dependence can be preserved while the Green's function grid size can be reduced by about two orders of magnitude by replacing the standard Matsubara frequency grid with a sparser grid and a set of interpolation coefficients. We benchmarked the accuracy of our algorithm as a function of a single parameter sensitive to the shape of the Green's function. Through numerous examples, we confirmed that our algorithm can be utilized in a systematically improvable, controlled, and black-box manner and highly accurate one- and two-body energies and one-particle density matrices can be obtained using only around 5% of the original grid points. Additionally, we established that to improve accuracy by an order of magnitude, the number of grid points needs to be double...
March, N. H.; Nagy, Á.
A fonnally exact integral equation theory for the exchange-only potential Vx(r) in density functional theory was recently set up by Howard and March [I.A. Howard, N.H. March, J. Chem. Phys. 119 (2003) 5789]. It involved a `closure' function P(r) satisfying the exact sum rule ∫ P(r) dr = 0. The simplest choice P(r) = 0 recovers then the approximation proposed by Della Sala and Görling [F. Della Sala, A. Görling, J. Chem. Phys. 115 (2001) 5718] and by Gritsenko and Baerends [O.V. Gritsenko, E.J. Baerends, Phys. Rev. A 64 (2001) 042506]. Here, refined choices of P(r) are proposed, the most direct being based on the KLI (Krieger-Li-Iafrate) approximation. A further choice given some attention is where P(r) involves frontier orbital properties. In particular, the introduction of the LUMO (lowest unoccupied molecular) orbital, along with the energy separation between HOMO (highest occupied molecular orbital) and LUMO levels, should prove a significant step beyond current approximations to the optimized potential method, all of which involve only single-particle occupied orbitals.
Institute of Scientific and Technical Information of China (English)
Yong Ping LIU; Chun Yuan SONG
2014-01-01
In this paper, we study the sharp Jackson inequality for the best approximation of f ∈L2,κ(Rd) by a subspace E2κ(σ) (SE2κ(σ)), which is a subspace of entire functions of exponential type (spherical exponential type) at most σ. Here L2,κ(Rd) denotes the space of all d-variate functions f endowed with the L2-norm with the weight vκ(x)=? ξ∈R+|(ξ, x)|2κ (ξ), which is defined by a positive subsystem R+ of a finite root system R ⊂ Rd and a function κ(ξ) : R → R+ invariant under the reflection group G(R) generated by R. In the case G(R)=Zd2 , we get some exact results. Moreover, the deviation of best approximation by the subspace E2κ(σ) (SE2κ(σ)) of some class of the smooth functions in the space L2,κ(Rd) is obtained.
Gonzalez, J; Rojas, I; Ortega, J; Pomares, H; Fernandez, F J; Diaz, A F
2003-01-01
This paper presents a multiobjective evolutionary algorithm to optimize radial basis function neural networks (RBFNNs) in order to approach target functions from a set of input-output pairs. The procedure allows the application of heuristics to improve the solution of the problem at hand by including some new genetic operators in the evolutionary process. These new operators are based on two well-known matrix transformations: singular value decomposition (SVD) and orthogonal least squares (OLS), which have been used to define new mutation operators that produce local or global modifications in the radial basis functions (RBFs) of the networks (the individuals in the population in the evolutionary procedure). After analyzing the efficiency of the different operators, we have shown that the global mutation operators yield an improved procedure to adjust the parameters of the RBFNNs.
Kwato-Njock, K
2002-01-01
A search is conducted for the determination of expectation values of r sup q between Dirac and quasirelativistic radial wave functions in the quantum-defect approximation. The phenomenological and supersymmetry-inspired quantum-defect models which have proven so far to yield accurate results are used. The recursive structure of formulae derived on the basis of the hypervirial theorem enables us to develop explicit relations for arbitrary values of q. Detailed numerical calculations concerning alkali-metal-like ions of the Li-, Na- and Cu-iso electronic sequences confirm the superiority of supersymmetry-based quantum-defect theory over quantum-defect orbital and exact orbital quantum number approximations. It is also shown that relativistic rather than quasirelativistic treatment may be used for consistent inclusion of relativistic effects.
B0 - anti-B0 mixing in the static approximation from the Schrodinger functional and twisted mass QCD
Palombi, Filippo; Peña, C; Wittig, H
2005-01-01
We discuss the renormalisation properties of parity-odd Delta B=2 operators with the heavy quark treated in the static approximation. Via twisted mass QCD (tmQCD), these operators provide the matrix elements relevant for the B0-B0bar mixing amplitude. The layout of a non-perturbative renormalisation programme for the operator basis, using Schroedinger Functional techniques, is described. Finally, we report our results for a one-loop perturbative study of various renormalisation schemes with Wilson-type lattice regularisations, which allows, in particular, to compute the NLO anomalous dimensions of the operators in the SF schemes of interest.
Kinoshita, T
1999-01-01
The contribution of the $\\alpha^3$ single electron-loop vacuum-polarization diagrams to the Lamb shift of the muonic hydrogen has been evaluated recently by two methods. One uses the exact parametric representation of the vacuum-polarization function while the other relies on the Padé approximation method. High numerical precision of these calculations enables us to examine the accuracy of the Monte-Carlo integration as well as that of the Padé method applied to the Lamb shift problem.
Lundengård, Karl; Javor, Vesna; Silvestrov, Sergei
2016-01-01
A multi-peaked version of the analytically extended function (AEF) intended for approximation of multi-peaked lightning current wave-forms will be presented along with some of its basic properties. A general framework for estimating the parameters of the AEF using the Marquardt least-squares method (MLSM) for a waveform with an arbitrary (finite) number of peaks as well as a given charge trans-fer and specific energy will also be described. This framework is used to find parameters for some common single-peak wave-forms and some advantages and disadvantages of the approach will be discussed.
一类算子的函数类逼近%On Approximation of Classes of Functions of Certain Operators
Institute of Scientific and Technical Information of China (English)
郭顺生; 陈金梅; 齐秋兰
2000-01-01
Feller operators are definded. Feller operators include some classical operators such as Bernstein,Szasz, Baskakov, Gamma, Weierstrass operators. Using some probabilitic methods, study the approximation of classes of functions for Feller operators and their modified forms,and obtain some general results.%定义了Feller算子，该类算子包括Bernstein,Szasz, Baskakov,Gamma,Weierstrass等算子．应用一些概率方法，研究Feller算子及其修正对函数类的逼近，得到了更一般化的结果．
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
Dalmasse, K; Gibson, S E; Fan, Y; Flyer, N
2016-01-01
The Coronal Multichannel Polarimeter (CoMP) routinely performs coronal polarimetric measurements using the Fe XIII 10747 $\\AA$ and 10798 $\\AA$ lines, which are sensitive to the coronal magnetic field. However, inverting such polarimetric measurements into magnetic field data is a difficult task because the corona is optically thin at these wavelengths and the observed signal is therefore the integrated emission of all the plasma along the line of sight. To overcome this difficulty, we take on a new approach that combines a parameterized 3D magnetic field model with forward modeling of the polarization signal. For that purpose, we develop a new, fast and efficient, optimization method for model-data fitting: the Radial-basis-functions Optimization Approximation Method (ROAM). Model-data fitting is achieved by optimizing a user-specified log-likelihood function that quantifies the differences between the observed polarization signal and its synthetic/predicted analogue. Speed and efficiency are obtained by comb...
Energy Technology Data Exchange (ETDEWEB)
Ribeiro, M., E-mail: ribeiro.jr@oorbit.com.br [Office of Operational Research for Business Intelligence and Technology, Principal Office, Buffalo, Wyoming 82834 (United States)
2015-06-21
Ab initio calculations of hydrogen-passivated Si nanowires were performed using density functional theory within LDA-1/2, to account for the excited states properties. A range of diameters was calculated to draw conclusions about the ability of the method to correctly describe the main trends of bandgap, quantum confinement, and self-energy corrections versus the diameter of the nanowire. Bandgaps are predicted with excellent accuracy if compared with other theoretical results like GW, and with the experiment as well, but with a low computational cost.
Hartley, Madeline K; Vine, Seanna; Walsh, Elizabeth; Avrantinis, Sara; Daub, G William; Cave, Robert J
2016-03-03
We investigate several representative density functional theory approaches for the calculation of relative activation energies and free energies of a set of model pericyclic reactions, some of which have been studied experimentally. In particular, we use a standard hybrid functional (B3LYP), the same hybrid functional augmented with a basis set superposition error and dispersion correction, a meta-hybrid functional developed to treat transition states and weak interactions (M06-2X), and the recently implemented random phase approximation (RPA) based on Kohn-Sham orbitals from conventional density functional theory by Furche and co-workers. We apply these methods to calculate relative activation energies and estimated free energies for the amide acetal Claisen rearrangement. We focus on relative activation energies to assess the effects of steric and weak interactions in the various methods and compare with experiment where possible. We also discuss the advantages of using this set of reactions as a test bed for the comparison of treatments of weak interactions. We conclude that all methods yield similar trends in relative reactivity, but the RPA yields results in best agreement with the experimental values.
Energy Technology Data Exchange (ETDEWEB)
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.
Tang, Yulin; Liang, Song; Wang, Juntao; Yu, Shuili; Wang, Yilong
2013-04-01
Amino-functionalized Fe3O4@mesoporous SiO2 core-shell composite microspheres NH2-MS in created in multiple synthesis steps have been investigated for Pb(II) and Cd(II) adsorption. The microspheres were characterized by transmission electron microscope (TEM), scanning electron microscope (SEM), N2 adsorption-desorption, zeta potential measurements and vibrating sample magnetometer. Batch adsorption tests indicated that NH2-MS exhibited higher adsorption affinity toward Pb(II) and Cd(II) than MS did. The Langmuir model could fit the adsorption isotherm very well with maximum adsorption capacity of 128.21 and 51.81 mg/g for Pb(II) and Cd(II), respectively, implying that adsorption processes involved monolayer adsorption. Pb(II) and Cd(II) adsorption could be well described by the pseudo second-order kinetics model, and was found to be strongly dependent on pH and humic acid. The Pb(II)- and Cd(II)-loaded microspheres were effectively desorbed using 0.01 mol/L HCl or EDTA solution. NH2-MS have promise for use as adsorbents in the removal of Pb(II) and Cd(II) in wastewater treatment processes.
APPROXIMATION OF CONVEX TYPE FUNCTION BY PARTIAL SUMS OF FOURIER SERIES%Fourier级数部分和对凸型函数的逼近
Institute of Scientific and Technical Information of China (English)
俞国华
2004-01-01
The concept of convex type function is introduced in this paper,from which a kind of convex-decomposition approach is proposed. As one of applications of this approach, the approximation of the convex type function by the partial sum of its Fourier series is investigated. Moreover,the order of approximation is described with the 2th continuous modulus.
Sharapudinov, I. I.
2016-07-01
We consider the space Lp(\\cdot)2π formed by 2π-periodic real measurable functions f for which the integral \\displaystyle\\int-ππ\\vert f(x)\\vertp(x) dx exists and is finite, where p(x), 1≤ p(x), is a 2π-periodic measurable function (a variable exponent). If p(x)≤ \\overline p0:\\int-ππ\\biggl\\vert\\frac{f(x)}{α\\biggr\\vertp(x) dx≤1\\biggr\\}. In the space Lp(\\cdot)2π we distinguish a subspace Wr,p(\\cdot)2π of Sobolev type. We investigate the approximation properties of the de la Vallée-Poussin means for trigonometric Fourier sums for functions in the space Wr,p(\\cdot)2π. In particular, we prove that if the variable exponent p=p(x) satisfies the Dini-Lipschitz condition \\vert p(x)-p(y)\\vert\\ln\\frac{2π}{\\vert x-y\\vert}≤ c and if f\\in Wr,p(\\cdot)2π, then the de la Vallée-Poussin means V_m^n(f)=V_m^n(f,x) with n≤ am satisfy \\displaystyle \\Vert f-V_m^n(f)\\Vert p(\\cdot)≤ \\frac{c_r(p,a)}{n^r}Ω\\biggl(f(r), \\frac1n\\biggr)p(\\cdot), where Ω(g,δ)p(\\cdot) is a modulus of continuity of the function g\\in Lp(\\cdot)2π defined in terms of the Steklov functions. It is proved that if 1, r≥1, f\\in Wr,p(\\cdot)2π and the Dini-Lipschitz condition holds, then \\displaystyle \\vert f(x)-V_m^n(f,x)\\vert≤\\frac{c_r(p)}{m+1}\\sumk=nn+m\\frac{E_k(f(r))p(\\cdot)}{(k+1)r-{{1/{p(x)}}}}, where E_k(g)p(\\cdot) stands for the best approximation to g\\in Lp(\\cdot)2π by trigonometric polynomials of order k. Bibliography: 19 titles.
Structure/Function/Dynamics of Photosystem II Plastoquinone Binding Sites
Lambreva, Maya D.; Russo, Daniela; Polticelli, Fabio; Scognamiglio, Viviana; Antonacci, Amina; Zobnina, Veranika; Campi, Gaetano; Rea, Giuseppina
2014-01-01
Photosystem II (PSII) continuously attracts the attention of researchers aiming to unravel the riddle of its functioning and efficiency fundamental for all life on Earth. Besides, an increasing number of biotechnological applications have been envisaged exploiting and mimicking the unique properties of this macromolecular pigment-protein complex. The PSII organization and working principles have inspired the design of electrochemical water splitting schemes and charge separating triads in energy storage systems as well as biochips and sensors for environmental, agricultural and industrial screening of toxic compounds. An intriguing opportunity is the development of sensor devices, exploiting native or manipulated PSII complexes or ad hoc synthesized polypeptides mimicking the PSII reaction centre proteins as bio-sensing elements. This review offers a concise overview of the recent improvements in the understanding of structure and function of PSII donor side, with focus on the interactions of the plastoquinone cofactors with the surrounding environment and operational features. Furthermore, studies focused on photosynthetic proteins structure/function/dynamics and computational analyses aimed at rational design of high-quality bio-recognition elements in biosensor devices are discussed. PMID:24678671
Functional Implications of Photosystem II Crystal Formation in Photosynthetic Membranes*
Tietz, Stefanie; Puthiyaveetil, Sujith; Enlow, Heather M.; Yarbrough, Robert; Wood, Magnus; Semchonok, Dmitry A.; Lowry, Troy; Li, Zhirong; Jahns, Peter; Boekema, Egbert J.; Lenhert, Steven; Niyogi, Krishna K.; Kirchhoff, Helmut
2015-01-01
The structural organization of proteins in biological membranes can affect their function. Photosynthetic thylakoid membranes in chloroplasts have the remarkable ability to change their supramolecular organization between disordered and semicrystalline states. Although the change to the semicrystalline state is known to be triggered by abiotic factors, the functional significance of this protein organization has not yet been understood. Taking advantage of an Arabidopsis thaliana fatty acid desaturase mutant (fad5) that constitutively forms semicrystalline arrays, we systematically test the functional implications of protein crystals in photosynthetic membranes. Here, we show that the change into an ordered state facilitates molecular diffusion of photosynthetic components in crowded thylakoid membranes. The increased mobility of small lipophilic molecules like plastoquinone and xanthophylls has implications for diffusion-dependent electron transport and photoprotective energy-dependent quenching. The mobility of the large photosystem II supercomplexes, however, is impaired, leading to retarded repair of damaged proteins. Our results demonstrate that supramolecular changes into more ordered states have differing impacts on photosynthesis that favor either diffusion-dependent electron transport and photoprotection or protein repair processes, thus fine-tuning the photosynthetic energy conversion. PMID:25897076
Functional Implications of Photosystem II Crystal Formation in Photosynthetic Membranes.
Tietz, Stefanie; Puthiyaveetil, Sujith; Enlow, Heather M; Yarbrough, Robert; Wood, Magnus; Semchonok, Dmitry A; Lowry, Troy; Li, Zhirong; Jahns, Peter; Boekema, Egbert J; Lenhert, Steven; Niyogi, Krishna K; Kirchhoff, Helmut
2015-05-29
The structural organization of proteins in biological membranes can affect their function. Photosynthetic thylakoid membranes in chloroplasts have the remarkable ability to change their supramolecular organization between disordered and semicrystalline states. Although the change to the semicrystalline state is known to be triggered by abiotic factors, the functional significance of this protein organization has not yet been understood. Taking advantage of an Arabidopsis thaliana fatty acid desaturase mutant (fad5) that constitutively forms semicrystalline arrays, we systematically test the functional implications of protein crystals in photosynthetic membranes. Here, we show that the change into an ordered state facilitates molecular diffusion of photosynthetic components in crowded thylakoid membranes. The increased mobility of small lipophilic molecules like plastoquinone and xanthophylls has implications for diffusion-dependent electron transport and photoprotective energy-dependent quenching. The mobility of the large photosystem II supercomplexes, however, is impaired, leading to retarded repair of damaged proteins. Our results demonstrate that supramolecular changes into more ordered states have differing impacts on photosynthesis that favor either diffusion-dependent electron transport and photoprotection or protein repair processes, thus fine-tuning the photosynthetic energy conversion.
Functional assessment of feet of patients with type II diabetes
Directory of Open Access Journals (Sweden)
Vinicius Saura Cardoso
2014-09-01
Full Text Available Objective: To evaluate the incidence of functional changes and risk of developing ulcers in type II diabetic patients seen in Primary Healthcare Units (Unidades Básicas de Saúde- UBS. Methods: A cross-sectional, quantitative and descriptive study comprising 80patients with type II diabetes mellitus (DM aged between 41 to 85 years and attended inthe UBS in the city of Parnaíba-PI. Volunteers responded to the identification form and theMichigan Neuropathy Screening Instrument (MNSI, followed by an evaluation of the lowerlimbs, as follows: achilles and patellar reflex, palpation of arterial pulses (dorsalis pedis and posterior tibial, tactile sensitivity (Monofilament 10g and vibration sensitivity (128Hz tuning fork; identification of the presence of changes such as ingrown toenails, calluses,claw toes and hair loss. Finally, using the information acquired from the assessment, subjects were classified according to the risk of developing wounds. Results: The sample consisted of 76 diabetic patients, with average age of 63.8 ± 10.4 years, 63 (82.8% were female, mean diagnostic time 8.8 ± 7.2 years, average body mass index (BMI 28.2 ± 5.4 kg/m2, with 15.7% of the sample being smokers. The myotatic reflexes and arterial pulses were reduced. Tactile sensitivity was identified in 81.5% and 13.1% did not feel the vibration of the tuning fork. The most dominant changes identified were calluses, 76.3% (n = 58. Risk level 2 of developing ulcers stood out, 52.6% (n = 40. Conclusion: Functional changes were detected in the sample and a classification of risk 2 for developing wounds was found in more than 50% of the assessed patients. doi:http://dx.doi.org/10.5020/18061230.2013.p563
Kr II and Xe II axial velocity distribution functions in a cross-field ion source
Lejeune, A.; Bourgeois, G.; Mazouffre, S.
2012-07-01
Laser induced fluorescence measurements were carried out in a cross-field ion source to examine the behaviour of the axial ion velocity distribution functions (VDFs) in the expanding plasma. In the present paper, we focus on the axial VDFs of Kr II and Xe II ions. We examine the contourplots in a 1D-phase space (x,vx) representation in front of the exhaust channel and along the centerline of the ion source. The main ion beam, whose momentum corresponds to the ions that are accelerated through the whole potential drop, is observed. A secondary structure reveals the ions coming from the opposite side of the channel. We show that the formation of the neutralized ion flow is governed by the annular geometry. The assumption of a collisionless shock or a double layer due to supersonic beam interaction is not necessary. A non-negligible fraction of slow ions originates in local ionization or charge-exchange collision events between ions of the expanding plasma and atoms of the background residual gas. Slow ions that are produced near the centerline in the vicinity of the exit plane are accelerated toward the source body with a negative velocity leading to a high sputtering of front face. On the contrary, the ions that are produced in the vicinity of the channel exit plane are partially accelerated by the extended electric field.
Jorgetto, Alexandre de Oliveira; Pereira, Silvana Pontes; Silva, Rafael Innocenti Vieira da; Saeki, Margarida Juri; Martines, Marco Antonio Utrera; Pedrosa, Valber de Albuquerque; Castro, Gustavo Rocha de
2015-01-01
This work reports the sol-gel synthesis of a SBA-15 silica, and its functionalization with 4-amino-2-mercaptopyrimidine to perform adsorption of metal species from aqueous media. The functionalization of the material was confirmed by FTIR and superficial area measurements. The final material was tested through batch experiments to uncover its adsorptive properties towards the adsorption of Cu(II), Cd(II), Zn(II), Pb(II) and Ni(II). Contact time and pH conditions were investigated, and the material presented slow adsorption kinetics, which was best described by the pseudo-second order model. In addition, at pH 5 - 6, the adsorption of the metal ions was favored. Under optimized conditions, the material had its maximum adsorption capacities determined for all metal species studied, and the obtained values were 13.0 µmol g(-1) for Zn(II), 12.3 µmol g(-1) for Cu(II), 3.45 µmol g(-1) for Ni(II), 2.45 µmol g(-1) for Pb(II) and 0.60 µmol g(-1) for Cd(II). The capacity differences between each metal ion were discussed in terms of their ionic radii and Person's soft/hard acids/bases concept.
Sato, Shunsuke A.; Taniguchi, Yasutaka; Shinohara, Yasushi; Yabana, Kazuhiro
2015-12-01
We develop methods to calculate electron dynamics in crystalline solids in real-time time-dependent density functional theory employing exchange-correlation potentials which reproduce band gap energies of dielectrics; a meta-generalized gradient approximation was proposed by Tran and Blaha [Phys. Rev. Lett. 102, 226401 (2009)] (TBm-BJ) and a hybrid functional was proposed by Heyd, Scuseria, and Ernzerhof [J. Chem. Phys. 118, 8207 (2003)] (HSE). In time evolution calculations employing the TB-mBJ potential, we have found it necessary to adopt the predictor-corrector step for a stable time evolution. We have developed a method to evaluate electronic excitation energy without referring to the energy functional which is unknown for the TB-mBJ potential. For the HSE functional, we have developed a method for the operation of the Fock-like term in Fourier space to facilitate efficient use of massive parallel computers equipped with graphic processing units. We compare electronic excitations in silicon and germanium induced by femtosecond laser pulses using the TB-mBJ, HSE, and a simple local density approximation (LDA). At low laser intensities, electronic excitations are found to be sensitive to the band gap energy: they are close to each other using TB-mBJ and HSE and are much smaller in LDA. At high laser intensities close to the damage threshold, electronic excitation energies do not differ much among the three cases.
Energy Technology Data Exchange (ETDEWEB)
Sato, Shunsuke A. [Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8571 (Japan); Taniguchi, Yasutaka [Center for Computational Science, University of Tsukuba, Tsukuba 305-8571 (Japan); Department of Medical and General Sciences, Nihon Institute of Medical Science, 1276 Shimogawara, Moroyama-Machi, Iruma-Gun, Saitama 350-0435 (Japan); Shinohara, Yasushi [Max Planck Institute of Microstructure Physics, 06120 Halle (Germany); Yabana, Kazuhiro [Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8571 (Japan); Center for Computational Science, University of Tsukuba, Tsukuba 305-8571 (Japan)
2015-12-14
We develop methods to calculate electron dynamics in crystalline solids in real-time time-dependent density functional theory employing exchange-correlation potentials which reproduce band gap energies of dielectrics; a meta-generalized gradient approximation was proposed by Tran and Blaha [Phys. Rev. Lett. 102, 226401 (2009)] (TBm-BJ) and a hybrid functional was proposed by Heyd, Scuseria, and Ernzerhof [J. Chem. Phys. 118, 8207 (2003)] (HSE). In time evolution calculations employing the TB-mBJ potential, we have found it necessary to adopt the predictor-corrector step for a stable time evolution. We have developed a method to evaluate electronic excitation energy without referring to the energy functional which is unknown for the TB-mBJ potential. For the HSE functional, we have developed a method for the operation of the Fock-like term in Fourier space to facilitate efficient use of massive parallel computers equipped with graphic processing units. We compare electronic excitations in silicon and germanium induced by femtosecond laser pulses using the TB-mBJ, HSE, and a simple local density approximation (LDA). At low laser intensities, electronic excitations are found to be sensitive to the band gap energy: they are close to each other using TB-mBJ and HSE and are much smaller in LDA. At high laser intensities close to the damage threshold, electronic excitation energies do not differ much among the three cases.
Value Function Approximation or Stopping Time Approximation
DEFF Research Database (Denmark)
Stentoft, Lars
2014-01-01
In their 2001 paper, Longstaff and Schwartz suggested a method for American option pricing using simulation and regression, and since then this method has rapidly gained importance. However, the idea of using regression and simulation for American option pricing was used at least as early as 1996......, by Carriere. In this paper, we provide a thorough comparison of these two methods and relate them to the work of Tsitsiklis and Van Roy. Although the methods are often considered to be similar, this analysis allows us to point out an important but often overlooked difference between them. We further show that...
Value Function Approximation or Stopping Time Approximation
DEFF Research Database (Denmark)
Stentoft, Lars
2014-01-01
In their 2001 paper, Longstaff and Schwartz suggested a method for American option pricing using simulation and regression, and since then this method has rapidly gained importance. However, the idea of using regression and simulation for American option pricing was used at least as early as 1996......, by Carriere. In this paper, we provide a thorough comparison of these two methods and relate them to the work of Tsitsiklis and Van Roy. Although the methods are often considered to be similar, this analysis allows us to point out an important but often overlooked difference between them.We further show that...
Value Function Approximation or Stopping Time Approximation
DEFF Research Database (Denmark)
Stentoft, Lars
2014-01-01
, by Carriere. In this paper, we provide a thorough comparison of these two methods and relate them to the work of Tsitsiklis and Van Roy. Although the methods are often considered to be similar, this analysis allows us to point out an important but often overlooked difference between them. We further show that...
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...
Scavenger receptor AI/II truncation, lung function and COPD
DEFF Research Database (Denmark)
Thomsen, M; Nordestgaard, B G; Tybjaerg-Hansen, A
2011-01-01
The scavenger receptor A-I/II (SRA-I/II) on alveolar macrophages is involved in recognition and clearance of modified lipids and inhaled particulates. A rare variant of the SRA-I/II gene, Arg293X, truncates the distal collagen-like domain, which is essential for ligand recognition. We tested whet...
Directory of Open Access Journals (Sweden)
Shyam Lal
2003-12-01
Full Text Available In this paper the degree of approximation of conjugate of a function belonging to Lip $ \\alpha$ class by $ K^\\lambda$-summability means of conjugate series of its Fourier series has been determined.
Kinza, Michael; Honerkamp, Carsten
2015-07-01
In the derivation of low-energy effective models for solids targeting the bands near the Fermi level, the constrained random-phase approximation (cRPA) has become an appreciated tool to compute the effective interactions. The Wick-ordered constrained functional renormalization group (cfRG) generalizes the cRPA approach by including all interaction channels in an unbiased way. Here we present applications of the cfRG to two simple multiband systems and compare the resulting effective interactions to the cRPA. First, we consider a multiband model for monolayer graphene, where we integrate out the σ bands to get an effective theory for π bands. It turns out that terms beyond cRPA are strongly suppressed by the different x y -plane reflection symmetry of the bands. In our model the cfRG corrections to cRPA become visible when one disturbs this symmetry difference slightly, however, without qualitative changes. This study shows that the embedding or layering of two-dimensional electronic systems can alter the effective interaction parameters beyond what is expected from screening considerations. The second example is a one-dimensional model for a diatomic system reminiscent of a CuO chain, where we consider an effective theory for Cu 3 d -like orbitals. Here the fRG data shows relevant and qualitative corrections compared to the cRPA results. We argue that the new interaction terms affect the magnetic properties of the low-energy model.
König, Carolin; Schlüter, Nicolas; Neugebauer, Johannes
2013-01-01
In subsystem time-dependent density functional theory (TDDFT) [J. Neugebauer, J. Chem. Phys. 126, 134116 (2007), 10.1063/1.2713754] localized excitations are used to calculate delocalized excitations in large chromophore aggregates. We have extended this formalism to allow for the Tamm-Dancoff approximation (TDA). The resulting response equations have a form similar to a perturbative configuration interaction singles (CIS) approach. Thus, the inter-subsystem matrix elements in subsystem TDA can, in contrast to the full subsystem-TDDFT case, directly be interpreted as exciton coupling matrix elements. Here, we present the underlying theory of subsystem TDDFT within the TDA as well as first applications. Since for some classes of pigments, such as linear polyenes and carotenoids, TDA has been reported to perform better than full TDDFT, we also report applications of this formalism to exciton couplings in dimers of such pigments and in mixed bacteriochlorophyll-carotenoid systems. The improved description of the exciton couplings can be traced back to a more balanced description of the involved local excitations.
Liu, Jie; Herbert, John M.
2015-07-01
A novel formulation of time-dependent density functional theory (TDDFT) is derived, based on non-orthogonal, absolutely-localized molecular orbitals (ALMOs). We call this approach TDDFT(MI), in reference to ALMO-based methods for describing molecular interactions (MI) that have been developed for ground-state applications. TDDFT(MI) is intended for efficient excited-state calculations in systems composed of multiple, weakly interacting chromophores. The efficiency is based upon (1) a local excitation approximation; (2) monomer-based, singly-excited basis states; (3) an efficient localization procedure; and (4) a one-step Davidson method to solve the TDDFT(MI) working equation. We apply this methodology to study molecular dimers, water clusters, solvated chromophores, and aggregates of naphthalene diimide that form the building blocks of self-assembling organic nanotubes. Absolute errors of 0.1-0.3 eV with respect to supersystem methods are achievable for these systems, especially for cases involving an excited chromophore that is weakly coupled to several explicit solvent molecules. Excited-state calculations in an aggregate of nine naphthalene diimide monomers are ˜40 times faster than traditional TDDFT calculations.
Cu(I)/Cu(II) templated functional pseudorotaxanes and rotaxanes
Indian Academy of Sciences (India)
Subrata Saha; Pradyut Ghosh
2012-11-01
Threaded complexes like pseudorotaxanes, rotaxanes based on Cu(I)/Cu(II) ions have shown to be promising for the construction of mechanically interlocked molecular-level architectures. In this short review, we focus on the synthetic strategies developed to construct pseudorotaxanes and rotaxanes using Cu(I)/Cu(II) ions as template. Further, brief discussions on chemical and mechanical properties associated with some of the selected to Cu(I)/Cu(II) based pseudorotaxanes and rotaxanes are presented.
The universal cut function and type II metrics
Energy Technology Data Exchange (ETDEWEB)
Kozameh, Carlos [FaMaF, University of Cordoba, Cordoba (Argentina); Newman, E T [Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260 (United States); Santiago-Santiago, J G [Facultad de Ciencias Fisico Matematicas de la Universidad Autonoma de Puebla, Apartado Postal 1152, 72001, Puebla, Pue. (Mexico); Silva-Ortigoza, Gilberto [Facultad de Ciencias Fisico Matematicas de la Universidad Autonoma de Puebla, Apartado Postal 1152, 72001, Puebla, Pue. (Mexico)
2007-04-21
In analogy with classical electromagnetic theory, where one determines the total charge and both electric and magnetic multipole moments of a source from certain surface integrals of the asymptotic (or far) fields, it has been known for many years-from the work of Hermann Bondi-that the energy and momentum of gravitational sources could be determined by similar integrals of the asymptotic Weyl tensor. Recently, we observed that there were certain overlooked structures, defined at future null infinity, that allowed one to determine (or define) further properties of both electromagnetic and gravitating sources. These structures, families of complex 'slices' or 'cuts' of Penrose's I{sup +}, are referred to as universal cut functions. In particular, one can define from these structures a (complex) centre of mass (and centre of charge) and its equations of motion-with rather surprising consequences. It appears as if these asymptotic structures contain, in their imaginary part, a well-defined total spin-angular momentum of the source. We apply these ideas to the type II algebraically special metrics, both twisting and twist free.
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
Gauge-independent Wigner functions. II. Inclusion of radiation reaction
Javanainen, J.; Varró, S.; Serimaa, O. T.
1987-04-01
We investigate the effects of quantized radiation reaction fields on the motion of a charged particle using the gauge-independent Wigner operator (GIWO) and gauge-independent Wigner function (GIWF) introduced earlier [Phys. Rev. A 33, 2913 (1986)]. To complement the equation of motion of the GIWO, the Heisenberg equations of motion of the quantized electromagnetic fields are solved within the Markov approximation. After considering the operator orderings and orders of magnitude of the radiation reaction terms, we eliminate the quantum fields from the evolution equation of the GIWO, and obtain for the GIWF a closed equation containing relaxation terms. As an example of the formalism we derive a Fokker-Planck equation (FPE) for the GIWF of a particle in a constant magnetic field. To the order ħ 0 the classical radiation damping ensues, and the first quantum correction proportional to ħ emerges as diffusion. The diffusion operator turns out to be indefinite and the FPE consequently defies our attempts at a complete analysis, but we demonstrate that at least the coherent states constructed from the Landau levels exhibit a manifestly physical time evolution under the FPE. We point out that the GIWF calculated with quantized electromagnetic fields is divergent even if the fields are in the vacuum state, and suggest that the GIWF should be associated with the particle state by ignoring the quantized fields altogether.
Functional properties of the oxygen evolving complex of photosystem II.
Vliet, van P.H.
1996-01-01
This Thesis presents the results of a study by electron paramagnetic resonance (EPR) and measurements of oxygen evolution of the Oxygen Evolving Complex of Photosystem 11 (PS-II) in PS-II enriched membranes from spinach.The experimental part of this Thesis is preceded by a general introduction (Chap
Cd(ii)-MOF-IM: post-synthesis functionalization of a Cd(ii)-MOF as a triphase transfer catalyst.
Wang, Jian-Cheng; Ma, Jian-Ping; Liu, Qi-Kui; Hu, Yu-Hong; Dong, Yu-Bin
2016-05-19
A robust and porous Cd(ii)-MOF based on a bent imidazole-bridged ligand was synthesized and post-synthetically functionalized with linear alkyl chains to afford imidazolium salt (IM)-type triphase transfer catalysts for organic transformations. The imidazolium salt decorated Cd(ii)-MOF-IM exhibits typical solid phase transfer catalytic behavior for the azidation and thiolation of bromoalkane between aqueous/organic phases. Moreover, they can be easily recovered and reused under the PTC conditions. Cd(ii)-MOF-IM herein created a versatile family of solid phase transfer catalysts for promoting a broad scope of reactions carried out in a biphasic mixture of two immiscible solvents.
Śmiga, Szymon; Fabiano, Eduardo; Constantin, Lucian A; Della Sala, Fabio
2017-02-14
The development of semilocal models for the kinetic energy density (KED) is an important topic in density functional theory (DFT). This is especially true for subsystem DFT, where these models are necessary to construct the required non-additive embedding contributions. In particular, these models can also be efficiently employed to replace the exact KED in meta-Generalized Gradient Approximation (meta-GGA) exchange-correlation functionals allowing to extend the subsystem DFT applicability to the meta-GGA level of theory. Here, we present a two-dimensional scan of semilocal KED models as linear functionals of the reduced gradient and of the reduced Laplacian, for atoms and weakly bound molecular systems. We find that several models can perform well but in any case the Laplacian contribution is extremely important to model the local features of the KED. Indeed a simple model constructed as the sum of Thomas-Fermi KED and 1/6 of the Laplacian of the density yields the best accuracy for atoms and weakly bound molecular systems. These KED models are tested within subsystem DFT with various meta-GGA exchange-correlation functionals for non-bonded systems, showing a good accuracy of the method.
Misra, R K; Jain, S K; Khatri, P K
2011-01-30
Iminodiacetic acid functionality has been introduced on styrene-divinyl benzene co-polymeric beads and characterized by FT-IR in order to develop weak acid based cation exchange resin. This resin was evaluated for the removal of different heavy metal ions namely Cd(II), Cr(VI), Ni(II) and Pb(II) from their aqueous solutions. The results showed greater affinity of resin towards Cr(VI) for which 99.7% removal achieved in optimal conditions following the order Ni(II)>Pb(II)>Cd(II) with 65%, 59% and 28% removal. Experiments were also directed towards kinetic studies of adsorption and found to follow first order reversible kinetic model with the overall rate constants 0.3250, 0.2393, 0.4290 and 0.2968 for Cr(VI), Ni(II), Pb(II) and Cd(II) removal respectively. Detailed studies of Cr(VI) removal has been carried out to see the effect of pH, resin dose and metal ion concentration on adsorption and concluded that complexation enhanced the chromium removal efficacy of resin drastically, which is strongly pH dependent. The findings were also supported by the comparison of FT-IR spectra of neat resin with the chromium-adsorbed resin.
Andreolotti, Alberto G; Bragado, Maria J; Tapia, Jose A; Jensen, Robert T; Garcia-Marin, Luis J
2003-12-01
Crk belongs to a family of adapter proteins whose structure allows interaction with tyrosine-phosphorylated proteins and is therefore an important modulator of downstream signals, representing a convergence of the actions of numerous stimuli. Recently, it was demonstrated that cholecystokinin (CCK) induced tyrosine phosphorylation of proteins related to fiber stress formation in rat pancreatic acini. Here, we investigated whether CCK receptor activation signals through CrkII and forms complexes with tyrosine-phosphorylated proteins in rat pancreatic acini. We demonstrated that CCK promoted the transient formation of CrkII-paxillin and CrkII-p130Cas complexes with maximal effect at 1 min. Additionally, CCK decreased the electrophoretic mobility of CrkII. This decrease was time- and concentration-dependent and inversely related with its function. Carbachol and bombesin also decreased CrkII electrophoretic mobility, whereas epidermal growth factor, vasoactive intestinal peptide, secretin or pituitary adenylate cyclase-activating polypeptide had no effect. CCK-induced CrkII electrophoretic shift was dependent on the Src family of tyrosine kinases and occurred in the intact animal, suggesting a physiological role of CrkII mediating CCK actions in the exocrine pancreas in vivo.
Directory of Open Access Journals (Sweden)
Xhevat Z. Krasniqi
2015-11-01
Full Text Available In this paper, using rest bounded variation sequences and head bounded variation sequences, some new results on approximation of functions (signals by almost generalized Nörlund means of their Fourier series are obtained. To our best knowledge this the first time to use such classes of sequences on approximations of the type treated in this paper. In addition, several corollaries are derived from our results as well as those obtained previously by others.
Directory of Open Access Journals (Sweden)
Xhevat Z. Krasniqi
2015-11-01
Full Text Available In this paper, using rest bounded variation sequences and head bounded variation sequences, some new results on approximation of functions (signals by almost generalized Nörlund means of their Fourier series are obtained. To our best knowledge this the first time to use such classes of sequences on approximations of the type treated in this paper. In addition, several corollaries are derived from our results as well as those obtained previously by others.
The relation of executive functioning to CVLT-II learning, memory, and process indexes.
Hill, Benjamin David; Alosco, Michael; Bauer, Lyndsey; Tremont, Geoffrey
2012-01-01
Previous research has found that executive functioning plays a role in memory performance. This study sought to determine the amount of variance accounted for in the California Verbal Learning Test-Second Edition (CVLT-II) by a global executive-functioning factor score. Archival data were extracted from 285 outpatients in a mixed neurologic sample. Measures used included: CVLT-II, Wisconsin Card-Sorting Test (Perseverative Errors), Trail-Making Test-Part B, Controlled Oral Word Association Test, Animal Naming, and Wechsler Adult Intelligence Scale-Third Edition Similarities. Executive data were reduced to a single executive-functioning factor score for each individual. Regression was used to determine the amount of variance accounted for by executive functioning in CVLT-II performance. Executive functioning accounted for minimal variance (0%-10%) in the following CVLT-II indexes: Total Learning (Trials 1-5), Semantic Clustering, Repetitions, Intrusions, and False Positives. However, executive functioning accounted for substantial variance (24%-31%) in CVLT-II performance for both Short- and Long-Delay Recall indexes and most discriminability indexes. CVLT-II indexes that would intuitively be associated with executive functioning accounted for a smaller-than-expected amount of variance. Additionally, level of executive functioning was related to level of CVLT-II performance. These results suggest that clinicians should consider executive deficits when interpreting mild-to-moderate memory impairments in recall and discriminability functions but that executive abilities have little effect on other aspects of memory.
Axon extension in the fast and slow lanes: substratum-dependent engagement of myosin II functions.
Ketschek, Andrea R; Jones, Steven L; Gallo, Gianluca
2007-09-01
Axon extension involves the coordinated regulation of the neuronal cytoskeleton. Actin filaments drive protrusion of filopodia and lamellipodia while microtubules invade the growth cone, thereby providing structural support for the nascent axon. Furthermore, in order for axons to extend the growth cone must attach to the substratum. Previous work indicates that myosin II activity inhibits the advance of microtubules into the periphery of growth cones, and myosin II has also been implicated in mediating integrin-dependent cell attachment. However, it is not clear how the functions of myosin II in regulating substratum attachment and microtubule advance are integrated during axon extension. We report that inhibition of myosin II function decreases the rate of axon extension on laminin, but surprisingly promotes extension rate on polylysine. The differential effects of myosin II inhibition on axon extension rate are attributable to myosin II having the primary function of mediating substratum attachment on laminin, but not on polylysine. Conversely, on polylysine the primary function of myosin II is to inhibit microtubule advance into growth cones. Thus, the substratum determines the role of myosin II in axon extension by controlling the functions of myosin II that contribute to extension.
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...
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
Consolidation of Military Pay and Personnel Functions (Copper). Volume II
1978-05-01
as in any system, the commander and staff must perform their roles in providing information in a timely and accurate manner. a. Concepts pertaining to...feminine genders . Exceptions to this use of the words "he" or "his" will be so noted. 8. RECOMMENDED CHANGES AND COMMENTS. Users of this manual are...II-lO-Aq3 S NO CAH TR TION NCL IN 0’ SECTION 2 co P ? PAGE YES YES II-10-A43 MAKE CORRECTIONS LOG IN OTL SEPARATE DOCUMENTS Orl, OTL DOCUMENTS ORIG
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.
Mohammadpour, Mozhdeh; Jamshidi, Zahra
2016-05-01
The prospect of challenges in reproducing and interpretation of resonance Raman properties of molecules interacting with metal clusters has prompted the present research initiative. Resonance Raman spectra based on the time-dependent gradient approximation are examined in the framework of density functional theory using different methods for representing the exchange-correlation functional. In this work the performance of different XC functionals in the prediction of ground state properties, excitation state energies, and gradients are compared and discussed. Resonance Raman properties based on time-dependent gradient approximation for the strongly low-lying charge transfer states are calculated and compared for different methods. We draw the following conclusions: (1) for calculating the binding energy and ground state geometry, dispersion-corrected functionals give the best performance in comparison to ab initio calculations, (2) GGA and meta GGA functionals give good accuracy in calculating vibrational frequencies, (3) excited state energies determined by hybrid and range-separated hybrid functionals are in good agreement with EOM-CCSD calculations, and (4) in calculating resonance Raman properties GGA functionals give good and reasonable performance in comparison to the experiment; however, calculating the excited state gradient by using the hybrid functional on the hessian of GGA improves the results of the hybrid functional significantly. Finally, we conclude that the agreement of charge-transfer surface enhanced resonance Raman spectra with experiment is improved significantly by using the excited state gradient approximation.
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...
Zhang, Zhongyang; Berti, Emanuele
2011-01-01
We study the effect of black hole spin on the accuracy of the post-Newtonian approximation. We focus on the gravitational energy flux for the quasicircular, equatorial, extreme mass-ratio inspiral of a compact object into a Kerr black hole of mass M and spin J. For a given dimensionless spin a=J/M^2 (in geometrical units), the energy flux depends only on the orbital velocity v or (equivalently) on the Boyer-Lindquist orbital radius r. We investigate the formal region of validity of the Taylor post-Newtonian expansion of the energy flux (which is known up to order v^8 beyond the quadrupole formula), generalizing previous work by two of us. The "error function" used to determine the region of validity of the post-Newtonian expansion can have two qualitatively different kinds of behavior, and we deal with these two cases separately. We find that, at any fixed post-Newtonian order, the edge of the region of validity (as measured by v/v_{ISCO}, where v_{ISCO} is the orbital velocity at the innermost stable circula...
Directory of Open Access Journals (Sweden)
Adewale Adewuyi
2016-11-01
Full Text Available Nitrilotriacetic acid functionalized Adansonia digitata (NFAD biosorbent has been synthesized using a simple and novel method. NFAD was characterized by X-ray Diffraction analysis technique (XRD, Scanning Electron Microscopy (SEM, Brunauer-Emmett-Teller (BET surface area analyzer, Fourier Transform Infrared spectrometer (FTIR, particle size dispersion, zeta potential, elemental analysis (CHNS/O analyzer, thermogravimetric analysis (TGA, differential thermal analysis (DTA, derivative thermogravimetric analysis (DTG and energy dispersive spectroscopy (EDS. The ability of NFAD as biosorbent was evaluated for the removal of Pb (II and Cu (II ions from aqueous solutions. The particle distribution of NFAD was found to be monomodal while SEM revealed the surface to be heterogeneous. The adsorption capacity of NFAD toward Pb (II ions was 54.417 mg/g while that of Cu (II ions was found to be 9.349 mg/g. The adsorption of these metals was found to be monolayer, second-order-kinetic, and controlled by both intra-particle diffusion and liquid film diffusion. The results of this study were compared better than some reported biosorbents in the literature. The current study has revealed NFAD to be an effective biosorbent for the removal of Pb (II and Cu (II from aqueous solution.
Adewuyi, Adewale; Pereira, Fabiano Vargas
2016-11-01
Nitrilotriacetic acid functionalized Adansonia digitata (NFAD) biosorbent has been synthesized using a simple and novel method. NFAD was characterized by X-ray Diffraction analysis technique (XRD), Scanning Electron Microscopy (SEM), Brunauer-Emmett-Teller (BET) surface area analyzer, Fourier Transform Infrared spectrometer (FTIR), particle size dispersion, zeta potential, elemental analysis (CHNS/O analyzer), thermogravimetric analysis (TGA), differential thermal analysis (DTA), derivative thermogravimetric analysis (DTG) and energy dispersive spectroscopy (EDS). The ability of NFAD as biosorbent was evaluated for the removal of Pb (II) and Cu (II) ions from aqueous solutions. The particle distribution of NFAD was found to be monomodal while SEM revealed the surface to be heterogeneous. The adsorption capacity of NFAD toward Pb (II) ions was 54.417 mg/g while that of Cu (II) ions was found to be 9.349 mg/g. The adsorption of these metals was found to be monolayer, second-order-kinetic, and controlled by both intra-particle diffusion and liquid film diffusion. The results of this study were compared better than some reported biosorbents in the literature. The current study has revealed NFAD to be an effective biosorbent for the removal of Pb (II) and Cu (II) from aqueous solution.
Calculus of Elementary Functions, Part II. Teacher's Commentary. Revised Edition.
Herriot, Sarah T.; And Others
This course is intended for students who have a thorough knowledge of college preparatory mathematics, including algebra, axiomatic geometry, trigonometry, and analytic geometry. This teacher's guide is for Part II of the course. It is designed to follow Part I of the text. The guide contains background information, suggested instructional…
Monotone Boolean approximation
Energy Technology Data Exchange (ETDEWEB)
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.
Smith, J. C.; Pribram-Jones, A.; Burke, K.
2016-06-01
Thermal density functional theory calculations often use the Mermin-Kohn-Sham scheme, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable nontrivial model, an asymmetric Hubbard dimer, we calculate the exact many-body energies and the exact Mermin-Kohn-Sham functionals for this system and extract the exact XC free energy. For moderate temperatures and weak correlation, we find this approximation to be excellent. We extract various exact free-energy correlation components and the exact adiabatic connection formula.
Bloomfield, Philip E
2005-05-01
The pulse-echo impulse-response format in the Field II formalism is generalized to separately located transmitter and receiver. To first order in sound velocity and density perturbations, identical results for the scattering-object function are obtained for the Morse-Ingard and the Chernov formulation in both the temporal and frequency domains: f(s)=-[2Delta(c/c)+(Delta(rho/rho))(1-cos(theta))] where for ultrasonic pulse-echo or transmission modality, cos(theta) approximately -1 or +1, respectively.
Lu, Yingdong
2008-01-01
Stochastic knapsack problem originally was a versatile model for controls in telecommunication networks. Recently, it draws attentions of revenue management community by serving as a basic model for allocating resources over time. We develop approximation schemes for knapsack problems in this paper, a system of nonlinear but solvable partial differential equations and stochastic partial differential equation are shown to be the limit of the process that following the optimal solution of the stochastic knapsack problem.
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.
Messica, A.
2016-10-01
The probability distribution function of a weighted sum of non-identical lognormal random variables is required in various fields of science and engineering and specifically in finance for portfolio management as well as exotic options valuation. Unfortunately, it has no known closed form and therefore has to be approximated. Most of the approximations presented to date are complex as well as complicated for implementation. This paper presents a simple, and easy to implement, approximation method via modified moments matching and a polynomial asymptotic series expansion correction for a central limit theorem of a finite sum. The method results in an intuitively-appealing and computation-efficient approximation for a finite sum of lognormals of at least ten summands and naturally improves as the number of summands increases. The accuracy of the method is tested against the results of Monte Carlo simulationsand also compared against the standard central limit theorem andthe commonly practiced Markowitz' portfolio equations.
Functional characterisation of a putative rhamnogalacturonan II specific xylosyltransferase.
Egelund, Jack; Damager, Iben; Faber, Kirsten; Olsen, Carl-Erik; Ulvskov, Peter; Petersen, Bent Larsen
2008-09-22
An Arabidopsis thaliana gene, At1g56550, was expressed in Pichia pastoris and the recombinant protein was shown to catalyse transfer of D-xylose from UDP-alpha-D-xylose onto methyl alpha-L-fucoside. The product formed was shown by 1D and 2D 1H NMR spectroscopy to be Me alpha-D-Xyl-(1,3)-alpha-L-Fuc, which is identical to the proposed target structure in the A-chain of rhamnogalacturonan II. Chemically synthesized methyl L-fucosides derivatized by methyl groups on either the 2-, 3- or 4 position were tested as acceptor substrates but only methyl 4-O-methyl-alpha-L-fucopyranoside acted as an acceptor, although to a lesser extent than methyl alpha-L-fucoside. At1g56550 is suggested to encode a rhamnogalacturonan II specific xylosyltransferase.
Energy Technology Data Exchange (ETDEWEB)
Ding, Dahu, E-mail: dingdahu@gmail.com [Graduate School of Life and Environmental Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8572 (Japan); Lei, Zhongfang; Yang, Yingnan [Graduate School of Life and Environmental Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8572 (Japan); Feng, Chuanping [School of Water Resources and Environment, China University of Geosciences (Beijing), Key Laboratory of Groundwater Circulation and Evolution, Ministry of Education, Beijing 100083 (China); Zhang, Zhenya, E-mail: zhang.zhenya.fu@u.tsukuba.ac.jp [Graduate School of Life and Environmental Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8572 (Japan)
2014-04-01
Highlights: • Novel biosorbent for cesium removal was derived from agricultural residue. • It could remove cesium effectively from aqueous solution. • Large size of granules makes it easy to be separated from solutions. • The volume of used biosorbent could be significantly reduced after incineration. • Incinerated biosorbent has a low volume and a low cost final disposal. - Abstract: A novel nickel (II) hexacyanoferrate (III) functionalized agricultural residue-walnut shell (Ni{sup II}HCF{sup III}-WS) was developed to selectively remove cesium ion (Cs{sup +}) from aqueous solutions. This paper showed the first integral study on Cs{sup +} removal behavior and waste reduction analysis by using biomass adsorption material. The results indicated that the removal process was rapid and reached saturation within 2 h. As a special characteristic of Ni{sup II}HCF{sup III}-WS, acidic condition was preferred for Cs{sup +} removal, which was useful for extending the application scope of the prepared biomass material in treating acidic radioactive liquid waste. The newly developed Ni{sup II}HCF{sup III}-WS could selectively remove Cs{sup +} though the coexisting ions (Na{sup +} and K{sup +} in this study) exhibited negative effects. In addition, approximately 99.8% (in volume) of the liquid waste was reduced by using Ni{sup II}HCF{sup III}-WS and furthermore 91.9% (in volume) of the spent biomass material (Cs-Ni{sup II}HCF{sup III}-WS) was reduced after incineration (at 500 °C for 2 h). Due to its relatively high distribution coefficient and significant volume reduction, Ni{sup II}HCF{sup III}-WS is expected to be a promising material for Cs{sup +} removal in practice.
Sun, Zhigang
2016-01-01
We proposed a distributed approximating functional method for efficiently describing the electronic dynamics in atoms and molecules in the presence of the Coulomb singularities, using the kernel of a grid representation derived by using the solutions of the Coulomb differential equation based upon the Schwartz's interpolation formula, and a grid representation using the Lobatto/Radau shape functions. The elements of the resulted Hamiltonian matrix are confined in a narrow diagonal band, which is similar to that using the (higher order) finite difference methods. However, the spectral convergence properties of the original grid representations are retained in the proposed distributed approximating functional method for solving the Schr\\"odinger equation involving the Coulomb singularity. Thus the method is effective for solving the electronic Schr\\"odinger equation using iterative methods where the action of the Hamiltonian matrix on the wave function need to evaluate many times. The method is investigated by ...
Directory of Open Access Journals (Sweden)
M. L. Mittal
2016-01-01
Full Text Available We prove two Theorems on approximation of functions belonging to Lipschitz class Lip(α,p in Lp-norm using Cesàro submethod. Further we discuss few corollaries of our Theorems and compare them with the existing results. We also note that our results give sharper estimates than the estimates in some of the known results.
Duifhuis, H
This letter concerns the paper "An approximate transfer function for the dual-resonance nonlinear filter model of auditory frequency selectivity" [E. A. Lopez-Poveda, J. Acoust. Soc. Am. 114, 2112-2117 (2003)]. It proposes a correction of the historical framework in which the paper is presented.
Ruthenium(II)-Catalyzed C-C Arylations and Alkylations: Decarbamoylative C-C Functionalizations.
Moselage, Marc; Li, Jie; Kramm, Frederik; Ackermann, Lutz
2017-04-05
Ruthenium(II)biscarboxylate catalysis enabled selective C-C functionalizations by means of decarbamoylative C-C arylations. The versatility of the ruthenium(II) catalysis was reflected by widely applicable C-C arylations and C-C alkylations of aryl amides, as well as acids with modifiable pyrazoles, through facile organometallic C-C activation.
Directory of Open Access Journals (Sweden)
Shrinivas Basavaraddi
2016-01-01
Full Text Available This case report describes the application of fixed functional appliance in the treatment of an adult female having Class II division 2 malocclusion with retroclination of upper incisors. Fixed functional appliance was used to correct the overjet after the uprighting of upper incisors. Fixed functional appliance was fitted on a rigid rectangular arch wire. Application of fixed functional appliance achieved a good Class I molar relationship along with Class I canine relationship with normal overjet and overbite. Fixed functional appliance is effective in the treatment of Class II malocclusions, even in adult patients, and can serve as an alternate choice of treatment instead of orthognathic surgery. This is a case; wherein, fixed functional appliance was successfully used to relieve deep bite and overjet that was ensued after leveling and aligning. We demonstrate that fixed functional appliance can act as a “noncompliant corrector” and use of Class II elastics can be avoided.
Basavaraddi, Shrinivas; Gandedkar, Narayan H; Belludi, Anup; Patil, Anand
2016-01-01
This case report describes the application of fixed functional appliance in the treatment of an adult female having Class II division 2 malocclusion with retroclination of upper incisors. Fixed functional appliance was used to correct the overjet after the uprighting of upper incisors. Fixed functional appliance was fitted on a rigid rectangular arch wire. Application of fixed functional appliance achieved a good Class I molar relationship along with Class I canine relationship with normal overjet and overbite. Fixed functional appliance is effective in the treatment of Class II malocclusions, even in adult patients, and can serve as an alternate choice of treatment instead of orthognathic surgery. This is a case; wherein, fixed functional appliance was successfully used to relieve deep bite and overjet that was ensued after leveling and aligning. We demonstrate that fixed functional appliance can act as a "noncompliant corrector" and use of Class II elastics can be avoided.
National Research Council Canada - National Science Library
Blahak, Ulrich
2008-01-01
... a simple moving sum of single-beam weighting functions. Assuming a Gaussian shape of a single pulse, a simple and easy-to-use parameterization of the effective beam weighting function is arrived at, which depends only on the single beamwidth and the ratio of the single beamwidth to the rotational angular averaging interval. The derived relation ...
Zhao, Qian; Hou, Jing; Chen, Bo; Shao, Xue; Zhu, Ruiming; Bu, Qian; Gu, Hui; Li, Yan; Zhang, Baolai; Du, Changman; Fu, Dengqi; Kong, Jueying; Luo, Li; Long, Hailei; Li, Hongyu; Deng, Yi; Zhao, Yinglan; Cen, Xiaobo
2015-10-01
Studies have showed that prenatal cocaine exposure (PCOC) can impair cognitive function and social behavior of the offspring; however, the mechanism underlying such effect is poorly understood. Insulin-like growth factor II (Igf-II), an imprinted gene, has a critical role in memory consolidation and enhancement. We hypothesized that epigenetic regulation of hippocampal Igf-II may attribute to the cognitive deficits of PCOC offspring. We used Morris water maze and open-field task to test the cognitive function in PCOC offspring. The epigenetic alteration involved in hippocampal Igf-II expression deficit in PCOC offspring was studied by determining Igf-II methylation status, DNA methyltransferases (DNMT) expressions and L-methionine level. Moreover, IGF-II rescue experiments were performed and the downstream signalings were investigated in PCOC offspring. In behavioral tests, we observed impaired spatial learning and memory and increased anxiety in PCOC offspring; moreover, hippocampal IGF-II mRNA and protein expressions were significantly decreased. Hippocampal methylation of cytosine-phospho-guanine (CpG) dinucleotides in differentially methylated region (DMR) 2 of Igf-II was elevated in PCOC offspring, which may be driven by the upregulation of L-methionine and DNA methyltransferase (DNMT) 1. Importantly, intra-hippocampal injection of recombinant IGF-II reactivated the repressed calcium calmodulin kinase II α (CaMKIIα) and reversed cognitive deficits in PCOC offspring. Collectively, our findings suggest that cocaine exposure during pregnancy impairs cognitive function of offspring through epigenetic modification of Igf-II gene. Enhancing IGF-II signaling may represent a novel therapeutical strategy for cocaine-induced cognitive impairment.
Nobile, F.
2015-10-30
In this work we provide a convergence analysis for the quasi-optimal version of the sparse-grids stochastic collocation method we presented in a previous work: “On the optimal polynomial approximation of stochastic PDEs by Galerkin and collocation methods” (Beck et al., Math Models Methods Appl Sci 22(09), 2012). The construction of a sparse grid is recast into a knapsack problem: a profit is assigned to each hierarchical surplus and only the most profitable ones are added to the sparse grid. The convergence rate of the sparse grid approximation error with respect to the number of points in the grid is then shown to depend on weighted summability properties of the sequence of profits. This is a very general argument that can be applied to sparse grids built with any uni-variate family of points, both nested and non-nested. As an example, we apply such quasi-optimal sparse grids to the solution of a particular elliptic PDE with stochastic diffusion coefficients, namely the “inclusions problem”: we detail the convergence estimates obtained in this case using polynomial interpolation on either nested (Clenshaw–Curtis) or non-nested (Gauss–Legendre) abscissas, verify their sharpness numerically, and compare the performance of the resulting quasi-optimal grids with a few alternative sparse-grid construction schemes recently proposed in the literature.
Petretto, Guido; Bruneval, Fabien
2015-12-01
The identification of defect levels from photoluminescence spectroscopy is a useful but challenging task. Density-functional theory (DFT) is a highly valuable tool to this aim. However, the semilocal approximations of DFT that are affected by a band gap underestimation are not reliable to evaluate defect properties, such as charge transition levels. It is now established that hybrid functional approximations to DFT improve the defect description in semiconductors. Here we demonstrate that the use of hybrid functionals systematically stabilizes donor defect states in the lower part of the band gap for many defects, impurities or vacancies, in III-V and in II-VI semiconductors, even though these defects are usually considered as acceptors. These donor defect states are a very general feature and, to the best of our knowledge, have been overlooked in previous studies. The states we identify here may challenge the older assignments to photoluminescent peaks. Though appealing to screen quickly through the possible stable charge states of a defect, semilocal approximations should not be trusted for that purpose.
Applications of Fitzpatrick functions for solving optimization problems II
Nashed, Z.; Raykov, I.
2015-10-01
This paper is a continuation of the paper [8] and presents more applications of Fitzpatrick functions for solving optimization problems. The main purpose of the present work is to introduce some new properties of Fitzpatrick functions useful for solving optimization problems, using also their already presented specific properties, as the maximal monotonicity, proper, convex and lower semi-continuity.
Correlation functions in conformal Toda field theory II
Fateev, V A
2009-01-01
This is the second part of the paper 0709.3806v2. Here we show that three-point correlation function with one semi-degenerate field in Toda field theory as well as four-point correlation function with one completely degenerate and one semi-degenerate field can be represented by the finite dimensional integrals.
几个总体均值函数的鞍点逼近%Saddlepoint Approximations for Function of Means from Several Populations
Institute of Scientific and Technical Information of China (English)
邢炳义; 李泽慧
2002-01-01
Saddlepoint approximations for marginal tail probabilities for a real-valued function of vector means fromseveral populations are developed. The approximations are then shown to give great numerical accuracy, whichare demonstrated in some numerical examples. Application to the bootstrap is also considered in order to avoidintensive Monte Carlo simulations.%本文发展了儿个总体的均值向量的函数的尾部概率的鞍点逼近方法,并应用它丁Bootstrap估计中,以代替Monto Carlo模拟,一些数值例子说明了其近似精度.
Energy Technology Data Exchange (ETDEWEB)
Buehring, W.
1983-03-01
Non-relativistic scattering phase shifts, bound state energies, and wave function normalization factors for a screened Coulomb potential of the Hulthen type are presented in the form of relatively simple analytic expressions. These formulae have been obtained by a suitable renormalization procedure applied to the quantities derived from an approximate Schroedinger equation which contains the exact Hulthen potential together with an approximate angular momentum term. When the screening exponent vanishes, our formulae reduce to the exact Coulomb expresions. The interrelation between our formulae and Pratt's analytic perturbation theory for screened Coulomb potentials' is discussed.
S-Approximation: A New Approach to Algebraic Approximation
Directory of Open Access Journals (Sweden)
M. R. Hooshmandasl
2014-01-01
Full Text Available We intend to study a new class of algebraic approximations, called S-approximations, and their properties. We have shown that S-approximations can be used for applied problems which cannot be modeled by inclusion based approximations. Also, in this work, we studied a subclass of S-approximations, called Sℳ-approximations, and showed that this subclass preserves most of the properties of inclusion based approximations but is not necessarily inclusionbased. The paper concludes by studying some basic operations on S-approximations and counting the number of S-min functions.
Enhanced removal of Hg(II) from acidic aqueous solution using thiol-functionalized biomass.
Chai, Liyuan; Wang, Qingwei; Li, Qingzhu; Yang, Zhihui; Wang, Yunyan
2010-01-01
Spent grain, the low-cost and abundant biomass produced in the brewing industry, was functionalized with thiol groups to be used as an adsorbent for Hg(II) removal from acidic aqueous solution. The adsorbents were characterized by the energy-dispersive X-ray analysis (EDAX) and Fourier transform infrared (FTIR) spectroscopy. Optimum pH for Hg(II) adsorption onto the thiol-functionalized spent grain (TFSG) was 2.0. The equilibrium and kinetics of the adsorption of Hg(II) onto TFSG from acidic aqueous solution were investigated. From the Langmuir isotherm model the maximum adsorption capacity of TFSG for Hg(II) was found to be 221.73 mg g(-1), which was higher than that of most various adsorbents reported in literature. Moreover, the adsorption of Hg(II) onto TFSG followed pseudo-second-order kinetic model.
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
Functional Implications of Photosystem II Crystal Formation in Photosynthetic Membranes
Tietz, Stefanie; Puthiyaveetil, Sujith; Enlow, Heather M; Yarbrough, Robert; Wood, Magnus; Semchonok, Dmitry A; Lowry, Troy; Li, Zhirong; Jahns, Peter; Boekema, Egbert J; Lenhert, Steven; Niyogi, Krishna K; Kirchhoff, Helmut
2015-01-01
The structural organization of proteins in biological membranes can affect their function. Photosynthetic thylakoid membranes in chloroplasts have the remarkable ability to change their supramolecular organization between disordered and semicrystalline states. Although the change to the semicrystall
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...
DEFF Research Database (Denmark)
Senjean, Bruno; Knecht, Stefan; Jensen, Hans Jørgen Aa
2015-01-01
Gross-Oliveira-Kohn density-functional theory (GOK-DFT) for ensembles is, in principle, very attractive but has been hard to use in practice. A practical model based on GOK-DFT for the calculation of electronic excitation energies is discussed. The model relies on two modifications of GOK-DFT: us...
Polymorphisms of mouse apolipoprotein A-II alter its physical and functional nature.
Directory of Open Access Journals (Sweden)
Timothy J Sontag
Full Text Available ApoA-II is the second most abundant protein on HDL making up ∼ 20% of the total protein but its functions have still only been partially characterized. Recent methodological improvements have allowed for the recombinant expression and characterization of human apoA-II which shares only 55% sequence homology with murine apoA-II. Here we describe the purification of the two most common polymorphic variants of apoA-II found in inbred mouse strains, differing at 3 amino acid sites. C57BL/6 mice having variant apoA-II(a have lower plasma HDL levels than FVB/N mice that have variant apoA-II(b. Characterization of the helical structure of these two variants reveals a more alpha-helical structure for the FVB/N apoA-II. These changes do not alter the lipid or HDL binding of the two apoA-II variants, but significantly increase the ability of the FVB/N variant to promote both ABCA1 and ABCG1 mediated cellular cholesterol efflux. These differences may be differentially altering plasma HDL apoA-II levels. In vivo, neither C57 nor FVB apoA-II protein levels are affected by the absence of apoE, while an apoE/apoA-I double deficiency results in a 50% decrease of plasma FVB apoA-II but results in undetectable levels of C57 apoA-II in the plasma. FVB apoA-II is able to form an HDL particle in the absence of apoE or apoA-I.
Veenhoff, L.M.; Geertsma, E.R.; Poolman, B.; Knol, J.
2000-01-01
The lactose transport protein (LacS) of Streptococcus thermophilus belongs to a family of transporters in which putative α-helices II and IV have been implicated in cation binding and the coupled transport of the substrate and the cation. Here, the analysis of site-directed mutants shows that a posi
Energy Technology Data Exchange (ETDEWEB)
Deng Xiaojiao; Lue Lili; Li Hongwei [Key Laboratory of Polyoxometalates Science of Ministry of Education, College of Chemistry, Northeast Normal University, Changchun 130024 (China); Luo Fang, E-mail: luof746@nenu.edu.cn [Key Laboratory of Polyoxometalates Science of Ministry of Education, College of Chemistry, Northeast Normal University, Changchun 130024 (China)
2010-11-15
The functionalized graphene (GNS{sup PF6}) was fabricated by simple and fast method of electrolysis with potassium hexafluorophosphate solution as electrolyte under the static potential of 15 V. The characterization results of transmission electron microscopy, atom force microscopy, X-ray photoelectron spectroscopy, X-ray powder diffraction, Raman spectroscopy and thermogravimetric analysis indicate that graphite rod was completely exfoliated to graphene layer containing 30 wt.% PF{sub 6}{sup -} with the average thickness ca. 1.0 nm. Our sample of GNS{sup PF6} was developed for the removal of Pb(II) or Cd(II) ions from water, and the determined adsorption capacities are 406.6 mg/g (pH = 5.1) for Pb(II) and 73.42 mg/g (pH = 6.2) for Cd(II), which is much higher than that by our previous sample of GNS{sup C8P} and carbon nanotube. The adsorption processes reach equilibrium in just 40 min and the adsorption isotherms are described well by Langmuir and Freundlich classical isotherms models.
Deng, Xiaojiao; Lü, Lili; Li, Hongwei; Luo, Fang
2010-11-15
The functionalized graphene (GNS(PF6)) was fabricated by simple and fast method of electrolysis with potassium hexafluorophosphate solution as electrolyte under the static potential of 15 V. The characterization results of transmission electron microscopy, atom force microscopy, X-ray photoelectron spectroscopy, X-ray powder diffraction, Raman spectroscopy and thermogravimetric analysis indicate that graphite rod was completely exfoliated to graphene layer containing 30 wt.% PF(6)- with the average thickness ca. 1.0 nm. Our sample of GNS(PF6) was developed for the removal of Pb(II) or Cd(II) ions from water, and the determined adsorption capacities are 406.6 mg/g (pH=5.1) for Pb(II) and 73.42 mg/g (pH=6.2) for Cd(II), which is much higher than that by our previous sample of GNS(C8P) and carbon nanotube. The adsorption processes reach equilibrium in just 40 min and the adsorption isotherms are described well by Langmuir and Freundlich classical isotherms models.
Functionalization of conducting polymer with novel Co(II) complex: Electroanalysis of ascorbic acid
Energy Technology Data Exchange (ETDEWEB)
Mohan, Swati [School of Materials Science and Technology, Institute of Technology, Banaras Hindu University, Varanasi 221005 (India); Prakash, Rajiv, E-mail: rajivprakash12@yahoo.com [School of Materials Science and Technology, Institute of Technology, Banaras Hindu University, Varanasi 221005 (India)
2010-06-15
We report for the first time the functionalization of a conducting polymer with a metal complex in order to develop a new type of catalytic material exhibiting better electronic communication through their delocalized {pi} electrons. The Co(II) complex having hydroxyl group as functional moiety is chemically coupled with carboxyl group of polyanthranilic acid which itself is a self doped conducting polymer. The covalent linkage between Co(II) and -OH group is confirmed using UV-vis, FT-IR and NMR spectroscopic techniques. The Co(II) complex functionalized polymer does exhibit excellent redox behavior and stability with mixed properties of Co(II) complex and {pi}-conjugated polymer. The material possesses potential benefits in sensors/biosensor applications and it is demonstrated for the electroanalysis of ascorbic acid at a level of nano molar concentration.
神经网络对φ-有界变差函数的逼近%Approximation of φ-bounded variations functions by neural network
Institute of Scientific and Technical Information of China (English)
石林蜜; 谢庭藩
2011-01-01
研究了以有界的sigmoidal函数σ为激活函数的单隐层神经网络对于在[a,b]上φ-有界变差函数f的逼近,得到的逼近偏差为‖σ‖φ-1(Vφ(f)[a,b]/n).倘若激活函数是Heaviside函数时,则逼近偏差为φ-1(Vφ(f)[a,b]/2n).此外,在第3节中,我们还将上述结果扩充到了全实轴上.%We studied the approximation of φ-bounded variation functions f on [a, b] by the feed-forward neural network with bounded sigmoidal functions σ, which the degree of approximation by single hidden layer neural network is ‖ σ ‖ φ- 1 (Vφ(f)[a,b])/n . If the active function was Heaviside function,We obtain that the degree of approximation is φ-1 (Vφ(f)[a,b] )/ 2n . Further more, we extend the results to the whole real axis in the section 3.
Rafal Podlaski; Francis .A. Roesch
2013-01-01
The goals of this study are (1) to analyse the accuracy of the approximation of empirical distributions of diameter at breast height (dbh) using two-component mixtures of either the Weibull distribution or the gamma distribution in two−cohort stands, and (2) to discuss the procedure of choosing goodness−of−fit tests. The study plots were...
Molecular determinants of angiotensin II type 1 receptor functional selectivity
DEFF Research Database (Denmark)
Aplin, Mark; Bonde, Marie Mi; Hansen, Jakob Lerche
2008-01-01
-independent recruitment of beta-arrestin-scaffolded signalling complexes that activate protein kinase pathways. Different states of receptor activation with preference for individual downstream pathways (functional selectivity) have been demonstrated in mutational studies of the AT(1) receptor and by pharmacological...... that selective blockade of G protein actions and simultaneous activation of G protein-independent signalling will prove to be a feasible strategy for improved cardiovascular therapy. The pharmacological perspectives of functional selectivity by receptors, such as the AT(1) receptor, urge the elucidation...
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 ...
Luenser, Arne; Kussmann, Jörg; Ochsenfeld, Christian
2016-09-01
We present a (sub)linear-scaling algorithm to determine indirect nuclear spin-spin coupling constants at the Hartree-Fock and Kohn-Sham density functional levels of theory. Employing efficient integral algorithms and sparse algebra routines, an overall (sub)linear scaling behavior can be obtained for systems with a non-vanishing HOMO-LUMO gap. Calculations on systems with over 1000 atoms and 20 000 basis functions illustrate the performance and accuracy of our reference implementation. Specifically, we demonstrate that linear algebra dominates the runtime of conventional algorithms for 10 000 basis functions and above. Attainable speedups of our method exceed 6 × in total runtime and 10 × in the linear algebra steps for the tested systems. Furthermore, a convergence study of spin-spin couplings of an aminopyrazole peptide upon inclusion of the water environment is presented: using the new method it is shown that large solvent spheres are necessary to converge spin-spin coupling values.
Luenser, Arne; Kussmann, Jörg; Ochsenfeld, Christian
2016-09-28
We present a (sub)linear-scaling algorithm to determine indirect nuclear spin-spin coupling constants at the Hartree-Fock and Kohn-Sham density functional levels of theory. Employing efficient integral algorithms and sparse algebra routines, an overall (sub)linear scaling behavior can be obtained for systems with a non-vanishing HOMO-LUMO gap. Calculations on systems with over 1000 atoms and 20 000 basis functions illustrate the performance and accuracy of our reference implementation. Specifically, we demonstrate that linear algebra dominates the runtime of conventional algorithms for 10 000 basis functions and above. Attainable speedups of our method exceed 6 × in total runtime and 10 × in the linear algebra steps for the tested systems. Furthermore, a convergence study of spin-spin couplings of an aminopyrazole peptide upon inclusion of the water environment is presented: using the new method it is shown that large solvent spheres are necessary to converge spin-spin coupling values.
Postlaunch Monitoring of Functional Foods - Methodology development (II)
Jong N de; Buurma-Rethans EJM; Fransen HP; Ocke MC; CVG
2005-01-01
Despite the availability of numerous cohort and monitoring studies in different populations in the Netherlands, the available information on functional food and/or supplement use on the whole from these studies is rather limited. Unfortunately, food intake data are vital for Post Launch Monitoring
Universality of the Distribution Functions of Random Matrix Theory. II
Tracy, Craig A.; Widom, Harold
1999-01-01
This paper is a brief review of recent developments in random matrix theory. Two aspects are emphasized: the underlying role of integrable systems and the occurrence of the distribution functions of random matrix theory in diverse areas of mathematics and physics.
Subharmonic functions and electric fields in ball layers. II
Directory of Open Access Journals (Sweden)
O. P. Gnatiuk
2011-03-01
Full Text Available In this sequel to cite{GK} we study a special case $BL(frac{1}{r},r$, $r>1$. Alsothe explicit representation of a subharmonic extension for a subharmonic function $u(x$ near a removable point is obtained. Moreover, the diverse Nevanlinna characteristics are compared.
Zhang, Yachao
2014-12-07
A first-principles study of critical temperatures (T(c)) of spin crossover (SCO) materials requires accurate description of the strongly correlated 3d electrons as well as much computational effort. This task is still a challenge for the widely used local density or generalized gradient approximations (LDA/GGA) and hybrid functionals. One remedy, termed density functional theory plus U (DFT+U) approach, introduces a Hubbard U term to deal with the localized electrons at marginal computational cost, while treats the delocalized electrons with LDA/GGA. Here, we employ the DFT+U approach to investigate the T(c) of a pair of iron(II) SCO molecular crystals (α and β phase), where identical constituent molecules are packed in different ways. We first calculate the adiabatic high spin-low spin energy splitting ΔE(HL) and molecular vibrational frequencies in both spin states, then obtain the temperature dependent enthalpy and entropy changes (ΔH and ΔS), and finally extract T(c) by exploiting the ΔH/T - T and ΔS - T relationships. The results are in agreement with experiment. Analysis of geometries and electronic structures shows that the local ligand field in the α phase is slightly weakened by the H-bondings involving the ligand atoms and the specific crystal packing style. We find that this effect is largely responsible for the difference in T(c) of the two phases. This study shows the applicability of the DFT+U approach for predicting T(c) of SCO materials, and provides a clear insight into the subtle influence of the crystal packing effects on SCO behavior.
Shrinivas Basavaraddi; Gandedkar, Narayan H; Anup Belludi; Anand Patil
2016-01-01
This case report describes the application of fixed functional appliance in the treatment of an adult female having Class II division 2 malocclusion with retroclination of upper incisors. Fixed functional appliance was used to correct the overjet after the uprighting of upper incisors. Fixed functional appliance was fitted on a rigid rectangular arch wire. Application of fixed functional appliance achieved a good Class I molar relationship along with Class I canine relationship with normal ov...
Directory of Open Access Journals (Sweden)
Witała H.
2010-04-01
Full Text Available For a sharply cut-oﬀ Coulomb potential we derive analytically the asymptotic form of the threedimensional wave function and the related scattering amplitude. We show a failure of the standard renormalization factor which is believed to be generally valid for any type of screening. We obtain also the asymptotic form of the corresponding three-dimensional half-shell t-matrix. Our results are fully supported by the numerical solutions of the three-dimensional Lippmann-Schwinger equation.
Immunophilins and their function in photosystem II assembly
Energy Technology Data Exchange (ETDEWEB)
Sheng Luan
2012-11-27
In the past funding period, the following lines of experiments have been conducted: to identify the partner proteins for FKBP20-2; to identify the mechanism of CYP38 function; studies on other FKBPs in the thylakoid lumen; to identify the partner proteins for FKBP20-2 using yeast two hybrid and transgenic lines expressing HA-FKBP20-2; to identify the partner protein of CYP38; studies on other FKBPs in the chloroplast.
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.
Magrini, Luciano A.; Domingues, Margarete O.; Mendes, Odim
2017-02-01
The presence of gaps is quite common in signals related to space science phenomena. Usually, this presence prevents the direct use of standard time-scale analysis because this analysis needs equally spaced data; it is affected by the time series borders (boundaries), and gaps can cause an increase of internal borders. Numerical approximations can be used to estimate the records whose entries are gaps. However, their use has limitations. In many practical cases, these approximations cannot faithfully reproduce the original signal behaviour. Alternatively, in this work, we compare an adapted wavelet technique (gaped wavelet transform), based on the continuous wavelet transform with Morlet wavelet analysing function, with two other standard approximation methods, namely, spline and Hermite cubic polynomials. This wavelet method does not require an approximation of the data on the gap positions, but it adapts the analysing wavelet function to deal with the gaps. To perform our comparisons, we use 120 magnetic field time series from a well-known space geophysical phenomena and we select and classify their gaps. Then, we analyse the influence of these methods in two time-scale tools. As conclusions, we observe that when the gaps are small (very few points sequentially missing), all the methods work well. However, with large gaps, the adapted wavelet method presents a better performance in the time-scale representation. Nevertheless, the cubic Hermite polynomial approximation is also an option when a reconstruction of the data is also needed, with the price of having a worse time-scale representation than the adapted wavelet method.
Magrini, Luciano A.; Domingues, Margarete O.; Mendes, Odim
2017-04-01
The presence of gaps is quite common in signals related to space science phenomena. Usually, this presence prevents the direct use of standard time-scale analysis because this analysis needs equally spaced data; it is affected by the time series borders (boundaries), and gaps can cause an increase of internal borders. Numerical approximations can be used to estimate the records whose entries are gaps. However, their use has limitations. In many practical cases, these approximations cannot faithfully reproduce the original signal behaviour. Alternatively, in this work, we compare an adapted wavelet technique (gaped wavelet transform), based on the continuous wavelet transform with Morlet wavelet analysing function, with two other standard approximation methods, namely, spline and Hermite cubic polynomials. This wavelet method does not require an approximation of the data on the gap positions, but it adapts the analysing wavelet function to deal with the gaps. To perform our comparisons, we use 120 magnetic field time series from a well-known space geophysical phenomena and we select and classify their gaps. Then, we analyse the influence of these methods in two time-scale tools. As conclusions, we observe that when the gaps are small (very few points sequentially missing), all the methods work well. However, with large gaps, the adapted wavelet method presents a better performance in the time-scale representation. Nevertheless, the cubic Hermite polynomial approximation is also an option when a reconstruction of the data is also needed, with the price of having a worse time-scale representation than the adapted wavelet method.
Grip, Helena; Tengman, Eva; Häger, Charlotte K
2015-07-16
Finite helical axis (FHA) measures of the knee joint during weight-bearing tasks may capture dynamic knee stability following Anterior Cruciate Ligament (ACL) injury. The aim was to investigate dynamic knee stability during two-leg squat (TLS) and one-leg side hop (SH) in a long-term follow-up of ACL injury, and to examine correlations with knee laxity (KT-1000), osteoarthritis (OA, Kellgren-Lawrence) and knee function (Lysholm score). Participants were injured 17-28 years ago and then treated with surgery (n=33, ACLR) or physiotherapy only (n=37, ACLPT) and healthy-knee controls (n=33) were tested. Movements were registered with an optical motion capture system. We computed three FHA inclination angles, its' Anterior-Posterior (A-P) position, and an index quantifying directional changes (DI), during stepwise knee flexion intervals of ∼15°. Injured knees were less stable compared to healthy controls' and to contralateral non-injured knees, regardless of treatment: the A-P intersection was more anterior (indicating a more anterior positioning of tibia relative to femur) positively correlating with high laxity/low knee function, and during SH, the FHA was more inclined relative to the flexion-extension axis, possibly due to reduced rotational stability. During the TLS, A-P intersection was more anterior in the non-injured knee than the injured, and DI was higher, probably related to higher load on the non-injured knee. ACLR had less anterior A-P intersection than ACLPT, suggesting that surgery enhanced stability, although rotational stability may remain reduced. More anterior A-P intersection and greater inclination between the FHA and the knee flexion-extension axis best revealed reduced dynamic stability ∼23 years post-injury.
Directory of Open Access Journals (Sweden)
Shuang Li
2015-06-01
Full Text Available This article concerns the existence of traveling wavefronts for a nonlocal diffusive predator-prey system with functional response of Holling type II. We first establish the existence principle for the system with a general functional response by using a fixed point theorem and upper-lower solution technique. We apply this result to a predator-prey model with Holling type II functional response. We deduce the existence of traveling wavefronts that connect the zero equilibrium and the positive equilibrium.
Karst geomorphology: From hydrological functioning to palaeoenvironmental reconstructions. Part II
De Waele, Jo; Gutierrez, Francisco; Audra, Philippe
2015-10-01
In January 2015, the first part of the special issue on karst, entitled "Karst geomorphology: From hydrological functioning to palaeoenvironmental reconstructions" was published (Geomorphology, Vol. 229). This second part of the special issue comprises seven research papers covering a broad geographical canvas including Japan, Slovenia, France, Spain, Croatia, and Poland-Ukraine. Both issues mainly emanate from the contributions presented in the Karst session of the 8th International Conference of Geomorphology (International Association of Geomorphologists), held in Paris in August 2013, enriched with some invited papers.
Tin(II)-functionalization of the archetypal {P8W48} polyoxotungstate.
Izarova, N V; Klaß, L; de Oliveira, P; Mbomekalle, I-M; Peters, V; Haarmann, F; Kögerler, P
2015-11-28
The synthesis of [K(4.5) ⊂ (ClSn(II))8P8W48O184](17.5-), featuring Sn(II) ions in trigonal-pyramidal SnO2Cl environment coordinating to the two inner rims of the wheel-shaped {P8W48}-type polyoxotungstate(vi) archetype, showcases how high chloride ligand concentrations as well as the control of the polyanion solubility via electrolytes and evaporation rates are essential to prevent numerous competing reactions that can hamper the Sn(ii) functionalization of polyoxometalates.
Energy Technology Data Exchange (ETDEWEB)
Hatch, C.E.
1995-05-01
This document is the Functional Design Criteria for Project W-252. Project W-252 provides the scope to provide BAT/AKART (best available technology...) to 200 Liquid Effluent Phase II streams (B-Plant). This revision (Rev. 2) incorporates a major descoping of the project. The descoping was done to reflect a combination of budget cutting measures allowed by a less stringent regulatory posture toward the Phase II streams
Directory of Open Access Journals (Sweden)
Jiashu Yao
Full Text Available Bipolar disorder types I (BD I and II (BD II behave differently in clinical manifestations, normal personality traits, responses to pharmacotherapies, biochemical backgrounds and neuroimaging activations. How the varied emotional states of BD I and II are related to the comorbid personality disorders remains to be settled.We therefore administered the Plutchick - van Praag Depression Inventory (PVP, the Mood Disorder Questionnaire (MDQ, the Hypomanic Checklist-32 (HCL-32, and the Parker Personality Measure (PERM in 37 patients with BD I, 34 BD II, and in 76 healthy volunteers.Compared to the healthy volunteers, patients with BD I and II scored higher on some PERM styles, PVP, MDQ and HCL-32 scales. In BD I, the PERM Borderline style predicted the PVP scale; and Antisocial predicted HCL-32. In BD II, Borderline, Dependent, Paranoid (- and Schizoid (- predicted PVP; Borderline predicted MDQ; Passive-Aggressive and Schizoid (- predicted HCL-32. In controls, Borderline and Narcissistic (- predicted PVP; Borderline and Dependent (- predicted MDQ.Besides confirming the different predictability of the 11 functioning styles of personality disorder to BD I and II, we found that the prediction was more common in BD II, which might underlie its higher risk of suicide and poorer treatment outcome.
Bone morphogenetic protein receptor II regulates pulmonary artery endothelial cell barrier function.
Burton, Victoria J; Ciuclan, Loredana I; Holmes, Alan M; Rodman, David M; Walker, Christoph; Budd, David C
2011-01-06
Mutations in bone morphogenetic protein receptor II (BMPR-II) underlie most heritable cases of pulmonary arterial hypertension (PAH). However, less than half the individuals who harbor mutations develop the disease. Interestingly, heterozygous null BMPR-II mice fail to develop PAH unless an additional inflammatory insult is applied, suggesting that BMPR-II plays a fundamental role in dampening inflammatory signals in the pulmonary vasculature. Using static- and flow-based in vitro systems, we demonstrate that BMPR-II maintains the barrier function of the pulmonary artery endothelial monolayer suppressing leukocyte transmigration. Similar findings were also observed in vivo using a murine model with loss of endothelial BMPR-II expression. In vitro, the enhanced transmigration of leukocytes after tumor necrosis factor α or transforming growth factor β1 stimulation was CXCR2 dependent. Our data define how loss of BMPR-II in the endothelial layer of the pulmonary vasculature could lead to a heightened susceptibility to inflammation by promoting the extravasation of leukocytes into the pulmonary artery wall. We speculate that this may be a key mechanism involved in the initiation of the disease in heritable PAH that results from defects in BMPR-II expression.
Yao, Jiashu; Xu, You; Qin, Yanhua; Liu, Jing; Shen, Yuedi; Wang, Wei; Chen, Wei
2015-01-01
Bipolar disorder types I (BD I) and II (BD II) behave differently in clinical manifestations, normal personality traits, responses to pharmacotherapies, biochemical backgrounds and neuroimaging activations. How the varied emotional states of BD I and II are related to the comorbid personality disorders remains to be settled. We therefore administered the Plutchick - van Praag Depression Inventory (PVP), the Mood Disorder Questionnaire (MDQ), the Hypomanic Checklist-32 (HCL-32), and the Parker Personality Measure (PERM) in 37 patients with BD I, 34 BD II, and in 76 healthy volunteers. Compared to the healthy volunteers, patients with BD I and II scored higher on some PERM styles, PVP, MDQ and HCL-32 scales. In BD I, the PERM Borderline style predicted the PVP scale; and Antisocial predicted HCL-32. In BD II, Borderline, Dependent, Paranoid (-) and Schizoid (-) predicted PVP; Borderline predicted MDQ; Passive-Aggressive and Schizoid (-) predicted HCL-32. In controls, Borderline and Narcissistic (-) predicted PVP; Borderline and Dependent (-) predicted MDQ. Besides confirming the different predictability of the 11 functioning styles of personality disorder to BD I and II, we found that the prediction was more common in BD II, which might underlie its higher risk of suicide and poorer treatment outcome.
Approximation of continuous functions by a class of neural network%一类神经网络对连续函数的逼近
Institute of Scientific and Technical Information of China (English)
高淇琦; 谢庭藩
2011-01-01
借助卷积逼近的工具研究前向神经网络对连续函数的逼近,构造了具有nd个神经元的一类神经网络,并证得用它逼近[0,1]d上的连续函数f(X)时,偏差是O(ω(f,n-1/(d+2))+n-1/(d+2)‖f‖∞).其中ω(f,δ)表示f(X)在[0,1]d上的连续模,‖f‖∞表示|f(X)|的极大值.%Discussed the approximation of continuous functions by the feed-forward artificial neural network with a tool of convolution approximation, which approximating the continuous function f(X) in[0,1]d is the (estimation error is O (ω (f,n-1/(d+2)) +n-1/(d+2) ‖ f ‖ ∞ ).Where ω(f,δ) is the continuity modulus of f(X) in [0,1]d and ‖ f ‖ ∞ is the maximum of ｜f(X)｜.
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.
International Conference Approximation Theory XV
Schumaker, Larry
2017-01-01
These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, a...
Laricchia, Savio; Constantin, Lucian A; Fabiano, Eduardo; Della Sala, Fabio
2014-01-14
We tested Laplacian-level meta-generalized gradient approximation (meta-GGA) noninteracting kinetic energy functionals based on the fourth-order gradient expansion (GE4). We considered several well-known Laplacian-level meta-GGAs from the literature (bare GE4, modified GE4, and the MGGA functional of Perdew and Constantin (Phys. Rev. B 2007,75, 155109)), as well as two newly designed Laplacian-level kinetic energy functionals (L0.4 and L0.6). First, a general assessment of the different functionals is performed to test them for model systems (one-electron densities, Hooke's atom, and different jellium systems) and atomic and molecular kinetic energies as well as for their behavior with respect to density-scaling transformations. Finally, we assessed, for the first time, the performance of the different functionals for subsystem density functional theory (DFT) calculations on noncovalently interacting systems. We found that the different Laplacian-level meta-GGA kinetic functionals may improve the description of different properties of electronic systems, but no clear overall advantage is found over the best GGA functionals. Concerning the subsystem DFT calculations, the here-proposed L0.4 and L0.6 kinetic energy functionals are competitive with state-of-the-art GGAs, whereas all other Laplacian-level functionals fail badly. The performance of the Laplacian-level functionals is rationalized thanks to a two-dimensional reduced-gradient and reduced-Laplacian decomposition of the nonadditive kinetic energy density.
Rüger, Robert; Heine, Thomas; Visscher, Lucas
2016-01-01
We propose a new method of calculating electronically excited states that combines a density functional theory (DFT) based ground state calculation with a linear response treatment that employs approximations used in the time-dependent density functional based tight binding (TD-DFTB) approach. The new method termed TD-DFT+TB does not rely on the DFTB parametrization and is therefore applicable to systems involving all combinations of elements. We show that the new method yields UV/Vis absorption spectra that are in excellent agreement with computationally much more expensive time-dependent density functional theory (TD-DFT) calculations. Errors in vertical excitation energies are reduced by a factor of two compared to TD-DFTB.
Laricchia, S; Fabiano, E; Della Sala, F
2014-01-01
We test Laplacian-level meta-generalized gradient approximation (meta-GGA) non-interacting kinetic energy functionals based on the fourth-order gradient expansion (GE4). We consider several well known Laplacian-level meta-GGAs from literature (bare GE4, modified GE4, and the MGGA functional of Perdew and Constantin [Phys. Rev. B \\textbf{75},155109 (2007)]), as well as two newly designed Laplacian-level kinetic energy functionals (named L0.4 and L0.6). First, a general assessment of the different functionals is performed, testing them for model systems (one-electron densities, Hooke's atom and different jellium systems), atomic and molecular kinetic energies as well as for their behavior with respect to density-scaling transformations. Finally, we assess, for the first time, the performance of the different functionals for Subsystem Density Functional Theory (DFT) calculations on non-covalently interacting systems. We find that the different Laplacian-level meta-GGA kinetic functionals may improve the descript...
BDD Minimization for Approximate Computing
Soeken, Mathias; Grosse, Daniel; Chandrasekharan, Arun; Drechsler, Rolf
2016-01-01
We present Approximate BDD Minimization (ABM) as a problem that has application in approximate computing. Given a BDD representation of a multi-output Boolean function, ABM asks whether there exists another function that has a smaller BDD representation but meets a threshold w.r.t. an error metric. We present operators to derive approximated functions and present algorithms to exactly compute the error metrics directly on the BDD representation. An experimental evaluation demonstrates the app...
El-Megharbel, Samy M.; Hamza, Reham Z.; Refat, Moamen S.
2015-01-01
The main task of our present study is the preparation of newly complexes of Mg(II), Ca(II), Sr(II) and Ba(II) with diclofenac which succeeded to great extent in alleviating the side effects of diclofenac alone and ameliorating the kidney function parameters and antioxidant capacities with respect to diclofenac treated group alone. The Mg(II), Ca(II), Sr(II) and Ba(II) with diclofenac have been synthesized and characterized using infrared, electronic and 1H NMR spectral, thermogravimetric and conductivity measurements. The diclofenac ligand has been found to act as bidentate chelating agent. Diclofenac complexes coordinate through the oxygen's of the carboxyl group. The molar ratio chelation is 1:2 (M2+-dic) with general formula [M(dic)2(H2O)2]ṡnH2O. Antibacterial screening of the alkaline earth metal complexes against Escherichia coli (Gram - ve), Bacillus subtilis (Gram + ve) and anti-fungal (Asperagillus oryzae, Asperagillus niger, Asperagillus flavus) were investigated. The kidney functions in male albino rats were ameliorated upon treatment with metal complexes of dic, which are represented by decreasing the levels of urea and uric acid to be located within normal values. The other looks bright spot in this article is the assessment of antioxidant defense system including SOD, CAT and MDA with the help of Sr2+, Mg2+ and Ca2+-dic complexes. The hormones related to kidney functions and stresses have been greatly ameliorated in groups treated with dic complexes in comparable with dic treated group.
El-Megharbel, Samy M; Hamza, Reham Z; Refat, Moamen S
2015-01-25
The main task of our present study is the preparation of newly complexes of Mg(II), Ca(II), Sr(II) and Ba(II) with diclofenac which succeeded to great extent in alleviating the side effects of diclofenac alone and ameliorating the kidney function parameters and antioxidant capacities with respect to diclofenac treated group alone. The Mg(II), Ca(II), Sr(II) and Ba(II) with diclofenac have been synthesized and characterized using infrared, electronic and (1)H NMR spectral, thermogravimetric and conductivity measurements. The diclofenac ligand has been found to act as bidentate chelating agent. Diclofenac complexes coordinate through the oxygen's of the carboxyl group. The molar ratio chelation is 1:2 (M(2+)-dic) with general formula [M(dic)2(H2O)2]⋅nH2O. Antibacterial screening of the alkaline earth metal complexes against Escherichia coli (Gram-ve), Bacillus subtilis (Gram+ve) and anti-fungal (Asperagillus oryzae, Asperagillus niger, Asperagillus flavus) were investigated. The kidney functions in male albino rats were ameliorated upon treatment with metal complexes of dic, which are represented by decreasing the levels of urea and uric acid to be located within normal values. The other looks bright spot in this article is the assessment of antioxidant defense system including SOD, CAT and MDA with the help of Sr(2+), Mg(2+) and Ca(2+)-dic complexes. The hormones related to kidney functions and stresses have been greatly ameliorated in groups treated with dic complexes in comparable with dic treated group.
Continuum quantum systems as limits of discrete quantum systems: II. State functions
Energy Technology Data Exchange (ETDEWEB)
Barker, Laurence [Department of Mathematics, Bilkent University, Bilkent, Ankara (Turkey)]. E-mail: barker@fen.bilkent.edu.tr
2001-06-08
In this second of four papers on the eponymous topic, pointwise convergence of a 'discrete' state function to a 'continuum' state function is shown to imply the algebraic criterion for convergence that was introduced in the prequel. As examples (and as a prerequisite for the sequels), the normal approximation theorem and the convergence of the Kravchuk functions to the Hermite-Gaussians are expressed in terms of the algebraic notion of convergence. (author)
Hierarchical low-rank approximation for high dimensional approximation
Nouy, Anthony
2016-01-07
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.
Kashinski, D O; Chase, G M; Nelson, R G; Di Nallo, O E; Scales, A N; VanderLey, D L; Byrd, E F C
2017-03-23
We propose new approximate global multiplicative scaling factors for the DFT calculation of ground state harmonic vibrational frequencies using functionals from the TPSS, M06, and M11 functional families with standard correlation consistent cc-pVxZ and aug-cc-pVxZ (x = D, T, and Q), 6-311G split valence family, Sadlej and Sapporo polarized triple-ζ basis sets. Results for B3LYP, CAM-B3LYP, B3PW91, PBE, and PBE0 functionals with these basis sets are also reported. A total of 99 harmonic frequencies were calculated for 26 gas-phase organic and nonorganic molecules typically found in detonated solid propellant residue. Our proposed approximate multiplicative scaling factors are determined using a least-squares approach comparing the computed harmonic frequencies to experimental counterparts well established in the scientific literature. A comparison of our work to previously published global scaling factors is made to verify method reliability and the applicability of our molecular test set.
Shapiro, Elsa G; Rudser, Kyle; Ahmed, Alia; Steiner, Robert D; Delaney, Kathleen A; Yund, Brianna; King, Kelly; Kunin-Batson, Alicia; Eisengart, Julie; Whitley, Chester B
2016-06-01
The behavioral, adaptive and quality of life characteristics of attenuated mucopolysaccharidosis type II (MPS II) have not been well studied. Understanding changes over time in the attenuated phenotype may assist in helping achieve better outcomes in long-term function. This longitudinal study investigates these outcomes in relation to age, somatic disease burden, and IQ. Specifically, somatic disease burden is a major challenge for these patients, even with treatment with enzyme replacement therapy. 15 patients, 10 between ages 6 and MPS II patients have increasing somatic disease burden and poor physical quality of life as they develop as well as decreasing self-esteem and sense of adequacy. Psychosocial quality of life, adaptive skills, and attention improve. Recognition of and intervention around these issues will be beneficial to MPS II attenuated patients who have the resources to use such assistance to improve their long-term outcomes.
Functional recombinant MHC class II molecules and high-throughput peptide-binding assays
DEFF Research Database (Denmark)
Justesen, Sune; Harndahl, Mikkel; Lamberth, Kasper
2009-01-01
of peptide-binding assay were developed including a homogeneous, non-radioactive, high-throughput (HTS) binding assay. Binding isotherms were generated allowing the affinities of interaction to be determined. The affinities of the best binders were found to be in the low nanomolar range. Recombinant MHC...... in the generation of MHC-II molecules as reagents to study and manipulate specific T helper cell responses. Methods to generate functional MHC-II molecules recombinantly, and measure their interaction with peptides, would be highly desirable; however, no consensus methodology has yet emerged. RESULTS: We generated....... CONCLUSION: We have successfully developed versatile MHC-II resources, which may assist in the generation of MHC class II -wide reagents, data, and tools....
Energy Technology Data Exchange (ETDEWEB)
Palombi, F.; Wittig, H. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Papinutto, M. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Pena, C. [European Organization for Nuclear Research, Geneva (Switzerland)
2005-09-01
We discuss the renormalisation properties of parity-odd {delta}B = 2 operators with the heavy quark treated in the static approximation. Via twisted mass QCD, these operators provide the matrix elements relevant for the B{sup 0} - B{sup 0} mixing amplitude. The layout of a non-perturbative renormalisation programme for the operator basis, using Schroedinger Functional techniques, is described. Finally, we report our results for a one-loop perturbative study of various renormalisation schemes with Wilson-type lattice regularisations, which allows, in particular, to compute the NLO anomalous dimensions of the operators in the SF schemes of interest. (orig.)
Indian Academy of Sciences (India)
KAUSHIK MAJI
2016-08-01
We propose a variant of the multiconfiguration time-dependent Hartree (MCTDH) method within the framework of Hermite-distributed approximating functional (HDAF) method. The discretized Hamiltonian is a highly banded Toeplitz matrix which significantly reduces computational cost in terms of both storage and number of operations. The method proposed is employed to carry out the study of tunnelling dynamics of two coupled double well oscillators. We have calculated the orthogonality time \\tau , which is a measure of the time interval for an initial state to evolve into its orthogonal state. It is observed that the coupling has a significant effect on \\tau .
Reliable Function Approximation and Estimation
2016-08-16
geometric mean inequality for products of three matrices. A Israel, F Krahmer, and R Ward. Linear Algebra and its Applications 488, 2016. 1-12. (O3...standard compressed sensing theory is valid only for a restrictive set of dictionaries, limiting the scope of applications . In this award, the PI developed...low-order interactions. The weighted sparsity model allows for more freedom than linear regression but provides sufficient structure to extend
[Functional analysis of transforming growth factor-beta type II dominant negative receptor].
Takarada, M
1996-06-01
The transforming growth factor-beta (TGF-beta) is a multifunctional homodimeric protein with an apparent molecular weight of 25 KDa. TGF-beta transduces signals by forming heteromeric complexes of their type-I (T beta R-I) and type-II (T beta R-II) serin/threonine kinase receptors. TGF-beta binds first to T beta R-II receptor, and then the ligand in this complex is recognized by T beta R-I, resulting in formation of a heteromeric receptor complex composed of T beta R-I and T beta R-II. Once received, T beta R-I becomes phosphorylated in the GS domain by the associated constitutively active T beta R-II and transmits the downstream signal. It has been reported that formation of the heteromeric complex is indispensible at least in epithelial cells for growth inhibition and extracellular matrix production induced by TGF-beta. In this study, the functional role of T beta R-II for the TGF-beta-induced signals in osteoblastic cells was investigated by using a dominant negative type of T beta R-II mutant receptors (T beta RIIDNR). ROS 17/2.8 and MG 63 cells were found to express T beta R-I, T beta R-II, and T beta R-III, and their cell growth was inhibited by TGF-beta, whereas alkaline phosphatase activity was stimulated. Cells that were stably transfected with the T beta RIIDNR plasmid showed decreased response to TGF-beta during growth and alkaline phosphatase activity. These results indicate that the intracellular serine/threonine kinase domain of T beta R-II is essential for signal transduction of the TGF-beta-induced alkaline phosphatase activity as well as growth inhibition.
Drechsler, Wolfgang; Havas, Peter; Rosenblum, Arnold
1984-02-01
In the preceding paper, the laws of motion were established for classical particles with spin which are monopole-dipole singularities of Yang-Mills-Higgs fields. In this paper, a systematic approximation scheme is developed for solving the coupled nonlinear field equations in any order and for determining the corresponding equations of motion. In zeroth order the potentials are taken as the usual Liénard-Wiechert and Bhabha-Harish-Chandra potentials (generalized to isospace); in this order the solutions are necessarily Abelian, since the isovector describing the charge is constant. The regularization necessary to obtain expressions finite on the world lines of the particles is achieved by the method of Riesz potentials. All fields are taken as retarded and are expressed in integral form. Omitting dipole interactions, the integrals for the various terms are carried out as far as possible for general motions, including radiation-reaction terms. In first order, the charge isovectors are no longer necessarily constant; thus the solutions are not necessarily Abelian, and it is possible for charge to be radiated away. The cases of time-symmetric field theory and of an action-at-a-distance formulation of the theory are discussed in an appendix.
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
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
Institute of Scientific and Technical Information of China (English)
G.R. Boroun; B. Rezaie
2007-01-01
We present the calculations of FL longitudinal structure functions from DGLAP evolution equation in leading order (LO) at low-x, assuming the Regge-like behaviour of gluon distribution at this limit. The calculated results are compared with the HI data and QCD fit. It is shown that the obtained results are very close to the mentioned methods. The proposed simple analytical relation for FL provides a t-evolution equation for the determination of the longitudinal structure function at low-x. All the results can consistently be described within the framework of perturbative QCD, which essentially shows increases as x decreases.
MERCURY(II) ADSORPTION FROM WASTEWATERS USING A THIOL FUNCTIONAL ADSORBENT
The removal of mercury(II) from wastewaters (coal-fired utility plant scrubber solutions) using a thiol functional organoceramic composite (SOL-AD-IV) is investigated. A simulant is employed as a surrogate to demonstrate the removal of mercury from real waste solutions. Equilibri...
WISC-IV and WIAT-II Profiles in Children with High-Functioning Autism
Mayes, Susan Dickerson; Calhoun, Susan L.
2008-01-01
Children with high-functioning autism earned above normal scores on the Wechsler Intelligence Scale for Children-Fourth Edition (WISC-IV) Perceptual Reasoning and Verbal Comprehension Indexes and below normal scores on the Working Memory and Processing Speed Indexes and Wechsler Individual Achievement Test-Second Edition (WIAT-II) Written…
Functional defecation disorders in children: comparing the Rome II with the Rome III criteria.
Burgers, Rosa; Levin, Alon D; Di Lorenzo, Carlo; Dijkgraaf, Marcel G W; Benninga, Marc A
2012-10-01
To evaluate the prevalence of pediatric functional defecation disorders (FDD) using the Rome III criteria and to compare these data with those obtained using Rome II criteria. A chart review was performed in patients referred to a tertiary outpatient clinic with symptoms of constipation and/or fecal incontinence. All patients received a standardized bowel questionnaire and physical examination, including rectal examination. The prevalence of pediatric FDD according to both Rome criteria sets was assessed. Patients with FDD (n = 336; 61% boys, mean age 6.3 ± 3.5 SD) were studied: 39% had a defecation frequency ≤ 2/wk, 75% had fecal incontinence, 75% displayed retentive posturing, 60% had pain during defecation, 49% passed large diameter stools, and 49% had a palpable rectal fecal mass. According to the Rome III criteria, 87% had functional constipation (FC) compared with only 34% fulfilling criteria for either FC or functional fecal retention based on the Rome II definitions (P criteria for functional nonretentive fecal incontinence according to both the Rome II and Rome III criteria. The pediatric Rome III criteria for FC are less restrictive than the Rome II criteria. The Rome III criteria are an important step forward in the definition and recognition of FDD in children. Copyright © 2012 Mosby, Inc. All rights reserved.
Comba, Peter; Dovalil, Nina; Gahan, Lawrence R; Haberhauer, Gebhard; Hanson, Graeme R; Noble, Christopher J; Seibold, Björn; Vadivelu, Prabha
2012-02-27
Two synthetic derivatives of the naturally occurring cyclic pseudooctapeptides patellamide A-F and ascidiacyclamide, that is, H(4)pat(2), H(4)pat(3), as well as their Cu(II) complexes are described. These cyclic peptide derivatives differ from the naturally occurring macrocycles by the variation of the incorporated heterocyclic donor groups and the configuration of the amino acids connecting the heterocycles. The exchange of the oxazoline and thiazole groups by dimethylimidazoles or methyloxazoles leads to more rigid macrocycles, and the changes in the configuration of the side chains leads to significant differences in the folding of the cyclic peptides. These variations allow a detailed study of the various possible structural changes on the chemistry of the Cu(II) complexes formed. The coordination of Cu(II) with these macrocyclic species was monitored by high-resolution electrospray mass spectrometry (ESI-MS), spectrophotometric (UV/Vis) and circular dichroic (CD) titrations, and electron paramagnetic resonance (EPR) spectroscopy. Density functional theory (DFT) calculations and molecular mechanics (MM) simulations have been used to model the structures of the Cu(II) complexes and provide a detailed understanding of their geometric preferences and conformational flexibility. This is related to the Cu(II) coordination chemistry and the reactivity of the dinuclear Cu(II) complexes towards CO(2) fixation. The variation observed between the natural and various synthetic peptide systems enables conclusions about structure-reactivity correlations, and our results also provide information on why nature might have chosen oxazolines and thiazoles as incorporated heterocycles.
Overlapping and non-overlapping functions of condensins I and II in neural stem cell divisions.
Directory of Open Access Journals (Sweden)
Kenji Nishide
2014-12-01
Full Text Available During development of the cerebral cortex, neural stem cells (NSCs divide symmetrically to proliferate and asymmetrically to generate neurons. Although faithful segregation of mitotic chromosomes is critical for NSC divisions, its fundamental mechanism remains unclear. A class of evolutionarily conserved protein complexes, known as condensins, is thought to be central to chromosome assembly and segregation among eukaryotes. Here we report the first comprehensive genetic study of mammalian condensins, demonstrating that two different types of condensin complexes (condensins I and II are both essential for NSC divisions and survival in mice. Simultaneous depletion of both condensins leads to severe defects in chromosome assembly and segregation, which in turn cause DNA damage and trigger p53-induced apoptosis. Individual depletions of condensins I and II lead to slower loss of NSCs compared to simultaneous depletion, but they display distinct mitotic defects: chromosome missegregation was observed more prominently in NSCs depleted of condensin II, whereas mitotic delays were detectable only in condensin I-depleted NSCs. Remarkably, NSCs depleted of condensin II display hyperclustering of pericentric heterochromatin and nucleoli, indicating that condensin II, but not condensin I, plays a critical role in establishing interphase nuclear architecture. Intriguingly, these defects are taken over to postmitotic neurons. Our results demonstrate that condensins I and II have overlapping and non-overlapping functions in NSCs, and also provide evolutionary insight into intricate balancing acts of the two condensin complexes.
Baber, Kari F; Anderson, Julia; Puzanovova, Martina; Walker, Lynn S
2008-09-01
The updated Rome III criteria for pediatric functional gastrointestinal disorders (FGIDs) include new FGID categories and changes to the Rome II criteria for various FGIDs. To our knowledge, the implications of these revisions for patient classification have not been identified. The purpose of this study was to compare classification results using Rome II versus Rome III criteria for FGIDs associated with chronic abdominal pain. Participants were 368 pediatric patients whose subspecialty evaluations for chronic abdominal pain yielded no evidence of organic disease. The children's gastrointestinal symptoms were assessed with the parent-report version of the Questionnaire on Pediatric Gastrointestinal Symptoms (QPGS). More patients met the criteria for a pediatric pain-related FGID according to the Rome III criteria (86.6%) than the Rome II criteria (68.0%). In comparison with the results from the Rome II criteria, the Rome III criteria classified a greater percentage of children as meeting criteria for Abdominal Migraine (23.1% vs 5.7%) and Functional Abdominal Pain (11.4% vs 2.7%). Irritable Bowel Syndrome was the most common diagnosis according to both Rome II (44.0%) and Rome III (45.1%). Changes to the Rome criteria make the Rome III criteria more inclusive, allowing classification of 86.6% of pediatric patients with medically unexplained chronic abdominal pain.
Functionality of in vitro reconstituted group II intron RmInt1-derived ribonucleoprotein particles
Directory of Open Access Journals (Sweden)
María Dolores Molina-Sánchez
2016-09-01
Full Text Available The functional unit of mobile group II introns is a ribonucleoprotein particle (RNP consisting of the intron-encoded protein (IEP and the excised intron RNA. The IEP has reverse transcriptase activity but also promotes RNA splicing, and the RNA-protein complex triggers site-specific DNA insertion by reverse splicing, in a process called retrohoming. In vitro reconstituted ribonucleoprotein complexes from the Lactococcus lactis group II intron Ll.LtrB, which produce a double strand break, have recently been studied as a means of developing group II intron-based gene targeting methods for higher organisms. The Sinorhizobium meliloti group II intron RmInt1 is an efficient mobile retroelement, the dispersal of which appears to be linked to transient single-stranded DNA during replication. The RmInt1IEP lacks the endonuclease domain (En and cannot cut the bottom strand to generate the 3’ end to initiate reverse transcription. We used an Escherichia coli expression system to produce soluble and active RmInt1 IEP and reconstituted RNPs with purified components in vitro. The RNPs generated were functional and reverse-spliced into a single-stranded DNA target. This work constitutes the starting point for the use of group II introns lacking DNA endonuclease domain-derived RNPs for highly specific gene targeting methods.
Pulmonary function testing in HTLV-I and HTLV-II infected humans: a cohort study
Directory of Open Access Journals (Sweden)
Garratty George
2003-07-01
Full Text Available Abstract Background HTLV-I infection has been linked to lung pathology and HTLV-II has been associated with an increased incidence of pneumonia and acute bronchitis. However it is unknown whether HTLV-I or -II infection alters pulmonary function. Methods We performed pulmonary function testing on HTLV-I, HTLV-II and HTLV seronegative subjects from the HTLV outcomes study (HOST, including vital capacity (VC, forced expiratory volume in one second (FEV1, and diffusing lung capacity for carbon monoxide (DLCO corrected for hemoglobin and lung volume. Multivariable analysis adjusted for differences in age, gender, race/ethnicity, height and smoking history. Results Mean (standard deviation pulmonary function values among the 257 subjects were as follows: FVC = 3.74 (0.89 L, FEV1 = 2.93 (0.67 L, DLCOcorr = 23.82 (5.89 ml/min/mmHg, alveolar ventilation (VA = 5.25 (1.20 L and DLCOcorr/VA = 4.54 (0.87 ml/min/mmHg/L. There were no differences in FVC, FEV1 and DLCOcorr/VA by HTLV status. For DLCOcorr, HTLV-I and HTLV-II subjects had slightly lower values than seronegatives, but neither difference was statistically significant after adjustment for confounding. Conclusions There was no difference in measured pulmonary function and diffusing capacity in generally healthy HTLV-I and HTLV-II subjects compared to seronegatives. These results suggest that previously described HTLV-associated abnormalities in bronchoalveolar cells and fluid may not affect pulmonary function.
Bild, Walther; Hritcu, Lucian; Stefanescu, Cristinel; Ciobica, Alin
2013-06-03
While it is now well established that the independent brain renin-angiotensin system (RAS) has some important central functions besides the vascular ones, the relevance of its main bioactive peptide angiotensin II (Ang II) on the memory processes, as well as on oxidative stress status is not completely understood. The purpose of the present work was to evaluate the effects of central Ang II administration, as well as the effects of Ang II inhibition with either AT1 and AT 2 receptor specific blockers (losartan and PD-123177, respectively) or an angiotensin-converting enzyme (ACE) inhibitor (captopril). These effects were studied on the short-term memory (assessed through Y-maze) or long-term memory (as determined in passive avoidance) and on the oxidative stress status of the hippocampus. Our results demonstrate memory deficits induced by the administration of Ang II, as showed by the significant decrease of the spontaneous alternation in Y-maze (p=0.015) and latency-time in passive avoidance task (p=0.001) when compared to saline. On the other side, the administration of all the aforementioned Ang II blockers significantly improved the spontaneous alternation in Y-maze task, while losartan also increased the latency time as compared to saline in step-through passive avoidance (p=0.042). Also, increased oxidative stress status was induced in the hippocampus by the administration of Ang II, as demonstrated by increased levels of lipid peroxidation markers (malondialdehyde-MDA concentration) (p0.0001) vs. saline. Moreover, significant correlations were found between all of the memory related behavioral parameters and the main oxidative stress markers from the hippocampus, which is known for its implication in the processes of memory and also where RAS components are well expressed. This could be relevant for the complex interactions between Ang II, behavioral processes and neuronal oxidative stress, and could generate important therapeutic approaches. Copyright
[Association of the insulin-like growth factor II (IGF2) gene with human cognitive functions].
Alfimova, M V; Lezheĭko, T V; Gritsenko, I K; Golimbet, V E
2012-08-01
Active search for candidate genes whose polymorphisms are associated with human cognitive functions has been in progress in the past years. The study focused on the role that the insulin-like growth factor II (IGF2) gene may play in the variation of cognitive processes related to executive functions. The ApaI polymorphism of the IGF2 gene was tested for association with selective attention during visual search, working memory/mental control, and semantic verbal fluency in a group of 182 healthy individuals. The ApaI polymorphism was associated with the general cognitive index and selective attention measure. Carriers of genotype AA displayed higher values of the two parameters than carriers of genotype GG. It was assumed that the ApaI polymorphism of the IGF2 gene influences the human cognitive functions, acting possibly via modulation of the IGF-II level in the central nervous system.
The long-term functional outcome of type II odontoid fractures managed non-operatively.
LENUS (Irish Health Repository)
Butler, J S
2010-10-01
Odontoid fractures currently account for 9-15% of all adult cervical spine fractures, with type II fractures accounting for the majority of these injuries. Despite recent advances in internal fixation techniques, the management of type II fractures still remains controversial with advocates still supporting non-rigid immobilization as the definitive treatment of these injuries. At the NSIU, over an 11-year period between 1 July 1996 and 30 June 2006, 66 patients (n = 66) were treated by external immobilization for type II odontoid fractures. The medical records, radiographs and CT scans of all patients identified were reviewed. Clinical follow-up evaluation was performed using the Cervical Spine Outcomes Questionnaire (CSOQ). The objectives of this study were to evaluate the long-term functional outcome of patients suffering isolated type II odontoid fractures managed non-operatively and to correlate patient age and device type with clinical and functional outcome. Of the 66 patients, there were 42 males and 24 females (M:F = 1.75:1) managed non-operatively for type II odontoid fractures. The mean follow-up time was 66 months. Advancing age was highly correlated with poorer long-term functional outcomes when assessing neck pain (r = 0.19, P = 0.1219), shoulder and arm pain (r = 0.41, P = 0.0007), physical symptoms (r = 0.25, P = 0.472), functional disability (r = 0.24, P = 0.0476) and psychological distress (r = 0.41, P = 0.0007). Patients >65 years displayed a higher rate of pseudoarthrosis (21.43 vs. 1.92%) and established non-union (7.14 vs. 0%) than patients <65 years. The non-operative management of type II odontoid fractures is an effective and satisfactory method of treating type II odontoid fractures, particularly those of a stable nature. However, patients of advancing age have been demonstrated to have significantly poorer functional outcomes in the long term. This may be linked to higher rates of non-union.
Finite elements and approximation
Zienkiewicz, O C
2006-01-01
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o
Energy Technology Data Exchange (ETDEWEB)
Mizutani, U; Inukai, M; Sato, H; Zijlstra, E S; Lin, Q
2014-05-16
There are three key electronic parameters in elucidating the physics behind the Hume–Rothery electron concentration rule: the square of the Fermi diameter (2kF)2, the square of the critical reciprocal lattice vector and the electron concentration parameter or the number of itinerant electrons per atom e/a. We have reliably determined these three parameters for 10 Rhombic Triacontahedron-type 2/1–2/1–2/1 (N = 680) and 1/1–1/1–1/1 (N = 160–162) approximants by making full use of the full-potential linearized augmented plane wave-Fourier band calculations based on all-electron density-functional theory. We revealed that the 2/1–2/1–2/1 approximants Al13Mg27Zn45 and Na27Au27Ga31 belong to two different sub-groups classified in terms of equal to 126 and 109 and could explain why they take different e/a values of 2.13 and 1.76, respectively. Among eight 1/1–1/1–1/1 approximants Al3Mg4Zn3, Al9Mg8Ag3, Al21Li13Cu6, Ga21Li13Cu6, Na26Au24Ga30, Na26Au37Ge18, Na26Au37Sn18 and Na26Cd40Pb6, the first two, the second two and the last four compounds were classified into three sub-groups with = 50, 46 and 42; and were claimed to obey the e/a = 2.30, 2.10–2.15 and 1.70–1.80 rules, respectively.
Mizutani, U.; Inukai, M.; Sato, H.; Zijlstra, E. S.; Lin, Q.
2014-08-01
There are three key electronic parameters in elucidating the physics behind the Hume-Rothery electron concentration rule: the square of the Fermi diameter (2kF)2, the square of the critical reciprocal lattice vector ? and the electron concentration parameter or the number of itinerant electrons per atom e/a. We have reliably determined these three parameters for 10 Rhombic Triacontahedron-type 2/1-2/1-2/1 (N = 680) and 1/1-1/1-1/1 (N = 160-162) approximants by making full use of the full-potential linearized augmented plane wave-Fourier band calculations based on all-electron density-functional theory. We revealed that the 2/1-2/1-2/1 approximants Al13Mg27Zn45 and Na27Au27Ga31 belong to two different sub-groups classified in terms of ? equal to 126 and 109 and could explain why they take different e/a values of 2.13 and 1.76, respectively. Among eight 1/1-1/1-1/1 approximants Al3Mg4Zn3, Al9Mg8Ag3, Al21Li13Cu6, Ga21Li13Cu6, Na26Au24Ga30, Na26Au37Ge18, Na26Au37Sn18 and Na26Cd40Pb6, the first two, the second two and the last four compounds were classified into three sub-groups with ? = 50, 46 and 42; and were claimed to obey the e/a = 2.30, 2.10-2.15 and 1.70-1.80 rules, respectively.
Enrichment of Pb(II) ions using phthalic acid functionalized XAD-16 resin as a sorbent.
Memon, Saima Q; Hasany, S M; Bhanger, M I; Khuhawar, M Y
2005-11-01
A simple and reliable method has been developed using polymeric material containing phthalic acid as a chelating agent to concentrate ultratrace amounts of lead ions in aqueous solutions. After characterization by CHN, IR, and thermal studies, the static and dynamic sorption behavior of Pb(II) ions onto new synthetic resin has been investigated. The sorption has been optimized with respect to pH, shaking speed, and contact time between the two phases. Maximum sorption is achieved from solution of pH 5-8 after 10 min agitation time. The lowest concentration for quantitative recovery is 5.8 ng cm(-3) with a preconcentration factor of approximately 850. The kinetics of sorption follows the first-order rate equation with the rate constant k=0.58+/-0.04 min(-1). The variation of the equilibrium constant K(c) with temperature between 10 and 50 degrees C yields values of DeltaH, 52.4+/-1.65 kJmol(-1), DeltaS, 186+/-5.21 Jmol(-1)K(-1), and DeltaG(303K), -4.15+/-0.002 kJmol(-1). The sorption data of Pb(II) ions in the concentration range from 2.41x10(-6) to 1.44x10(-4) molL(-1) follows the Langmuir, Freundlich, and Dubinin-Radushkevich (D-R) isotherms at all temperatures investigated. The sorption of Pb(II) ions onto synthesized resin in the presence of common anions and cations has also been measured. The possible sorption mechanism of Pb(II) ions onto phthalic acid modified XAD-16 is also discussed. The sorption procedure is utilized to preconcentrate Pb(II) ions prior to their determination in automobile exhaust particulates by atomic absorption spectrometry using direct and standard addition methods.
Anirudhan, Thayyath Sreenivasan; Divya, Lekshmi; Rijith, Sreenivasan
2010-07-01
This study explored the feasibility of utilizing a novel adsorbent, poly(hydroxyethylmethacrylate)-grafted coconut coir pith with carboxyl functionality (PGCP-COOH) for the removal of cadmium(II) from water and wastewater. Maximum removal of 99.9% was observed for an initial concentration of 25 mg/L at pH 6.0 and adsorbent dose of 2.0 g/L. The first-order reversible kinetic model and Langmuir isotherm model were resulted in high correlation coefficients and described well the adsorption of Cd(II) onto PGCP-COOH. The complete removal of 22.4 mg/L Cd(II) from fertilizer industry wastewater was achieved by 2.0 g/L PGCP-COOH. The reusability of the PGCP-COOH for several cycles was demonstrated using 0.1 M HCl solution.
Therapeutic approach to Class II, Division 1 malocclusion with maxillary functional orthopedics
de Bittencourt, Aristeu Corrêa; Saga, Armando Yukio; Pacheco, Ariel Adriano Reyes; Tanaka, Orlando
2015-01-01
INTRODUCTION: Interceptive treatment of Class II, Division 1 malocclusion is a challenge orthodontists commonly face due to the different growth patterns they come across and the different treatment strategies they have available. OBJECTIVE: To report five cases of interceptive orthodontics performed with the aid of Klammt's elastic open activator (KEOA) to treat Class II, Division 1 malocclusion. METHODS: Treatment comprehends one or two phases; and the use of functional orthopedic appliances, whenever properly recommended, is able to minimize dentoskeletal discrepancies with consequent improvement in facial esthetics during the first stage of mixed dentition. The triad of diagnosis, correct appliance manufacture and patient's compliance is imperative to allow KEOA to contribute to Class II malocclusion treatment. RESULTS: Cases reported herein showed significant improvement in skeletal, dental and profile aspects, as evinced by cephalometric analysis and clinical photographs taken before, during and after interceptive orthodontics. PMID:26352852
Kraisler, Eli; Kelson, Itzhak
2010-01-01
The total energies and the spin states for atoms and their first ions with Z = 1-86 are calculated within the the local spin-density approximation (LSDA) and the generalized-gradient approximation (GGA) to the exchange-correlation (xc) energy in density-functional theory. Atoms and ions for which the ground-state density is not pure-state v-representable, are treated as ensemble v- representable with fractional occupations of the Kohn-Sham system. A newly developed algorithm which searches over ensemble v-representable densities [E. Kraisler et al., Phys. Rev. A 80, 032115 (2009)] is employed in calculations. It is found that for many atoms the ionization energies obtained with the GGA are only modestly improved with respect to experimental data, as compared to the LSDA. However, even in those groups of atoms where the improvement is systematic, there remains a non-negligible difference with respect to the experiment. The ab-initio electronic configuration in the Kohn-Sham reference system does not always equ...
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...
Fractal Trigonometric Polynomials for Restricted Range Approximation
Chand, A. K. B.; Navascués, M. A.; Viswanathan, P.; Katiyar, S. K.
2016-05-01
One-sided approximation tackles the problem of approximation of a prescribed function by simple traditional functions such as polynomials or trigonometric functions that lie completely above or below it. In this paper, we use the concept of fractal interpolation function (FIF), precisely of fractal trigonometric polynomials, to construct one-sided uniform approximants for some classes of continuous functions.
Pérez, Alejandro; Tuckerman, Mark E.; Müser, Martin H.
2009-05-01
The problems of ergodicity and internal consistency in the centroid and ring-polymer molecular dynamics methods are addressed in the context of a comparative study of the two methods. Enhanced sampling in ring-polymer molecular dynamics (RPMD) is achieved by first performing an equilibrium path integral calculation and then launching RPMD trajectories from selected, stochastically independent equilibrium configurations. It is shown that this approach converges more rapidly than periodic resampling of velocities from a single long RPMD run. Dynamical quantities obtained from RPMD and centroid molecular dynamics (CMD) are compared to exact results for a variety of model systems. Fully converged results for correlations functions are presented for several one dimensional systems and para-hydrogen near its triple point using an improved sampling technique. Our results indicate that CMD shows very similar performance to RPMD. The quality of each method is further assessed via a new χ2 descriptor constructed by transforming approximate real-time correlation functions from CMD and RPMD trajectories to imaginary time and comparing these to numerically exact imaginary time correlation functions. For para-hydrogen near its triple point, it is found that adiabatic CMD and RPMD both have similar χ2 error.
Energy Technology Data Exchange (ETDEWEB)
Korytar, Richard; Lorente, Nicolas, E-mail: rkorytar@cin2.es [Centro de investigacion en nanociencia y nanotecnologIa (CSIC-ICN), Campus de la UAB, E-08193 Bellaterra (Spain)
2011-09-07
We have developed a multi-orbital approach to compute the electronic structure of a quantum impurity using the non-crossing approximation. The calculation starts with a mean-field evaluation of the system's electronic structure using a standard quantum chemistry code; here we use density functional theory (DFT). We transformed the one-electron structure into an impurity Hamiltonian by using maximally localized Wannier functions. Hence, we have developed a method to study the Kondo effect in systems based on an initial one-electron calculation. We have applied our methodology to a copper phthalocyanine molecule chemisorbed on Ag(100), and we have described its spectral function for three different cases where the molecule presents a single spin or two spins with ferro- and anti-ferromagnetic exchange couplings. We find that the use of broken-symmetry mean-field theories such as Kohn-Sham DFT cannot deal with the complexity of the spin of open-shell molecules on metal surfaces and extra modeling is needed. (paper)
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.
P-cadherin counteracts myosin II-B function: implications in melanoma progression
Directory of Open Access Journals (Sweden)
De Wever Olivier
2010-09-01
Full Text Available Abstract Background Malignant transformation of melanocytes is frequently attended by a switch in cadherin expression profile as shown for E- and N-cadherin. For P-cadherin, downregulation in metastasizing melanoma has been demonstrated, and over-expression of P-cadherin in melanoma cell lines has been shown to inhibit invasion. The strong invasive and metastatic nature of cutaneous melanoma implies a deregulated interplay between intercellular adhesion and migration-related molecules Results In this study we performed a microarray analysis to compare the mRNA expression profile of an invasive BLM melanoma cell line (BLM LIE and the non-invasive P-cadherin over-expression variant (BLM P-cad. Results indicate that nonmuscle myosin II-B is downregulated in BLM P-cad. Moreover, myosin II-B plays a major role in melanoma migration and invasiveness by retracting the tail during the migratory cycle, as shown by the localization of myosin II-B stress fibers relative to Golgi and the higher levels of phosphorylated myosin light chain. Analysis of P-cadherin and myosin II-B in nodular melanoma sections and in a panel of melanoma cell lines further confirmed that there is an inverse relationship between both molecules. Conclusions Therefore, we conclude that P-cadherin counteracts the expression and function of myosin II-B, resulting in the suppression of the invasive and migratory behaviour of BLM melanoma cells
Energy Technology Data Exchange (ETDEWEB)
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.
Buschow, S.I.; Balkom, B.W.M. van; Aalberts, M.; Heck, A.J.R. van; Wauben, M.; Stoorvogel, W.
2010-01-01
Professional antigen-presenting cells secrete major histocompatibility complex class II (MHC II) carrying exosomes with unclear physiological function(s). Exosomes are first generated as the intraluminal vesicles (ILVs) of a specific type of multivesicular body, and are then secreted by fusion of th
Adsorption of Co(II) by a carboxylate-functionalized polyacrylamide grafted lignocellulosics.
Shibi, I G; Anirudhan, T S
2005-02-01
A new adsorbent (PGBS-COOH) having carboxylate functional group at the chain end was synthesized by graft copolymerization of acrylamide onto banana stalk, BS (Musa Paradisiaca) using ferrous ammonium sulphate/H2O2 redox initiator system. The efficiency of the adsorbent in the removal of cobalt [Co(II)] from water was investigated using batch adsorption technique. The adsorbent exhibits very high adsorption potential for Co(II) and under optimum conditions more than 99% removal was achieved. The maximum adsorption capacity was observed at the pH range 6.5-9.0. The equilibrium isotherm data were analysed using three isotherm models, Langmuir, Freundlich and Scatchard, to determine the best fit equation for the sorption of Co(II) on the PGBS-COOH. A comparative study with a commercial cation exchanger, Ceralite IRC-50, having carboxylate functional group showed that PGBS-COOH is 2.8 times more effective compared to Ceralite IRC-50 at 30 degrees C. Synthetic nuclear power plant coolant water samples were also treated by the adsorbent to demonstrate its efficiency in removing Co(II) from water in the presence of other metal ions. Acid regeneration was tried for several cycles to recover the adsorbed metal ions and also to restore the sorbent to its original state.
Roper, Ian P E; Besley, Nicholas A
2016-03-21
The simulation of X-ray emission spectra of transition metal complexes with time-dependent density functional theory (TDDFT) is investigated. X-ray emission spectra can be computed within TDDFT in conjunction with the Tamm-Dancoff approximation by using a reference determinant with a vacancy in the relevant core orbital, and these calculations can be performed using the frozen orbital approximation or with the relaxation of the orbitals of the intermediate core-ionised state included. Both standard exchange-correlation functionals and functionals specifically designed for X-ray emission spectroscopy are studied, and it is shown that the computed spectral band profiles are sensitive to the exchange-correlation functional used. The computed intensities of the spectral bands can be rationalised by considering the metal p orbital character of the valence molecular orbitals. To compute X-ray emission spectra with the correct energy scale allowing a direct comparison with experiment requires the relaxation of the core-ionised state to be included and the use of specifically designed functionals with increased amounts of Hartree-Fock exchange in conjunction with high quality basis sets. A range-corrected functional with increased Hartree-Fock exchange in the short range provides transition energies close to experiment and spectral band profiles that have a similar accuracy to those from standard functionals.
Tree wavelet approximations with applications
Institute of Scientific and Technical Information of China (English)
XU Yuesheng; ZOU Qingsong
2005-01-01
We construct a tree wavelet approximation by using a constructive greedy scheme(CGS). We define a function class which contains the functions whose piecewise polynomial approximations generated by the CGS have a prescribed global convergence rate and establish embedding properties of this class. We provide sufficient conditions on a tree index set and on bi-orthogonal wavelet bases which ensure optimal order of convergence for the wavelet approximations encoded on the tree index set using the bi-orthogonal wavelet bases. We then show that if we use the tree index set associated with the partition generated by the CGS to encode a wavelet approximation, it gives optimal order of convergence.
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.
Approximate Bayesian computation.
Directory of Open Access Journals (Sweden)
Mikael Sunnåker
Full Text Available Approximate Bayesian computation (ABC constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology.
Structure and function of Cu(I)- and Zn(II)-ATPases
DEFF Research Database (Denmark)
Sitsel, Oleg; Grønberg, Christina; Autzen, Henriette
2015-01-01
membranes at the expense of ATP. Recent biochemical studies and crystal structures have significantly improved our understanding of the transport mechanisms of these proteins, but many details about their structure and function remain elusive. Here we compare the Cu(I)- and Zn(II)-ATPases, scrutinizing......Copper and zinc are micronutrients essential for the function of many enzymes while also being toxic at elevated concentrations. Cu(I)- and Zn(II)-transporting P-type ATPases of subclass 1B are of key importance for the homeostasis of these transition metals, allowing ion transport across cellular...... the molecular differences that allow transport of these two distinct metal types, and discuss possible future directions of research in the field....
Correction of Skeletal Class II Malocclusion using Functional-Fixed Appliance Therapy
Directory of Open Access Journals (Sweden)
Ashok Surana
2012-01-01
Full Text Available Single-phase treatment started during late mixed dentition using functional followed by fixed appliance therapy has proven to be the most effective approach to achieve correction of Class II malocclusion. This case report demonstrates the use of this treatment approach in an 11-year-old girl with skeletal and dental Class II malocclusion, large overjet, deep overbite, increased incisor exposure and a gummy smile. She was given a functional appliance for 1 year which was immediately followed by fixed mechanotherapy for final finishing and detailing of the occlusion. The magnitude of skeletal and dental correction achieved, along with the dramatic improvement in facial appearance of the patient, provides a strong case for establishing the efficacy of this treatment modality.
De Mello, Walmor C; Gerena, Yamil
2017-01-01
The molecular mechanisms related to the effect of angiotensin II, its level on cardiac tissues, as well as its overexpression represent an important aspect of cardiovascular pharmacology and pathology. Severe alterations of cardiac functions are induced by hypertension including activation of circulating and local cardiac renin angiotensin systems. In this chapter, we are providing the methods and materials necessary for further investigation of this important topic.
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...
Yuan, Shifei; Jiang, Lei; Yin, Chengliang; Wu, Hongjie; Zhang, Xi
2017-06-01
To guarantee the safety, high efficiency and long lifetime for lithium-ion battery, an advanced battery management system requires a physics-meaningful yet computationally efficient battery model. The pseudo-two dimensional (P2D) electrochemical model can provide physical information about the lithium concentration and potential distributions across the cell dimension. However, the extensive computation burden caused by the temporal and spatial discretization limits its real-time application. In this research, we propose a new simplified electrochemical model (SEM) by modifying the boundary conditions for electrolyte diffusion equations, which significantly facilitates the analytical solving process. Then to obtain a reduced order transfer function, the Padé approximation method is adopted to simplify the derived transcendental impedance solution. The proposed model with the reduced order transfer function can be briefly computable and preserve physical meanings through the presence of parameters such as the solid/electrolyte diffusion coefficients (Ds&De) and particle radius. The simulation illustrates that the proposed simplified model maintains high accuracy for electrolyte phase concentration (Ce) predictions, saying 0.8% and 0.24% modeling error respectively, when compared to the rigorous model under 1C-rate pulse charge/discharge and urban dynamometer driving schedule (UDDS) profiles. Meanwhile, this simplified model yields significantly reduced computational burden, which benefits its real-time application.
Quasi-chemical approximation for polyatomic mixtures
Dávila, M V; Matoz-Fernandez, D A; Ramirez-Pastor, A J
2016-01-01
The statistical thermodynamics of binary mixtures of polyatomic species was developed on a generalization in the spirit of the lattice-gas model and the quasi-chemical approximation (QCA). The new theoretical framework is obtained by combining: (i) the exact analytical expression for the partition function of non-interacting mixtures of linear $k$-mers and $l$-mers (species occupying $k$ sites and $l$ sites, respectively) adsorbed in one dimension, and its extension to higher dimensions; and (ii) a generalization of the classical QCA for multicomponent adsorbates and multisite-occupancy adsorption. The process is analyzed through the partial adsorption isotherms corresponding to both species of the mixture. Comparisons with analytical data from Bragg-Williams approximation (BWA) and Monte Carlo simulations are performed in order to test the validity of the theoretical model. Even though a good fitting is obtained from BWA, it is found that QCA provides a more accurate description of the phenomenon of adsorpti...
Casida, Mark E.; Salahub, Dennis R.
2000-11-01
The time-dependent density functional theory (TD-DFT) calculation of excitation spectra places certain demands on the DFT exchange-correlation potential, vxc, that are not met by the functionals normally used in molecular calculations. In particular, for high-lying excitations, it is crucial that the asymptotic behavior of vxc be correct. In a previous paper, we introduced a novel asymptotic-correction approach which we used with the local density approximation (LDA) to yield an asymptotically corrected LDA (AC-LDA) potential [Casida, Casida, and Salahub, Int. J. Quantum Chem. 70, 933 (1998)]. The present paper details the theory underlying this asymptotic correction approach, which involves a constant shift to incorporate the effect of the derivative discontinuity (DD) in the bulk region of finite systems, and a spliced asymptotic correction in the large r region. This is done without introducing any adjustable parameters. We emphasize that correcting the asymptotic behavior of vxc is not by itself sufficient to improve the overall form of the potential unless the effect of the derivative discontinuity is taken into account. The approach could be used to correct vxc from any of the commonly used gradient-corrected functionals. It is here applied to the LDA, using the asymptotically correct potential of van Leeuwen and Baerends (LB94) in the large r region. The performance of our AC-LDA vxc is assessed for the calculation of TD-DFT excitation energies for a large number of excitations, including both valence and Rydberg states, for each of four small molecules: N2, CO, CH2O, and C2H4. The results show a significant improvement over those from either the LB94 or the LDA functionals. This confirms that the DD is indeed an important element in the design of functionals. The quality of TDLDA/LB94 and TDLDA/AC-LDA oscillator strengths were also assessed in what we believe to be the first rigorous assessment of TD-DFT molecular oscillator strengths in comparison with
Szmulowicz, F.; Haugan, H.; Brown, G. J.
2004-04-01
We develop a modified 8×8 envelope-function approximation (EFA) formalism for the noncommon-atom (NCA) superlattices (SL’s), incorporating the effect of anisotropic and other interface (IF) interactions that go beyond the standard EFA. The boundary conditions in the presence of IF interactions are used to set up a secular equation (including a transfer matrix derivation) whose physical transparency makes possible a number of valuable insights (possibility of IF bound states, analytic solutions, indirect gaps, etc.). We show that the heavy-hole spin-orbit IF coupling is very important due to the IF localization of the SO wave function components and the ability of the IF potential to potentially bind a hole at the IF’s, all of which pose convergence problems for perturbative solutions. With two adjustable parameter for the two possible IF’s, we find a very good agreement between experiment and theory for the band gaps of several sets of very long-infrared and midinfrared InAs/GaSb SL’s grown at several laboratories and by us. The band gaps as a function of GaSb and InAs widths are explained in terms of variations of the HH and conduction (C) band bandwidths. We show that the cut-off wavelengths can be reduced by increasing the GaSb layer width. Thus, a consistent application of the EFA method with the inclusion of well established IF effects can provide useful physical insights and possesses good predictive capacity in the design of NCA SL’s.
Ma, Fang; Qu, Rongjun; Sun, Changmei; Wang, Chunhua; Ji, Chunnuan; Zhang, Ying; Yin, Ping
2009-12-30
The adsorption behaviors of Hg(II) on adsorbents, chitosan functionalized by generation 1.0-3.0 of amino-terminated hyperbranched polyamidoamine polymers (denoted as CTS-1.0, CTS-2.0 and CTS-3.0, respectively), were studied. The optimum pH corresponding to the maximum adsorption capacities was found to be 5.0 for the three adsorbents. The experimental equilibrium data of Hg(II) on the three adsorbents were fitted to the Freundlich and the Langmuir models, and it is found that the Langmuir isotherm was the best fitting model to describe the equilibrium adsorption. The kinetics data indicated that the adsorption process of Hg(II) ions on CTS-1.0, CTS-2.0 and CTS-3.0 were governed by the film diffusion and followed pseudo-second-order rate model. Thermodynamic analysis and FTIR analysis revealed that the adsorption behaviors of Hg(II) ions on the three adsorbents could be considered as spontaneous, endothermic and chemical sorption process, resulting in their higher adsorption capacities at higher temperature.
Study on the adsorption of Cu(II) by folic acid functionalized magnetic graphene oxide
Wang, Cuicui; Ge, Heyi; Zhao, Yueying; Liu, Shanshan; Zou, Yu; Zhang, Wenbo
2017-02-01
The folic acid functionalized magnetic graphene oxide (FA-mGO) as a new adsorbent has been synthesized in this work for the elimination of Cu(II) from waste water. The as-prepared FA-mGO was tested by SEM, TEM, particle size analyzer, FTIR, XRD, Roman spectrum, TGA and magnetic properties analyzer. Some factors, such as adsorbent dose, pH, contact time, initial concentration of adsorbate and temperature were explored. The results showed that the FA-mGO had the better adsorption performance than mGO. After 40 min, the adsorption equilibrium could be reached. Furthermore, the adsorption property obeyed the pseudo-second order kinetic model and the Temkin isotherms well. The maximum adsorption capacity was 283.29 mg/g for Cu(II) from Pseudo-second-order model at pH=5 and 318 K. The chelation action between FA and Cu(II) along with electrostatic incorporation between GO and Cu(II) determined the favourable adsorption property. Besides, thermodynamic studies results ∆G00, ∆S0>0 suggested that the adsorption mechanism was an endothermic and spontaneous process essentially. Finally, desorption and reusability studies imply FA-mGO has an excellent reproducibility and is benefit to environmental protection and resource conservation.