International Nuclear Information System (INIS)
Pollock, M.D.
1988-01-01
In quantum cosmology, a wave function Ψ for a given theory can be obtained by solving the Wheeler-DeWitt equation, using the semi-classical approximation to the path integral over euclidean metrics to impose the boundary condition, as described by Hawking and his collaborators. If the universe is expanding as a quasi-de Sitter space-time, then it is possible to derive a Fokker-Planck equation for the probability distribution P, as shown by Starobinsky. Arguing by analogy with quantum mechanics in flat space-time, one would expect that P ∝ ΨΨ * . We examine this assertion by reference to the scale-invariant theory L = -1/24 βR 2 , whose wave function has been calculated in mini-superspace by Horowitz, and whose classical solutions are de Sitter space-times. It appears that deviations from the relation P ∝ ΨΨ * are attributable to long-wavelength fluctuations δΦ e ≅ H/2π in the effective inflaton field Φ c =√(βR)=√(12β) H. Their existence is taken into account in the derivation of the Fokker-Planck equation, but not in the derivation of Ψ when this is restricted to mini-superspace. In the limit β → ∞, we find that δΦ e /Φ c → 0 and that P ∝ ΨΨ * . The scale-invariant theory L = (1/2εφ 2 R-1/4λΦ 4 ) can be similarly analyzed. Inclusion of a kinetic term 1/2Φ; k Φ ;k destroys this similarity, which is restored however upon addition of a term (-1/24βR 2 ). (orig.)
Approximate Networking for Universal Internet Access
Directory of Open Access Journals (Sweden)
Junaid Qadir
2017-12-01
Full Text Available Despite the best efforts of networking researchers and practitioners, an ideal Internet experience is inaccessible to an overwhelming majority of people the world over, mainly due to the lack of cost-efficient ways of provisioning high-performance, global Internet. In this paper, we argue that instead of an exclusive focus on a utopian goal of universally accessible “ideal networking” (in which we have a high throughput and quality of service as well as low latency and congestion, we should consider providing “approximate networking” through the adoption of context-appropriate trade-offs. In this regard, we propose to leverage the advances in the emerging trend of “approximate computing” that rely on relaxing the bounds of precise/exact computing to provide new opportunities for improving the area, power, and performance efficiency of systems by orders of magnitude by embracing output errors in resilient applications. Furthermore, we propose to extend the dimensions of approximate computing towards various knobs available at network layers. Approximate networking can be used to provision “Global Access to the Internet for All” (GAIA in a pragmatically tiered fashion, in which different users around the world are provided a different context-appropriate (but still contextually functional Internet experience.
Function approximation of tasks by neural networks
International Nuclear Information System (INIS)
Gougam, L.A.; Chikhi, A.; Mekideche-Chafa, F.
2008-01-01
For several years now, neural network models have enjoyed wide popularity, being applied to problems of regression, classification and time series analysis. Neural networks have been recently seen as attractive tools for developing efficient solutions for many real world problems in function approximation. The latter is a very important task in environments where computation has to be based on extracting information from data samples in real world processes. In a previous contribution, we have used a well known simplified architecture to show that it provides a reasonably efficient, practical and robust, multi-frequency analysis. We have investigated the universal approximation theory of neural networks whose transfer functions are: sigmoid (because of biological relevance), Gaussian and two specified families of wavelets. The latter have been found to be more appropriate to use. The aim of the present contribution is therefore to use a m exican hat wavelet a s transfer function to approximate different tasks relevant and inherent to various applications in physics. The results complement and provide new insights into previously published results on this problem
Measure Fields for Function Approximation
1993-06-01
intelligence research is provided by ONR contract N00014-91-J-4038 J.L. Marroquin was supported in part by a grant from the Consejo Nacional de Ciencia y ... Tecnologia , Mexico. _ 93-28011 9-3 -- -" nnuM IInu 4 0 0 0 1 Introduction imating functions are always discontinuous, and the dis- continuities are...capacity and generalization capabili- is present panel (a) of figure 1 shows a function z(z, y ) ties. that is equal to a tilted plane inside an L
Nonlinear Ritz approximation for Fredholm functionals
Directory of Open Access Journals (Sweden)
Mudhir A. Abdul Hussain
2015-11-01
Full Text Available In this article we use the modify Lyapunov-Schmidt reduction to find nonlinear Ritz approximation for a Fredholm functional. This functional corresponds to a nonlinear Fredholm operator defined by a nonlinear fourth-order differential equation.
Polynomial approximation of functions in Sobolev spaces
International Nuclear Information System (INIS)
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 polynomical 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
Semiclassical initial value approximation for Green's function.
Kay, Kenneth G
2010-06-28
A semiclassical initial value approximation is obtained for the energy-dependent Green's function. For a system with f degrees of freedom the Green's function expression has the form of a (2f-1)-dimensional integral over points on the energy surface and an integral over time along classical trajectories initiated from these points. This approximation is derived by requiring an integral ansatz for Green's function to reduce to Gutzwiller's semiclassical formula when the integrations are performed by the stationary phase method. A simpler approximation is also derived involving only an (f-1)-dimensional integral over momentum variables on a Poincare surface and an integral over time. The relationship between the present expressions and an earlier initial value approximation for energy eigenfunctions is explored. Numerical tests for two-dimensional systems indicate that good accuracy can be obtained from the initial value Green's function for calculations of autocorrelation spectra and time-independent wave functions. The relative advantages of initial value approximations for the energy-dependent Green's function and the time-dependent propagator are discussed.
RATIONAL APPROXIMATIONS TO GENERALIZED HYPERGEOMETRIC FUNCTIONS.
Under weak restrictions on the various free parameters, general theorems for rational representations of the generalized hypergeometric functions...and certain Meijer G-functions are developed. Upon specialization, these theorems yield a sequency of rational approximations which converge to the
Smooth function approximation using neural networks.
Ferrari, Silvia; Stengel, Robert F
2005-01-01
An algebraic approach for representing multidimensional nonlinear functions by feedforward neural networks is presented. In this paper, the approach is implemented for the approximation of smooth batch data containing the function's input, output, and possibly, gradient information. The training set is associated to the network adjustable parameters by nonlinear weight equations. The cascade structure of these equations reveals that they can be treated as sets of linear systems. Hence, the training process and the network approximation properties can be investigated via linear algebra. Four algorithms are developed to achieve exact or approximate matching of input-output and/or gradient-based training sets. Their application to the design of forward and feedback neurocontrollers shows that algebraic training is characterized by faster execution speeds and better generalization properties than contemporary optimization techniques.
Multidimensional stochastic approximation using locally contractive functions
Lawton, W. M.
1975-01-01
A Robbins-Monro type multidimensional stochastic approximation algorithm which converges in mean square and with probability one to the fixed point of a locally contractive regression function is developed. The algorithm is applied to obtain maximum likelihood estimates of the parameters for a mixture of multivariate normal distributions.
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.
When Density Functional Approximations Meet Iron Oxides.
Meng, Yu; Liu, Xing-Wu; Huo, Chun-Fang; Guo, Wen-Ping; Cao, Dong-Bo; Peng, Qing; Dearden, Albert; Gonze, Xavier; Yang, Yong; Wang, Jianguo; Jiao, Haijun; Li, Yongwang; Wen, Xiao-Dong
2016-10-11
Three density functional approximations (DFAs), PBE, PBE+U, and Heyd-Scuseria-Ernzerhof screened hybrid functional (HSE), were employed to investigate the geometric, electronic, magnetic, and thermodynamic properties of four iron oxides, namely, α-FeOOH, α-Fe 2 O 3 , Fe 3 O 4 , and FeO. Comparing our calculated results with available experimental data, we found that HSE (a = 0.15) (containing 15% "screened" Hartree-Fock exchange) can provide reliable values of lattice constants, Fe magnetic moments, band gaps, and formation energies of all four iron oxides, while standard HSE (a = 0.25) seriously overestimates the band gaps and formation energies. For PBE+U, a suitable U value can give quite good results for the electronic properties of each iron oxide, but it is challenging to accurately get other properties of the four iron oxides using the same U value. Subsequently, we calculated the Gibbs free energies of transformation reactions among iron oxides using the HSE (a = 0.15) functional and plotted the equilibrium phase diagrams of the iron oxide system under various conditions, which provide reliable theoretical insight into the phase transformations of iron oxides.
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.
Function approximation with polynomial regression slines
International Nuclear Information System (INIS)
Urbanski, P.
1996-01-01
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)
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.
Forecasting with Universal Approximators and a Learning Algorithm
DEFF Research Database (Denmark)
Kock, Anders Bredahl
2011-01-01
to the performance of the best single model in the set of models combined from. The use of universal approximators along with a combination scheme for which explicit loss bounds exist should give a solid theoretical foundation to the way the forecasts are performed. The practical performance will be investigated...... combination has a long history in econometrics focus has not been on proving loss bounds for the combination rules applied. We apply the Weighted Average Algorithm (WAA) of Kivinen & Warmuth (1999) for which such loss bounds exist. Specifically, one can bound the worst case performance of the WAA compared...
Forecasting with Universal Approximators and a Learning Algorithm
DEFF Research Database (Denmark)
Kock, Anders Bredahl
bounds for the combination rules applied. We apply the Weighted Average Algorithm (WAA) of Kivinen and Warmuth (1999) for which such loss bounds exist. Specifically, one can bound the worst case performance of the WAA compared to the performance of the best single model in the set of models combined from....... The use of universal approximators along with a combination scheme for which explicit loss bounds exist should give a solid theoretical foundation to the way the forecasts are performed. The practical performance will be investigated by considering various monthly postwar macroeconomic data sets for the G...
Fuzzy Universal Model Approximator for Distributed Solar Collector Field Control
Elmetennani, Shahrazed
2014-07-01
This paper deals with the control of concentrating parabolic solar collectors by forcing the outlet oil temperature to track a set reference. A fuzzy universal approximate model is introduced in order to accurately reproduce the behavior of the system dynamics. The proposed model is a low order state space representation derived from the partial differential equation describing the oil temperature evolution using fuzzy transform theory. The resulting set of ordinary differential equations simplifies the system analysis and the control law design and is suitable for real time control implementation. Simulation results show good performance of the proposed model.
Universal approximation in p-mean by neural networks
Burton, R.M; Dehling, H.G
A feedforward neural net with d input neurons and with a single hidden layer of n neurons is given by [GRAPHICS] where a(j), theta(j), w(ji) is an element of R. In this paper we study the approximation of arbitrary functions f: R-d --> R by a neural net in an L-p(mu) norm for some finite measure mu
Discontinuous approximate molecular electronic wave-functions
International Nuclear Information System (INIS)
Stuebing, E.W.; Weare, J.H.; Parr, R.G.
1977-01-01
Following Kohn, Schlosser and Marcus and Weare and Parr an energy functional is defined for a molecular problem which is stationary in the neighborhood of the exact solution and permits the use of trial functions that are discontinuous. The functional differs from the functional of the standard Rayleigh--Ritz method in the replacement of the usual kinetic energy operators circumflex T(μ) with operators circumflex T'(μ) = circumflex T(μ) + circumflex I(μ) generates contributions from surfaces of nonsmooth behavior. If one uses the nabla PSI . nabla PSI way of writing the usual kinetic energy contributions, one must add surface integrals of the product of the average of nabla PSI and the change of PSI across surfaces of discontinuity. Various calculations are carried out for the hydrogen molecule-ion and the hydrogen molecule. It is shown that ab initio calculations on molecules can be carried out quite generally with a basis of atomic orbitals exactly obeying the zero-differential overlap (ZDO) condition, and a firm basis is thereby provided for theories of molecular electronic structure invoking the ZDO aoproximation. It is demonstrated that a valence bond theory employing orbitals exactly obeying ZDO can provide an adequate account of chemical bonding, and several suggestions are made regarding molecular orbital methods
An inductive algorithm for smooth approximation of functions
International Nuclear Information System (INIS)
Kupenova, T.N.
2011-01-01
An inductive algorithm is presented for smooth approximation of functions, based on the Tikhonov regularization method and applied to a specific kind of the Tikhonov parametric functional. The discrepancy principle is used for estimation of the regularization parameter. The principle of heuristic self-organization is applied for assessment of some parameters of the approximating function
Comparison of four support-vector based function approximators
de Kruif, B.J.; de Vries, Theodorus J.A.
2004-01-01
One of the uses of the support vector machine (SVM), as introduced in V.N. Vapnik (2000), is as a function approximator. The SVM and approximators based on it, approximate a relation in data by applying interpolation between so-called support vectors, being a limited number of samples that have been
Quasi-fractional approximation to the Bessel functions
International Nuclear Information System (INIS)
Guerrero, P.M.L.
1989-01-01
In this paper the authors presents a simple Quasi-Fractional Approximation for Bessel Functions J ν (x), (- 1 ≤ ν < 0.5). This has been obtained by extending a method published which uses simultaneously power series and asymptotic expansions. Both functions, exact and approximated, coincide in at least two digits for positive x, and ν between - 1 and 0,4
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…
On root mean square approximation by exponential functions
Sharipov, Ruslan
2014-01-01
The problem of root mean square approximation of a square integrable function by finite linear combinations of exponential functions is considered. It is subdivided into linear and nonlinear parts. The linear approximation problem is solved. Then the nonlinear problem is studied in some particular example.
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.
Legendre-tau approximations for functional differential equations
Ito, K.; Teglas, R.
1986-01-01
The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.
Precise analytic approximations for the Bessel function J1 (x)
Maass, Fernando; Martin, Pablo
2018-03-01
Precise and straightforward analytic approximations for the Bessel function J1 (x) have been found. Power series and asymptotic expansions have been used to determine the parameters of the approximation, which is as a bridge between both expansions, and it is a combination of rational and trigonometric functions multiplied with fractional powers of x. Here, several improvements with respect to the so called Multipoint Quasirational Approximation technique have been performed. Two procedures have been used to determine the parameters of the approximations. The maximum absolute errors are in both cases smaller than 0.01. The zeros of the approximation are also very precise with less than 0.04 per cent for the first one. A second approximation has been also determined using two more parameters, and in this way the accuracy has been increased to less than 0.001.
Teaching Function at University
Directory of Open Access Journals (Sweden)
Alma Elena Figueroa Rubalcava
2008-08-01
Full Text Available A peremptory change in education and the higher education at universities is occurriyng. Since 60´s to date theoretical issues on the role of education are continuously on modification more rapidly than the teaching and learning practices that need more time to be realized. In this paper is presented a broad scope of main national and international organizations that propose, promote and systematize those educational changes since a half century ago and specially, those that impact the formation tendency based on competences. On other side, and not pretending be exhaustive, in this paper is highlighted a list of educational competences that teachers need to develop if they pretend to realize their teaching functions with high quality standards, mainly those related with velocity involvement as curriculum constructor.
Efficient approximation of black-box functions and Pareto sets
Rennen, G.
2009-01-01
In the case of time-consuming simulation models or other so-called black-box functions, we determine a metamodel which approximates the relation between the input- and output-variables of the simulation model. To solve multi-objective optimization problems, we approximate the Pareto set, i.e. the
Reducing Approximation Error in the Fourier Flexible Functional Form
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Tristan D. Skolrud
2017-12-01
Full Text Available The Fourier Flexible form provides a global approximation to an unknown data generating process. In terms of limiting function specification error, this form is preferable to functional forms based on second-order Taylor series expansions. The Fourier Flexible form is a truncated Fourier series expansion appended to a second-order expansion in logarithms. By replacing the logarithmic expansion with a Box-Cox transformation, we show that the Fourier Flexible form can reduce approximation error by 25% on average in the tails of the data distribution. The new functional form allows for nested testing of a larger set of commonly implemented functional forms.
On approximation and energy estimates for delta 6-convex functions.
Saleem, Muhammad Shoaib; Pečarić, Josip; Rehman, Nasir; Khan, Muhammad Wahab; Zahoor, Muhammad Sajid
2018-01-01
The smooth approximation and weighted energy estimates for delta 6-convex functions are derived in this research. Moreover, we conclude that if 6-convex functions are closed in uniform norm, then their third derivatives are closed in weighted [Formula: see text]-norm.
On approximation and energy estimates for delta 6-convex functions
Directory of Open Access Journals (Sweden)
Muhammad Shoaib Saleem
2018-02-01
Full Text Available Abstract The smooth approximation and weighted energy estimates for delta 6-convex functions are derived in this research. Moreover, we conclude that if 6-convex functions are closed in uniform norm, then their third derivatives are closed in weighted L2 $L^{2}$-norm.
Cheap contouring of costly functions: the Pilot Approximation Trajectory algorithm
International Nuclear Information System (INIS)
Huttunen, Janne M J; Stark, Philip B
2012-01-01
The Pilot Approximation Trajectory (PAT) contour algorithm can find the contour of a function accurately when it is not practical to evaluate the function on a grid dense enough to use a standard contour algorithm, for instance, when evaluating the function involves conducting a physical experiment or a computationally intensive simulation. PAT relies on an inexpensive pilot approximation to the function, such as interpolating from a sparse grid of inexact values, or solving a partial differential equation (PDE) numerically using a coarse discretization. For each level of interest, the location and ‘trajectory’ of an approximate contour of this pilot function are used to decide where to evaluate the original function to find points on its contour. Those points are joined by line segments to form the PAT approximation of the contour of the original function. Approximating a contour numerically amounts to estimating a lower level set of the function, the set of points on which the function does not exceed the contour level. The area of the symmetric difference between the true lower level set and the estimated lower level set measures the accuracy of the contour. PAT measures its own accuracy by finding an upper confidence bound for this area. In examples, PAT can estimate a contour more accurately than standard algorithms, using far fewer function evaluations than standard algorithms require. We illustrate PAT by constructing a confidence set for viscosity and thermal conductivity of a flowing gas from simulated noisy temperature measurements, a problem in which each evaluation of the function to be contoured requires solving a different set of coupled nonlinear PDEs. (paper)
Complexity of Gaussian-Radial-Basis Networks Approximating Smooth Functions
Czech Academy of Sciences Publication Activity Database
Kainen, P.C.; Kůrková, Věra; Sanguineti, M.
2009-01-01
Roč. 25, č. 1 (2009), s. 63-74 ISSN 0885-064X R&D Projects: GA ČR GA201/08/1744 Institutional research plan: CEZ:AV0Z10300504 Keywords : Gaussian-radial-basis-function networks * rates of approximation * model complexity * variation norms * Bessel and Sobolev norms * tractability of approximation Subject RIV: IN - Informatics, Computer Science Impact factor: 1.227, year: 2009
Mathieu functions and its useful approximation for elliptical waveguides
Pillay, Shamini; Kumar, Deepak
2017-11-01
The standard form of the Mathieu differential equation is where a and q are real parameters and q > 0. In this paper we obtain closed formula for the generic term of expansions of modified Mathieu functions in terms of Bessel and modified Bessel functions in the following cases: Let ξ0 = ξ0, where i can take the values 1 and 2 corresponding to the first and the second boundary. These approximations also provide alternative methods for numerical evaluation of Mathieu functions.
Using function approximation to determine neural network accuracy
International Nuclear Information System (INIS)
Wichman, R.F.; Alexander, J.
2013-01-01
Many, if not most, control processes demonstrate nonlinear behavior in some portion of their operating range and the ability of neural networks to model non-linear dynamics makes them very appealing for control. Control of high reliability safety systems, and autonomous control in process or robotic applications, however, require accurate and consistent control and neural networks are only approximators of various functions so their degree of approximation becomes important. In this paper, the factors affecting the ability of a feed-forward back-propagation neural network to accurately approximate a non-linear function are explored. Compared to pattern recognition using a neural network for function approximation provides an easy and accurate method for determining the network's accuracy. In contrast to other techniques, we show that errors arising in function approximation or curve fitting are caused by the neural network itself rather than scatter in the data. A method is proposed that provides improvements in the accuracy achieved during training and resulting ability of the network to generalize after training. Binary input vectors provided a more accurate model than with scalar inputs and retraining using a small number of the outlier x,y pairs improved generalization. (author)
Analytical approximations to seawater optical phase functions of scattering
Haltrin, Vladimir I.
2004-11-01
This paper proposes a number of analytical approximations to the classic and recently measured seawater light scattering phase functions. The three types of analytical phase functions are derived: individual representations for 15 Petzold, 41 Mankovsky, and 91 Gulf of Mexico phase functions; collective fits to Petzold phase functions; and analytical representations that take into account dependencies between inherent optical properties of seawater. The proposed phase functions may be used for problems of radiative transfer, remote sensing, visibility and image propagation in natural waters of various turbidity.
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.
Approximation of the Doppler broadening function by Frobenius method
International Nuclear Information System (INIS)
Palma, Daniel A.P.; Martinez, Aquilino S.; Silva, Fernando C.
2005-01-01
An analytical approximation of the Doppler broadening function ψ(x,ξ) is proposed. This approximation is based on the solution of the differential equation for ψ(x,ξ) using the methods of Frobenius and the parameters variation. The analytical form derived for ψ(x,ξ) in terms of elementary functions is very simple and precise. It can be useful for applications related to the treatment of nuclear resonances mainly for the calculations of multigroup parameters and self-protection factors of the resonances, being the last used to correct microscopic cross-sections measurements by the activation technique. (author)
Approximate convex hull of affine iterated function system attractors
International Nuclear Information System (INIS)
Mishkinis, Anton; Gentil, Christian; Lanquetin, Sandrine; Sokolov, Dmitry
2012-01-01
Highlights: ► We present an iterative algorithm to approximate affine IFS attractor convex hull. ► Elimination of the interior points significantly reduces the complexity. ► To optimize calculations, we merge the convex hull images at each iteration. ► Approximation by ellipses increases speed of convergence to the exact convex hull. ► We present a method of the output convex hull simplification. - Abstract: In this paper, we present an algorithm to construct an approximate convex hull of the attractors of an affine iterated function system (IFS). We construct a sequence of convex hull approximations for any required precision using the self-similarity property of the attractor in order to optimize calculations. Due to the affine properties of IFS transformations, the number of points considered in the construction is reduced. The time complexity of our algorithm is a linear function of the number of iterations and the number of points in the output approximate convex hull. The number of iterations and the execution time increases logarithmically with increasing accuracy. In addition, we introduce a method to simplify the approximate convex hull without loss of accuracy.
Integral approximants for functions of higher monodromic dimension
Energy Technology Data Exchange (ETDEWEB)
Baker, G.A. Jr.
1987-01-01
In addition to the description of multiform, locally analytic functions as covering a many sheeted version of the complex plane, Riemann also introduced the notion of considering them as describing a space whose ''monodromic'' dimension is the number of linearly independent coverings by the monogenic analytic function at each point of the complex plane. I suggest that this latter concept is natural for integral approximants (sub-class of Hermite-Pade approximants) and discuss results for both ''horizontal'' and ''diagonal'' sequences of approximants. Some theorems are now available in both cases and make clear the natural domain of convergence of the horizontal sequences is a disk centered on the origin and that of the diagonal sequences is a suitably cut complex-plane together with its identically cut pendant Riemann sheets. Some numerical examples have also been computed.
Sequential function approximation on arbitrarily distributed point sets
Wu, Kailiang; Xiu, Dongbin
2018-02-01
We present a randomized iterative method for approximating unknown function sequentially on arbitrary point set. The method is based on a recently developed sequential approximation (SA) method, which approximates a target function using one data point at each step and avoids matrix operations. The focus of this paper is on data sets with highly irregular distribution of the points. We present a nearest neighbor replacement (NNR) algorithm, which allows one to sample the irregular data sets in a near optimal manner. We provide mathematical justification and error estimates for the NNR algorithm. Extensive numerical examples are also presented to demonstrate that the NNR algorithm can deliver satisfactory convergence for the SA method on data sets with high irregularity in their point distributions.
Pade approximants for entire functions with regularly decreasing Taylor coefficients
International Nuclear Information System (INIS)
Rusak, V N; Starovoitov, A P
2002-01-01
For a class of entire functions the asymptotic behaviour of the Hadamard determinants D n,m as 0≤m≤m(n)→∞ and n→∞ is described. This enables one to study the behaviour of parabolic sequences from Pade and Chebyshev tables for many individual entire functions. The central result of the paper is as follows: for some sequences {(n,m(n))} in certain classes of entire functions (with regular Taylor coefficients) the Pade approximants {π n,m(n) }, which provide the locally best possible rational approximations, converge to the given function uniformly on the compact set D={z:|z|≤1} with asymptotically best rate
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
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…
Approximate Solutions for Indifference Pricing under General Utility Functions
Chen, A.; Pelsser, A.; Vellekoop, M.
2007-01-01
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
Applications exponential approximation by integer shifts of Gaussian functions
Directory of Open Access Journals (Sweden)
S. M. Sitnik
2013-01-01
Full Text Available In this paper we consider approximations of functions using integer shifts of Gaussians – quadratic exponentials. A method is proposed to find coefficients of node functions by solving linear systems of equations. The explicit formula for the determinant of the system is found, based on it solvability of linear system under consideration is proved and uniqueness of its solution. We compare results with known ones and briefly indicate applications to signal theory.
Are there approximate relations among transverse momentum dependent distribution functions?
Energy Technology Data Exchange (ETDEWEB)
Harutyun AVAKIAN; Anatoli Efremov; Klaus Goeke; Andreas Metz; Peter Schweitzer; Tobias Teckentrup
2007-10-11
Certain {\\sl exact} relations among transverse momentum dependent parton distribution functions due to QCD equations of motion turn into {\\sl approximate} ones upon the neglect of pure twist-3 terms. On the basis of available data from HERMES we test the practical usefulness of one such ``Wandzura-Wilczek-type approximation'', namely of that connecting $h_{1L}^{\\perp(1)a}(x)$ to $h_L^a(x)$, and discuss how it can be further tested by future CLAS and COMPASS data.
Strong semiclassical approximation of Wigner functions for the Hartree dynamics
Athanassoulis, Agissilaos; Paul, Thierry; Pezzotti, Federica; Pulvirenti, Mario
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.
Quantal density functional theory II. Approximation methods and applications
International Nuclear Information System (INIS)
Sahni, Viraht
2010-01-01
This book is on approximation methods and applications of Quantal Density Functional Theory (QDFT), a new local effective-potential-energy theory of electronic structure. What distinguishes the theory from traditional density functional theory is that the electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and the correlation contribution to the kinetic energy -- the Correlation-Kinetic effects -- are separately and explicitly defined. As such it is possible to study each property of interest as a function of the different electron correlations. Approximations methods based on the incorporation of different electron correlations, as well as a many-body perturbation theory within the context of QDFT, are developed. The applications are to the few-electron inhomogeneous electron gas systems in atoms and molecules, as well as to the many-electron inhomogeneity at metallic surfaces. (orig.)
Approximation methods for the partition functions of anharmonic systems
International Nuclear Information System (INIS)
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
On the approximation of the limit cycles function
Directory of Open Access Journals (Sweden)
L. Cherkas
2007-11-01
Full Text Available We consider planar vector fields depending on a real parameter. It is assumed that this vector field has a family of limit cycles which can be described by means of the limit cycles function $l$. We prove a relationship between the multiplicity of a limit cycle of this family and the order of a zero of the limit cycles function. Moreover, we present a procedure to approximate $l(x$, which is based on the Newton scheme applied to the Poincaré function and represents a continuation method. Finally, we demonstrate the effectiveness of the proposed procedure by means of a Liénard system.
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.
Approximate models for the analysis of laser velocimetry correlation functions
International Nuclear Information System (INIS)
Robinson, D.P.
1981-01-01
Velocity distributions in the subchannels of an eleven pin test section representing a slice through a Fast Reactor sub-assembly were measured with a dual beam laser velocimeter system using a Malvern K 7023 digital photon correlator for signal processing. Two techniques were used for data reduction of the correlation function to obtain velocity and turbulence values. Whilst both techniques were in excellent agreement on the velocity, marked discrepancies were apparent in the turbulence levels. As a consequence of this the turbulence data were not reported. Subsequent investigation has shown that the approximate technique used as the basis of Malvern's Data Processor 7023V is restricted in its range of application. In this note alternative approximate models are described and evaluated. The objective of this investigation was to develop an approximate model which could be used for on-line determination of the turbulence level. (author)
Approximation of the exponential integral (well function) using sampling methods
Baalousha, Husam Musa
2015-04-01
Exponential integral (also known as well function) is often used in hydrogeology to solve Theis and Hantush equations. Many methods have been developed to approximate the exponential integral. Most of these methods are based on numerical approximations and are valid for a certain range of the argument value. This paper presents a new approach to approximate the exponential integral. The new approach is based on sampling methods. Three different sampling methods; Latin Hypercube Sampling (LHS), Orthogonal Array (OA), and Orthogonal Array-based Latin Hypercube (OA-LH) have been used to approximate the function. Different argument values, covering a wide range, have been used. The results of sampling methods were compared with results obtained by Mathematica software, which was used as a benchmark. All three sampling methods converge to the result obtained by Mathematica, at different rates. It was found that the orthogonal array (OA) method has the fastest convergence rate compared with LHS and OA-LH. The root mean square error RMSE of OA was in the order of 1E-08. This method can be used with any argument value, and can be used to solve other integrals in hydrogeology such as the leaky aquifer integral.
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.
Universal resources for approximate and stochastic measurement-based quantum computation
International Nuclear Information System (INIS)
Mora, Caterina E.; Piani, Marco; Miyake, Akimasa; Van den Nest, Maarten; Duer, Wolfgang; Briegel, Hans J.
2010-01-01
We investigate which quantum states can serve as universal resources for approximate and stochastic measurement-based quantum computation in the sense that any quantum state can be generated from a given resource by means of single-qubit (local) operations assisted by classical communication. More precisely, we consider the approximate and stochastic generation of states, resulting, for example, from a restriction to finite measurement settings or from possible imperfections in the resources or local operations. We show that entanglement-based criteria for universality obtained in M. Van den Nest et al. [New J. Phys. 9, 204 (2007)] for the exact, deterministic case can be lifted to the much more general approximate, stochastic case. This allows us to move from the idealized situation (exact, deterministic universality) considered in previous works to the practically relevant context of nonperfect state preparation. We find that any entanglement measure fulfilling some basic requirements needs to reach its maximum value on some element of an approximate, stochastic universal family of resource states, as the resource size grows. This allows us to rule out various families of states as being approximate, stochastic universal. We prove that approximate, stochastic universality is in general a weaker requirement than deterministic, exact universality and provide resources that are efficient approximate universal, but not exact deterministic universal. We also study the robustness of universal resources for measurement-based quantum computation under realistic assumptions about the (imperfect) generation and manipulation of entangled states, giving an explicit expression for the impact that errors made in the preparation of the resource have on the possibility to use it for universal approximate and stochastic state preparation. Finally, we discuss the relation between our entanglement-based criteria and recent results regarding the uselessness of states with a high
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.
Approximate Treatment of the Dirac Equation with Hyperbolic Potential Function
Durmus, Aysen
2018-03-01
The time independent Dirac equation is solved analytically for equal scalar and vector hyperbolic potential function in the presence of Greene and Aldrich approximation scheme. The bound state energy equation and spinor wave functions expressed by the hypergeometric function have been obtained in detail with asymptotic iteration approach. In order to indicate the accuracy of this different approach proposed to solve second order linear differential equations, we present that in the non-relativistic limit, analytical solutions of the Dirac equation converge to those of the Schrödinger one. We introduce numerical results of the theoretical analysis for hyperbolic potential function. Bound states corresponding to arbitrary values of n and l are reported for potential parameters covering a wide range of interaction. Also, we investigate relativistic vibrational energy spectra of alkali metal diatomic molecules in the different electronic states. It is observed that theoretical vibrational energy values are consistent with experimental Rydberg-Klein-Rees (RKR) results and vibrational energies of NaK, K_2 and KRb diatomic molecules interacting with hyperbolic potential smoothly converge to the experimental dissociation limit D_e=2508cm^{-1}, 254cm^{-1} and 4221cm^{-1}, respectively.
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.
Singlet structure function F_1 in double-logarithmic approximation
Ermolaev, B. I.; Troyan, S. I.
2018-03-01
The conventional ways to calculate the perturbative component of the DIS singlet structure function F_1 involve approaches based on BFKL which account for the single-logarithmic contributions accompanying the Born factor 1 / x. In contrast, we account for the double-logarithmic (DL) contributions unrelated to 1 / x and because of that they were disregarded as negligibly small. We calculate the singlet F_1 in the double-logarithmic approximation (DLA) and account at the same time for the running α _s effects. We start with a total resummation of both quark and gluon DL contributions and obtain the explicit expression for F_1 in DLA. Then, applying the saddle-point method, we calculate the small- x asymptotics of F_1, which proves to be of the Regge form with the leading singularity ω _0 = 1.066. Its large value compensates for the lack of the factor 1 / x in the DLA contributions. Therefore, this Reggeon can be identified as a new Pomeron, which can be quite important for the description of all QCD processes involving the vacuum (Pomeron) exchanges at very high energies. We prove that the expression for the small- x asymptotics of F_1 scales: it depends on a single variable Q^2/x^2 only instead of x and Q^2 separately. Finally, we show that the small- x asymptotics reliably represent F_1 at x ≤ 10^{-6}.
A learning rule for very simple universal approximators consisting of a single layer of perceptrons.
Auer, Peter; Burgsteiner, Harald; Maass, Wolfgang
2008-06-01
One may argue that the simplest type of neural networks beyond a single perceptron is an array of several perceptrons in parallel. In spite of their simplicity, such circuits can compute any Boolean function if one views the majority of the binary perceptron outputs as the binary output of the parallel perceptron, and they are universal approximators for arbitrary continuous functions with values in [0,1] if one views the fraction of perceptrons that output 1 as the analog output of the parallel perceptron. Note that in contrast to the familiar model of a "multi-layer perceptron" the parallel perceptron that we consider here has just binary values as outputs of gates on the hidden layer. For a long time one has thought that there exists no competitive learning algorithm for these extremely simple neural networks, which also came to be known as committee machines. It is commonly assumed that one has to replace the hard threshold gates on the hidden layer by sigmoidal gates (or RBF-gates) and that one has to tune the weights on at least two successive layers in order to achieve satisfactory learning results for any class of neural networks that yield universal approximators. We show that this assumption is not true, by exhibiting a simple learning algorithm for parallel perceptrons - the parallel delta rule (p-delta rule). In contrast to backprop for multi-layer perceptrons, the p-delta rule only has to tune a single layer of weights, and it does not require the computation and communication of analog values with high precision. Reduced communication also distinguishes our new learning rule from other learning rules for parallel perceptrons such as MADALINE. Obviously these features make the p-delta rule attractive as a biologically more realistic alternative to backprop in biological neural circuits, but also for implementations in special purpose hardware. We show that the p-delta rule also implements gradient descent-with regard to a suitable error measure
An improvement of speed control performances of a two-mass system using a universal approximator
DEFF Research Database (Denmark)
Lee, Kyo Beum; Blåbjerg, Frede
2007-01-01
A new control scheme using a universal approximator based on a radial basis ti.tnction network (RBFN) is proposed and investigated for improving the control characteristics of the high-performance motion control system. This control method presents better performance in the corresponding speed vi...
Śmiga, Szymon; Fabiano, Eduardo; Laricchia, Savio; Constantin, Lucian A; Della Sala, Fabio
2015-04-21
We analyze the methodology and the performance of subsystem density functional theory (DFT) with meta-generalized gradient approximation (meta-GGA) exchange-correlation functionals for non-bonded molecular systems. Meta-GGA functionals depend on the Kohn-Sham kinetic energy density (KED), which is not known as an explicit functional of the density. Therefore, they cannot be directly applied in subsystem DFT calculations. We propose a Laplacian-level approximation to the KED which overcomes this limitation and provides a simple and accurate way to apply meta-GGA exchange-correlation functionals in subsystem DFT calculations. The so obtained density and energy errors, with respect to the corresponding supermolecular calculations, are comparable with conventional approaches, depending almost exclusively on the approximations in the non-additive kinetic embedding term. An embedding energy error decomposition explains the accuracy of our method.
A novel single neuron perceptron with universal approximation and XOR computation properties.
Lotfi, Ehsan; Akbarzadeh-T, M-R
2014-01-01
We propose a biologically motivated brain-inspired single neuron perceptron (SNP) with universal approximation and XOR computation properties. This computational model extends the input pattern and is based on the excitatory and inhibitory learning rules inspired from neural connections in the human brain's nervous system. The resulting architecture of SNP can be trained by supervised excitatory and inhibitory online learning rules. The main features of proposed single layer perceptron are universal approximation property and low computational complexity. The method is tested on 6 UCI (University of California, Irvine) pattern recognition and classification datasets. Various comparisons with multilayer perceptron (MLP) with gradient decent backpropagation (GDBP) learning algorithm indicate the superiority of the approach in terms of higher accuracy, lower time, and spatial complexity, as well as faster training. Hence, we believe the proposed approach can be generally applicable to various problems such as in pattern recognition and classification.
Wavelet series approximation using wavelet function with compactly ...
African Journals Online (AJOL)
The Wavelets generated by Scaling Function with Compactly Support are useful in various applications especially for reconstruction of functions. Generally, the computational process will be faster if Scaling Function support descends, so computational errors are summarized from one level to another level. In this article, 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.
Multi-level methods and approximating distribution functions
International Nuclear Information System (INIS)
Wilson, D.; Baker, R. E.
2016-01-01
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.
Multi-level methods and approximating distribution functions
Energy Technology Data Exchange (ETDEWEB)
Wilson, D., E-mail: daniel.wilson@dtc.ox.ac.uk; Baker, R. E. [Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG (United Kingdom)
2016-07-15
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....
Directory of Open Access Journals (Sweden)
Jie Shen
2015-01-01
Full Text Available We describe an extension of the redistributed technique form classical proximal bundle method to the inexact situation for minimizing nonsmooth nonconvex functions. The cutting-planes model we construct is not the approximation to the whole nonconvex function, but to the local convexification of the approximate objective function, and this kind of local convexification is modified dynamically in order to always yield nonnegative linearization errors. Since we only employ the approximate function values and approximate subgradients, theoretical convergence analysis shows that an approximate stationary point or some double approximate stationary point can be obtained under some mild conditions.
Approximate scattering wave functions for few-particle continua
International Nuclear Information System (INIS)
Briggs, J.S.
1990-01-01
An operator identity which allows the wave operator for N particles interacting pairwise to be expanded as products of operators in which fewer than N particles interact is given. This identity is used to derive appproximate scattering wave functions for N-particle continua that avoid certain difficulties associated with Faddeev-type expansions. For example, a derivation is given of a scattering wave function used successfully recently to describe the three-particle continuum occurring in the electron impact ionization of the hydrogen atom
Approximate formulas for elasticity of the Tornquist functions and some their advantages
Issin, Meyram
2017-09-01
In this article functions of demand for prime necessity, second necessity and luxury goods depending on the income are considered. These functions are called Tornquist functions. By means of the return model the demand for prime necessity goods and second necessity goods are approximately described. Then on the basis of a method of the smallest squares approximate formulas for elasticity of these Tornquist functions are received. To receive an approximate formula for elasticity of function of demand for luxury goods, the linear asymptotic formula is constructed for this function. Some benefits of approximate formulas for elasticity of Tornquist functions are specified.
Bayesian Parameter Estimation via Filtering and Functional Approximations
Matthies, Hermann G.
2016-11-25
The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation and updating of parameters in a computational model. This is a filter acting on random variables, and while its Monte Carlo variant --- the Ensemble Kalman Filter (EnKF) --- is fairly straightforward, we subsequently only sketch its implementation with the help of functional representations.
Bayesian Parameter Estimation via Filtering and Functional Approximations
Matthies, Hermann G.; Litvinenko, Alexander; Rosic, Bojana V.; Zander, Elmar
2016-01-01
The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation and updating of parameters in a computational model. This is a filter acting on random variables, and while its Monte Carlo variant --- the Ensemble Kalman Filter (EnKF) --- is fairly straightforward, we subsequently only sketch its implementation with the help of functional representations.
International Nuclear Information System (INIS)
Cafiero, Mauricio; Gonzalez, Carlos
2005-01-01
We show that potentials for exchange-correlation functionals within the Kohn-Sham density-functional-theory framework may be written as potentials for simpler functionals multiplied by a factor close to unity, and in a self-consistent field calculation, these effective potentials find the correct self-consistent solutions. This simple theory is demonstrated with self-consistent exchange-only calculations of the atomization energies of some small molecules using the Perdew-Kurth-Zupan-Blaha (PKZB) meta-generalized-gradient-approximation (meta-GGA) exchange functional. The atomization energies obtained with our method agree with or surpass previous meta-GGA calculations performed in a non-self-consistent manner. The results of this work suggest the utility of this simple theory to approximate exchange-correlation potentials corresponding to energy functionals too complicated to generate closed forms for their potentials. We hope that this method will encourage the development of complex functionals which have correct boundary conditions and are free of self-interaction errors without the worry that the functionals are too complex to differentiate to obtain potentials
H4: A challenging system for natural orbital functional approximations
International Nuclear Information System (INIS)
Ramos-Cordoba, Eloy; Lopez, Xabier; 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 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 4 D 4h /D 2h potential energy surface (PES). 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 actually interpair nondynamic correlation is the key to a cusp-free qualitatively correct description of H 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
H4: A challenging system for natural orbital functional approximations
Ramos-Cordoba, Eloy; Lopez, Xabier; Piris, Mario; Matito, Eduard
2015-10-01
The correct description of nondynamic correlation by electronic structure methods not belonging to the multireference family is a challenging issue. The transition of D2h to D4h symmetry in H4 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 H4 D4h/D2h potential energy surface (PES). Thus far, the wrongful behavior of single-reference methods at the D2h-D4h transition of H4 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 H4 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.
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
Approximate relativistic corrections to atomic radial wave functions
International Nuclear Information System (INIS)
Cowan, R.D.; Griffin, D.C.
1976-01-01
The mass-velocity and Darwin terms of the one-electron-atom Pauli equation have been added to the Hartree-Fock differential equations by using the HX formula to calculate a local central field potential for use in these terms. Introduction of the quantum number j is avoided by omitting the spin-orbit term of the Pauli equation. The major relativistic effects, both direct and indirect, are thereby incorporated into the wave functions, while allowing retention of the commonly used nonrelativistic formulation of energy level calculations. The improvement afforded in calculated total binding energies, excitation energies, spin-orbit parameters, and expectation values of r/sub m/ is comparable with that provided by fully relativistic Dirac-Hartree-Fock calculations
Analytic approximation for the modified Bessel function I -2/3(x)
Martin, Pablo; Olivares, Jorge; Maass, Fernando
2017-12-01
In the present work an analytic approximation to modified Bessel function of negative fractional order I -2/3(x) is presented. The validity of the approximation is for every positive value of the independent variable. The accuracy is high in spite of the small number (4) of parameters used. The approximation is a combination of elementary functions with rational ones. Power series and assymptotic expansions are simultaneously used to obtain the approximation.
High-Dimensional Function Approximation With Neural Networks for Large Volumes of Data.
Andras, Peter
2018-02-01
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.
Universality for 1d Random Band Matrices: Sigma-Model Approximation
Shcherbina, Mariya; Shcherbina, Tatyana
2018-02-01
The paper continues the development of the rigorous supersymmetric transfer matrix approach to the random band matrices started in (J Stat Phys 164:1233-1260, 2016; Commun Math Phys 351:1009-1044, 2017). We consider random Hermitian block band matrices consisting of W× W random Gaussian blocks (parametrized by j,k \\in Λ =[1,n]^d\\cap Z^d ) with a fixed entry's variance J_{jk}=δ _{j,k}W^{-1}+β Δ _{j,k}W^{-2} , β >0 in each block. Taking the limit W→ ∞ with fixed n and β , we derive the sigma-model approximation of the second correlation function similar to Efetov's one. Then, considering the limit β , n→ ∞, we prove that in the dimension d=1 the behaviour of the sigma-model approximation in the bulk of the spectrum, as β ≫ n , is determined by the classical Wigner-Dyson statistics.
International Nuclear Information System (INIS)
Sato, M.
1991-01-01
The Saha equation for a plasma in thermodynamic equilibrium (TE) is approximately solved to give the temperature as an explicit function of population densities. It is shown that the derived expressions for the Saha temperature are valid approximations to the exact solution. An application of the approximate temperature to the calculation of TE plasma parameters is also described. (orig.)
Directory of Open Access Journals (Sweden)
H. K. Hetman
2011-01-01
Full Text Available A number of functions for approximating the universal magnetic curve and its derivatives, their accuracy and conformity to the requirements put forward by the authors have been studied.
International Nuclear Information System (INIS)
Gougam, L.A.; Taibi, H.; Chikhi, A.; Mekideche-Chafa, F.
2009-01-01
The problem of determining the analytical description for a set of data arises in numerous sciences and applications and can be referred to as data modeling or system identification. Neural networks are a convenient means of representation because they are known to be universal approximates that can learn data. The desired task is usually obtained by a learning procedure which consists in adjusting the s ynaptic weights . For this purpose, many learning algorithms have been proposed to update these weights. The convergence for these learning algorithms is a crucial criterion for neural networks to be useful in different applications. The aim of the present contribution is to use a training algorithm for feed forward wavelet networks used for function approximation. The training is based on the minimization of the least-square cost function. The minimization is performed by iterative second order gradient-based methods. We make use of the Levenberg-Marquardt algorithm to train the architecture of the chosen network and, then, the training procedure starts with a simple gradient method which is followed by a BFGS (Broyden, Fletcher, Glodfarb et Shanno) algorithm. The performances of the two algorithms are then compared. Our method is then applied to determine the energy of the ground state associated to a sextic potential. In fact, the Schrodinger equation does not always admit an exact solution and one has, generally, to solve it numerically. To this end, the sextic potential is, firstly, approximated with the above outlined wavelet network and, secondly, implemented into a numerical scheme. Our results are in good agreement with the ones found in the literature.
DEFF Research Database (Denmark)
Ruban, Andrei; Skriver, Hans Lomholt
2002-01-01
We have used the locally self-consistent Green's-function (LSGF) method in supercell calculations to establish the distribution of the net charges assigned to the atomic spheres of the alloy components in metallic alloys with different compositions and degrees of order. This allows us to determine......-site local interaction zone. We demonstrate that the basic mechanism that governs the charge distribution is the screening of the net charges of the alloy components that makes the direct Coulomb interactions short ranged. In the atomic-sphere approximation, this screening appears to be almost independent...
International Nuclear Information System (INIS)
Gaj, E.V.; Badikov, S.A.; Gusejnov, M.A.; Rabotnov, N.S.
1988-01-01
Possible applications of rational functions in the analysis of neutron cross sections, angular distributions and neutron constants generation are described. Results of investigations made in this direction, which have been obtained after the preceding conference in Kiev, are presented: the method of simultaneous treatment of several cross sections for one compound nucleus in the resonance range; the use of the Pade approximation for elastically scattered neutron angular distribution approximation; obtaining of subgroup constants on the basis of rational approximation of cross section functional dependence on dilution cross section; the first experience in function approximation by two variables
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.
Spacetimes admitting a universal redshift function
International Nuclear Information System (INIS)
Dautcourt, G.
1987-01-01
The conditions are given for a velocity congruence in a Riemannian spacetime admitting a universal redshift function R. This function allows to calculate in a simple way (as a quotient of R values taken at the emission and registration event) the redshift or blueshift connected with an emitter and observer both following the congruence. Spacetimes and congruences with an universal redshift function are shortly discussed. (author)
Approximation Of Multi-Valued Inverse Functions Using Clustering And Sugeno Fuzzy Inference
Walden, Maria A.; Bikdash, Marwan; Homaifar, Abdollah
1998-01-01
Finding the inverse of a continuous function can be challenging and computationally expensive when the inverse function is multi-valued. Difficulties may be compounded when the function itself is difficult to evaluate. We show that we can use fuzzy-logic approximators such as Sugeno inference systems to compute the inverse on-line. To do so, a fuzzy clustering algorithm can be used in conjunction with a discriminating function to split the function data into branches for the different values of the forward function. These data sets are then fed into a recursive least-squares learning algorithm that finds the proper coefficients of the Sugeno approximators; each Sugeno approximator finds one value of the inverse function. Discussions about the accuracy of the approximation will be included.
The varying cosmological constant: a new approximation to the Friedmann equations and universe model
Öztaş, Ahmet M.; Dil, Emre; Smith, Michael L.
2018-05-01
We investigate the time-dependent nature of the cosmological constant, Λ, of the Einstein Field Equation (EFE). Beginning with the Einstein-Hilbert action as our fundamental principle we develop a modified version of the EFE allowing the value of Λ to vary as a function of time, Λ(t), indirectly, for an expanding universe. We follow the evolving Λ presuming four-dimensional space-time and a flat universe geometry and present derivations of Λ(t) as functions of the Hubble constant, matter density, and volume changes which can be traced back to the radiation epoch. The models are more detailed descriptions of the Λ dependence on cosmological factors than previous, allowing calculations of the important parameters, Ωm and Ωr, to deep lookback times. Since we derive these without the need for extra dimensions or other special conditions our derivations are useful for model evaluation with astronomical data. This should aid resolution of several difficult problems of astronomy such as the best value for the Hubble constant at present and at recombination.
Giuliani, Matteo; Mason, Emanuele; Castelletti, Andrea; Pianosi, Francesca
2014-05-01
The optimal operation of water resources systems is a wide and challenging problem due to non-linearities in the model and the objectives, high dimensional state-control space, and strong uncertainties in the hydroclimatic regimes. The application of classical optimization techniques (e.g., SDP, Q-learning, gradient descent-based algorithms) is strongly limited by the dimensionality of the system and by the presence of multiple, conflicting objectives. This study presents a novel approach which combines Direct Policy Search (DPS) and Multi-Objective Evolutionary Algorithms (MOEAs) to solve high-dimensional state and control space problems involving multiple objectives. DPS, also known as parameterization-simulation-optimization in the water resources literature, is a simulation-based approach where the reservoir operating policy is first parameterized within a given family of functions and, then, the parameters optimized with respect to the objectives of the management problem. The selection of a suitable class of functions to which the operating policy belong to is a key step, as it might restrict the search for the optimal policy to a subspace of the decision space that does not include the optimal solution. In the water reservoir literature, a number of classes have been proposed. However, many of these rules are based largely on empirical or experimental successes and they were designed mostly via simulation and for single-purpose reservoirs. In a multi-objective context similar rules can not easily inferred from the experience and the use of universal function approximators is generally preferred. In this work, we comparatively analyze two among the most common universal approximators: artificial neural networks (ANN) and radial basis functions (RBF) under different problem settings to estimate their scalability and flexibility in dealing with more and more complex problems. The multi-purpose HoaBinh water reservoir in Vietnam, accounting for hydropower
International Nuclear Information System (INIS)
Marrero, S. I.; Turibus, S. N.; Assis, J. T. De; Monin, V. I.
2011-01-01
Data processing of the most of diffraction experiments is based on determination of diffraction line position and measurement of broadening of diffraction profile. High precision and digitalisation of these procedures can be resolved by approximation of experimental diffraction profiles by analytical functions. There are various functions for these purposes both simples, like Gauss function, but no suitable for wild range of experimental profiles and good approximating functions but complicated for practice using, like Vougt or PersonVII functions. Proposed analytical function is modified Cauchy function which uses two variable parameters allowing describing any experimental diffraction profile. In the presented paper modified function was applied for approximation of diffraction lines of steels after various physical and mechanical treatments and simulation of diffraction profiles applied for study of stress gradients and distortions of crystal structure. (Author)
Winkler, David A; Le, Tu C
2017-01-01
Neural networks have generated valuable Quantitative Structure-Activity/Property Relationships (QSAR/QSPR) models for a wide variety of small molecules and materials properties. They have grown in sophistication and many of their initial problems have been overcome by modern mathematical techniques. QSAR studies have almost always used so-called "shallow" neural networks in which there is a single hidden layer between the input and output layers. Recently, a new and potentially paradigm-shifting type of neural network based on Deep Learning has appeared. Deep learning methods have generated impressive improvements in image and voice recognition, and are now being applied to QSAR and QSAR modelling. This paper describes the differences in approach between deep and shallow neural networks, compares their abilities to predict the properties of test sets for 15 large drug data sets (the kaggle set), discusses the results in terms of the Universal Approximation theorem for neural networks, and describes how DNN may ameliorate or remove troublesome "activity cliffs" in QSAR data sets. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
A new way of obtaining analytic approximations of Chandrasekhar's H function
International Nuclear Information System (INIS)
Vukanic, J.; Arsenovic, D.; Davidovic, D.
2007-01-01
Applying the mean value theorem for definite integrals in the non-linear integral equation for Chandrasekhar's H function describing conservative isotropic scattering, we have derived a new, simple analytic approximation for it, with a maximal relative error below 2.5%. With this new function as a starting-point, after a single iteration in the corresponding integral equation, we have obtained a new, highly accurate analytic approximation for the H function. As its maximal relative error is below 0.07%, it significantly surpasses the accuracy of other analytic approximations
International Nuclear Information System (INIS)
Ramazanov, A.-R K
2005-01-01
Necessary and sufficient conditions for the best polynomial approximation with an arbitrary and, generally speaking, unbounded sign-sensitive weight to a continuous function are obtained; the components of the weight can also take infinite values, therefore the conditions obtained cover, in particular, approximation with interpolation at fixed points and one-sided approximation; in the case of the weight with components equal to 1 one arrives at Chebyshev's classical alternation theorem.
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.
Delta-function Approximation SSC Model in 3C 273 S. J. Kang1 ...
Indian Academy of Sciences (India)
Abstract. We obtain an approximate analytical solution using δ 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 ...
Aarts, Ronald M; Janssen, Augustus J E M
2016-12-01
The Struve functions H n (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 H 1 (z) as (2/π)-J 0 (z)+(2/π) I(z), where J 0 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 H 0 (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,t̂ 0 ] and [t̂ 0 ,1] with t̂ 0 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 H 0 and H 1 . 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 H 0 and of 2.6 for H 1 . Recursion relations satisfied by Struve functions, initialized with the approximations of H 0 and H 1 , yield approximations for higher order Struve functions.
Approximation of functions in two variables by some linear positive operators
Directory of Open Access Journals (Sweden)
Mariola Skorupka
1995-12-01
Full Text Available We introduce some linear positive operators of the Szasz-Mirakjan type in the weighted spaces of continuous functions in two variables. We study the degree of the approximation of functions by these operators. The similar results for functions in one variable are given in [5]. Some operators of the Szasz-Mirakjan type are examined also in [3], [4].
National Research Council Canada - National Science Library
Franke, Richard
2001-01-01
.... It was found that for all levels the approximation of the covariance data for pressure height innovations by Legendre functions led to positive coefficients for up to 25 terms except at the some low and high levels...
Bisetti, Fabrizio
2012-01-01
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
International Nuclear Information System (INIS)
Capelle, K.; Gross, E.
1997-01-01
It is shown that the exchange-correlation functional of spin-density functional theory is identical, on a certain set of densities, with the exchange-correlation functional of current-density functional theory. This rigorous connection is used to construct new approximations of the exchange-correlation functionals. These include a conceptually new generalized-gradient spin-density functional and a nonlocal current-density functional. copyright 1997 The American Physical Society
The universal function in color dipole model
Jalilian, Z.; Boroun, G. R.
2017-10-01
In this work we review color dipole model and recall properties of the saturation and geometrical scaling in this model. Our primary aim is determining the exact universal function in terms of the introduced scaling variable in different distance than the saturation radius. With inserting the mass in calculation we compute numerically the contribution of heavy productions in small x from the total structure function by the fraction of universal functions and show the geometrical scaling is established due to our scaling variable in this study.
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. PMID:24379744
Monotone Approximations of Minimum and Maximum Functions and Multi-objective Problems
International Nuclear Information System (INIS)
Stipanović, Dušan M.; Tomlin, Claire J.; Leitmann, George
2012-01-01
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.
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.
Rational function approximation method for discrete ordinates problems in slab geometry
International Nuclear Information System (INIS)
Leal, Andre Luiz do C.; Barros, Ricardo C.
2009-01-01
In this work we use rational function approaches to obtain the transfer functions that appear in the spectral Green's function (SGF) auxiliary equations for one-speed isotropic scattering SN equations in one-dimensional Cartesian geometry. For this task we use the computation of the Pade approximants to compare the results with the standard SGF method's applied to deep penetration problems in homogeneous domains. This work is a preliminary investigation of a new proposal for handling leakage terms that appear in the two transverse integrated one-dimensional SN equations in the exponential SGF method (SGF-ExpN). Numerical results are presented to illustrate the rational function approximation accuracy. (author)
Correlation energy functional within the GW -RPA: Exact forms, approximate forms, and challenges
Ismail-Beigi, Sohrab
2010-05-01
In principle, the Luttinger-Ward Green’s-function formalism allows one to compute simultaneously the total energy and the quasiparticle band structure of a many-body electronic system from first principles. We present approximate and exact expressions for the correlation energy within the GW -random-phase approximation that are more amenable to computation and allow for developing efficient approximations to the self-energy operator and correlation energy. The exact form is a sum over differences between plasmon and interband energies. The approximate forms are based on summing over screened interband transitions. We also demonstrate that blind extremization of such functionals leads to unphysical results: imposing physical constraints on the allowed solutions (Green’s functions) is necessary. Finally, we present some relevant numerical results for atomic systems.
Mini wave function for the Universe
International Nuclear Information System (INIS)
Maslanka, K.
1989-01-01
The Friedman radiation filled world model can formally be treated as an oscillator with frequency determined by the cosmological constant and with an external force connected with the space curvature. The wave function for such a universe is constructed. By using Feynman's sum-over-histories method, the initial fundamental indeterminacy in the state of the universe is propagated forward in time. 5 refs. (author)
Universality of correlation functions in random matrix models of QCD
International Nuclear Information System (INIS)
Jackson, A.D.; Sener, M.K.; Verbaarschot, J.J.M.
1997-01-01
We demonstrate the universality of the spectral correlation functions of a QCD inspired random matrix model that consists of a random part having the chiral structure of the QCD Dirac operator and a deterministic part which describes a schematic temperature dependence. We calculate the correlation functions analytically using the technique of Itzykson-Zuber integrals for arbitrary complex supermatrices. An alternative exact calculation for arbitrary matrix size is given for the special case of zero temperature, and we reproduce the well-known Laguerre kernel. At finite temperature, the microscopic limit of the correlation functions are calculated in the saddle-point approximation. The main result of this paper is that the microscopic universality of correlation functions is maintained even though unitary invariance is broken by the addition of a deterministic matrix to the ensemble. (orig.)
Optimized implementations of rational approximations for the Voigt and complex error function
International Nuclear Information System (INIS)
Schreier, Franz
2011-01-01
Rational functions are frequently used as efficient yet accurate numerical approximations for real and complex valued functions. For the complex error function w(x+iy), whose real part is the Voigt function K(x,y), code optimizations of rational approximations are investigated. An assessment of requirements for atmospheric radiative transfer modeling indicates a y range over many orders of magnitude and accuracy better than 10 -4 . Following a brief survey of complex error function algorithms in general and rational function approximations in particular the problems associated with subdivisions of the x, y plane (i.e., conditional branches in the code) are discussed and practical aspects of Fortran and Python implementations are considered. Benchmark tests of a variety of algorithms demonstrate that programming language, compiler choice, and implementation details influence computational speed and there is no unique ranking of algorithms. A new implementation, based on subdivision of the upper half-plane in only two regions, combining Weideman's rational approximation for small |x|+y<15 and Humlicek's rational approximation otherwise is shown to be efficient and accurate for all x, y.
Many-body perturbation theory using the density-functional concept: beyond the GW approximation.
Bruneval, Fabien; Sottile, Francesco; Olevano, Valerio; Del Sole, Rodolfo; Reining, Lucia
2005-05-13
We propose an alternative formulation of many-body perturbation theory that uses the density-functional concept. Instead of the usual four-point integral equation for the polarizability, we obtain a two-point one, which leads to excellent optical absorption and energy-loss spectra. The corresponding three-point vertex function and self-energy are then simply calculated via an integration, for any level of approximation. Moreover, we show the direct impact of this formulation on the time-dependent density-functional theory. Numerical results for the band gap of bulk silicon and solid argon illustrate corrections beyond the GW approximation for the self-energy.
Physical Applications of a Simple Approximation of Bessel Functions of Integer Order
Barsan, V.; Cojocaru, S.
2007-01-01
Applications of a simple approximation of Bessel functions of integer order, in terms of trigonometric functions, are discussed for several examples from electromagnetism and optics. The method may be applied in the intermediate regime, bridging the "small values regime" and the "asymptotic" one, and covering, in this way, an area of great…
Agarwal, Mukul
2018-01-01
It is proved that the limit of the normalized rate-distortion functions of block independent approximations of an irreducible, aperiodic Markoff chain is independent of the initial distribution of the Markoff chain and thus, is also equal to the rate-distortion function of the Markoff chain.
Local density approximation for exchange in excited-state density functional theory
Harbola, Manoj K.; Samal, Prasanjit
2004-01-01
Local density approximation for the exchange energy is made for treatment of excited-states in density-functional theory. It is shown that taking care of the state-dependence of the LDA exchange energy functional leads to accurate excitation energies.
Bessel harmonic analysis and approximation of functions on the half-line
International Nuclear Information System (INIS)
Platonov, Sergei S
2007-01-01
We study problems of approximation of functions on [0,+∞) in the metric of L p with power weight using generalized Bessel shifts. We prove analogues of direct Jackson theorems for the modulus of smoothness of arbitrary order defined in terms of generalized Bessel shifts. We establish the equivalence of the modulus of smoothness and the K-functional. We define function spaces of Nikol'skii-Besov type and describe them in terms of best approximations. As a tool for approximation, we use a certain class of entire functions of exponential type. In this class, we prove analogues of Bernstein's inequality and others for the Bessel differential operator and its fractional powers. The main tool we use to solve these problems is Bessel harmonic analysis
Big geo data surface approximation using radial basis functions: A comparative study
Majdisova, Zuzana; Skala, Vaclav
2017-12-01
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for big scattered datasets in n-dimensional space. It is a non-separable approximation, as it is based on the distance between two points. This method leads to the solution of an overdetermined linear system of equations. In this paper the RBF approximation methods are briefly described, a new approach to the RBF approximation of big datasets is presented, and a comparison for different Compactly Supported RBFs (CS-RBFs) is made with respect to the accuracy of the computation. The proposed approach uses symmetry of a matrix, partitioning the matrix into blocks and data structures for storage of the sparse matrix. The experiments are performed for synthetic and real datasets.
Numerical analysis of different neural transfer functions used for best approximation
International Nuclear Information System (INIS)
Gougam, L.A.; Chikhi, A.; Biskri, S.; Chafa, F.
2006-01-01
It is widely recognised that the choice of transfer functions in neural networks is of en importance to their performance. In this paper, different neural transfer functions usec approximation are discussed. We begin with sigmoi'dal functions used most often by diffi authors . At a second step, we use Gaussian functions as previously suggested in refere Finally, we deal with a specified wavelet family. A comparison between the three cases < above is made exhibiting therefore the advantages of each transfer function. The approa< function improves as the dimension N of the elementary task basis increases
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. Copyright © 2016 The Author(s). Published by Elsevier Ltd.. All rights reserved.
International Nuclear Information System (INIS)
Lee, M.W.; Bigeleisen, J.
1978-01-01
The MINIMAX finite polynomial approximation to an arbitrary function has been generalized to include a weighting function (WINIMAX). It is suggested that an exponential is a reasonable weighting function for the logarithm of the reduced partition function of a harmonic oscillator. Comparison of the error function for finite orthogonal polynomial (FOP), MINIMAX, and WINIMAX expansions of the logarithm of the reduced vibrational partition function show WINIMAX to be the best of the three approximations. A condensed table of WINIMAX coefficients is presented. The FOP, MINIMAX, and WINIMAX approximations are compared with exact calculations of the logarithm of the reduced partition function ratios for isotopic substitution in H 2 O, CH 4 , CH 2 O, C 2 H 4 , and C 2 H 6 at 300 0 K. Both deuterium and heavy atom isotope substitution are studied. Except for a third order expansion involving deuterium substitution, the WINIMAX method is superior to FOP and MINIMAX. At the level of a second order expansion WINIMAX approximations to ln(s/s')f are good to 2.5% and 6.5% for deuterium and heavy atom substitution, respectively
FUNPACK-2, Subroutine Library, Bessel Function, Elliptical Integrals, Min-max Approximation
International Nuclear Information System (INIS)
Cody, W.J.; Garbow, Burton S.
1975-01-01
1 - Description of problem or function: FUNPACK is a collection of FORTRAN subroutines to evaluate certain special functions. The individual subroutines are (Identification/Description): NATSI0 F2I0 Bessel function I 0 ; NATSI1 F2I1 Bessel function I 1 ; NATSJ0 F2J0 Bessel function J 0 ; NATSJ1 F2J1 Bessel function J 1 ; NATSK0 F2K0 Bessel function K 0 ; NATSK1 F2K1 Bessel function K 1 ; NATSBESY F2BY Bessel function Y ν ; DAW F1DW Dawson's integral; DELIPK F1EK Complete elliptic integral of the first kind; DELIPE F1EE Complete elliptic integral of the second kind; DEI F1EI Exponential integrals; NATSPSI F2PS Psi (logarithmic derivative of gamma function); MONERR F1MO Error monitoring package . 2 - Method of solution: FUNPACK uses evaluation of min-max approximations
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.
International Nuclear Information System (INIS)
Haeggblom, H.
1968-08-01
The method of calculating the resonance interaction effect by series expansions has been studied. Starting from the assumption that the neutron flux in a homogeneous mixture is inversely proportional to the total cross section, the expression for the flux can be simplified by series expansions. Two types of expansions are investigated and it is shown that only one of them is generally applicable. It is also shown that this expansion gives sufficient accuracy if the approximate resonance line shape function is reasonably representative. An investigation is made of the approximation of the resonance shape function with a Gaussian function which in some cases has been used to calculate the interaction effect. It is shown that this approximation is not sufficiently accurate in all cases which can occur in practice. Then, a rational approximation is introduced which in the first order approximation gives the same order of accuracy as a practically exact shape function. The integrations can be made analytically in the complex plane and the method is therefore very fast compared to purely numerical integrations. The method can be applied both to statistically correlated and uncorrelated resonances
Energy Technology Data Exchange (ETDEWEB)
Haeggblom, H
1968-08-15
The method of calculating the resonance interaction effect by series expansions has been studied. Starting from the assumption that the neutron flux in a homogeneous mixture is inversely proportional to the total cross section, the expression for the flux can be simplified by series expansions. Two types of expansions are investigated and it is shown that only one of them is generally applicable. It is also shown that this expansion gives sufficient accuracy if the approximate resonance line shape function is reasonably representative. An investigation is made of the approximation of the resonance shape function with a Gaussian function which in some cases has been used to calculate the interaction effect. It is shown that this approximation is not sufficiently accurate in all cases which can occur in practice. Then, a rational approximation is introduced which in the first order approximation gives the same order of accuracy as a practically exact shape function. The integrations can be made analytically in the complex plane and the method is therefore very fast compared to purely numerical integrations. The method can be applied both to statistically correlated and uncorrelated resonances.
Bridge density functional approximation for non-uniform hard core repulsive Yukawa fluid
International Nuclear Information System (INIS)
Zhou Shiqi
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. (condensed matter: structure, thermal and mechanical properties)
Balancing Exchange Mixing in Density-Functional Approximations for Iron Porphyrin.
Berryman, Victoria E J; Boyd, Russell J; Johnson, Erin R
2015-07-14
Predicting the correct ground-state multiplicity for iron(II) porphyrin, a high-spin quintet, remains a significant challenge for electronic-structure methods, including commonly employed density functionals. An even greater challenge for these methods is correctly predicting favorable binding of O2 to iron(II) porphyrin, due to the open-shell singlet character of the adduct. In this work, the performance of a modest set of contemporary density-functional approximations is assessed and the results interpreted using Bader delocalization indices. It is found that inclusion of greater proportions of Hartree-Fock exchange, in hybrid or range-separated hybrid functionals, has opposing effects; it improves the ability of the functional to identify the ground state but is detrimental to predicting favorable dioxygen binding. Because of the uncomplementary nature of these properties, accurate prediction of both the relative spin-state energies and the O2 binding enthalpy eludes conventional density-functional approximations.
Directory of Open Access Journals (Sweden)
Irina-Carmen ANDREI
2017-09-01
Full Text Available Following the demands of the design and performance analysis in case of liquid fuel propelled rocket engines, as well as the trajectory optimization, the development of efficient codes, which frequently need to call the Fuel Combustion Charts, became an important matter. This paper presents an efficient solution to the issue; the author has developed an original approach to determine the non-linear approximation function of two variables: the chamber pressure and the nozzle exit pressure ratio. The numerical algorithm based on this two variable approximation function is more efficient due to its simplicity, capability to providing numerical accuracy and prospects for an increased convergence rate of the optimization codes.
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.
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.
A full scale approximation of covariance functions for large spatial data sets
Sang, Huiyan; Huang, Jianhua Z.
2011-01-01
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.
Yang, Jingjing; Cox, Dennis D; Lee, Jong Soo; Ren, Peng; Choi, Taeryon
2017-12-01
Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected on discretized grids with measurement errors. In order to accurately smooth noisy functional observations and deal with the issue of high-dimensional observation grids, we propose a novel Bayesian method based on the Bayesian hierarchical model with a Gaussian-Wishart process prior and basis function representations. We first derive an induced model for the basis-function coefficients of the functional data, and then use this model to conduct posterior inference through Markov chain Monte Carlo methods. Compared to the standard Bayesian inference that suffers serious computational burden and instability in analyzing high-dimensional functional data, our method greatly improves the computational scalability and stability, while inheriting the advantage of simultaneously smoothing raw observations and estimating the mean-covariance functions in a nonparametric way. In addition, our method can naturally handle functional data observed on random or uncommon grids. Simulation and real studies demonstrate that our method produces similar results to those obtainable by the standard Bayesian inference with low-dimensional common grids, while efficiently smoothing and estimating functional data with random and high-dimensional observation grids when the standard Bayesian inference fails. In conclusion, our method can efficiently smooth and estimate high-dimensional functional data, providing one way to resolve the curse of dimensionality for Bayesian functional data analysis with Gaussian-Wishart processes. © 2017, The International Biometric Society.
CSIR Research Space (South Africa)
Kok, S
2012-07-01
Full Text Available continuously as the correlation function hyper-parameters approach zero. Since the global minimizer of the maximum likelihood function is an asymptote in this case, it is unclear if maximum likelihood estimation (MLE) remains valid. Numerical ill...
DEFF Research Database (Denmark)
Øjelund, Henrik; Sadegh, Payman
2000-01-01
be obtained. This paper presents a new approach for system modelling under partial (global) information (or the so called Gray-box modelling) that seeks to perserve the benefits of the global as well as local methodologies sithin a unified framework. While the proposed technique relies on local approximations......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...... 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....
A new formulation for the Doppler broadening function relaxing the approximations of Beth–Plackzec
International Nuclear Information System (INIS)
Palma, Daniel A.P.; Gonçalves, Alessandro C.; Martinez, Aquilino S.; Mesquita, Amir Z.
2016-01-01
Highlights: • One of the Beth–Placzek approximation were relaxed. • An additional term in the form of an integral is obtained. • A new mathematical formulation for the Doppler broadening function is proposed. - Abstract: In all nuclear reactors some neutrons can be absorbed in the resonance region and, in the design of these reactors, an accurate treatment of the resonant absorptions is essential. Apart from that, the resonant absorption varies with fuel temperature due to the Doppler broadening of the resonances. The thermal agitation movement in the reactor core is adequately represented in the microscopic cross-section of the neutron-core interaction through the Doppler broadening function. This function is calculated numerically in modern systems for the calculation of macro-group constants, necessary to determine the power distribution of a nuclear reactor. It can also be applied to the calculation of self-shielding factors to correct the measurements of the microscopic cross-sections through the activation technique and used for the approximate calculations of the resonance integrals in heterogeneous fuel cells. In these types of application we can point at the need to develop precise analytical approximations for the Doppler broadening function to be used in the calculation codes that calculate the values of this function. However, the Doppler broadening function is based on a series of approximations proposed by Beth–Plackzec. In this work a relaxation of these approximations is proposed, generating an additional term in the form of an integral. Analytical solutions of this additional term are discussed. The results obtained show that the new term is important for high temperatures.
On the functional integral approach in quantum statistics. 1. Some approximations
International Nuclear Information System (INIS)
Dai Xianxi.
1990-08-01
In this paper the susceptibility of a Kondo system in a fairly wide temperature region is calculated in the first harmonic approximation in a functional integral approach. The comparison with that of the renormalization group theory shows that in this region the two results agree quite well. The expansion of the partition function with infinite independent harmonics for the Anderson model is studied. Some symmetry relations are generalized. It is a challenging problem to develop a functional integral approach including diagram analysis, mixed mode effects and some exact relations in the Anderson system proved in the functional integral approach. These topics will be discussed in the next paper. (author). 22 refs, 1 fig
International Nuclear Information System (INIS)
Lublinsky, Michael
2004-01-01
A simple analytic expression for the nonsinglet structure function f NS is given. The expression is derived from the result of Ermolaev, Manaenkov, and Ryskin obtained by low x resummation of the quark ladder diagrams in the double logarithmic approximation of perturbative QCD
On the universality of MOG weak field approximation at galaxy cluster scale
Directory of Open Access Journals (Sweden)
Ivan De Martino
2017-07-01
Full Text Available In its weak field limit, Scalar-tensor-vector gravity theory introduces a Yukawa-correction to the gravitational potential. Such a correction depends on the two parameters, α which accounts for the modification of the gravitational constant, and μ⁎−1 which represents the scale length on which the scalar field propagates. These parameters were found to be universal when the modified gravitational potential was used to fit the galaxy rotation curves and the mass profiles of galaxy clusters, both without Dark Matter. We test the universality of these parameters using the temperature anisotropies due to the thermal Sunyaev–Zeldovich effect. In our model the intra-cluster gas is in hydrostatic equilibrium within the modified gravitational potential well and it is described by a polytropic equation of state. We predict the thermal Sunyaev–Zeldovich temperature anisotropies produced by Coma cluster, and we compare them with those obtained using the Planck 2013 Nominal maps. In our analysis, we find α and the scale length, respectively, to be consistent and to depart from their universal values. Our analysis points out that the assumption of the universality of the Yukawa-correction to the gravitational potential is ruled out at more than 3.5σ at galaxy clusters scale, while demonstrating that such a theory of gravity is capable to fit the cluster profile if the scale dependence of the gravitational potential is restored.
APPROX, 1-D and 2-D Function Approximation by Polynomials, Splines, Finite Elements Method
International Nuclear Information System (INIS)
Tollander, Bengt
1975-01-01
1 - Nature of physical problem solved: Approximates one- and two- dimensional functions using different forms of the approximating function, as polynomials, rational functions, Splines and (or) the finite element method. Different kinds of transformations of the dependent and (or) the independent variables can easily be made by data cards using a FORTRAN-like language. 2 - Method of solution: Approximations by polynomials, Splines and (or) the finite element method are made in L2 norm using the least square method by which the answer is directly given. For rational functions in one dimension the result given in L(infinite) norm is achieved by iterations moving the zero points of the error curve. For rational functions in two dimensions, the norm is L2 and the result is achieved by iteratively changing the coefficients of the denominator and then solving the coefficients of the numerator by the least square method. The transformation of the dependent and (or) independent variables is made by compiling the given transform data card(s) to an array of integers from which the transformation can be made
Piecewise quadratic Lyapunov functions for stability verification of approximate explicit MPC
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Morten Hovd
2010-04-01
Full Text Available Explicit MPC of constrained linear systems is known to result in a piecewise affine controller and therefore also piecewise affine closed loop dynamics. The complexity of such analytic formulations of the control law can grow exponentially with the prediction horizon. The suboptimal solutions offer a trade-off in terms of complexity and several approaches can be found in the literature for the construction of approximate MPC laws. In the present paper a piecewise quadratic (PWQ Lyapunov function is used for the stability verification of an of approximate explicit Model Predictive Control (MPC. A novel relaxation method is proposed for the LMI criteria on the Lyapunov function design. This relaxation is applicable to the design of PWQ Lyapunov functions for discrete-time piecewise affine systems in general.
Approximated calculation of the vacuum wave function and vacuum energy of the LGT with RPA method
International Nuclear Information System (INIS)
Hui Ping
2004-01-01
The coupled cluster method is improved with the random phase approximation (RPA) to calculate vacuum wave function and vacuum energy of 2 + 1 - D SU(2) lattice gauge theory. In this calculating, the trial wave function composes of single-hollow graphs. The calculated results of vacuum wave functions show very good scaling behaviors at weak coupling region l/g 2 >1.2 from the third order to the sixth order, and the vacuum energy obtained with RPA method is lower than the vacuum energy obtained without RPA method, which means that this method is a more efficient one
Zeng, Lang; He, Yu; Povolotskyi, Michael; Liu, XiaoYan; Klimeck, Gerhard; Kubis, Tillmann
2013-06-01
In this work, the low rank approximation concept is extended to the non-equilibrium Green's function (NEGF) method to achieve a very efficient approximated algorithm for coherent and incoherent electron transport. This new method is applied to inelastic transport in various semiconductor nanodevices. Detailed benchmarks with exact NEGF solutions show (1) a very good agreement between approximated and exact NEGF results, (2) a significant reduction of the required memory, and (3) a large reduction of the computational time (a factor of speed up as high as 150 times is observed). A non-recursive solution of the inelastic NEGF transport equations of a 1000 nm long resistor on standard hardware illustrates nicely the capability of this new method.
Deep-inelastic structure functions in an approximation to the bag theory
International Nuclear Information System (INIS)
Jaffe, R.L.
1975-01-01
A cavity approximation to the bag theory developed earlier is extended to the treatment of forward virtual Compton scattering. In the Bjorken limit and for small values of ω (ω = vertical-bar2p center-dot q/q 2 vertical-bar) it is argued that the operator nature of the bag boundaries might be ignored. Structure functions are calculated in one and three dimensions. Bjorken scaling is obtained. The model provides a realization of light-cone current algebra and possesses a parton interpretation. The structure functions show a quasielastic peak. The spreading of the structure functions about the peak is associated with confinement. As expected, Regge behavior is not obtained for large ω. The ''momentum sum rule'' is saturated, indicating that the hadron's charged constituents carry all the momentum in this model. νW/subL/ is found to scale and is calculable. Application of the model to the calculation of spin-dependent and chiral-symmetry--violating structure functions is proposed. The nature of the intermediate states in this approximation is discussed. Problems associated with the cavity approximation are also discussed
Two site spin correlation function in Bethe-Peierls approximation for Ising model
Energy Technology Data Exchange (ETDEWEB)
Kumar, D [Roorkee Univ. (India). Dept. of Physics
1976-07-01
Two site spin correlation function for an Ising model above Curie temperature has been calculated by generalising Bethe-Peierls approximation. The results derived by a graphical method due to Englert are essentially the same as those obtained earlier by Elliott and Marshall, and Oguchi and Ono. The earlier results were obtained by a direct generalisation of the cluster method of Bethe, while these results are derived by retaining that class of diagrams , which is exact on Bethe lattice.
APPROXIMATIONS TO THE USES OF TWITTER BY UNIVERSITY LIBRARIES IN ARGENTINA.
Directory of Open Access Journals (Sweden)
Claudia Nora Laudano
2016-07-01
Full Text Available This article analyses the main uses of the social media Twitter in university libraries in Argentina. After revising existing literature, we outline the research methods used to identify whether libraries are currently adopting Twitter and how it is being used. We focus on the following areas: the starting date of the activity, basic institutional data, visibility and access to Twitter from the library web, the quantity of tweets over time, those "followed" and those "following" and quantity and type of posts during the period of time selected for research. The results show that few libraries have used Twitter and their use of this media tool has generally been unplanned, mostly for spreading information rather than interaction. It also stresses that despite an extensive literature on what are considered good practices, generally they are not taken by the institutions. At last, we propose further research in this area to widen our knowledge of the daily use of Twitter among librarians.
The approximation function of bridge deck vibration derived from the measured eigenmodes
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Sokol Milan
2017-12-01
Full Text Available This article deals with a method of how to acquire approximate displacement vibration functions. Input values are discrete, experimentally obtained mode shapes. A new improved approximation method based on the modal vibrations of the deck is derived using the least-squares method. An alternative approach to be employed in this paper is to approximate the displacement vibration function by a sum of sine functions whose periodicity is determined by spectral analysis adapted for non-uniformly sampled data and where the parameters of scale and phase are estimated as usual by the least-squares method. Moreover, this periodic component is supplemented by a cubic regression spline (fitted on its residuals that captures individual displacements between piers. The statistical evaluation of the stiffness parameter is performed using more vertical modes obtained from experimental results. The previous method (Sokol and Flesch, 2005, which was derived for near the pier areas, has been enhanced to the whole length of the bridge. The experimental data describing the mode shapes are not appropriate for direct use. Especially the higher derivatives calculated from these data are very sensitive to data precision.
International Nuclear Information System (INIS)
D’Amore, L; Campagna, R; Murli, A; Galletti, A; Marcellino, L
2012-01-01
The scientific and application-oriented interest in the Laplace transform and its inversion is testified by more than 1000 publications in the last century. Most of the inversion algorithms available in the literature assume that the Laplace transform function is available everywhere. Unfortunately, such an assumption is not fulfilled in the applications of the Laplace transform. Very often, one only has a finite set of data and one wants to recover an estimate of the inverse Laplace function from that. We propose a fitting model of data. More precisely, given a finite set of measurements on the real axis, arising from an unknown Laplace transform function, we construct a dth degree generalized polynomial smoothing spline, where d = 2m − 1, such that internally to the data interval it is a dth degree polynomial complete smoothing spline minimizing a regularization functional, and outside the data interval, it mimics the Laplace transform asymptotic behavior, i.e. it is a rational or an exponential function (the end behavior model), and at the boundaries of the data set it joins with regularity up to order m − 1, with the end behavior model. We analyze in detail the generalized polynomial smoothing spline of degree d = 3. This choice was motivated by the (ill)conditioning of the numerical computation which strongly depends on the degree of the complete spline. We prove existence and uniqueness of this spline. We derive the approximation error and give a priori and computable bounds of it on the whole real axis. In such a way, the generalized polynomial smoothing spline may be used in any real inversion algorithm to compute an approximation of the inverse Laplace function. Experimental results concerning Laplace transform approximation, numerical inversion of the generalized polynomial smoothing spline and comparisons with the exponential smoothing spline conclude the work. (paper)
Long-range-corrected Rung 3.5 density functional approximations
Janesko, Benjamin G.; Proynov, Emil; Scalmani, Giovanni; Frisch, Michael J.
2018-03-01
Rung 3.5 functionals are a new class of approximations for density functional theory. They provide a flexible intermediate between exact (Hartree-Fock, HF) exchange and semilocal approximations for exchange. Existing Rung 3.5 functionals inherit semilocal functionals' limitations in atomic cores and density tails. Here we address those limitations using range-separated admixture of HF exchange. We present three new functionals. LRC-ωΠLDA combines long-range HF exchange with short-range Rung 3.5 ΠLDA exchange. SLC-ΠLDA combines short- and long-range HF exchange with middle-range ΠLDA exchange. LRC-ωΠLDA-AC incorporates a combination of HF, semilocal, and Rung 3.5 exchange in the short range, based on an adiabatic connection. We test these in a new Rung 3.5 implementation including up to analytic fourth derivatives. LRC-ωΠLDA and SLC-ΠLDA improve atomization energies and reaction barriers by a factor of 8 compared to the full-range ΠLDA. LRC-ωΠLDA-AC brings further improvement approaching the accuracy of standard long-range corrected schemes LC-ωPBE and SLC-PBE. The new functionals yield highest occupied orbital energies closer to experimental ionization potentials and describe correctly the weak charge-transfer complex of ethylene and dichlorine and the hole-spin distribution created by an Al defect in quartz. This study provides a framework for more flexible range-separated Rung 3.5 approximations.
Many-body perturbation theory using the density-functional concept: beyond the GW approximation
Bruneval, Fabien; Sottile, Francesco; Olevano, Valerio; Del Sole, Rodolfo; Reining, Lucia
2005-01-01
We propose an alternative formulation of Many-Body Perturbation Theory that uses the density-functional concept. Instead of the usual four-point integral equation for the polarizability, we obtain a two-point one, that leads to excellent optical absorption and energy loss spectra. The corresponding three-point vertex function and self-energy are then simply calculated via an integration, for any level of approximation. Moreover, we show the direct impact of this formulation on the time-depend...
International Nuclear Information System (INIS)
Lobanov, Yu.Yu.; Shidkov, E.P.
1987-01-01
The method for numerical evaluation of path integrals in Eucledean quantum mechanics without lattice discretization is elaborated. The method is based on the representation of these integrals in the form of functional integrals with respect to the conditional Wiener measure and on the use of the derived approximate exact on a class of polynomial functionals of a given degree. By the computations of non-perturbative characteristics, concerned the topological structure of vacuum, the advantages of this method versus lattice Monte-Carlo calculations are demonstrated
Exact solutions for fermionic Green's functions in the Bloch-Nordsieck approximation of QED
International Nuclear Information System (INIS)
Kernemann, A.; Stefanis, N.G.
1989-01-01
A set of new closed-form solutions for fermionic Green's functions in the Bloch-Nordsieck approximation of QED is presented. A manifestly covariant phase-space path-integral method is applied for calculating the n-fermion Green's function in a classical external field. In the case of one and two fermions, explicit expressions for the full Green's functions are analytically obtained, with renormalization carried out in the modified minimal subtraction scheme. The renormalization constants and the corresponding anomalous dimensions are determined. The mass-shell behavior of the two-fermion Green's function is investigated in detail. No assumptions are made concerning the structure of asymptotic states and no IR cutoff is used in the calculations
On Approximation of Hyper-geometric Function Values of a Special Class
Directory of Open Access Journals (Sweden)
P. L. Ivankov
2017-01-01
Full Text Available Investigations of arithmetic properties of the hyper-geometric function values make it possible to single out two trends, namely, Siegel’s method and methods based on the effective construction of a linear approximating form. There are also methods combining both approaches mentioned. The Siegel’s method allows obtaining the most general results concerning the abovementioned problems. In many cases it was used to establish the algebraic independence of the values of corresponding functions. Although the effective methods do not allow obtaining propositions of such generality they have nevertheless some advantages. Among these advantages one can distinguish at least two: a higher precision of the quantitative results obtained by effective methods and a possibility to study the hyper-geometric functions with irrational parameters.In this paper we apply the effective construction to estimate a measure of the linear independence of the hyper-geometric function values over the imaginary quadratic field. The functions themselves were chosen by a special way so that it could be possible to demonstrate a new approach to the effective construction of a linear approximating form. This approach makes it possible also to extend the well-known effective construction methods of the linear approximating forms for poly-logarithms to the functions of more general type.To obtain the arithmetic result we had to establish a linear independence of the functions under consideration over the field of rational functions. It is apparently impossible to apply directly known theorems containing sufficient (and in some cases needful and sufficient conditions for the system of functions appearing in the theorems mentioned. For this reason, a special technique has been developed to solve this problem.The paper presents the obtained arithmetic results concerning the values of integral functions, but, with appropriate alterations, the theorems proved can be adapted to
A universal approximation to grain size from images of non-cohesive sediment
Buscombe, D.; Rubin, D.M.; Warrick, J.A.
2010-01-01
The two-dimensional spectral decomposition of an image of sediment provides a direct statistical estimate, grid-by-number style, of the mean of all intermediate axes of all single particles within the image. We develop and test this new method which, unlike existing techniques, requires neither image processing algorithms for detection and measurement of individual grains, nor calibration. The only information required of the operator is the spatial resolution of the image. The method is tested with images of bed sediment from nine different sedimentary environments (five beaches, three rivers, and one continental shelf), across the range 0.1 mm to 150 mm, taken in air and underwater. Each population was photographed using a different camera and lighting conditions. We term it a “universal approximation” because it has produced accurate estimates for all populations we have tested it with, without calibration. We use three approaches (theory, computational experiments, and physical experiments) to both understand and explore the sensitivities and limits of this new method. Based on 443 samples, the root-mean-squared (RMS) error between size estimates from the new method and known mean grain size (obtained from point counts on the image) was found to be ±≈16%, with a 95% probability of estimates within ±31% of the true mean grain size (measured in a linear scale). The RMS error reduces to ≈11%, with a 95% probability of estimates within ±20% of the true mean grain size if point counts from a few images are used to correct bias for a specific population of sediment images. It thus appears it is transferable between sedimentary populations with different grain size, but factors such as particle shape and packing may introduce bias which may need to be calibrated for. For the first time, an attempt has been made to mathematically relate the spatial distribution of pixel intensity within the image of sediment to the grain size.
Combi, Carlo; Mantovani, Matteo; Sabaini, Alberto; Sala, Pietro; Amaddeo, Francesco; Moretti, Ugo; Pozzi, Giuseppe
2015-07-01
Functional dependencies (FDs) typically represent associations over facts stored by a database, such as "patients with the same symptom get the same therapy." In more recent years, some extensions have been introduced to represent both temporal constraints (temporal functional dependencies - TFDs), as "for any given month, patients with the same symptom must have the same therapy, but their therapy may change from one month to the next one," and approximate properties (approximate functional dependencies - AFDs), as "patients with the same symptomgenerallyhave the same therapy." An AFD holds most of the facts stored by the database, enabling some data to deviate from the defined property: the percentage of data which violate the given property is user-defined. According to this scenario, in this paper we introduce approximate temporal functional dependencies (ATFDs) and use them to mine clinical data. Specifically, we considered the need for deriving new knowledge from psychiatric and pharmacovigilance data. ATFDs may be defined and measured either on temporal granules (e.g.grouping data by day, week, month, year) or on sliding windows (e.g.a fixed-length time interval which moves over the time axis): in this regard, we propose and discuss some specific and efficient data mining techniques for ATFDs. We also developed two running prototypes and showed the feasibility of our proposal by mining two real-world clinical data sets. The clinical interest of the dependencies derived considering the psychiatry and pharmacovigilance domains confirms the soundness and the usefulness of the proposed techniques. Copyright © 2014 Elsevier Ltd. All rights reserved.
Eikonal Approximation in AdS/CFT From Shock Waves to Four-Point Functions
Cornalba, L; Costa, Miguel S; Penedones, Joao; Cornalba, Lorenzo; Costa, M S; Penedones, J; Schiappa, Ricardo
2007-01-01
We initiate a program to generalize the standard eikonal approximation to compute amplitudes in Anti-de Sitter spacetimes. Inspired by the shock wave derivation of the eikonal amplitude in flat space, we study the two-point function E ~ _{shock} in the presence of a shock wave in Anti-de Sitter, where O_1 is a scalar primary operator in the dual conformal field theory. At tree level in the gravitational coupling, we relate the shock two-point function E to the discontinuity across a kinematical branch cut of the conformal field theory four-point function A ~ , where O_2 creates the shock geometry in Anti-de Sitter. Finally, we extend the above results by computing E in the presence of shock waves along the horizon of Schwarzschild BTZ black holes. This work gives new tools for the study of Planckian physics in Anti-de Sitter spacetimes.
Spherical Bessel transform via exponential sum approximation of spherical Bessel function
Ikeno, Hidekazu
2018-02-01
A new algorithm for numerical evaluation of spherical Bessel transform is proposed in this paper. In this method, the spherical Bessel function is approximately represented as an exponential sum with complex parameters. This is obtained by expressing an integral representation of spherical Bessel function in complex plane, and discretizing contour integrals along steepest descent paths and a contour path parallel to real axis using numerical quadrature rule with the double-exponential transformation. The number of terms in the expression is reduced using the modified balanced truncation method. The residual part of integrand is also expanded by exponential functions using Prony-like method. The spherical Bessel transform can be evaluated analytically on arbitrary points in half-open interval.
Efficient approximation of the incomplete gamma function for use in cloud model applications
Directory of Open Access Journals (Sweden)
U. Blahak
2010-07-01
Full Text Available This paper describes an approximation to the lower incomplete gamma function γ_{l}(a,x which has been obtained by nonlinear curve fitting. It comprises a fixed number of terms and yields moderate accuracy (the absolute approximation error of the corresponding normalized incomplete gamma function P is smaller than 0.02 in the range 0.9 ≤ a ≤ 45 and x≥0. Monotonicity and asymptotic behaviour of the original incomplete gamma function is preserved.
While providing a slight to moderate performance gain on scalar machines (depending on whether a stays the same for subsequent function evaluations or not compared to established and more accurate methods based on series- or continued fraction expansions with a variable number of terms, a big advantage over these more accurate methods is the applicability on vector CPUs. Here the fixed number of terms enables proper and efficient vectorization. The fixed number of terms might be also beneficial on massively parallel machines to avoid load imbalances, caused by a possibly vastly different number of terms in series expansions to reach convergence at different grid points. For many cloud microphysical applications, the provided moderate accuracy should be enough. However, on scalar machines and if a is the same for subsequent function evaluations, the most efficient method to evaluate incomplete gamma functions is perhaps interpolation of pre-computed regular lookup tables (most simple example: equidistant tables.
Guliyev , Namig; Ismailov , Vugar
2016-01-01
The possibility of approximating a continuous function on a compact subset of the real line by a feedforward single hidden layer neural network with a sigmoidal activation function has been studied in many papers. Such networks can approximate an arbitrary continuous function provided that an unlimited number of neurons in a hidden layer is permitted. In this paper, we consider constructive approximation on any finite interval of $\\mathbb{R}$ by neural networks with only one neuron in the hid...
International Nuclear Information System (INIS)
Huh, Jae Sung; Kwak, Byung Man
2011-01-01
Robust optimization or reliability-based design optimization are some of the methodologies that are employed to take into account the uncertainties of a system at the design stage. For applying such methodologies to solve industrial problems, accurate and efficient methods for estimating statistical moments and failure probability are required, and further, the results of sensitivity analysis, which is needed for searching direction during the optimization process, should also be accurate. The aim of this study is to employ the function approximation moment method into the sensitivity analysis formulation, which is expressed as an integral form, to verify the accuracy of the sensitivity results, and to solve a typical problem of reliability-based design optimization. These results are compared with those of other moment methods, and the feasibility of the function approximation moment method is verified. The sensitivity analysis formula with integral form is the efficient formulation for evaluating sensitivity because any additional function calculation is not needed provided the failure probability or statistical moments are calculated
Mejia-Rodriguez, Daniel; Trickey, S. B.
2017-11-01
We explore the simplification of widely used meta-generalized-gradient approximation (mGGA) exchange-correlation functionals to the Laplacian level of refinement by use of approximate kinetic-energy density functionals (KEDFs). Such deorbitalization is motivated by the prospect of reducing computational cost while recovering a strictly Kohn-Sham local potential framework (rather than the usual generalized Kohn-Sham treatment of mGGAs). A KEDF that has been rather successful in solid simulations proves to be inadequate for deorbitalization, but we produce other forms which, with parametrization to Kohn-Sham results (not experimental data) on a small training set, yield rather good results on standard molecular test sets when used to deorbitalize the meta-GGA made very simple, Tao-Perdew-Staroverov-Scuseria, and strongly constrained and appropriately normed functionals. We also study the difference between high-fidelity and best-performing deorbitalizations and discuss possible implications for use in ab initio molecular dynamics simulations of complicated condensed phase systems.
Energy Technology Data Exchange (ETDEWEB)
Rudolph, E [Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (F.R. Germany)
1975-01-01
As a model for gravitational radiation damping of a planet the electromagnetic radiation damping of an extended charged body moving in an external gravitational field is calculated in harmonic coordinates using a weak field, slowing-motion approximation. Special attention is paid to the case where this gravitational field is a weak Schwarzschild field. Using Green's function methods for this purpose it is shown that in a slow-motion approximation there is a strange connection between the tail part and the sharp part: radiation reaction terms of the tail part can cancel corresponding terms of the sharp part. Due to this cancelling mechanism the lowest order electromagnetic radiation damping force in an external gravitational field in harmonic coordinates remains the flat space Abraham Lorentz force. It is demonstrated in this simplified model that a naive slow-motion approximation may easily lead to divergent higher order terms. It is shown that this difficulty does not arise up to the considered order.
Fall with linear drag and Wien's displacement law: approximate solution and Lambert function
International Nuclear Information System (INIS)
Vial, Alexandre
2012-01-01
We present an approximate solution for the downward time of travel in the case of a mass falling with a linear drag force. We show how a quasi-analytical solution implying the Lambert function can be found. We also show that solving the previous problem is equivalent to the search for Wien's displacement law. These results can be of interest for undergraduate students, as they show that some transcendental equations found in physics may be solved without purely numerical methods. Moreover, as will be seen in the case of Wien's displacement law, solutions based on series expansion can be very accurate even with few terms. (paper)
A Method of Approximating Expectations of Functions of Sums of Independent Random Variables
Klass, Michael J.
1981-01-01
Let $X_1, X_2, \\cdots$ be a sequence of independent random variables with $S_n = \\sum^n_{i = 1} X_i$. Fix $\\alpha > 0$. Let $\\Phi(\\cdot)$ be a continuous, strictly increasing function on $\\lbrack 0, \\infty)$ such that $\\Phi(0) = 0$ and $\\Phi(cx) \\leq c^\\alpha\\Phi(x)$ for all $x > 0$ and all $c \\geq 2$. Suppose $a$ is a real number and $J$ is a finite nonempty subset of the positive integers. In this paper we are interested in approximating $E \\max_{j \\in J} \\Phi(|a + S_j|)$. We construct a nu...
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.
Garza, Alejandro J.
Perhaps the most important approximations to the electronic structure problem in quantum chemistry are those based on coupled cluster and density functional theories. Coupled cluster theory has been called the ``gold standard'' of quantum chemistry due to the high accuracy that it achieves for weakly correlated systems. Kohn-Sham density functionals based on semilocal approximations are, without a doubt, the most widely used methods in chemistry and material science because of their high accuracy/cost ratio. The root of the success of coupled cluster and density functionals is their ability to efficiently describe the dynamic part of the electron correlation. However, both traditional coupled cluster and density functional approximations may fail catastrophically when substantial static correlation is present. This severely limits the applicability of these methods to a plethora of important chemical and physical problems such as, e.g., the description of bond breaking, transition states, transition metal-, lanthanide- and actinide-containing compounds, and superconductivity. In an attempt to tackle this problem, nonstandard (single-reference) coupled cluster-based techniques that aim to describe static correlation have been recently developed: pair coupled cluster doubles (pCCD) and singlet-paired coupled cluster doubles (CCD0). The ability to describe static correlation in pCCD and CCD0 comes, however, at the expense of important amounts of dynamic correlation so that the high accuracy of standard coupled cluster becomes unattainable. Thus, the reliable and efficient description of static and dynamic correlation in a simultaneous manner remains an open problem for quantum chemistry and many-body theory in general. In this thesis, different ways to combine pCCD and CCD0 with density functionals in order to describe static and dynamic correlation simultaneously (and efficiently) are explored. The combination of wavefunction and density functional methods has a long
Impaired neural networks for approximate calculation in dyscalculic children: a functional MRI study
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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.
Hinuma, Yoyo; Hayashi, Hiroyuki; Kumagai, Yu; Tanaka, Isao; Oba, Fumiyasu
2017-09-01
High-throughput first-principles calculations based on density functional theory (DFT) are a powerful tool in data-oriented materials research. The choice of approximation to the exchange-correlation functional is crucial as it strongly affects the accuracy of DFT calculations. This study compares performance of seven approximations, six of which are based on Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) with and without Hubbard U and van der Waals corrections (PBE, PBE+U, PBED3, PBED3+U, PBEsol, and PBEsol+U), and the strongly constrained and appropriately normed (SCAN) meta-GGA on the energetics and crystal structure of elementary substances and binary oxides. For the latter, only those with closed-shell electronic structures are considered, examples of which include C u2O , A g2O , MgO, ZnO, CdO, SnO, PbO, A l2O3 , G a2O3 , I n2O3 , L a2O3 , B i2O3 , Si O2 , Sn O2 , Pb O2 , Ti O2 , Zr O2 , Hf O2 , V2O5 , N b2O5 , T a2O5 , Mo O3 , and W O3 . Prototype crystal structures are selected from the Inorganic Crystal Structure Database (ICSD) and cation substitution is used to make a set of existing and hypothetical oxides. Two indices are proposed to quantify the extent of lattice and internal coordinate relaxation during a calculation. The former is based on the second invariant and determinant of the transformation matrix of basis vectors from before relaxation to after relaxation, and the latter is derived from shifts of internal coordinates of atoms in the unit cell. PBED3, PBEsol, and SCAN reproduce experimental lattice parameters of elementary substances and oxides well with few outliers. Notably, PBEsol and SCAN predict the lattice parameters of low dimensional structures comparably well with PBED3, even though these two functionals do not explicitly treat van der Waals interactions. SCAN gives formation enthalpies and Gibbs free energies closest to experimental data, with mean errors (MEs) of 0.01 and -0.04 eV, respectively, and root
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.
Random phase approximations for the screening function in high Tc superconductors
International Nuclear Information System (INIS)
Lopez-Aguilar, F.; Costa-Quintana, J.; Sanchez, A.; Puig, T.; Aurell, M.T.; Martinez, L.M.; Munoz, J.S.
1990-01-01
This paper reports on the electronic transferences from the CuO 2 sheets toward the CuO 3 linear chain, which locate electrons in the orbitals p y /p z of O4/O1 and d z 2 -y 2 of Cu1, and holes in the orbitals d x 2 -y 2 - P z /p y of Cu2 - P2/O3. These holes states present large interatomic overlapping. In this paper, we determine the screening function within the random phase approximation applied to the high-T c superconductors. This screening function is vanishing for determined values of the frequency which correspond to renormalized plasmon frequencies. These frequencies depends on the band parameters and their knowledge is essential for determining the self energy. This self energy is deduced and it contain independent terms for each of the channels for the localization
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.
Global Approximations to Cost and Production Functions using Artificial Neural Networks
Directory of Open Access Journals (Sweden)
Efthymios G. Tsionas
2009-06-01
Full Text Available The estimation of cost and production functions in economics relies on standard specifications which are less than satisfactory in numerous situations. However, instead of fitting the data with a pre-specified model, Artificial Neural Networks (ANNs let the data itself serve as evidence to support the modelrs estimation of the underlying process. In this context, the proposed approach combines the strengths of economics, statistics and machine learning research and the paper proposes a global approximation to arbitrary cost and production functions, respectively, given by ANNs. Suggestions on implementation are proposed and empirical application relies on standard techniques. All relevant measures such as Returns to Scale (RTS and Total Factor Productivity (TFP may be computed routinely.
Single image super-resolution based on approximated Heaviside functions and iterative refinement
Wang, Xin-Yu; Huang, Ting-Zhu; Deng, Liang-Jian
2018-01-01
One method of solving the single-image super-resolution problem is to use Heaviside functions. This has been done previously by making a binary classification of image components as “smooth” and “non-smooth”, describing these with approximated Heaviside functions (AHFs), and iteration including l1 regularization. We now introduce a new method in which the binary classification of image components is extended to different degrees of smoothness and non-smoothness, these components being represented by various classes of AHFs. Taking into account the sparsity of the non-smooth components, their coefficients are l1 regularized. In addition, to pick up more image details, the new method uses an iterative refinement for the residuals between the original low-resolution input and the downsampled resulting image. Experimental results showed that the new method is superior to the original AHF method and to four other published methods. PMID:29329298
Shiju, S.; Sumitra, S.
2017-12-01
In this paper, the multiple kernel learning (MKL) is formulated as a supervised classification problem. We dealt with binary classification data and hence the data modelling problem involves the computation of two decision boundaries of which one related with that of kernel learning and the other with that of input data. In our approach, they are found with the aid of a single cost function by constructing a global reproducing kernel Hilbert space (RKHS) as the direct sum of the RKHSs corresponding to the decision boundaries of kernel learning and input data and searching that function from the global RKHS, which can be represented as the direct sum of the decision boundaries under consideration. In our experimental analysis, the proposed model had shown superior performance in comparison with that of existing two stage function approximation formulation of MKL, where the decision functions of kernel learning and input data are found separately using two different cost functions. This is due to the fact that single stage representation helps the knowledge transfer between the computation procedures for finding the decision boundaries of kernel learning and input data, which inturn boosts the generalisation capacity of the model.
International Nuclear Information System (INIS)
Galatolo, Stefano; Monge, Maurizio; Nisoli, Isaia
2016-01-01
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. (paper)
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 L 1 norm or even sub-linear potentials corresponding to quasinorms L p (0application 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.
The problem of the universal density functional and the density matrix functional theory
International Nuclear Information System (INIS)
Bobrov, V. B.; Trigger, S. A.
2013-01-01
The analysis in this paper shows that the Hohenberg-Kohn theorem is the constellation of two statements: (i) the mathematically rigorous Hohenberg-Kohn lemma, which demonstrates that the same ground-state density cannot correspond to two different potentials of an external field, and (ii) the hypothesis of the existence of the universal density functional. Based on the obtained explicit expression for the nonrel-ativistic particle energy in a local external field, we prove that the energy of the system of more than two non-interacting electrons cannot be a functional of the inhomogeneous density. This result is generalized to the system of interacting electrons. It means that the Hohenberg-Kohn lemma cannot provide justification of the universal density functional for fermions. At the same time, statements of the density functional theory remain valid when considering any number of noninteracting ground-state bosons due to the Bose condensation effect. In the framework of the density matrix functional theory, the hypothesis of the existence of the universal density matrix functional corresponds to the cases of noninteracting particles and to interaction in the Hartree-Fock approximation.
Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng
2018-03-01
In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.
Ito, Kazufumi; Teglas, Russell
1987-01-01
The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.
Ito, K.; Teglas, R.
1984-01-01
The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.
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.
Salajegheh, Maral; Nejad, S. Mohammad Moosavi; Khanpour, Hamzeh; Tehrani, S. Atashbar
2018-05-01
In this paper, we present SMKA18 analysis, which is a first attempt to extract the set of next-to-next-leading-order (NNLO) spin-dependent parton distribution functions (spin-dependent PDFs) and their uncertainties determined through the Laplace transform technique and Jacobi polynomial approach. Using the Laplace transformations, we present an analytical solution for the spin-dependent Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NNLO approximation. The results are extracted using a wide range of proton g1p(x ,Q2) , neutron g1n(x ,Q2) , and deuteron g1d(x ,Q2) spin-dependent structure functions data set including the most recent high-precision measurements from COMPASS16 experiments at CERN, which are playing an increasingly important role in global spin-dependent fits. The careful estimations of uncertainties have been done using the standard Hessian error propagation. We will compare our results with the available spin-dependent inclusive deep inelastic scattering data set and other results for the spin-dependent PDFs in literature. The results obtained for the spin-dependent PDFs as well as spin-dependent structure functions are clearly explained both in the small and large values of x .
International Nuclear Information System (INIS)
Wyatt, Robert E.; Kouri, Donald J.; Hoffman, David K.
2000-01-01
The quantum trajectory method (QTM) was recently developed to solve the hydrodynamic equations of motion in the Lagrangian, moving-with-the-fluid, picture. In this approach, trajectories are integrated for N fluid elements (particles) moving under the influence of both the force from the potential surface and from the quantum potential. In this study, distributed approximating functionals (DAFs) are used on a uniform grid to compute the necessary derivatives in the equations of motion. Transformations between the physical grid where the particle coordinates are defined and the uniform grid are handled through a Jacobian, which is also computed using DAFs. A difficult problem associated with computing derivatives on finite grids is the edge problem. This is handled effectively by using DAFs within a least squares approach to extrapolate from the known function region into the neighboring regions. The QTM-DAF is then applied to wave packet transmission through a one-dimensional Eckart potential. Emphasis is placed upon computation of the transmitted density and wave function. A problem that develops when part of the wave packet reflects back into the reactant region is avoided in this study by introducing a potential ramp to sweep the reflected particles away from the barrier region. (c) 2000 American Institute of Physics
Use of universal functional optimisation for TL glow curve analysis
International Nuclear Information System (INIS)
Pernicka, F.; Linh, H.Q.
1996-01-01
The effective use of any TL instrument requires an efficient software package to be able to fulfil different tasks required by research and practical applications. One of the standard features of the package used at the NPI Prague is the application of the interactive modular system Universal Functional Optimisation (UFO) for glow curve deconvolution. The whole system has been tested on standard glow curves using different models of the TL process (a single peak described by the Podgorsak approximation, first order kinetics and/or general order kinetics). Calculated values of basic TL parameters (E and s) show a good agreement with the results obtained by other authors. The main advantage of the system is in its modularity that enables flexible changes in the TL model and mathematical procedures of the glow curve analysis. (author)
International Nuclear Information System (INIS)
Askar, S.S.; Alnowibet, K.
2016-01-01
Isoelastic demand function have been used in literature to study the dynamic features of systems constructed based on economic market structure. In this paper, we adopt the so-called Cobb–Douglas production function and study its impact on the steady state of an oligopolistic game that consists of four oligopolistic competitors or firms. Briefly, the paper handles three different scenarios. The first scenario introduces four oligopolistic firms who plays rational against each other in market. The firms use the myopic mechanism (or bounded rational) to update their production in the next time unit. The steady state of the obtained system in this scenario, which is the Nash equilibrium, is unique and its characteristics are investigated. Based on a local monopolistic approximation (LMA) strategy, one competitor prefers to play against the three rational firms and this is illustrated in the second scenario. The last scenario discusses the case when three competitors use the LMA strategy against a rational one. For all scenarios discrete dynamical systems are used to describe the game introduced in all scenarios. The stability analysis of the Nash equilibrium is investigated analytically and some numerical simulations are used to confirm the obtained analytical results.
A point-value enhanced finite volume method based on approximate delta functions
Xuan, Li-Jun; Majdalani, Joseph
2018-02-01
We revisit the concept of an approximate delta function (ADF), introduced by Huynh (2011) [1], in the form of a finite-order polynomial that holds identical integral properties to the Dirac delta function when used in conjunction with a finite-order polynomial integrand over a finite domain. We show that the use of generic ADF polynomials can be effective at recovering and generalizing several high-order methods, including Taylor-based and nodal-based Discontinuous Galerkin methods, as well as the Correction Procedure via Reconstruction. Based on the ADF concept, we then proceed to formulate a Point-value enhanced Finite Volume (PFV) method, which stores and updates the cell-averaged values inside each element as well as the unknown quantities and, if needed, their derivatives on nodal points. The sharing of nodal information with surrounding elements saves the number of degrees of freedom compared to other compact methods at the same order. To ensure conservation, cell-averaged values are updated using an identical approach to that adopted in the finite volume method. Here, the updating of nodal values and their derivatives is achieved through an ADF concept that leverages all of the elements within the domain of integration that share the same nodal point. The resulting scheme is shown to be very stable at successively increasing orders. Both accuracy and stability of the PFV method are verified using a Fourier analysis and through applications to the linear wave and nonlinear Burgers' equations in one-dimensional space.
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.
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.
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.
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.
International Nuclear Information System (INIS)
Palma, Daniel A.; Goncalves, Alessandro C.; Martinez, Aquilino S.; Silva, Fernando C.
2008-01-01
The activation technique allows much more precise measurements of neutron intensity, relative or absolute. The technique requires the knowledge of the Doppler broadening function ψ(x,ξ) to determine the resonance self-shielding factors in the epithermal range G epi (τ,ξ). Two new analytical approximations for the Doppler broadening function ψ(x,ξ) are proposed. The approximations proposed are compared with other methods found in literature for the calculation of the ψ(x,ξ) function, that is, the 4-pole Pade method and the Frobenius method, when applied to the calculation of G epi (τ,ξ). The results obtained provided satisfactory accuracy. (authors)
Building a universal nuclear energy density functional
International Nuclear Information System (INIS)
Bertsch, G F
2007-01-01
This talk describes a new project in SciDAC II in the area of low-energy nuclear physics. The motivation and goals of the SciDAC are presented as well as an outline of the theoretical and computational methodology that will be employed. An important motivation is to have more accurate and reliable predictions of nuclear properties including their binding energies and low-energy reaction rates. The theoretical basis is provided by density functional theory, which the only available theory that can be systematically applied to all nuclei. However, other methodologies based on wave function methods are needed to refine the functionals and to make applications to dynamic processes
Wave function of the Universe as a leaking system
International Nuclear Information System (INIS)
Suen, W.; Young, K.
1989-01-01
We propose a path-integral formulation for the wave function of the Universe which requires neither the Euclidean nor the conformal rotation. The boundary condition is taken to be that ''all possible boundaries are included.'' The resulting wave function in a simple model is shown to have the following properties: (i) the wave function tends to zero as the scale factor of the Universe tends to zero; (ii) in the semiclassical regime, it contains only the expanding component; (iii) it favors inflation
Energy Technology Data Exchange (ETDEWEB)
Larin, S.A.; Ritbergen, T. van; Vermaseren, J.A.M.
1993-12-01
We obtain the analytic next-next-to-leading perturbative QCD corrections in the leading twist approximation for the moments N = 2, 4, 6, 8 of the non-singlet deep inelastic structure functions F{sub 2} and F{sub L}. We calculate the three-loop anomalous dimensions of the corresponding non-singlet operators and the three-loop coefficient functions of the structure function F{sub L}. (orig.).
International Nuclear Information System (INIS)
Larin, S.A.; Ritbergen, T. van; Vermaseren, J.A.M.
1993-12-01
We obtain the analytic next-next-to-leading perturbative QCD corrections in the leading twist approximation for the moments N = 2, 4, 6, 8 of the non-singlet deep inelastic structure functions F 2 and F L . We calculate the three-loop anomalous dimensions of the corresponding non-singlet operators and the three-loop coefficient functions of the structure function F L . (orig.)
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.
Gabor, A.F.; Ommeren, van J.C.W.
2006-01-01
In this article we focus on approximation algorithms for facility location problems with subadditive costs. As examples of such problems, we present three facility location problems with stochastic demand and exponential servers, respectively inventory. We present a (1+e,1)-reduction of the facility
Gabor, Adriana F.; van Ommeren, Jan C.W.
2006-01-01
In this article we focus on approximation algorithms for facility location problems with subadditive costs. As examples of such problems, we present three facility location problems with stochastic demand and exponential servers, respectively inventory. We present a $(1+\\varepsilon, 1)$-reduction of
Approximation algorithms for facility location problems with discrete subadditive cost functions
Gabor, A.F.; van Ommeren, Jan C.W.
2005-01-01
In this article we focus on approximation algorithms for facility location problems with subadditive costs. As examples of such problems, we present two facility location problems with stochastic demand and exponential servers, respectively inventory. We present a $(1+\\epsilon,1)$- reduction of the
International Nuclear Information System (INIS)
Tang Xiangyang; Hsieh Jiang
2007-01-01
A cone-angle-based window function is defined in this manuscript for image reconstruction using helical cone beam filtered backprojection (CB-FBP) algorithms. Rather than defining the window boundaries in a two-dimensional detector acquiring projection data for computed tomographic imaging, the cone-angle-based window function deals with data redundancy by selecting rays with the smallest cone angle relative to the reconstruction plane. To be computationally efficient, an asymptotic approximation of the cone-angle-based window function is also given and analyzed in this paper. The benefit of using such an asymptotic approximation also includes the avoidance of functional discontinuities that cause artifacts in reconstructed tomographic images. The cone-angle-based window function and its asymptotic approximation provide a way, equivalent to the Tam-Danielsson-window, for helical CB-FBP reconstruction algorithms to deal with data redundancy, regardless of where the helical pitch is constant or dynamically variable during a scan. By taking the cone-parallel geometry as an example, a computer simulation study is conducted to evaluate the proposed window function and its asymptotic approximation for helical CB-FBP reconstruction algorithm to handle data redundancy. The computer simulated Forbild head and thorax phantoms are utilized in the performance evaluation, showing that the proposed cone-angle-based window function and its asymptotic approximation can deal with data redundancy very well in cone beam image reconstruction from projection data acquired along helical source trajectories. Moreover, a numerical study carried out in this paper reveals that the proposed cone-angle-based window function is actually equivalent to the Tam-Danielsson-window, and rigorous mathematical proofs are being investigated
Energy Technology Data Exchange (ETDEWEB)
Palma, Daniel A.P. [Centro Federal de Educacao Tecnologica de Quimica de Nilopolis/RJ (CEFET), RJ (Brazil)]. E-mail: dpalma@cefeteq.br; Martinez, Aquilino S.; Silva, Fernando C. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear]. E-mail: aquilino@lmp.ufrj.br; fernando@lmn.con.ufrj.br
2005-07-01
An analytical approximation of the Doppler broadening function {psi}(x,{xi}) is proposed. This approximation is based on the solution of the differential equation for {psi}(x,{xi}) using the methods of Frobenius and the parameters variation. The analytical form derived for {psi}(x,{xi}) in terms of elementary functions is very simple and precise. It can be useful for applications related to the treatment of nuclear resonances mainly for the calculations of multigroup parameters and self-protection factors of the resonances, being the last used to correct microscopic cross-sections measurements by the activation technique. (author)
Building a Universal Nuclear Energy Density Functional
Energy Technology Data Exchange (ETDEWEB)
Carlson, Joe A. [Michigan State Univ., East Lansing, MI (United States); Furnstahl, Dick; Horoi, Mihai; Lust, Rusty; Nazaewicc, Witek; Ng, Esmond; Thompson, Ian; Vary, James
2012-12-30
During the period of Dec. 1 2006 – Jun. 30, 2012, the UNEDF collaboration carried out a comprehensive study of all nuclei, based on the most accurate knowledge of the strong nuclear interaction, the most reliable theoretical approaches, the most advanced algorithms, and extensive computational resources, with a view towards scaling to the petaflop platforms and beyond. The long-term vision initiated with UNEDF is to arrive at a comprehensive, quantitative, and unified description of nuclei and their reactions, grounded in the fundamental interactions between the constituent nucleons. We seek to replace current phenomenological models of nuclear structure and reactions with a well-founded microscopic theory that delivers maximum predictive power with well-quantified uncertainties. Specifically, the mission of this project has been three-fold: First, to find an optimal energy density functional (EDF) using all our knowledge of the nucleonic Hamiltonian and basic nuclear properties; Second, to apply the EDF theory and its extensions to validate the functional using all the available relevant nuclear structure and reaction data; Third, to apply the validated theory to properties of interest that cannot be measured, in particular the properties needed for reaction theory.
International Nuclear Information System (INIS)
Johnson, E.
1977-01-01
A theory for site-site pair distribution functions of molecular fluids is derived from the Ornstein-Zernike equation. Atom-atom pair distribution functions of this theory which were obtained by using different approximations for the Percus-Yevick site-site direct correlation functions are compared
Frydel, Derek; Ma, Manman
2016-06-01
Using the adiabatic connection, we formulate the free energy in terms of the correlation function of a fictitious system, h_{λ}(r,r^{'}), in which interactions λu(r,r^{'}) are gradually switched on as λ changes from 0 to 1. The function h_{λ}(r,r^{'}) is then obtained from the inhomogeneous Ornstein-Zernike equation and the two equations constitute a general liquid-state framework for treating inhomogeneous fluids. The two equations do not yet constitute a closed set. In the present work we use the closure c_{λ}(r,r^{'})≈-λβu(r,r^{'}), known as the random-phase approximation (RPA). We demonstrate that the RPA is identical with the variational Gaussian approximation derived within the field-theoretical framework, originally derived and used for charged particles. We apply our generalized RPA approximation to the Gaussian core model and Coulomb charges.
Tempel, David G; Aspuru-Guzik, Alán
2012-01-01
We prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practical standpoint this opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quantities (i.e. as density functionals). Additionally, we also demonstrate that TDDFT provides an exact prescription for simulating universal Hamiltonians with other universal Hamiltonians that have different, and possibly easier-to-realize two-qubit interactions. This establishes the foundations of TDDFT for quantum computation and opens the possibility of developing density functionals for use in quantum algorithms.
International Nuclear Information System (INIS)
Song Lina; Wang Weiguo
2010-01-01
In this Letter, an enhanced Adomian decomposition method which introduces the h-curve of the homotopy analysis method into the standard Adomian decomposition method is proposed. Some examples prove that this method can derive successfully approximate rational Jacobi elliptic function solutions of the fractional differential equations.
International Nuclear Information System (INIS)
Lublinsky, M.
2004-01-01
A simple analytic expression for the non-singlet structure function fns is given. The expression is derived from the result of B. I. Ermolaev et al. (1996) obtained by low x resummation of the quark ladder diagrams in the double logarithmic approximation of perturbative QCD. (orig.)
Rosolen, A.; Peco, C.; Arroyo, M.
2013-01-01
We present an adaptive meshfree method to approximate phase-field models of biomembranes. In such models, the Helfrich curvature elastic energy, the surface area, and the enclosed volume of a vesicle are written as functionals of a continuous phase-field, which describes the interface in a smeared manner. Such functionals involve up to second-order spatial derivatives of the phase-field, leading to fourth-order Euler–Lagrange partial differential equations (PDE). The solutions develop sharp i...
Csordás, András; Graham, Robert; Szépfalusy, Péter
1997-01-01
The Bogoliubov equations of the quasi-particle excitations in a weakly interacting trapped Bose-condensate are solved in the WKB approximation in an isotropic harmonic trap, determining the discrete quasi-particle energies and wave functions by torus (Bohr-Sommerfeld) quantization of the integrable classical quasi-particle dynamics. The results are used to calculate the position and strengths of the peaks in the dynamic structure function which can be observed by off-resonance inelastic light...
Uniform approximations of Bernoulli and Euler polynomials in terms of hyperbolic functions
J.L. López; N.M. Temme (Nico)
1998-01-01
textabstractBernoulli and Euler polynomials are considered for large values of the order. Convergent expansions are obtained for $B_n(nz+1/2)$ and $E_n(nz+1/2)$ in powers of $n^{-1$, with coefficients being rational functions of $z$ and hyperbolic functions of argument $1/2z$. These expansions are
Directory of Open Access Journals (Sweden)
Juana Rubio Romero
2015-07-01
Full Text Available This paper pretends to understand the success of the WhatsApp phenomenon among the university youths, exploring the keys of its conquest, and also the attitudes provoked by its use when compared with other commonly used virtual communication systems. In order to do that, apart from carrying out a review of reports and studies on this issue, this study is based on the results obtained from the qualitative Observatory Youth and Communication at Nebrija University and on a research ad hoc based on interviews and group dynamics with university youths.
Mobile heterotopia: movement, circulation and the function of the university
Directory of Open Access Journals (Sweden)
Bradley Rink
Full Text Available This paper explores the function of the university through the lens of mobility as seen from a South African perspective. Understanding the role of the university as one that requires the movement and circulation of academic bodies in the form of students and staff, and bodies of academic knowledge in the form of teaching, research and academic content, I use a theoretical framework from the interdisciplinary field of mobilities in order to understand the role of movement in the university and to highlight what is ruptured and catalysed by frictions enacted through power geometry, austerity and disruption. Sighted from the perspective of the University of the Western Cape in South Africa, this paper poses a series of provocations that reveal the obligations of presence that comprise the production and transfer of knowledge in the twenty-first-century university. I discuss how disruption and austerity, amongst other embedded mobility limitations, impact on the multiple/intersecting universes of the university; how the austere and disrupted university influences our engagement at various scales from local to global; and, finally, how disruption and austerity act to fix academic bodies in place even as they may allow virtual mobility to replace the face-to-face engagement that is the hallmark of the academic project. This paper demonstrates the critical role of mobility in the institution of the university and concludes that the university is a form of Foucauldian heterotopia mobilising diverse academic bodies and bodies of knowledge.
International Nuclear Information System (INIS)
Jung, J.; Alvarellos, J.E.; Garcia-Gonzalez, P.; Godby, R.W.
2004-01-01
The complex nature of electron-electron correlations is made manifest in the very simple but nontrivial problem of two electrons confined within a sphere. The description of highly nonlocal correlation and self-interaction effects by widely used local and semilocal exchange-correlation energy density functionals is shown to be unsatisfactory in most cases. Even the best such functionals exhibit significant errors in the Kohn-Sham potentials and density profiles
Juana Rubio Romero; Marta Perlado Lamo de Espinosa
2015-01-01
This paper pretends to understand the success of the WhatsApp phenomenon among the university youths, exploring the keys of its conquest, and also the attitudes provoked by its use when compared with other commonly used virtual communication systems. In order to do that, apart from carrying out a review of reports and studies on this issue, this study is based on the results obtained from the qualitative Observatory Youth and Communication at Nebrija University and on a research ad hoc based ...
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.
Energy Technology Data Exchange (ETDEWEB)
Palma, Daniel A. [CEFET QUIMICA de Nilopolis/RJ, Rio de Janeiro (Brazil); Goncalves, Alessandro C.; Martinez, Aquilino S.; Silva, Fernando C. [COPPE/UFRJ - Programa de Engenharia Nuclear, Rio de Janeiro (Brazil)
2008-07-01
The activation technique allows much more precise measurements of neutron intensity, relative or absolute. The technique requires the knowledge of the Doppler broadening function psi(x,xi) to determine the resonance self-shielding factors in the epithermal range G{sub epi} (tau,xi). Two new analytical approximations for the Doppler broadening function psi(x,xi) are proposed. The approximations proposed are compared with other methods found in literature for the calculation of the psi(x,xi) function, that is, the 4-pole Pade method and the Frobenius method, when applied to the calculation of G{sub epi} (tau,xi). The results obtained provided satisfactory accuracy. (authors)
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.
Fast generation of macro basis functions for LEGO through the adaptive cross approximation
Lancellotti, V.
2015-01-01
We present a method for the fast generation of macro basis functions in the context of the linear embedding via Green's operators approach (LEGO) which is a domain decomposition technique based on the combination of electromagnetic bricks in turn described by means of scattering operators. We show
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.
Kryven, I.; Röblitz, S; Schütte, C.
2015-01-01
Background: The chemical master equation is the fundamental equation of stochastic chemical kinetics. This differential-difference equation describes temporal evolution of the probability density function for states of a chemical system. A state of the system, usually encoded as a vector, represents
The Functions of Function Discourse--University Mathematics Teaching from a Commognitive Standpoint
Viirman, Olov
2014-01-01
This paper addresses a topic within university mathematics education which has been somewhat underexplored: the teaching practices actually used by university mathematics teachers when giving lectures. The study investigates the teaching practices of seven Swedish university teachers on the topic of functions using a discursive approach, the…
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.
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.
Short-distance behavior of the Bethe--Salpeter wave function in the ladder approximation
International Nuclear Information System (INIS)
Guth, A.H.; Soper, D.E.
1975-01-01
We investigate the short-distance behavior of the (Wick-rotated) Bethe--Salpeter wave function for the two spin-1/2 quarks bound by the exchange of a massive vector meson. We use the ladder-model kernel, which has the same p -4 scaling behavior as the true kernel in a theory with a fixed point of the renormalization group at g not equal to 0. For a bound state with the quantum numbers of the pion, the leading asymptotic behavior is chi (q/sup μ/) approx. cq/sup -4 + epsilon(g)/γ 5 , where epsilon (g) =1- (1-g 2 /π 2 ) 1 / 2 . Our method also provides the full asymptotic series, although it should be noted that the nonleading terms will depend on the nonleading behavior of the ladder-model kernel. A general term has the form cq - /sup a/(lnq)/sup n/phi (q/sup μ/), where c is an unknown constant, a may be integral or nonintegral, n is an integer, and phi (q/sup μ/) is a representation function of the rotation group in four dimensions
Bulk and interface dielectric functions: New results within the tight-binding approximation
International Nuclear Information System (INIS)
Elvira, V.D.; Duran, J.C.
1991-01-01
A tight-binding approach is used to analyze the dielectric behaviour of bulk semiconductors and semiconductor interfaces. This time interactions between second nearest neighbours are taken into account and several electrostatic models are proposed for the induced charge density around the atoms. The bulk dielectric function of different semiconductors (Si, Ge, GaAs and AlAs) are obtained and compared with other theoretical and experimental results. Finally, the energy band offset for GaAs-AlAs(1,0,0) interface is obtained and related to bulk properties of both semiconductors. The results presented in this paper show how the use of very simple but more realistic electrostatic models improve the analysis of the screening properties in semiconductors, giving a new support to the consistent tight-binding method for studying characteristics related to those properties. (Author)
Li, Chen; Requist, Ryan; Gross, E. K. U.
2018-02-01
We perform model calculations for a stretched LiF molecule, demonstrating that nonadiabatic charge transfer effects can be accurately and seamlessly described within a density functional framework. In alkali halides like LiF, there is an abrupt change in the ground state electronic distribution due to an electron transfer at a critical bond length R = Rc, where an avoided crossing of the lowest adiabatic potential energy surfaces calls the validity of the Born-Oppenheimer approximation into doubt. Modeling the R-dependent electronic structure of LiF within a two-site Hubbard model, we find that nonadiabatic electron-nuclear coupling produces a sizable elongation of the critical Rc by 0.5 bohr. This effect is very accurately captured by a simple and rigorously derived correction, with an M-1 prefactor, to the exchange-correlation potential in density functional theory, M = reduced nuclear mass. Since this nonadiabatic term depends on gradients of the nuclear wave function and conditional electronic density, ∇Rχ(R) and ∇Rn(r, R), it couples the Kohn-Sham equations at neighboring R points. Motivated by an observed localization of nonadiabatic effects in nuclear configuration space, we propose a local conditional density approximation—an approximation that reduces the search for nonadiabatic density functionals to the search for a single function y(n).
Directory of Open Access Journals (Sweden)
Jiameng Wu
2018-01-01
Full Text Available The infinite depth free surface Green function (GF and its high order derivatives for diffraction and radiation of water waves are considered. Especially second order derivatives are essential requirements in high-order panel method. In this paper, concerning the classical representation, composed of a semi-infinite integral involving a Bessel function and a Cauchy singularity, not only the GF and its first order derivatives but also second order derivatives are derived from four kinds of analytical series expansion and refined division of whole calculation domain. The approximations of special functions, particularly the hypergeometric function and the algorithmic applicability with different subdomains are implemented. As a result, the computation accuracy can reach 10-9 in whole domain compared with conventional methods based on direct numerical integration. Furthermore, numerical efficiency is almost equivalent to that with the classical method.
Mcclelland, J.; Silk, J.
1979-01-01
The evolution of the two-point correlation function for the large-scale distribution of galaxies in an expanding universe is studied on the assumption that the perturbation densities lie in a Gaussian distribution centered on any given mass scale. The perturbations are evolved according to the Friedmann equation, and the correlation function for the resulting distribution of perturbations at the present epoch is calculated. It is found that: (1) the computed correlation function gives a satisfactory fit to the observed function in cosmological models with a density parameter (Omega) of approximately unity, provided that a certain free parameter is suitably adjusted; (2) the power-law slope in the nonlinear regime reflects the initial fluctuation spectrum, provided that the density profile of individual perturbations declines more rapidly than the -2.4 power of distance; and (3) both positive and negative contributions to the correlation function are predicted for cosmological models with Omega less than unity.
Directory of Open Access Journals (Sweden)
Yanqi Hao
2015-07-01
Full Text Available Alternative splicing acts on transcripts from almost all human multi-exon genes. Notwithstanding its ubiquity, fundamental ramifications of splicing on protein expression remain unresolved. The number and identity of spliced transcripts that form stably folded proteins remain the sources of considerable debate, due largely to low coverage of experimental methods and the resulting absence of negative data. We circumvent this issue by developing a semi-supervised learning algorithm, positive unlabeled learning for splicing elucidation (PULSE; http://www.kimlab.org/software/pulse, which uses 48 features spanning various categories. We validated its accuracy on sets of bona fide protein isoforms and directly on mass spectrometry (MS spectra for an overall AU-ROC of 0.85. We predict that around 32% of “exon skipping” alternative splicing events produce stable proteins, suggesting that the process engenders a significant number of previously uncharacterized proteins. We also provide insights into the distribution of positive isoforms in various functional classes and into the structural effects of alternative splicing.
International Nuclear Information System (INIS)
Frishman, A.; Hoffman, D.K.; Kouri, D.J.
1997-01-01
We report a distributed approximating functional (DAF) fit of the ab initio potential-energy data of Liu [J. Chem. Phys. 58, 1925 (1973)] and Siegbahn and Liu [ibid. 68, 2457 (1978)]. The DAF-fit procedure is based on a variational principle, and is systematic and general. Only two adjustable parameters occur in the DAF leading to a fit which is both accurate (to the level inherent in the input data; RMS error of 0.2765 kcal/mol) and smooth (open-quotes well-tempered,close quotes in DAF terminology). In addition, the LSTH surface of Truhlar and Horowitz based on this same data [J. Chem. Phys. 68, 2466 (1978)] is itself approximated using only the values of the LSTH surface on the same grid coordinate points as the ab initio data, and the same DAF parameters. The purpose of this exercise is to demonstrate that the DAF delivers a well-tempered approximation to a known function that closely mimics the true potential-energy surface. As is to be expected, since there is only roundoff error present in the LSTH input data, even more significant figures of fitting accuracy are obtained. The RMS error of the DAF fit, of the LSTH surface at the input points, is 0.0274 kcal/mol, and a smooth fit, accurate to better than 1cm -1 , can be obtained using more than 287 input data points. copyright 1997 American Institute of Physics
Heßelmann, Andreas
2015-04-14
Molecular excitation energies have been calculated with time-dependent density-functional theory (TDDFT) using random-phase approximation Hessians augmented with exact exchange contributions in various orders. It has been observed that this approach yields fairly accurate local valence excitations if combined with accurate asymptotically corrected exchange-correlation potentials used in the ground-state Kohn-Sham calculations. The inclusion of long-range particle-particle with hole-hole interactions in the kernel leads to errors of 0.14 eV only for the lowest excitations of a selection of three alkene, three carbonyl, and five azabenzene molecules, thus surpassing the accuracy of a number of common TDDFT and even some wave function correlation methods. In the case of long-range charge-transfer excitations, the method typically underestimates accurate reference excitation energies by 8% on average, which is better than with standard hybrid-GGA functionals but worse compared to range-separated functional approximations.
The integration of quality management functions within a university ...
African Journals Online (AJOL)
According to a recent study, institutions of higher learning in South Africa fail to a great extent to integrate the key management functions that are fundamental to effective quality management. This article argues that the effective promotion of quality of a university's core business depends to a large extent on the ability of an ...
Gauss-Arnoldi quadrature for -1φ,φ> and rational Pade-type approximation for Markov-type functions
International Nuclear Information System (INIS)
Knizhnerman, L A
2008-01-01
The efficiency of Gauss-Arnoldi quadrature for the calculation of the quantity -1 φ,φ> is studied, where A is a bounded operator in a Hilbert space and φ is a non-trivial vector in this space. A necessary and a sufficient conditions are found for the efficiency of the quadrature in the case of a normal operator. An example of a non-normal operator for which this quadrature is inefficient is presented. It is shown that Gauss-Arnoldi quadrature is related in certain cases to rational Pade-type approximation (with the poles at Ritz numbers) for functions of Markov type and, in particular, can be used for the localization of the poles of a rational perturbation. Error estimates are found, which can also be used when classical Pade approximation does not work or it may not be efficient. Theoretical results and conjectures are illustrated by numerical experiments. Bibliography: 44 titles
Fujiwara, Takeo; Nishino, Shinya; Yamamoto, Susumu; Suzuki, Takashi; Ikeda, Minoru; Ohtani, Yasuaki
2018-06-01
A novel tight-binding method is developed, based on the extended Hückel approximation and charge self-consistency, with referring the band structure and the total energy of the local density approximation of the density functional theory. The parameters are so adjusted by computer that the result reproduces the band structure and the total energy, and the algorithm for determining parameters is established. The set of determined parameters is applicable to a variety of crystalline compounds and change of lattice constants, and, in other words, it is transferable. Examples are demonstrated for Si crystals of several crystalline structures varying lattice constants. Since the set of parameters is transferable, the present tight-binding method may be applicable also to molecular dynamics simulations of large-scale systems and long-time dynamical processes.
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.
Kwato-Njock, M G; Oumarou, B
2002-01-01
A search is conducted for the determination of expectation values of $r^q$ 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.
Vega Corona, Antonio; Zárate Banda, Magdalena; Barron Adame, Jose Miguel; Martínez Celorio, René Alfredo; Andina de la Fuente, Diego
2008-01-01
The present study describes the design of an Artificial Neural Network to synthesize the Approximation Function of a Pedometer for the Healthy Life Style Promotion. Experimentally, the approximation function is synthesized using three basic digital pedometers of low cost, these pedometers were calibrated with an advanced pedometer that calculates calories consumed and computes distance travelled with personal stride input. The synthesized approximation function by means of the designed neural...
Universal Probability Distribution Function for Bursty Transport in Plasma Turbulence
International Nuclear Information System (INIS)
Sandberg, I.; Benkadda, S.; Garbet, X.; Ropokis, G.; Hizanidis, K.; Castillo-Negrete, D. del
2009-01-01
Bursty transport phenomena associated with convective motion present universal statistical characteristics among different physical systems. In this Letter, a stochastic univariate model and the associated probability distribution function for the description of bursty transport in plasma turbulence is presented. The proposed stochastic process recovers the universal distribution of density fluctuations observed in plasma edge of several magnetic confinement devices and the remarkable scaling between their skewness S and kurtosis K. Similar statistical characteristics of variabilities have been also observed in other physical systems that are characterized by convection such as the x-ray fluctuations emitted by the Cygnus X-1 accretion disc plasmas and the sea surface temperature fluctuations.
International Nuclear Information System (INIS)
Kutzler, F.W.; Painter, G.S.
1992-01-01
A fully self-consistent series of nonlocal (gradient) density-functional calculations has been carried out using the augmented-Gaussian-orbital method to determine the magnitude of gradient corrections to the potential-energy curves of the first-row diatomics, Li 2 through F 2 . Both the Langreth-Mehl-Hu and the Perdew-Wang gradient-density functionals were used in calculations of the binding energy, bond length, and vibrational frequency for each dimer. Comparison with results obtained in the local-spin-density approximation (LSDA) using the Vosko-Wilk-Nusair functional, and with experiment, reveals that bond lengths and vibrational frequencies are rather insensitive to details of the gradient functionals, including self-consistency effects, but the gradient corrections reduce the overbinding commonly observed in the LSDA calculations of first-row diatomics (with the exception of Li 2 , the gradient-functional binding-energy error is only 50--12 % of the LSDA error). The improved binding energies result from a large differential energy lowering, which occurs in open-shell atoms relative to the diatomics. The stabilization of the atom arises from the use of nonspherical charge and spin densities in the gradient-functional calculations. This stabilization is negligibly small in LSDA calculations performed with nonspherical densities
Effects of Cigarettes Smoking on Pulmonary Function among University Students
Directory of Open Access Journals (Sweden)
Hariri Azian
2017-01-01
Full Text Available Pulmonary function testing is a physiological test that measures how an individual inhales or exhales volumes of air as a function of time. Smoking is greatly associated with reduction of pulmonary function. This research is aimed to estimate the values of peak expiratory flow (PEF, forced expiratory volume in first second (FEV1, forced vital capacity (FVC and ratio between FEV1/FVC among smoking and non-smoking students in Universiti Tun Hussein Onn Malaysia. Smoking is often related to obstructive disorder with low value of FVC, FEV1 and FEV1/FVC. These pulmonary functions were analyzed based on several variables such as; the number of cigarette smoked per day, duration of smoking, age, and body mass index (BMI values. 70 healthy volunteers consist of smoking and non- smoking students was selected through several sessions. Students were interviewed to answer questionnaire on demographic, lifestyles and their smoking habit. The pulmonary function tests were conducted according to American Thoracic Society (ATS standards. The results of the pulmonary functions were analyzed by using SPSS software to compare the pulmonary functions between the smoker and the non-smoker students. The results of the studies showed that the number of cigarettes smoked by respondent and the BMI values were the significant predictors of the decrease in FEV1/FVC values among university students
International Nuclear Information System (INIS)
Lorenzana, J.; Grynberg, M.D.; Yu, L.; Yonemitsu, K.; Bishop, A.R.
1992-11-01
The ground state energy, and static and dynamic correlation functions are investigated in the inhomogeneous Hartree-Fock (HF) plus random phase approximation (RPA) approach applied to a one-dimensional spinless fermion model showing self-trapped doping states at the mean field level. Results are compared with homogeneous HF and exact diagonalization. RPA fluctuations added to the generally inhomogeneous HF ground state allows the computation of dynamical correlation functions that compare well with exact diagonalization results. The RPA correction to the ground state energy agrees well with the exact results at strong and weak coupling limits. We also compare it with a related quasi-boson approach. The instability towards self-trapped behaviour is signaled by a RPA mode with frequency approaching zero. (author). 21 refs, 10 figs
Peck, Charles C.; Dhawan, Atam P.; Meyer, Claudia M.
1991-01-01
A genetic algorithm is used to select the inputs to a neural network function approximator. In the application considered, modeling critical parameters of the space shuttle main engine (SSME), the functional relationship between measured parameters is unknown and complex. Furthermore, the number of possible input parameters is quite large. Many approaches have been used for input selection, but they are either subjective or do not consider the complex multivariate relationships between parameters. Due to the optimization and space searching capabilities of genetic algorithms they were employed to systematize the input selection process. The results suggest that the genetic algorithm can generate parameter lists of high quality without the explicit use of problem domain knowledge. Suggestions for improving the performance of the input selection process are also provided.
Kataev, A. L.; Kazantsev, A. E.; Stepanyantz, K. V.
2018-01-01
We calculate the Adler D-function for N = 1 SQCD in the three-loop approximation using the higher covariant derivative regularization and the NSVZ-like subtraction scheme. The recently formulated all-order relation between the Adler function and the anomalous dimension of the matter superfields defined in terms of the bare coupling constant is first considered and generalized to the case of an arbitrary representation for the chiral matter superfields. The correctness of this all-order relation is explicitly verified at the three-loop level. The special renormalization scheme in which this all-order relation remains valid for the D-function and the anomalous dimension defined in terms of the renormalized coupling constant is constructed in the case of using the higher derivative regularization. The analytic expression for the Adler function for N = 1 SQCD is found in this scheme to the order O (αs2). The problem of scheme-dependence of the D-function and the NSVZ-like equation is briefly discussed.
Directory of Open Access Journals (Sweden)
A.L. Kataev
2018-01-01
Full Text Available We calculate the Adler D-function for N=1 SQCD in the three-loop approximation using the higher covariant derivative regularization and the NSVZ-like subtraction scheme. The recently formulated all-order relation between the Adler function and the anomalous dimension of the matter superfields defined in terms of the bare coupling constant is first considered and generalized to the case of an arbitrary representation for the chiral matter superfields. The correctness of this all-order relation is explicitly verified at the three-loop level. The special renormalization scheme in which this all-order relation remains valid for the D-function and the anomalous dimension defined in terms of the renormalized coupling constant is constructed in the case of using the higher derivative regularization. The analytic expression for the Adler function for N=1 SQCD is found in this scheme to the order O(αs2. The problem of scheme-dependence of the D-function and the NSVZ-like equation is briefly discussed.
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.
International Nuclear Information System (INIS)
Ribeiro, M.
2015-01-01
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
Tamosiunaite, Minija; Asfour, Tamim; Wörgötter, Florentin
2009-03-01
Reinforcement learning methods can be used in robotics applications especially for specific target-oriented problems, for example the reward-based recalibration of goal directed actions. To this end still relatively large and continuous state-action spaces need to be efficiently handled. The goal of this paper is, thus, to develop a novel, rather simple method which uses reinforcement learning with function approximation in conjunction with different reward-strategies for solving such problems. For the testing of our method, we use a four degree-of-freedom reaching problem in 3D-space simulated by a two-joint robot arm system with two DOF each. Function approximation is based on 4D, overlapping kernels (receptive fields) and the state-action space contains about 10,000 of these. Different types of reward structures are being compared, for example, reward-on- touching-only against reward-on-approach. Furthermore, forbidden joint configurations are punished. A continuous action space is used. In spite of a rather large number of states and the continuous action space these reward/punishment strategies allow the system to find a good solution usually within about 20 trials. The efficiency of our method demonstrated in this test scenario suggests that it might be possible to use it on a real robot for problems where mixed rewards can be defined in situations where other types of learning might be difficult.
Fromager, Emmanuel; Toulouse, Julien; Jensen, Hans Jørgen Aa.
2007-02-01
In many cases, the dynamic correlation can be calculated quite accurately and at a fairly low computational cost in Kohn-Sham density-functional theory (KS-DFT), using current standard approximate functionals. However, in general, KS-DFT does not treat static correlation effects (near degeneracy) adequately which, on the other hand, can be described in wave-function theory (WFT), for example, with a multiconfigurational self-consistent field (MCSCF) model. It is therefore of high interest to develop a hybrid model which combines the best of both WFT and DFT approaches. The merge of WFT and DFT can be achieved by splitting the two-electron interaction into long-range and short-range parts. The long-range part is then treated by WFT and the short-range part by DFT. In this work the authors consider the so-called "erf" long-range interaction erf(μr12)/r12, which is based on the standard error function, and where μ is a free parameter which controls the range of the long-/short-range decomposition. In order to formulate a general method, they propose a recipe for the definition of an optimal μopt parameter, which is independent of the approximate short-range functional and the approximate wave function, and they discuss its universality. Calculations on a test set consisting of He, Be, Ne, Mg, H2, N2, and H2O yield μopt≈0.4a.u.. A similar analysis on other types of test systems such as actinide compounds is currently in progress. Using the value of 0.4a.u. for μ, encouraging results are obtained with the hybrid MCSCF-DFT method for the dissociation energies of H2, N2, and H2O, with both short-range local-density approximation and PBE-type functionals.
Green's function for the scalar field in the early Universe
International Nuclear Information System (INIS)
Chowdhury, A.; Mallik, S.
1987-01-01
We derive the thermal Green's function for the scalar field in a de Sitter space-time and apply it to the problem of the early Universe. Field fluctuations relevant for inflation arise predominantly from wavelengths of the order of the inverse Hubble constant. Sufficient inflation is obtained in a Coleman-Weinberg model, provided the coupling constant is small enough. The results are insensitive to the choice of the vacuum of the field theory
Directory of Open Access Journals (Sweden)
HU Qi-guo
2017-01-01
Full Text Available For reducing the vehicle compartment low frequency noise, the Optimal Latin hypercube sampling method was applied to perform experimental design for sampling in the factorial design space. The thickness parameters of the panels with larger acoustic contribution was considered as factors, as well as the vehicle mass, seventh rank modal frequency of body, peak sound pressure of test point and sound pressure root-mean-square value as responses. By using the RBF(radial basis function neuro-network method, an approximation model of four responses about six factors was established. Further more, error analysis of established approximation model was performed in this paper. To optimize the panel’s thickness parameter, the adaptive simulated annealing algorithm was im-plemented. Optimization results show that the peak sound pressure of driver’s head was reduced by 4.45dB and 5.47dB at frequency 158HZ and 134Hz respec-tively. The test point pressure were significantly reduced at other frequency as well. The results indicate that through the optimization the vehicle interior cavity noise was reduced effectively, and the acoustical comfort of the vehicle was im-proved significantly.
THE MANAGEMENT AND CONTENT OF MANAGERIAL FUNCTIONS IN ROMANIAN UNIVERSITIES
Directory of Open Access Journals (Sweden)
AVRAM MARIOARA
2013-12-01
Full Text Available Although pan-European universities became autonomous institutions, their governance structure is still organized under the laws of each state, which expressly states the functions and management structures together with their attributions. For the past two years, the Romanian academic environment experienced a consistent reform. The old ground of the educative system was reinforced by the new Law of National Education which represented, for our country, the starting of the modernization of the academic education. By modifying the regulation framework, certain key-objectives were envisaged, such as: the modernization of higher education institutions management, reinforcing university autonomy and the public liability, insuring quality in academic education, enforcing measures for stating university ethics, competition financing, supporting performant private education, developing trans-borders cooperation, both at the Community level and globally. In the university management, the changes followed: a review of governance structures and leaving behind the traditional self-governance model, focusing on the new models, which re-distribute the decision making power and responsibilities between stakeholders, internal and external. Now, Romanian academic education can be found in the middle of the crossroad since the reform is not completed but must go on in order to improve educational results.
Coupling functions: Universal insights into dynamical interaction mechanisms
Stankovski, Tomislav; Pereira, Tiago; McClintock, Peter V. E.; Stefanovska, Aneta
2017-10-01
The dynamical systems found in nature are rarely isolated. Instead they interact and influence each other. The coupling functions that connect them contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how an interaction occurs. A coherent and comprehensive review is presented encompassing the rapid progress made recently in the analysis, understanding, and applications of coupling functions. The basic concepts and characteristics of coupling functions are presented through demonstrative examples of different domains, revealing the mechanisms and emphasizing their multivariate nature. The theory of coupling functions is discussed through gradually increasing complexity from strong and weak interactions to globally coupled systems and networks. A variety of methods that have been developed for the detection and reconstruction of coupling functions from measured data is described. These methods are based on different statistical techniques for dynamical inference. Stemming from physics, such methods are being applied in diverse areas of science and technology, including chemistry, biology, physiology, neuroscience, social sciences, mechanics, and secure communications. This breadth of application illustrates the universality of coupling functions for studying the interaction mechanisms of coupled dynamical systems.
International Nuclear Information System (INIS)
Al-Hawat, Sh; Naddaf, M
2005-01-01
The electron energy distribution function (EEDF) was determined from the second derivative of the I-V Langmuir probe characteristics and, thereafter, theoretically calculated by solving the plasma kinetic equation, using the black wall (BW) approximation, in the positive column of a neon glow discharge. The pressure has been varied from 0.5 to 4 Torr and the current from 10 to 30 mA. The measured electron temperature, density and electric field strength were used as input data for solving the kinetic equation. Comparisons were made between the EEDFs obtained from experiment, the BW approach, the Maxwellian distribution and the Rutcher solution of the kinetic equation in the elastic energy range. The best conditions for the BW approach are found to be under the discharge conditions: current density j d = 4.45 mA cm -2 and normalized electric field strength E/p = 1.88 V cm -1 Torr -1
Al-Hawat, Sh; Naddaf, M.
2005-04-01
The electron energy distribution function (EEDF) was determined from the second derivative of the I-V Langmuir probe characteristics and, thereafter, theoretically calculated by solving the plasma kinetic equation, using the black wall (BW) approximation, in the positive column of a neon glow discharge. The pressure has been varied from 0.5 to 4 Torr and the current from 10 to 30 mA. The measured electron temperature, density and electric field strength were used as input data for solving the kinetic equation. Comparisons were made between the EEDFs obtained from experiment, the BW approach, the Maxwellian distribution and the Rutcher solution of the kinetic equation in the elastic energy range. The best conditions for the BW approach are found to be under the discharge conditions: current density jd = 4.45 mA cm-2 and normalized electric field strength E/p = 1.88 V cm-1 Torr-1.
International Nuclear Information System (INIS)
Dalmasse, Kevin; Nychka, Douglas W.; Gibson, Sarah E.; Fan, Yuhong; Flyer, Natasha
2016-01-01
The Coronal Multichannel Polarimeter (CoMP) routinely performs coronal polarimetric measurements using the Fe XIII 10747 and 10798 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 analog. Speed and efficiency are obtained by combining sparse evaluation of the magnetic model with radial-basis-function (RBF) decomposition of the log-likelihood function. The RBF decomposition provides an analytical expression for the log-likelihood function that is used to inexpensively estimate the set of parameter values optimizing it. We test and validate ROAM on a synthetic test bed of a coronal magnetic flux rope and show that it performs well with a significantly sparse sample of the parameter space. We conclude that our optimization method is well-suited for fast and efficient model-data fitting and can be exploited for converting coronal polarimetric measurements, such as the ones provided by CoMP, into coronal magnetic field data.
International Nuclear Information System (INIS)
Ginsburg, C.A.
1980-01-01
In many problems, a desired property A of a function f(x) is determined by the behaviour of f(x) approximately equal to g(x,A) as x→xsup(*). In this letter, a method for resuming the power series in x of f(x) and approximating A (modulated Pade approximant) is presented. This new approximant is an extension of a resumation method for f(x) in terms of rational functions. (author)
Universal Spatial Correlation Functions for Describing and Reconstructing Soil Microstructure
Skvortsova, Elena B.; Mallants, Dirk
2015-01-01
Structural features of porous materials such as soil define the majority of its physical properties, including water infiltration and redistribution, multi-phase flow (e.g. simultaneous water/air flow, or gas exchange between biologically active soil root zone and atmosphere) and solute transport. To characterize soil microstructure, conventional soil science uses such metrics as pore size and pore-size distributions and thin section-derived morphological indicators. However, these descriptors provide only limited amount of information about the complex arrangement of soil structure and have limited capability to reconstruct structural features or predict physical properties. We introduce three different spatial correlation functions as a comprehensive tool to characterize soil microstructure: 1) two-point probability functions, 2) linear functions, and 3) two-point cluster functions. This novel approach was tested on thin-sections (2.21×2.21 cm2) representing eight soils with different pore space configurations. The two-point probability and linear correlation functions were subsequently used as a part of simulated annealing optimization procedures to reconstruct soil structure. Comparison of original and reconstructed images was based on morphological characteristics, cluster correlation functions, total number of pores and pore-size distribution. Results showed excellent agreement for soils with isolated pores, but relatively poor correspondence for soils exhibiting dual-porosity features (i.e. superposition of pores and micro-cracks). Insufficient information content in the correlation function sets used for reconstruction may have contributed to the observed discrepancies. Improved reconstructions may be obtained by adding cluster and other correlation functions into reconstruction sets. Correlation functions and the associated stochastic reconstruction algorithms introduced here are universally applicable in soil science, such as for soil classification
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......, due to this difference, it is possible to provide arguments favoring the method of Longstaff and Schwartz. Finally, we compare the methods in a realistic numerical setting and show that practitioners would do well to choose the method of Longstaff and Schwartz instead of the methods of Carriere...
International Nuclear Information System (INIS)
Bricka, M.
1962-03-01
This report addresses the problem of determination of neutron spectrum by using a set of detectors. The spectrum approximation method based on a polygonal function is more particularly studied. The author shows that the coefficients of the usual mathematical model can be simply formulated and assessed. The study of spectra approximation by a polygonal function shows that dose can be expressed by a linear function of the activity of the different detectors [fr
Executive functioning and alcohol binge drinking in university students.
Parada, María; Corral, Montserrat; Mota, Nayara; Crego, Alberto; Rodríguez Holguín, Socorro; Cadaveira, Fernando
2012-02-01
Binge drinking (BD) is prevalent among college students. Studies on alcoholism have shown that the prefrontal cortex is vulnerable to the neurotoxic effects of alcohol. The prefrontal cortex undergoes both structural and functional changes during adolescence and young adulthood. Sex differences have been observed in brain maturation and in alcohol-induced damage. The objective of the present study was to analyze the relationship between BD and cognitive functions subserved by the prefrontal cortex in male and female university students. The sample comprised 122 undergraduates (aged 18 to 20 years): 62 BD (30 females) and 60 non-BD (29 females). Executive functions were assessed by WMS-III (Backward Digit Span and Backward Spatial Span), SOPT (abstract designs), Letter Fluency (PMR), BADS (Zoo Map and Key Search) and WCST-3. BD students scored lower in the Backward Digit Span Subtest and generated more perseverative responses in the SOPT In relation to interaction BD by sex, BD males scored lower in the Backward Digit Span test than BD females and non-BD males. BD is associated with poorer performance of executive functions subserved by the dorsolateral prefrontal cortex. The results do not support enhanced vulnerability of women to alcohol neurotoxic effects. These difficulties may reflect developmental delay or frontal lobe dysfunction. Copyright © 2011 Elsevier Ltd. All rights reserved.
Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions
Cornalba, L; Penedones, J; Schiappa, R; Cornalba, Lorenzo; Costa, Miguel S.; Penedones, Joao; Schiappa, Ricardo
2007-01-01
We introduce the impact-parameter representation for conformal field theory correlators of the form A ~ . This representation is appropriate in the eikonal kinematical regime, and approximates the conformal partial-wave decomposition in the limit of large spin and dimension of the exchanged primary. Using recent results on the two-point function _{shock} in the presence of a shock wave in Anti-de Sitter, and its relation to the discontinuity of the four-point amplitude A across a kinematical branch-cut, we find the high spin and dimension conformal partial- wave decomposition of all tree-level Anti-de Sitter Witten diagrams. We show that, as in flat space, the eikonal kinematical regime is dominated by the T-channel exchange of the massless particle with highest spin (graviton dominance). We also compute the anomalous dimensions of the high-spin O_1 O_2 composites. Finally, we conjecture a formula re-summing crossed-ladder Witten diagrams to all orders in the gravitational coupling.
Perlt, Eva; Ray, Promit; Hansen, Andreas; Malberg, Friedrich; Grimme, Stefan; Kirchner, Barbara
2018-05-01
Ionic liquids raise interesting but complicated questions for theoretical investigations due to the fact that a number of different inter-molecular interactions, e.g., hydrogen bonding, long-range Coulomb interactions, and dispersion interactions, need to be described properly. Here, we present a detailed study on the ionic liquids ethylammonium nitrate and 1-ethyl-3-methylimidazolium acetate, in which we compare different dispersion corrected density functional approximations to accurate local coupled cluster data in static calculations on ionic liquid clusters. The efficient new composite method B97-3c is tested and has been implemented in CP2K for future studies. Furthermore, tight-binding based approaches which may be used in large scale simulations are assessed. Subsequently, ab initio as well as classical molecular dynamics simulations are conducted and structural analyses are presented in order to shed light on the different short- and long-range structural patterns depending on the method and the system size considered in the simulation. Our results indicate the presence of strong hydrogen bonds in ionic liquids as well as the aggregation of alkyl side chains due to dispersion interactions.
Energy Technology Data Exchange (ETDEWEB)
Al-Hawat, Sh; Naddaf, M [Physics Department, Atomic Energy Commission, PO Box 6091, Damascus (Syrian Arab Republic)
2005-04-21
The electron energy distribution function (EEDF) was determined from the second derivative of the I-V Langmuir probe characteristics and, thereafter, theoretically calculated by solving the plasma kinetic equation, using the black wall (BW) approximation, in the positive column of a neon glow discharge. The pressure has been varied from 0.5 to 4 Torr and the current from 10 to 30 mA. The measured electron temperature, density and electric field strength were used as input data for solving the kinetic equation. Comparisons were made between the EEDFs obtained from experiment, the BW approach, the Maxwellian distribution and the Rutcher solution of the kinetic equation in the elastic energy range. The best conditions for the BW approach are found to be under the discharge conditions: current density j{sub d} = 4.45 mA cm{sup -2} and normalized electric field strength E/p = 1.88 V cm{sup -1} Torr{sup -1}.
Eikonal approximation in AdS/CFT: Conformal partial waves and finite N four-point functions
International Nuclear Information System (INIS)
Cornalba, Lorenzo; Costa, Miguel S.; Penedones, Joao; Schiappa, Ricardo
2007-01-01
We introduce the impact parameter representation for conformal field theory correlators of the form A∼ 1 O 2 O 1 O 2 >. This representation is appropriate in the eikonal kinematical regime, and approximates the conformal partial wave decomposition in the limit of large spin and dimension of the exchanged primary. Using recent results on the two-point function 1 O 1 > shock in the presence of a shock wave in anti-de Sitter, and its relation to the discontinuity of the four-point amplitude A across a kinematical branch cut, we find the high spin and dimension conformal partial wave decomposition of all tree-level anti-de Sitter Witten diagrams. We show that, as in flat space, the eikonal kinematical regime is dominated by the T-channel exchange of the massless particle with highest spin (graviton dominance). We also compute the anomalous dimensions of the high spin O 1 O 2 composites. Finally, we conjecture a formula re-summing crossed-ladder Witten diagrams to all orders in the gravitational coupling
Li, Zhendong; Liu, Wenjian
2010-08-14
The spin-adaptation of single-reference quantum chemical methods for excited states of open-shell systems has been nontrivial. The primary reason is that the configuration space, generated by a truncated rank of excitations from only one component of a reference multiplet, is spin-incomplete. Those "missing" configurations are of higher ranks and can, in principle, be recaptured by a particular class of excitation operators. However, the resulting formalisms are then quite involved and there are situations [e.g., time-dependent density functional theory (TD-DFT) under the adiabatic approximation] that prevent one from doing so. To solve this issue, we propose here a tensor-coupling scheme that invokes all the components of a reference multiplet (i.e., a tensor reference) rather than increases the excitation ranks. A minimal spin-adapted n-tuply excited configuration space can readily be constructed by tensor products between the n-tuple tensor excitation operators and the chosen tensor reference. Further combined with the tensor equation-of-motion formalism, very compact expressions for excitation energies can be obtained. As a first application of this general idea, a spin-adapted open-shell random phase approximation is first developed. The so-called "translation rule" is then adopted to formulate a spin-adapted, restricted open-shell Kohn-Sham (ROKS)-based TD-DFT (ROKS-TD-DFT). Here, a particular symmetry structure has to be imposed on the exchange-correlation kernel. While the standard ROKS-TD-DFT can access only excited states due to singlet-coupled single excitations, i.e., only some of the singly excited states of the same spin (S(i)) as the reference, the new scheme can capture all the excited states of spin S(i)-1, S(i), or S(i)+1 due to both singlet- and triplet-coupled single excitations. The actual implementation and computation are very much like the (spin-contaminated) unrestricted Kohn-Sham-based TD-DFT. It is also shown that spin-contaminated spin
Approximations of Fuzzy Systems
Directory of Open Access Journals (Sweden)
Vinai K. Singh
2013-03-01
Full Text Available A fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy. Such results can be viewed as an existence of optimal fuzzy systems. Li-Xin Wang discussed a similar problem using Gaussian membership function and Stone-Weierstrass Theorem. He established that fuzzy systems, with product inference, centroid defuzzification and Gaussian functions are capable of approximating any real continuous function on a compact set to arbitrary accuracy. In this paper we study a similar approximation problem by using exponential membership functions
The universal wave function interpretation of string theory
International Nuclear Information System (INIS)
Gang, Dr. Sha Zhi; Xiu, Rulin
2016-01-01
In this work, we will show that a deeper understanding of space-time provided by both quantum physics and general relativity can lead to a new way to understand string theory. This new way of understanding and applying string theory, the universal wave function interpretation of string theory (UWFIST), may yield to a more powerful string theory and testable prediction. We will show how to derive UWFIST and what new result we can obtain from UWFIST. We will demonstrate that UWFIST indicates that the observed space-time and all phenomena are the projections from the world-sheet hologram. UWFIST provides the possible source for dark energy and dark matter and the explanation about why the dark energy and dark matter is beyond the detection of our current detector. We will show that UWFIST may also yield correct prediction of the cosmological constant to be of the order 10-121 in the unit of Planck scale. It may also help us understand and derive the energy source for inflation and the flatness of our observed 4-dimensional universe. UWFIST may also make other testable predictions that may be detected by interferometers. We conclude that UWFIST has the potential to make string theory a more powerful physics theory that can yield testable predictions. It is worth further investigation by more physicists
CONTRIBUTIONS TO RATIONAL APPROXIMATION,
Some of the key results of linear Chebyshev approximation theory are extended to generalized rational functions. Prominent among these is Haar’s...linear theorem which yields necessary and sufficient conditions for uniqueness. Some new results in the classic field of rational function Chebyshev...Furthermore a Weierstrass type theorem is proven for rational Chebyshev approximation. A characterization theorem for rational trigonometric Chebyshev approximation in terms of sign alternation is developed. (Author)
International Nuclear Information System (INIS)
De Backer, A; Sand, A; Ortiz, C J; Domain, C; Olsson, P; Berthod, E; Becquart, C S
2016-01-01
The damage produced by primary knock-on atoms (PKA) in W has been investigated from the threshold displacement energy (TDE) where it produces one self interstitial atom–vacancy pair to larger energies, up to 100 keV, where a large molten volume is formed. The TDE has been determined in different crystal directions using the Born–Oppenheimer density functional molecular dynamics (DFT-MD). A significant difference has been observed without and with the semi-core electrons. Classical MD has been used with two different empirical potentials characterized as ‘soft’ and ‘hard’ to obtain statistics on TDEs. Cascades of larger energy have been calculated, with these potentials, using a model that accounts for electronic losses (Sand et al 2013 Europhys. Lett. 103 46003). Two other sets of cascades have been produced using the binary collision approximation (BCA): a Monte Carlo BCA using SDTrimSP (Eckstein et al 2011 SDTrimSP: Version 5.00. Report IPP 12/8) (similar to SRIM www.srim.org) and MARLOWE (RSICC Home Page. (https://rsicc.ornl.gov/codes/psr/psr1/psr-137.html) (accessed May, 2014)). The comparison of these sets of cascades gave a recombination distance equal to 12 Å which is significantly larger from the one we reported in Hou et al (2010 J. Nucl. Mater. 403 89) because, here, we used bulk cascades rather than surface cascades which produce more defects (Stoller 2002 J. Nucl. Mater. 307 935, Nordlund et al 1999 Nature 398 49). Investigations on the defect clustering aspect showed that the difference between BCA and MD cascades is considerably reduced after the annealing of the cascade debris at 473 K using our Object Kinetic Monte Carlo model, LAKIMOCA (Domain et al 2004 J. Nucl. Mater. 335 121). (paper)
Exposure to air pollution and pulmonary function in university students.
Hong, Yun-Chul; Leem, Jong-Han; Lee, Kwan-Hee; Park, Dong-Hyun; Jang, Jae-Yeon; Kim, Sun-Tae; Ha, Eun-Hee
2005-03-01
Exposure to air pollution has been reported to be associated with increase in pulmonary disease. The aims of the present study were to examine the use of personal nitrogen dioxide (NO(2)) samplers as a means of measuring exposure to air pollution and to investigate the relationship between personal exposure to air pollution and pulmonary function. We measured individual exposures to NO(2) using passive personal NO(2) samplers for 298 healthy university students. Questionnaire interview was conducted for traffic-related factors, and spirometry was performed when the samplers were returned after 1 day. Personal NO(2) concentrations varied, depending on the distance between residence and a main road (P=0.029). Students who used transportation for more than 1 h were exposed to higher levels of NO(2) than those using transportation for less than 1 h (P=0.032). In terms of transportation, riding in a bus or subway caused significantly higher exposure than not using them (P=0.046). NO(2) exposure was not significantly associated with forced vital capacity (FVC) or forced expiratory volume in 1 s (FEV(1)) but was associated with the ratio of FEV(1)/FVC and mid-expiratory flow between 25% and 75% of the forced vital capacity (FEF(25-75)) (Ppollution and are associated with decreased pulmonary function.
Approximating distributions from moments
Pawula, R. F.
1987-11-01
A method based upon Pearson-type approximations from statistics is developed for approximating a symmetric probability density function from its moments. The extended Fokker-Planck equation for non-Markov processes is shown to be the underlying foundation for the approximations. The approximation is shown to be exact for the beta probability density function. The applicability of the general method is illustrated by numerous pithy examples from linear and nonlinear filtering of both Markov and non-Markov dichotomous noise. New approximations are given for the probability density function in two cases in which exact solutions are unavailable, those of (i) the filter-limiter-filter problem and (ii) second-order Butterworth filtering of the random telegraph signal. The approximate results are compared with previously published Monte Carlo simulations in these two cases.
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.
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...
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.
Statistical universals reveal the structures and functions of human music.
Savage, Patrick E; Brown, Steven; Sakai, Emi; Currie, Thomas E
2015-07-21
Music has been called "the universal language of mankind." Although contemporary theories of music evolution often invoke various musical universals, the existence of such universals has been disputed for decades and has never been empirically demonstrated. Here we combine a music-classification scheme with statistical analyses, including phylogenetic comparative methods, to examine a well-sampled global set of 304 music recordings. Our analyses reveal no absolute universals but strong support for many statistical universals that are consistent across all nine geographic regions sampled. These universals include 18 musical features that are common individually as well as a network of 10 features that are commonly associated with one another. They span not only features related to pitch and rhythm that are often cited as putative universals but also rarely cited domains including performance style and social context. These cross-cultural structural regularities of human music may relate to roles in facilitating group coordination and cohesion, as exemplified by the universal tendency to sing, play percussion instruments, and dance to simple, repetitive music in groups. Our findings highlight the need for scientists studying music evolution to expand the range of musical cultures and musical features under consideration. The statistical universals we identified represent important candidates for future investigation.
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...
Schmidt, Wolfgang M
1980-01-01
"In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approxi- mations to algebraic numbers. The present volume is an ex- panded and up-dated version of the original mimeographed notes on the course. As an introduction to the author's own remarkable achievements relating to the Thue-Siegel-Roth theory, the text can hardly be bettered and the tract can already be regarded as a classic in its field."(Bull.LMS) "Schmidt's work on approximations by algebraic numbers belongs to the deepest and most satisfactory parts of number theory. These notes give the best accessible way to learn the subject. ... this book is highly recommended." (Mededelingen van het Wiskundig Genootschap)
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.
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.
Traa, M.R.M.J.; Traa, M.R.M.J.; Caspers, W.J.; Caspers, W.J.; Banning, E.J.; Banning, E.J.
1994-01-01
In this paper the Hubbard-Anderson model on a square lattice with two holes is studied. The ground state (GS) is approximated by a variational RVB-type wave function. The holes interact by exchange of a localized spin excitation (SE), which is created or absorbed if a hole moves to a
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.
Nobile, F.; Tamellini, L.; Tempone, Raul
2015-01-01
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.
Li, Shaohong L; Truhlar, Donald G
2015-07-14
Time-dependent density functional theory (TDDFT) with conventional local and hybrid functionals such as the local and hybrid generalized gradient approximations (GGA) seriously underestimates the excitation energies of Rydberg states, which limits its usefulness for applications such as spectroscopy and photochemistry. We present here a scheme that modifies the exchange-enhancement factor to improve GGA functionals for Rydberg excitations within the TDDFT framework while retaining their accuracy for valence excitations and for the thermochemical energetics calculated by ground-state density functional theory. The scheme is applied to a popular hybrid GGA functional and tested on data sets of valence and Rydberg excitations and atomization energies, and the results are encouraging. The scheme is simple and flexible. It can be used to correct existing functionals, and it can also be used as a strategy for the development of new functionals.
Cendagorta, Joseph R; Bačić, Zlatko; Tuckerman, Mark E
2018-03-14
We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.
Cendagorta, Joseph R.; Bačić, Zlatko; Tuckerman, Mark E.
2018-03-01
We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.
Self-similar factor approximants
International Nuclear Information System (INIS)
Gluzman, S.; Yukalov, V.I.; Sornette, D.
2003-01-01
The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving an improved type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approximants, because of their form, are called self-similar factor approximants. These complement the obtained earlier self-similar exponential approximants and self-similar root approximants. The specific feature of self-similar factor approximants is that their control functions, providing convergence of the computational algorithm, are completely defined from the accuracy-through-order conditions. These approximants contain the Pade approximants as a particular case, and in some limit they can be reduced to the self-similar exponential approximants previously introduced by two of us. It is proved that the self-similar factor approximants are able to reproduce exactly a wide class of functions, which include a variety of nonalgebraic functions. For other functions, not pertaining to this exactly reproducible class, the factor approximants provide very accurate approximations, whose accuracy surpasses significantly that of the most accurate Pade approximants. This is illustrated by a number of examples showing the generality and accuracy of the factor approximants even when conventional techniques meet serious difficulties
On reversible Turing machines and their function universality
DEFF Research Database (Denmark)
Axelsen, Holger Bock; Glück, Robert
2016-01-01
We provide a treatment of the reversible Turing machines (RTMs) under a strict function semantics. Unlike many existing reversible computation models, we distinguish strictly between computing the function backslashlambda x.f(x) $ x . f ( x ) and computing the function backslashlambda x. (x, f(x)...
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: use...... promising results have been obtained for both single (including charge transfer) and double excitations with spin-independent short-range local and semilocal functionals. Even at the Kohn-Sham ensemble DFT level, which is recovered when the range-separation parameter is set to 0, LIM performs better than...
International Nuclear Information System (INIS)
Giricheva, N.I.; Girichev, G.V.; Smorodin, S.V.
2007-01-01
Scanning of potential energy surface in the LaI 3 molecule along normal coordinates are realized using the B3LYP/SDD,SDD method. The most anharmonicity is shown to have a potential function of non-planar oscillation ν 2 (A 2 ''). Effect of anharmonicity on the value of mean-square oscillation amplitudes and oscillation spectrum of the molecule is established. It is noted that the account of anharmonicity of potential functions leads to decreasing mean-square oscillation amplitudes [ru
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
Self-Assessment of the University Teaching Staff Functions
Duarte Clemente, Mariana Vilela; Ferrándiz-Vindel, Isabel-María
2012-01-01
The Higher Education institutions should offer excellence teaching and qualification opportunities for the university teaching staff. La Facultad Integrada de Pernambuco (FACIPE) (the Integrated School of Pernambuco) in Brazil, following the global trend, has been involved in implementing changes to help improve the quality of education in our…
Tutu, Hiroki
2011-06-01
Stochastic resonance (SR) enhanced by time-delayed feedback control is studied. The system in the absence of control is described by a Langevin equation for a bistable system, and possesses a usual SR response. The control with the feedback loop, the delay time of which equals to one-half of the period (2π/Ω) of the input signal, gives rise to a noise-induced oscillatory switching cycle between two states in the output time series, while its average frequency is just smaller than Ω in a small noise regime. As the noise intensity D approaches an appropriate level, the noise constructively works to adapt the frequency of the switching cycle to Ω, and this changes the dynamics into a state wherein the phase of the output signal is entrained to that of the input signal from its phase slipped state. The behavior is characterized by power loss of the external signal or response function. This paper deals with the response function based on a dichotomic model. A method of delay-coordinate series expansion, which reduces a non-Markovian transition probability flux to a series of memory fluxes on a discrete delay-coordinate system, is proposed. Its primitive implementation suggests that the method can be a potential tool for a systematic analysis of SR phenomenon with delayed feedback loop. We show that a D-dependent behavior of poles of a finite Laplace transform of the response function qualitatively characterizes the structure of the power loss, and we also show analytical results for the correlation function and the power spectral density.
Chen, Xin; Xie, Penghuan; Xiong, Yonghua; He, Yong; Wu, Min
2015-01-01
Adaptive Dynamic Programming (ADP) with critic-actor architecture is an effective way to perform online learning control. To avoid the subjectivity in the design of a neural network that serves as a critic network, kernel-based adaptive critic design (ACD) was developed recently. There are two essential issues for a static kernel-based model: how to determine proper hyperparameters in advance and how to select right samples to describe the value function. They all rely on the assessment of sa...
Spherical Approximation on Unit Sphere
Directory of Open Access Journals (Sweden)
Eman Samir Bhaya
2018-01-01
Full Text Available In this paper we introduce a Jackson type theorem for functions in LP spaces on sphere And study on best approximation of functions in spaces defined on unit sphere. our central problem is to describe the approximation behavior of functions in spaces for by modulus of smoothness of functions.
Mewes, Stefanie A; Plasser, Felix; Dreuw, Andreas
2017-03-16
The exciton size of the lowest singlet excited state in a diverse set of organic π-conjugated polymers is studied and found to be a universal, system-independent quantity of approximately 7 Å in the single-chain picture. With time-dependent density functional theory (TDDFT), its value as well as the overall description of the exciton is almost exclusively governed by the amount of nonlocal orbital exchange. This is traced back to the lack of the Coulomb attraction between the electron and hole quasiparticles in pure TDDFT, which is reintroduced only with the admixture of nonlocal orbital exchange.
Sergeev, A.; Alharbi, F. H.; Jovanovic, R.; Kais, S.
2016-04-01
The gradient expansion of the kinetic energy density functional, when applied to atoms or finite systems, usually grossly overestimates the energy in the fourth order and generally diverges in the sixth order. We avoid the divergence of the integral by replacing the asymptotic series including the sixth order term in the integrand by a rational function. Padé approximants show moderate improvements in accuracy in comparison with partial sums of the series. The results are discussed for atoms and Hooke’s law model for two-electron atoms.
Condensins: universal organizers of chromosomes with diverse functions.
Hirano, Tatsuya
2012-08-01
Condensins are multisubunit protein complexes that play a fundamental role in the structural and functional organization of chromosomes in the three domains of life. Most eukaryotic species have two different types of condensin complexes, known as condensins I and II, that fulfill nonoverlapping functions and are subjected to differential regulation during mitosis and meiosis. Recent studies revealed that the two complexes contribute to a wide variety of interphase chromosome functions, such as gene regulation, recombination, and repair. Also emerging are their cell type- and tissue-specific functions and relevance to human disease. Biochemical and structural analyses of eukaryotic and bacterial condensins steadily uncover the mechanisms of action of this class of highly sophisticated molecular machines. Future studies on condensins will not only enhance our understanding of chromosome architecture and dynamics, but also help address a previously underappreciated yet profound set of questions in chromosome biology.
Directory of Open Access Journals (Sweden)
Xin Chen
2015-01-01
Full Text Available Adaptive Dynamic Programming (ADP with critic-actor architecture is an effective way to perform online learning control. To avoid the subjectivity in the design of a neural network that serves as a critic network, kernel-based adaptive critic design (ACD was developed recently. There are two essential issues for a static kernel-based model: how to determine proper hyperparameters in advance and how to select right samples to describe the value function. They all rely on the assessment of sample values. Based on the theoretical analysis, this paper presents a two-phase simultaneous learning method for a Gaussian-kernel-based critic network. It is able to estimate the values of samples without infinitively revisiting them. And the hyperparameters of the kernel model are optimized simultaneously. Based on the estimated sample values, the sample set can be refined by adding alternatives or deleting redundances. Combining this critic design with actor network, we present a Gaussian-kernel-based Adaptive Dynamic Programming (GK-ADP approach. Simulations are used to verify its feasibility, particularly the necessity of two-phase learning, the convergence characteristics, and the improvement of the system performance by using a varying sample set.
Functional diversification of Argonautes in nematodes: an expanding universe.
Buck, Amy H; Blaxter, Mark
2013-08-01
In the last decade, many diverse RNAi (RNA interference) pathways have been discovered that mediate gene silencing at epigenetic, transcriptional and post-transcriptional levels. The diversity of RNAi pathways is inherently linked to the evolution of Ago (Argonaute) proteins, the central protein component of RISCs (RNA-induced silencing complexes). An increasing number of diverse Agos have been identified in different species. The functions of most of these proteins are not yet known, but they are generally assumed to play roles in development, genome stability and/or protection against viruses. Recent research in the nematode Caenorhabditis elegans has expanded the breadth of RNAi functions to include transgenerational epigenetic memory and, possibly, environmental sensing. These functions are inherently linked to the production of secondary siRNAs (small interfering RNAs) that bind to members of a clade of WAGOs (worm-specific Agos). In the present article, we review briefly what is known about the evolution and function of Ago proteins in eukaryotes, including the expansion of WAGOs in nematodes. We postulate that the rapid evolution of WAGOs enables the exceptional functional plasticity of nematodes, including their capacity for parasitism.
Goode, Adam P; Ni, Pengshend; Jette, Alan; Fitzgerald, G Kelley
2018-04-19
Pragmatic studies have gained popularity, thus emphasizing the need for patient-reported outcomes (PRO) to be integrated into electronic health records. This study describes the development of a customized short form from the Boston University Osteoarthritis Functional Assessment PRO (BU-OA-PRO) for a specific pragmatic clinical trial. A Functional Pain Short Form was created from an existing item bank of deidentified data in the BU-OA-PRO. Item response theory (IRT) methods were used to select items. Reliability was measured with the Cronbach alpha, then with IRT simulation methods. To examine validity, ceiling and floor effects, correlations between the short-form scores and scores from the BU-OA-PRO and the Western Ontario McMasters University Osteoarthritis Index (WOMAC) Pain and Difficulty subscales, and the area under the curve (AUC) were calculated. A minimum detectable change at 90% confidence (MDC90) was calculated based on a calibration sample. The BU-OA PRO was reduced from 126 items to 10 items to create the BU-OA Functional Pain Short Form (BU-OA-FPS). The Cronbach alpha indicated high internal consistency (0.91), and reliability distribution estimates were 0.96 (uniform) and 0.92 (normal). Low ceiling effects (4.57%), and floor effects (0%) were found. Moderate-to-high correlations between the BU-OA PRO and BU-OA-FPS were found with WOMAC Pain (BU-OA-FPS = 0.67; BU-OA-PRO = 0.64) and Difficulty (BU-OA-FPS = 0.73; BU-OA-PRO = 0.69) subscales. The correlation between the BU-OA-PRO and BU-OA-FPS was 0.94. The AUC ranged from 0.80 to 0.88. The MDC90 was approximately 6 standardized points. The BU-OA-FPS provides reliable and valid measurement of functional pain. Pragmatic studies may consider the BU-OA-FPS for use in electronic health records to capture outcomes.
Microscopic universality of complex matrix model correlation functions at weak non-Hermiticity
International Nuclear Information System (INIS)
Akemann, G.
2002-01-01
The microscopic correlation functions of non-chiral random matrix models with complex eigenvalues are analyzed for a wide class of non-Gaussian measures. In the large-N limit of weak non-Hermiticity, where N is the size of the complex matrices, we can prove that all k-point correlation functions including an arbitrary number of Dirac mass terms are universal close to the origin. To this aim we establish the universality of the asymptotics of orthogonal polynomials in the complex plane. The universality of the correlation functions then follows from that of the kernel of orthogonal polynomials and a mapping of massive to massless correlators
Methods of Approximation Theory in Complex Analysis and Mathematical Physics
Saff, Edward
1993-01-01
The book incorporates research papers and surveys written by participants ofan International Scientific Programme on Approximation Theory jointly supervised by Institute for Constructive Mathematics of University of South Florida at Tampa, USA and the Euler International Mathematical Instituteat St. Petersburg, Russia. The aim of the Programme was to present new developments in Constructive Approximation Theory. The topics of the papers are: asymptotic behaviour of orthogonal polynomials, rational approximation of classical functions, quadrature formulas, theory of n-widths, nonlinear approximation in Hardy algebras,numerical results on best polynomial approximations, wavelet analysis. FROM THE CONTENTS: E.A. Rakhmanov: Strong asymptotics for orthogonal polynomials associated with exponential weights on R.- A.L. Levin, E.B. Saff: Exact Convergence Rates for Best Lp Rational Approximation to the Signum Function and for Optimal Quadrature in Hp.- H. Stahl: Uniform Rational Approximation of x .- M. Rahman, S.K. ...
Building a universal nuclear energy density functional (UNEDF)
Energy Technology Data Exchange (ETDEWEB)
Nazarewicz, Witold [Univ. of Tennessee, Knoxville, TN (United States)
2012-07-01
The long-term vision initiated with UNEDF is to arrive at a comprehensive, quantitative, and unified description of nuclei and their reactions, grounded in the fundamental interactions between the constituent nucleons. We seek to replace current phenomenological models of nuclear structure and reactions with a well-founded microscopic theory that delivers maximum predictive power with well-quantified uncertainties. Specifically, the mission of this project has been three-fold: First, to find an optimal energy density functional (EDF) using all our knowledge of the nucleonic Hamiltonian and basic nuclear properties. Second, to apply the EDF theory and its extensions to validate the functional using all the available relevant nuclear structure and reaction data. Third, to apply the validated theory to properties of interest that cannot be measured, in particular the properties needed for reaction theory.
Executive function in different groups of university students
Prosen, Simona; Smrtnik Vitulić, Helena
2015-01-01
The present study analyses the executive function (EF) skills of 369 students of primary education (n = 116), preschool education (n = 72), social pedagogy (n = 54), and biology (n = 128). It explores how the different groups of students use selected executive skills and whether there are any differences between the groups in this respect. Eleven EF skills were self-assessed using the Executive Skills Questionnaire for Students (Dawson & Guare, 2010). All of the groups of students experien...
Building A Universal Nuclear Energy Density Functional (UNEDF)
Energy Technology Data Exchange (ETDEWEB)
Carlson, Joe [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Furnstahl, Dick [The Ohio State Univ., Columbus, OH (United States); Horoi, Mihai [Central Michigan Univ., Mount Pleasant, MI (United States); Lusk, Rusty [Argonne National Lab. (ANL), Argonne, IL (United States); Nazarewicz, Witek [Univ. of Tennessee, Knoxville, TN (United States); Ng, Esmond [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Thompson, Ian [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Vary, James [Iowa State Univ., Ames, IA (United States)
2012-09-30
During the period of Dec. 1 2006 - Jun. 30, 2012, the UNEDF collaboration carried out a comprehensive study of all nuclei, based on the most accurate knowledge of the strong nuclear interaction, the most reliable theoretical approaches, the most advanced algorithms, and extensive computational resources, with a view towards scaling to the petaflop platforms and beyond. The long-term vision initiated with UNEDF is to arrive at a comprehensive, quantitative, and unified description of nuclei and their reactions, grounded in the fundamental interactions between the constituent nucleons. We seek to replace current phenomenological models of nuclear structure and reactions with a well-founded microscopic theory that delivers maximum predictive power with well-quantified uncertainties. Specifically, the mission of this project has been three-fold: first, to find an optimal energy density functional (EDF) using all our knowledge of the nucleonic Hamiltonian and basic nuclear properties; second, to apply the EDF theory and its extensions to validate the functional using all the available relevant nuclear structure and reaction data; third, to apply the validated theory to properties of interest that cannot be measured, in particular the properties needed for reaction theory. The main physics areas of UNEDF, defined at the beginning of the project, were: ab initio structure; ab initio functionals; DFT applications; DFT extensions; reactions.
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...
Energy Technology Data Exchange (ETDEWEB)
Rüger, Robert, E-mail: rueger@scm.com [Scientific Computing & Modelling NV, De Boelelaan 1083, 1081 HV Amsterdam (Netherlands); Department of Theoretical Chemistry, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam (Netherlands); Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Linnéstr. 2, 04103 Leipzig (Germany); Lenthe, Erik van [Scientific Computing & Modelling NV, De Boelelaan 1083, 1081 HV Amsterdam (Netherlands); Heine, Thomas [Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Linnéstr. 2, 04103 Leipzig (Germany); Visscher, Lucas [Department of Theoretical Chemistry, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam (Netherlands)
2016-05-14
We propose a new method of calculating electronically excited states that combines a density functional theory 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 time-dependent density functional theory 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 TD-DFT calculations. Errors in vertical excitation energies are reduced by a factor of two compared to TD-DFTB.
ÜNAL, Aslıhan; YILDIZ, Mehmet Selami
2017-01-01
University libraries have a great importance in accessing information fortheir intermediary role. In today’s world, developments in various areas leadsto new user needs and expectations. Libraries are obliged to improve currentservices and to adapt new developments. The purpose of this research is tocontribute to the improvement of the library services of Duzce University -astate university, was founded in 2006- by following Quality Function Deploymentmethodology. As a result of the research ...
Rank of quantized universal enveloping algebras and modular functions
International Nuclear Information System (INIS)
Majid, S.; Soibelman, Ya.S.
1991-01-01
We compute an intrinsic rank invariant for quasitriangular Hopf algebras in the case of general quantum groups U q (g). As a function of q the rank has remarkable number theoretic properties connected with modular covariance and Galois theory. A number of examples are treated in detail, including rank (U q (su(3)) and rank (U q (e 8 )). We briefly indicate a physical interpretation as relating Chern-Simons theory with the theory of a quantum particle confined to an alcove of g. (orig.)
Compact baby universe model in ten dimension and probability function of quantum gravity
International Nuclear Information System (INIS)
Yan Jun; Hu Shike
1991-01-01
The quantum probability functions are calculated for ten-dimensional compact baby universe model. The authors find that the probability for the Yang-Mills baby universe to undergo a spontaneous compactification down to a four-dimensional spacetime is greater than that to remain in the original homogeneous multidimensional state. Some questions about large-wormhole catastrophe are also discussed
Rasero Causil, Diego; Ortega López, César; Espitia Rico, Miguel
2018-04-01
Computational calculations of total energy based on density functional theory were used to investigate the structural, electronic, and magnetic properties of the DyB2 compounds in the hexagonal structure. The calculations were carried out by means of the full-potential linearized augmented plane wave (FP-LAPW) method, employing the computational Wien2k package. The local density approximation (LDA) and the generalized gradient approximation (GGA) were used for the electron-electron interactions. Additionally, we used the functional hybrid PBE0 for a better description the electronic and magnetic properties, because the DyB2 compound is a strongly-correlated system. We found that the calculated lattice constant agrees well with the values reported theoretically and experimentally. The density of states (DOS) calculation shows that the compound exhibits a metallic behavior and has magnetic properties, with a total magnetic moment of 5.47 μ0/cell determined mainly by the 4f states of the rare earth elements. The functional PBE0 shows a strong localization of the Dy-4f orbitals.
Cioslowski, Jerzy; Strasburger, Krzysztof
2018-04-01
Electronic properties of several states of the five- and six-electron harmonium atoms are obtained from large-scale calculations employing explicitly correlated basis functions. The high accuracy of the computed energies (including their components), natural spinorbitals, and their occupation numbers makes them suitable for testing, calibration, and benchmarking of approximate formalisms of quantum chemistry and solid state physics. In the case of the five-electron species, the availability of the new data for a wide range of the confinement strengths ω allows for confirmation and generalization of the previously reached conclusions concerning the performance of the presently known approximations for the electron-electron repulsion energy in terms of the 1-matrix that are at heart of the density matrix functional theory (DMFT). On the other hand, the properties of the three low-lying states of the six-electron harmonium atom, computed at ω = 500 and ω = 1000, uncover deficiencies of the 1-matrix functionals not revealed by previous studies. In general, the previously published assessment of the present implementations of DMFT being of poor accuracy is found to hold. Extending the present work to harmonically confined systems with even more electrons is most likely counterproductive as the steep increase in computational cost required to maintain sufficient accuracy of the calculated properties is not expected to be matched by the benefits of additional information gathered from the resulting benchmarks.
International Nuclear Information System (INIS)
Cai Qi; Shang Yanlong; Chen Lisheng; Zhao Yuguang
2013-01-01
Vector-universal generating function was presented to analyze the availability of thermodynamic system with multiple performance parameters. Vector-universal generating function of component's performance was defined, the arithmetic model based on vector-universal generating function was derived for the thermodynamic system, and the calculation method was given for state probability of multi-state component. With the stochastic simulation of the degeneration trend of the multiple factors, the system availability with multiple performance parameters was obtained under composite factors. It is shown by an example that the results of the availability obtained by the binary availability analysis method are somewhat conservative, and the results considering parameter failure based on vector-universal generating function reflect the operation characteristics of the thermodynamic system better. (authors)
Practice-Oriented Research: The Extended Function of Dutch Universities of Applied Sciences
de Weert, Egbert; Leijnse, Frans; Kyvik, Svein; Lepori, Benedetto
2010-01-01
This chapter seeks to analyse the legitimate research claims of Dutch universities of applied sciences. It subsequently analyses how the research function has been conceived in national policies, the emerging funding schemes for research, strategies developed by these institutions regarding
Hierarchical low-rank approximation for high dimensional approximation
Nouy, Anthony
2016-01-01
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.
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.
DEFF Research Database (Denmark)
Fromager, Emmanuel; Toulouse, Julien; Jensen, Hans Jørgen Aagaard
2007-01-01
In many cases, the dynamic correlation can be calculated quite accurately and at a fairly low computational cost in Kohn-Sham density-functional theory (KS-DFT), using current standard approximate functionals. However, in general, KS-DFT does not treat static correlation effects (near degeneracy...
Reliable Function Approximation and Estimation
2016-08-16
compressed sensing results to a wide class of infinite -dimensional problems. We discuss four key application domains for the methods developed in this... infinite -dimensional problems. We discuss four key findings arising from this project, as related to uncertainty quantification, image processing, matrix...compressed sensing results to a wide class of infinite -dimensional problems. We discuss four key application domains for the methods developed in this project
Hanson-Heine, Magnus W. D.; George, Michael W.; Besley, Nicholas A.
2018-06-01
The restricted excitation subspace approximation is explored as a basis to reduce the memory storage required in linear response time-dependent density functional theory (TDDFT) calculations within the Tamm-Dancoff approximation. It is shown that excluding the core orbitals and up to 70% of the virtual orbitals in the construction of the excitation subspace does not result in significant changes in computed UV/vis spectra for large molecules. The reduced size of the excitation subspace greatly reduces the size of the subspace vectors that need to be stored when using the Davidson procedure to determine the eigenvalues of the TDDFT equations. Furthermore, additional screening of the two-electron integrals in combination with a reduction in the size of the numerical integration grid used in the TDDFT calculation leads to significant computational savings. The use of these approximations represents a simple approach to extend TDDFT to the study of large systems and make the calculations increasingly tractable using modest computing resources.
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
Hutter, Jürg
2003-03-01
An efficient formulation of time-dependent linear response density functional theory for the use within the plane wave basis set framework is presented. The method avoids the transformation of the Kohn-Sham matrix into the canonical basis and references virtual orbitals only through a projection operator. Using a Lagrangian formulation nuclear derivatives of excited state energies within the Tamm-Dancoff approximation are derived. The algorithms were implemented into a pseudo potential/plane wave code and applied to the calculation of adiabatic excitation energies, optimized geometries and vibrational frequencies of three low lying states of formaldehyde. An overall good agreement with other time-dependent density functional calculations, multireference configuration interaction calculations and experimental data was found.
Garza, Alejandro J.; Bulik, Ireneusz W.; Alencar, Ana G. Sousa; Sun, Jianwei; Perdew, John P.; Scuseria, Gustavo E.
2016-04-01
Contrary to standard coupled cluster doubles (CCD) and Brueckner doubles (BD), singlet-paired analogues of CCD and BD (denoted here as CCD0 and BD0) do not break down when static correlation is present, but neglect substantial amounts of dynamic correlation. In fact, CCD0 and BD0 do not account for any contributions from multielectron excitations involving only same-spin electrons at all. We exploit this feature to add - without introducing double counting, self-interaction, or increase in cost - the missing correlation to these methods via meta-GGA (generalised gradient approximation) density functionals (Tao-Perdew-Staroverov-Scuseria and strongly constrained and appropriately normed). Furthermore, we improve upon these CCD0+DFT blends by invoking range separation: the short- and long-range correlations absent in CCD0/BD0 are evaluated with density functional theory and the direct random phase approximation, respectively. This corrects the description of long-range van der Waals forces. Comprehensive benchmarking shows that the combinations presented here are very accurate for weakly correlated systems, while also providing a reasonable description of strongly correlated problems without resorting to symmetry breaking.
Diophantine approximation and badly approximable sets
DEFF Research Database (Denmark)
Kristensen, S.; Thorn, R.; Velani, S.
2006-01-01
. The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...
On the approximation by single hidden layer feedforward neural networks with fixed weights
Guliyev, Namig J.; Ismailov, Vugar E.
2017-01-01
International audience; Feedforward neural networks have wide applicability in various disciplines of science due to their universal approximation property. Some authors have shown that single hidden layer feedforward neural networks (SLFNs) with fixed weights still possess the universal approximation property provided that approximated functions are univariate. But this phenomenon does not lay any restrictions on the number of neurons in the hidden layer. The more this number, the more the p...
Ziegler, Tom; Krykunov, Mykhaylo; Autschbach, Jochen
2014-09-09
The random phase approximation (RPA) equation of adiabatic time dependent density functional ground state response theory (ATDDFT) has been used extensively in studies of excited states. It extracts information about excited states from frequency dependent ground state response properties and avoids, thus, in an elegant way, direct Kohn-Sham calculations on excited states in accordance with the status of DFT as a ground state theory. Thus, excitation energies can be found as resonance poles of frequency dependent ground state polarizability from the eigenvalues of the RPA equation. ATDDFT is approximate in that it makes use of a frequency independent energy kernel derived from the ground state functional. It is shown in this study that one can derive the RPA equation of ATDDFT from a purely variational approach in which stationary states above the ground state are located using our constricted variational DFT (CV-DFT) method and the ground state functional. Thus, locating stationary states above the ground state due to one-electron excitations with a ground state functional is completely equivalent to solving the RPA equation of TDDFT employing the same functional. The present study is an extension of a previous work in which we demonstrated the equivalence between ATDDFT and CV-DFT within the Tamm-Dancoff approximation.
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)
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.
Prestack wavefield approximations
Alkhalifah, Tariq
2013-01-01
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.
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.
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.
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.
An improved saddlepoint approximation.
Gillespie, Colin S; Renshaw, Eric
2007-08-01
Given a set of third- or higher-order moments, not only is the saddlepoint approximation the only realistic 'family-free' technique available for constructing an associated probability distribution, but it is 'optimal' in the sense that it is based on the highly efficient numerical method of steepest descents. However, it suffers from the problem of not always yielding full support, and whilst [S. Wang, General saddlepoint approximations in the bootstrap, Prob. Stat. Lett. 27 (1992) 61.] neat scaling approach provides a solution to this hurdle, it leads to potentially inaccurate and aberrant results. We therefore propose several new ways of surmounting such difficulties, including: extending the inversion of the cumulant generating function to second-order; selecting an appropriate probability structure for higher-order cumulants (the standard moment closure procedure takes them to be zero); and, making subtle changes to the target cumulants and then optimising via the simplex algorithm.
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.
International Nuclear Information System (INIS)
Fatima, A.; Tanveer, F.; Ahmed, A.; Gillani, S.A.
2017-01-01
To determine an association of pain intensity with quality of life and functional disability in university students with lumbago. Methodology: In this cross sectional study 213 students participated. Standard questionnaire Numeric pain rating scale, Utian quality of life scale Oswestry Low Back Pain Disability Questionnaire were used for the data collection. Results: Mean age of students was 21.0 +- 1.970 years (range 18-24). Out of 213 students, 143 had lower quality of life. There was an association between pain intensity and quality of life (p=0.006). Out of 213 students, 120 had minimal disability with lower quality of life. There was strong association (p=0.015) between quality of life and functional disability. Conclusion: There was a strong association between pain intensity and quality of life, pain intensity and functional disability, quality of life and functional disability in university students with low back ache. (author)
Polynomial approximation on polytopes
Totik, Vilmos
2014-01-01
Polynomial approximation on convex polytopes in \\mathbf{R}^d is considered in uniform and L^p-norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the L^p-case so called strong direct and converse results are also verified. The equivalence of the moduli of smoothness with an appropriate K-functional follows as a consequence. The results solve a problem that was left open since the mid 1980s when some of the present findings were established for special, so-called simple polytopes.
Dzhamalova, Bika B.; Timonin, Andrey I.; Kolesov, Vladimir I.; Pavlov, Vladimir V.; Evstegneeva, Anastasiia A.
2016-01-01
This article is focused on the development of the structure and content of consolidating orientation of pedagogical functions of university teachers in international students' training. The leading method of research is the modeling method that allows producing of the established structure's and content's justification of consolidating orientation…
Yee, Ng Kin; Lam, Toh Tin
2008-01-01
This paper reports on students' errors in performing integration of rational functions, a topic of calculus in the pre-university mathematics classrooms. Generally the errors could be classified as those due to the students' weak algebraic concepts and their lack of understanding of the concept of integration. With the students' inability to link…
Towards Total Quality Management in Universities: Quality Function Deployment Paradigm and Beyond
Al-Fuqaha, Isam Najib
2014-01-01
This paper is an endeavor to develop a customised and computerized matrix of Quality Function Deployment paradigm (QFD) that has been applied in industry, with the aim of probing quality assurance and enhancement in Universities. Results of testing the new matrix proved that, it is efficient and time-saving while compared with a detailed field…
The Integration of Quality Management Functions within a University: A Systems Approach
Brits, H. J.
2011-01-01
According to a recent study, institutions of higher learning in South Africa fail to a great extent to integrate the key management functions that are fundamental to effective quality management. This article argues that the effective promotion of quality of a university's core business depends to a large extent on the ability of an institution's…
The black-body radiation inversion problem, its instability and a new universal function set method
International Nuclear Information System (INIS)
Ye, JiPing; Ji, FengMin; Wen, Tao; Dai, Xian-Xi; Dai, Ji-Xin; Evenson, William E.
2006-01-01
The black-body radiation inversion (BRI) problem is ill-posed and requires special techniques to achieve stable solutions. In this Letter, the universal function set method (UFS), is developed in BRI. An improved unique existence theorem is proposed. Asymptotic behavior control (ABC) is introduced. A numerical example shows that practical calculations are possible with UFS
Severina, Wambeti Njagi; Edabu, Paul; Kimani, Cecilia
2016-01-01
Women working in Kenyan universities should be provided with the many benefits of sponsorship, a mentorship function. Mentors should for example give their mentees challenging assignments which prepare them for top leadership positions. But it is possible that women may not be getting this support from their mentors. Therefore, the researcher did…
Universal recovery map for approximate Markov chains.
Sutter, David; Fawzi, Omar; Renner, Renato
2016-02-01
A central question in quantum information theory is to determine how well lost information can be reconstructed. Crucially, the corresponding recovery operation should perform well without knowing the information to be reconstructed. In this work, we show that the quantum conditional mutual information measures the performance of such recovery operations. More precisely, we prove that the conditional mutual information I ( A : C | B ) of a tripartite quantum state ρ ABC can be bounded from below by its distance to the closest recovered state [Formula: see text], where the C -part is reconstructed from the B -part only and the recovery map [Formula: see text] merely depends on ρ BC . One particular application of this result implies the equivalence between two different approaches to define topological order in quantum systems.
2009-01-01
The Universe, is one book in the Britannica Illustrated Science Library Series that is correlated to the science curriculum in grades 5-8. The Britannica Illustrated Science Library is a visually compelling set that covers earth science, life science, and physical science in 16 volumes. Created for ages 10 and up, each volume provides an overview on a subject and thoroughly explains it through detailed and powerful graphics-more than 1,000 per volume-that turn complex subjects into information that students can grasp. Each volume contains a glossary with full definitions for vocabulary help and an index.
Rollout sampling approximate policy iteration
Dimitrakakis, C.; Lagoudakis, M.G.
2008-01-01
Several researchers have recently investigated the connection between reinforcement learning and classification. We are motivated by proposals of approximate policy iteration schemes without value functions, which focus on policy representation using classifiers and address policy learning as a
International Nuclear Information System (INIS)
Li, J H; Dai, X D; Wang, T L; Liu, B X
2007-01-01
We propose a two-parameter binomial truncation function for the second-moment approximation of the tight-binding (TB-SMA) interatomic potential and illustrate in detail the procedure of constructing the potentials for binary and ternary transition metal systems. For the ternary Ni-Hf-Ti system, the lattice constants, cohesion energies, elastic constants and bulk moduli of six binary compounds, i.e. L1 2 Ni 3 Hf, NiHf 3 , Ni 3 Ti, NiTi 3 , Hf 3 Ti and HfTi 3 , are firstly acquired by ab initio calculations and then employed to derive the binomial-truncated TB-SMA Ni-Hf-Ti potential. Applying the ab initio derived Ni-Hf-Ti potential, the lattice constants, cohesive energy, elastic constants and bulk moduli of another six binary compounds, i.e. D0 3 NiHf 3 , NiTi 3 HfTi 3 , and B2 NiHf, NiTi, HfTi, and two ternary compounds, i.e. C1 b NiHfTi, L2 1 Ni 2 HfTi, are calculated, respectively. It is found that, for the eight binary compounds studied, the calculated lattice constants and cohesion energies are in excellent agreement with those directly acquired from ab initio calculations and that the elastic constants and bulk moduli calculated from the potential are also qualitatively consistent with the results from ab initio calculations
International Nuclear Information System (INIS)
Yuste, Santos Bravo; Abad, Enrique
2011-01-01
We present an iterative method to obtain approximations to Bessel functions of the first kind J p (x) (p > -1) via the repeated application of an integral operator to an initial seed function f 0 (x). The class of seed functions f 0 (x) leading to sets of increasingly accurate approximations f n (x) is considerably large and includes any polynomial. When the operator is applied once to a polynomial of degree s, it yields a polynomial of degree s + 2, and so the iteration of this operator generates sets of increasingly better polynomial approximations of increasing degree. We focus on the set of polynomial approximations generated from the seed function f 0 (x) = 1. This set of polynomials is useful not only for the computation of J p (x) but also from a physical point of view, as it describes the long-time decay modes of certain fractional diffusion and diffusion-wave problems.
Limitations of shallow nets approximation.
Lin, Shao-Bo
2017-10-01
In this paper, we aim at analyzing the approximation abilities of shallow networks in reproducing kernel Hilbert spaces (RKHSs). We prove that there is a probability measure such that the achievable lower bound for approximating by shallow nets can be realized for all functions in balls of reproducing kernel Hilbert space with high probability, which is different with the classical minimax approximation error estimates. This result together with the existing approximation results for deep nets shows the limitations for shallow nets and provides a theoretical explanation on why deep nets perform better than shallow nets. Copyright © 2017 Elsevier Ltd. All rights reserved.
Endurance Capacity Is Not Correlated with Endothelial Function in Male University Students
Wu, Fang; Su, Chen; Fan, Zhen-guo; Zhu, Zhu; Tao, Jun; Huang, Yi-jun
2014-01-01
Background Endurance capacity, assessed by 1000-meter (1000 m) run of male university students, is an indicator of cardiovascular fitness in Chinese students physical fitness surveillance. Although cardiovascular fitness is related to endothelial function closely in patients with cardiovascular diseases, it remains unclear whether endurance capacity correlates with endothelial function, especially with circulating endothelial microparticles (EMPs), a new sensitive marker of endothelial dysfunction in young students. The present study aimed to investigate the relationship between endurance capacity and endothelial function in male university students. Methods Forty-seven healthy male university students (mean age, 20.1±0.6 years; mean height, 172.4±6.3 cm; and mean weight, 60.0±8.2 kg) were recruited in this study. The measurement procedure of 1000 m run time was followed to Chinese national students Constitutional Health Criterion. Endothelium function was assessed by flow-mediated vasodilation (FMD) in the brachial artery measured by ultrasonic imaging, and the level of circulating EMPs was measured by flow cytometry. Cardiovascular fitness indicator - maximal oxygen uptake (VO2 max) - was also measured on a cycle ergometer using a portable gas analyzer. Results 1000 m run time was correlated with VO2max (r = −0.399, p0.05). Conclusion The correlations between endurance capacity or cardiovascular fitness and endothelial function were not found in healthy Chinese male university students. These results suggest that endurance capacity may not reflect endothelial function in healthy young adults with well preserved FMD and low level of circulating CD31+/CD42-EMPs. PMID:25101975
Approximate Dynamic Programming: Combining Regional and Local State Following Approximations.
Deptula, Patryk; Rosenfeld, Joel A; Kamalapurkar, Rushikesh; Dixon, Warren E
2018-06-01
An infinite-horizon optimal regulation problem for a control-affine deterministic system is solved online using a local state following (StaF) kernel and a regional model-based reinforcement learning (R-MBRL) method to approximate the value function. Unlike traditional methods such as R-MBRL that aim to approximate the value function over a large compact set, the StaF kernel approach aims to approximate the value function in a local neighborhood of the state that travels within a compact set. In this paper, the value function is approximated using a state-dependent convex combination of the StaF-based and the R-MBRL-based approximations. As the state enters a neighborhood containing the origin, the value function transitions from being approximated by the StaF approach to the R-MBRL approach. Semiglobal uniformly ultimately bounded (SGUUB) convergence of the system states to the origin is established using a Lyapunov-based analysis. Simulation results are provided for two, three, six, and ten-state dynamical systems to demonstrate the scalability and performance of the developed method.
Entropy function and universality of entropy-area relation for small black holes
International Nuclear Information System (INIS)
Cai Ronggen; Chen, C.-M.; Maeda, Kei-ichi; Ohta, Nobuyoshi; Pang Dawei
2008-01-01
We discuss the entropy-area relation for the small black holes with higher curvature corrections by using the entropy function formalism and field redefinition method. We show that the entropy S BH of the small black hole is proportional to its horizon area A. In particular, we find a universal result that S BH =A/2G, the ratio is 2 times of Bekenstein-Hawking entropy-area formula in many cases of physical interest. In four dimensions, the universal relation is always true irrespective of the coefficients of the higher-order terms if the dilaton couplings are the same, which is the case for string effective theory, while in five dimensions, the relation again holds irrespective of the overall coefficient if the higher-order corrections are in the GB combination. We also discuss how this result generalizes to known physically interesting cases with Lovelock correction terms in various dimensions, and possible implications of the universal relation.
Wave function of the Universe in the early stage of its evolution
International Nuclear Information System (INIS)
Maydanyuk, Sergei P.
2008-01-01
In quantum cosmological models, constructed in the framework of Friedmann-Robertson-Walker metrics, a nucleation of the Universe with its further expansion is described as a tunneling transition through an effective barrier between regions with small and large values of the scale factor a at non-zero (or zero) energy. The approach for describing this tunneling consists of constructing a wave function satisfying an appropriate boundary condition. There are various ways for defining the boundary condition that lead to different estimates of the barrier penetrability and the tunneling time. In order to describe the escape from the tunneling region as accurately as possible and to construct the total wave function on the basis of its two partial solutions unambiguously, we use the tunneling boundary condition that the total wave function must represent only the outgoing wave at the point of escape from the barrier, where the following definition for the wave is introduced: the wave is represented by the wave function whose modulus changes minimally under a variation of the scale factor a. We construct a new method for a direct non-semiclassical calculation of the total stationary wave function of the Universe, analyze the behavior of this wave function in the tunneling region, near the escape point and in the asymptotic region, and estimate the barrier penetrability. We observe oscillations of the modulus of the wave function in the external region starting from the turning point which decrease with increasing of a and which are not shown in semiclassical calculations. The period of such an oscillation decreases uniformly with increasing a and can be used as a fully quantum dynamical characteristic of the expansion of the Universe. (orig.)
Functions of Russian University During Formation of Innovation-Based Economy
Directory of Open Access Journals (Sweden)
Malika A. Kurdova
2017-09-01
Full Text Available Introduction: the formation of innovation-based model of the Russian economy promotes the appearance of new functions of higher education institutions’ activities aimed at sustainable development. The article analyzes various classifications of the above functions in the changed conditions of modern Russia. Materials and Methods: the authors draw on the publications by famous scientists, methods of logical analysis and synthesis, generalisation, sociological and statistical studies: a survey, expert evaluation method, documentation analysis, etc. Results: the authors’ classification of higher education institutions’ functions formed during transition to innovation-oriented model of economic development for training innovation-oriented experts is presented. The aim of new approaches is to generate innovative ideas, to transfer knowledge, to foster the skills of entrepreneurship, to ensure the competitiveness and the employability of graduates. The analysis of implementation of new functions on the example of the universities of the Penza region of the Russian Federation is made. Discussion and Conclusions: the modernisation of higher education, accompanied by update of its content and functions, involves the formation of a new national University model that reflects the specifics of modern stage of the country’s socio-economic development. Therefore changes in higher education affecting the processes of functioning of higher educational institutions are revealed. The influence of rapidly changing factors in the external and internal environment led to the formation of new and transformation of basic functions of Russian universities, the effective implementation of which will contribute to improving the quality of professional training of specialists and formation of innovative potential of new economy.
A discrete stress-strength interference model based on universal generating function
International Nuclear Information System (INIS)
An Zongwen; Huang Hongzhong; Liu Yu
2008-01-01
Continuous stress-strength interference (SSI) model regards stress and strength as continuous random variables with known probability density function. This, to some extent, results in a limitation of its application. In this paper, stress and strength are treated as discrete random variables, and a discrete SSI model is presented by using the universal generating function (UGF) method. Finally, case studies demonstrate the validity of the discrete model in a variety of circumstances, in which stress and strength can be represented by continuous random variables, discrete random variables, or two groups of experimental data
Correlation function for density perturbations in an expanding universe. I. Linear theory
International Nuclear Information System (INIS)
McClelland, J.; Silk, J.
1977-01-01
We derive analytic solutions for the evolution of linearized adiabatic spherically symmetric density perturbations and the two-point correlation function in two regimes of the early universe: the radiation-dominated regime prior to decoupling, and the matter-dominated regime after decoupling. The solutions are for an Einstein--de Sitter universe, and include pressure effects. In the radiation era, we find that individual spherically symmetric adiabatic density perturbations smaller than the Jeans length flow outward like water waves instead of oscillating as infinite plane waves. It seems likely that the only primordial structures on scales smaller than the maximum Jeans length which could survive are very regular waves such as infinite plane waves. However, structure does build up in the correlation function over distances comparable with the maximum Jeans length in the radiation regime, and could lead to the eventual formation of galaxy superclusters. This scale (approx.10 17 Ω -2 M/sub sun)/therefore provides a natural dimension for large-scale structure arising out of the early universe. A general technique is described for constructing solutions for the evolution of the two-point correlation function, and applied to study white noise and power-law initial conditions for primordial inhomogeneities
Rational approximation of vertical segments
Salazar Celis, Oliver; Cuyt, Annie; Verdonk, Brigitte
2007-08-01
In many applications, observations are prone to imprecise measurements. When constructing a model based on such data, an approximation rather than an interpolation approach is needed. Very often a least squares approximation is used. Here we follow a different approach. A natural way for dealing with uncertainty in the data is by means of an uncertainty interval. We assume that the uncertainty in the independent variables is negligible and that for each observation an uncertainty interval can be given which contains the (unknown) exact value. To approximate such data we look for functions which intersect all uncertainty intervals. In the past this problem has been studied for polynomials, or more generally for functions which are linear in the unknown coefficients. Here we study the problem for a particular class of functions which are nonlinear in the unknown coefficients, namely rational functions. We show how to reduce the problem to a quadratic programming problem with a strictly convex objective function, yielding a unique rational function which intersects all uncertainty intervals and satisfies some additional properties. Compared to rational least squares approximation which reduces to a nonlinear optimization problem where the objective function may have many local minima, this makes the new approach attractive.
Tanaka, Shoji; Kirino, Eiji
2016-01-01
Conceiving concrete mental imagery is critical for skillful musical expression and performance. The precuneus, a core component of the default mode network (DMN), is a hub of mental image processing that participates in functions such as episodic memory retrieval and imagining future events. The precuneus connects with many brain regions in the frontal, parietal, temporal, and occipital cortices. The aim of this study was to examine the effects of long-term musical training on the resting-state functional connectivity of the precuneus. Our hypothesis was that the functional connectivity of the precuneus is altered in musicians. We analyzed the functional connectivity of the precuneus using resting-state functional magnetic resonance imaging (fMRI) data recorded in female university students majoring in music and nonmusic disciplines. The results show that the music students had higher functional connectivity of the precuneus with opercular/insular regions, which are associated with interoceptive and emotional processing; Heschl's gyrus (HG) and the planum temporale (PT), which process complex tonal information; and the lateral occipital cortex (LOC), which processes visual information. Connectivity of the precuneus within the DMN did not differ between the two groups. Our finding suggests that functional connections between the precuneus and the regions outside of the DMN play an important role in musical performance. We propose that a neural network linking the precuneus with these regions contributes to translate mental imagery into information relevant to musical performance.
A search for parameters of universal sub-barrier fusion excitation function
Energy Technology Data Exchange (ETDEWEB)
Qu, W.W. [Medical College of Soochow University, School of Radiation Medicine and Protection, Soochow (China); Zhang, G.L. [Beihang University, School of Physics and Nuclear Energy Engineering, Beijing (China); Wolski, R. [Henryk Niewodniczanski Institute of Nuclear Physics PAS, Cracow (Poland)
2016-11-15
Many fusion experimental data have been analyzed in terms of a simple universal function which could be used for predictions of fusion cross section below the barrier for arbitrary systems. Sub-barrier fusions based on the concept of Q -fusion value dependence were studied. It is attempted to parameterize the energy-reduced fusion excitation functions around the Coulomb barriers by an analytical phenomenological function. It was found that the speed of driving nuclei towards fusion is faster with the increase of mass asymmetry of colliding systems and those systems with a large difference of the ratio of neutrons to protons. However, a general trend with respect to total mass has not been observed. An exposition of more qualitative conclusions is hindered by apparent inconsistencies of measured fusion cross sections. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Alan M Kaplan
2012-10-12
This grant will be used to augment the equipment infrastructure and core support at the University of Kentucky and the University of Alabama particularly in the areas of genomics/informatics, molecular analysis and cell separation. In addition, we will promote collaborative research interactions through scientific workshops and exchange of scientists, as well as joint exploration of the role of immune receptors as targets in autoimmunity and host defense, innate and adaptive immune responses, and mucosal immunity in host defense.
STRUCTURAL AND FUNCTIONAL MODEL OF FORMING INFORMATIONAL COMPETENCE OF TECHNICAL UNIVERSITY STUDENTS
Directory of Open Access Journals (Sweden)
Taras Ostapchuk
2016-11-01
Full Text Available The article elaborates and analyses the structural and functional model of formation of information competence of technical university students. The system and mutual relationships between its elements are revealed. It is found out that the presence of the target structure of the proposed model, process and result-evaluative blocks ensure its functioning and the opportunity to optimize the learning process for technical school students’ information training. It is established that the formation of technical university students’ information competence based on components such as motivational value, as well as operational activity, cognitive, and reflexive one. These criteria (motivation, operational and activity, cognitive, reflective, indexes and levels (reproductive, technologized, constructive forming technical university students’ information competence are disclosed. Expediency of complex organizational and educational conditions in the stages of information competence is justified. The complex organizational and pedagogical conditions include: orientation in the organization and implementation of class work for technical university students’ positive value treatment; the issue of forming professionalism; informatization of educational and socio-cultural environment of higher technical educational institutions; orientation of technical university students’ training to the demands of European and international standards on information competence as a factor in the formation of competitiveness at the labor market; introducing a special course curriculum that will provide competence formation due to the use of information technology in professional activities. Forms (lecture, visualization, problem lecture, combined lecture, scientific online conference, recitals, excursions, etc., tools (computer lab, multimedia projector, interactive whiteboard, multimedia technology (audio, video, the Internet technologies; social networks, etc
Wave function of the Universe, preferred reference frame effects and metric signature transition
International Nuclear Information System (INIS)
Ghaffarnejad, Hossein
2015-01-01
Gravitational model of non-minimally coupled Brans Dicke (BD) scalar field 0 with dynamical unit time-like four vector field is used to study flat Robertson Walker (RW) cosmology in the presence of variable cosmological parameter V (ϕ) = Λϕ. Aim of the paper is to seek cosmological models which exhibit metric signature transition. The problem is studied in both classical and quantum cosmological approach with large values of BD parameter ω >> 1. Scale factor of RW metric is obtained as which describes nonsingular inflationary universe in Lorentzian signature sector. Euclidean signature sector of our solution describes a re-collapsing universe and is obtained from analytic continuation of the Lorentzian sector by exchanging . Dynamical vector field together with the BD scalar field are treated as fluid with time dependent barotropic index. They have regular (dark) matter dominance in the Euclidean (Lorentzian) sector. We solved Wheeler De Witt (WD) quantum wave equation of the cosmological system. Assuming a discrete non-zero ADM mass we obtained solutions of the WD equation as simple harmonic quantum Oscillator eigen functionals described by Hermite polynomials. Absolute values of these eigen functionals have nonzero values on the hypersurface in which metric field has signature degeneracy. Our eigen functionals describe nonzero probability of the space time with Lorentzian (Euclidean) signature for . Maximal probability corresponds to the ground state j = 0. (paper)
Total reflection coefficients of low-energy photons presented as universal functions
Directory of Open Access Journals (Sweden)
Ljubenov Vladan
2010-01-01
Full Text Available The possibility of expressing the total particle and energy reflection coefficients of low-energy photons in the form of universal functions valid for different shielding materials is investigated in this paper. The analysis is based on the results of Monte Carlo simulations of photon reflection by using MCNP, FOTELP, and PENELOPE codes. The normal incidence of the narrow monoenergetic photon beam of the unit intensity and of initial energies from 20 keV up to 100 keV is considered, and particle and energy reflection coefficients from the plane homogenous targets of water, aluminum, and iron are determined and compared. The representations of albedo coefficients on the initial photon energy, on the probability of large-angle photon scattering, and on the mean number of photon scatterings are examined. It is found out that only the rescaled albedo coefficients dependent on the mean number of photon scatterings have the form of universal functions and these functions are determined by applying the least square method.
Do light nuclei display a universal γ-ray strength function-
International Nuclear Information System (INIS)
Guttormsen, M.; Larsen, A.C.; Buerger, A.
2012-01-01
Particle-γ coincidences from the bombardment of 15 MeV and 32 MeV protons on a 46 Ti target are utilized to obtain γ-ray spectra as a function of excitation energy for 44,45,46 Ti. The Oslo method has been used to extract simultaneously level density and γ-ray strength functions (γ-SFs). The rich 46 Ti data set of 110 million events allows analysis of the coincidence data for many independent data sets. As expected, the results are consistent with one common level density. A method to study the evolution of the deduced γ-SFs as a function of excitation energy will be described. The γ-SFs are found to display strong variations for different initial and final excitation energies if transitions to the lowest states are involved. The differences in the γ-SFs can be explained as a consequence of Porter-Thomas fluctuations of individual intensities, and shows that this energy region cannot be used for determination of the universal γ-RSF. Even though, the deduced γ-SFs based on transitions within the quasi-continuum still indicate that the decay is governed by a universal γ-SF
Approximate symmetries of Hamiltonians
Chubb, Christopher T.; Flammia, Steven T.
2017-08-01
We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.
Directory of Open Access Journals (Sweden)
Dirk Hoyer
Full Text Available Fetal brain development involves the development of the neuro-vegetative (autonomic control that is mediated by the autonomic nervous system (ANS. Disturbances of the fetal brain development have implications for diseases in later postnatal life. In that context, the fetal functional brain age can be altered. Universal principles of developmental biology applied to patterns of autonomic control may allow a functional age assessment. The work aims at the development of a fetal autonomic brain age score (fABAS based on heart rate patterns. We analysed n = 113 recordings in quiet sleep, n = 286 in active sleep, and n = 29 in active awakeness from normals. We estimated fABAS from magnetocardiographic recordings (21.4-40.3 weeks of gestation preclassified in quiet sleep (n = 113, 63 females and active sleep (n = 286, 145 females state by cross-validated multivariate linear regression models in a cross-sectional study. According to universal system developmental principles, we included indices that address increasing fluctuation range, increasing complexity, and pattern formation (skewness, power spectral ratio VLF/LF, pNN5. The resulting models constituted fABAS. fABAS explained 66/63% (coefficient of determination R(2 of training and validation set of the variance by age in quiet, while 51/50% in active sleep. By means of a logistic regression model using fluctuation range and fetal age, quiet and active sleep were automatically reclassified (94.3/93.1% correct classifications. We did not find relevant gender differences. We conclude that functional brain age can be assessed based on universal developmental indices obtained from autonomic control patterns. fABAS reflect normal complex functional brain maturation. The presented normative data are supplemented by an explorative study of 19 fetuses compromised by intrauterine growth restriction. We observed a shift in the state distribution towards active awakeness. The lower WGA
Directory of Open Access Journals (Sweden)
Byungseok Lee
2018-01-01
Full Text Available Motions using Leap Motion controller are not standardized while the use of it is spreading in media contents. Each content defines its own motions, thereby creating confusion for users. Therefore, to alleviate user inconvenience, this study categorized the commonly used motion by Amusement and Functional Contents and defined the Structural Motion Grammar that can be universally used based on the classification. To this end, the Motion Lexicon was defined, which is a fundamental motion vocabulary, and an algorithm that enables real-time recognition of Structural Motion Grammar was developed. Moreover, the proposed method was verified by user evaluation and quantitative comparison tests.
Campos, Jorge; Barbado, Elena; Maldonado, Mariano; Andreu, Gemma; López de Fuentes, Pilar
2016-04-01
As it well-known, agricultural soil fertilization increases the rate of greenhouse gas (GHG) emission production such as CO2, CH4 and N2O. Participation share of this activity on the climate change is currently under study, as well as the mitigation possibilities. In this context, we considered that it would be interesting to know how this share is in the case of organic farming. In relation to this, a field experiment was carried out at the organic garden of the School of Agricultural, Food and Biosystems Engineering (ETSIAAB) in the Technical University of Madrid (UPM). The orchard included different management growing areas, corresponding to different schools of organic farming. Soil and gas samples were taken from these different sites. Gas samples were collected throughout the growing season from an accumulated atmosphere inside static chambers inserted into the soil. Then, these samples were carried to the laboratory and there analyzed. The results obtained allow knowing approximately how ecological fertilization contributes to air pollution due to greenhouse gases.
International Nuclear Information System (INIS)
Hansen, R.
1982-01-01
Within the framework of this thesis, X-ray pictures have been made of 430 gold or amalgam fillings in order to measure the gap between approximal cavity margin and filling margin. With amalgam fillings, the gap width measured after a residence time of half a year was 9.3 μm and widened to 136.9 μm after 8 years, which represents an increase to the 14-fold. The gap widths measured with gold inlays only doubled within this period, increasing from 38.8 μm after half a year to 77.4 μm after 8 years. The number of retention spots found in the approximal-cervical space with amalgam fillings was at least twice that found for gold fillings. From this it is concluded that gold inlays are by far the better solution for dental restorations. (orig./MG) [de
Nuclear Hartree-Fock approximation testing and other related approximations
International Nuclear Information System (INIS)
Cohenca, J.M.
1970-01-01
Hartree-Fock, and Tamm-Dancoff approximations are tested for angular momentum of even-even nuclei. Wave functions, energy levels and momenta are comparatively evaluated. Quadripole interactions are studied following the Elliott model. Results are applied to Ne 20 [pt
Approximate Implicitization Using Linear Algebra
Directory of Open Access Journals (Sweden)
Oliver J. D. Barrowclough
2012-01-01
Full Text Available We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD systems. We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms. We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.
Jingyu Shi; Lu Wang; Yuhong Yao; Na Su; Xudong Zhao; Xudong Zhao; Xudong Zhao; Chenyu Zhan
2017-01-01
This study examines the association between family function and self-esteem of Chinese university students with grandparenting experience, and explores the moderating effects of social support in this link. Two thousand five hundred thirty university students (1372 males and 1158 females) from a Chinese university completed the Perceived Social Support Scale, the Rosenberg’s Self-esteem Scale, and the Family Assessment Device (FAD). Six hundred and forty-five (25.69%) students reported grandp...
The correlation function for density perturbations in an expanding universe. I - Linear theory
Mcclelland, J.; Silk, J.
1977-01-01
The evolution of the two-point correlation function for adiabatic density perturbations in the early universe is studied. Analytical solutions are obtained for the evolution of linearized spherically symmetric adiabatic density perturbations and the two-point correlation function for these perturbations in the radiation-dominated portion of the early universe. The results are then extended to the regime after decoupling. It is found that: (1) adiabatic spherically symmetric perturbations comparable in scale with the maximum Jeans length would survive the radiation-dominated regime; (2) irregular fluctuations are smoothed out up to the scale of the maximum Jeans length in the radiation era, but regular fluctuations might survive on smaller scales; (3) in general, the only surviving structures for irregularly shaped adiabatic density perturbations of arbitrary but finite scale in the radiation regime are the size of or larger than the maximum Jeans length in that regime; (4) infinite plane waves with a wavelength smaller than the maximum Jeans length but larger than the critical dissipative damping scale could survive the radiation regime; and (5) black holes would also survive the radiation regime and might accrete sufficient mass after decoupling to nucleate the formation of galaxies.
Expectation Consistent Approximate Inference
DEFF Research Database (Denmark)
Opper, Manfred; Winther, Ole
2005-01-01
We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood from replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability dis...
Approximate reasoning in decision analysis
Energy Technology Data Exchange (ETDEWEB)
Gupta, M M; Sanchez, E
1982-01-01
The volume aims to incorporate the recent advances in both theory and applications. It contains 44 articles by 74 contributors from 17 different countries. The topics considered include: membership functions; composite fuzzy relations; fuzzy logic and inference; classifications and similarity measures; expert systems and medical diagnosis; psychological measurements and human behaviour; approximate reasoning and decision analysis; and fuzzy clustering algorithms.
Vaughn, Kelley; Hales, Cindy; Bush, Marta; Fox, James
1998-01-01
Describes implementation of functional behavioral assessment (FBA) through collaboration between a university (East Tennessee State University) and the local school system. Discusses related issues such as factors in team training, team size, FBA adaptations, and replicability of the FBA team model. (Author/DB)
Energy Technology Data Exchange (ETDEWEB)
Lisenko, S A; Kugeiko, M M [Belarusian State University, Minsk (Belarus)
2014-03-28
Approximating expressions are derived to calculate spectral and spatial characteristics of diffuse reflection of light from a two-layer medium mimicking human skin. The effectiveness of the use of these expressions in the optical diagnosis of skin biophysical parameters (tissue scattering parameters, concentration of melanin in the epidermis, concentration of total haemoglobin and bilirubin in the tissues of the dermis) and content of haemoglobin derivatives in blood (oxy-, deoxy-, met-, carboxy- and sulfhaemoglobin) is analysed numerically. The methods are proposed to determine in realtime these parameters without contact of the measuring instrument with the patient's body. (biophotonics)
Lisenko, S. A.; Kugeiko, M. M.
2014-03-01
Approximating expressions are derived to calculate spectral and spatial characteristics of diffuse reflection of light from a two-layer medium mimicking human skin. The effectiveness of the use of these expressions in the optical diagnosis of skin biophysical parameters (tissue scattering parameters, concentration of melanin in the epidermis, concentration of total haemoglobin and bilirubin in the tissues of the dermis) and content of haemoglobin derivatives in blood (oxy-, deoxy-, met-, carboxy- and sulfhaemoglobin) is analysed numerically. The methods are proposed to determine in realtime these parameters without contact of the measuring instrument with the patient's body.
Remizovich, V. S.
2010-06-01
It is commonly accepted that the Schwarzschild-Schuster two-flux approximation (1905, 1914) can be employed only for the calculation of the energy characteristics of the radiation field (energy density and energy flux density) and cannot be used to characterize the angular distribution of radiation field. However, such an inference is not valid. In several cases, one can calculate the radiation intensity inside matter and the reflected radiation with the aid of this simplest approximation in the transport theory. In this work, we use the results of the simplest one-parameter variant of the two-flux approximation to calculate the angular distribution (reflection function) of the radiation reflected by a semi-infinite isotropically scattering dissipative medium when a relatively broad beam is incident on the medium at an arbitrary angle relative to the surface. We do not employ the invariance principle and demonstrate that the reflection function exhibits the multiplicative property. It can be represented as a product of three functions: the reflection function corresponding to the single scattering and two identical h functions, which have the same physical meaning as the Ambartsumyan-Chandrasekhar function ( H) has. This circumstance allows a relatively easy derivation of simple analytical expressions for the H function, total reflectance, and reflection function. We can easily determine the relative contribution of the true single scattering in the photon backscattering at an arbitrary probability of photon survival Λ. We compare all of the parameters of the backscattered radiation with the data resulting from the calculations using the exact theory of Ambartsumyan, Chandrasekhar, et al., which was developed decades after the two-flux approximation. Thus, we avoid the application of fine mathematical methods (the Wiener-Hopf method, the Case method of singular functions, etc.) and obtain simple analytical expressions for the parameters of the scattered radiation
Ciofi degli Atti, Claudio; Morita, Hiko
2017-12-01
Background: The nuclear spectral function is a fundamental quantity that describes the mean-field and short-range correlation dynamics of nucleons embedded in the nuclear medium; its knowledge is a prerequisite for the interpretation of various electroweak scattering processes off nuclear targets aimed at providing fundamental information on strong and weak interactions. Whereas in the case of the three-nucleon and, partly, the four-nucleon systems, the spectral function can be calculated ab initio within a nonrelativistic many-body Schroedinger approach, in the case of complex nuclei only models of the correlated, high-momentum part of the spectral function are available so far. Purpose: The purpose of this paper is to present a new approach such that the spectral function for a specific nucleus can be obtained from a reliable many-body calculation based upon realistic nucleon-nucleon interactions, thus avoiding approximations leading to adjustable parameters. Methods: The expectation value of the nuclear many-body Hamiltonian, containing realistic nucleon-nucleon interaction of the Argonne family, is evaluated variationally by a normalization-conserving linked-cluster expansion and the resulting many-body correlated wave functions are used to calculate the one-nucleon and the two-nucleon momentum distributions; by analyzing the high-momentum behavior of the latter, the spectral function can be expressed in terms of a transparent convolution formula involving the relative and center-of-mass (c.m.) momentum distributions in specific regions of removal energy E and momentum k . Results: It is found that as a consequence of the factorization of the many-body wave functions at short internucleon separations, the high-momentum behavior of the two-nucleon momentum distributions in A =3 ,4 ,12 ,16 ,40 nuclei factorizes, at proper values of the relative and c.m. momenta, into the c.m. and relative momentum distributions, with the latter exhibiting a universal A
Functional capacity associated with work ability in older university staff employed by the state
Directory of Open Access Journals (Sweden)
Juleimar Soares Coelho de Amorim
Full Text Available Abstract Introduction: The increase in numbers of older adults in the workplace and in the number of years they spend in work prior to retiring has challenged health professionals to provide enable health conditions such that they may undertake occupational activity. Objective: To analyze the variables for functional ability, associated with work ability, in older adults who were government employees at a university. Methods: A cross-sectional design, with older workers aged 60 years old or over, located in different university centers and departments. A structured sociodemographic questionnaire was used to characterize the sample, and the Work Ability Index was used as an outcome variable for the associations, using the Timed Up and Go test, the handgrip strength test, the walking speed test and the chair sit to stand test. The Chi-squared test and Pearson correlation coefficient were used in the statistical analysis. The association of the factors of functional capacity was based on the odds ratio and 95% confidence interval, calculated using the Logistic Regression Model, as part of the SPSS statistical package for Windows. Results: A total of 258 staff participated in the investigation, with men (57.7% and a lower age range (60 to 62 years old predominating. Women differed in relation to falls after the age of 60 (p = 0.007 and in the last 12 months (p = 0.017. The mean Work Ability Index was 39.70 ± 5.64 points and a statistical association was ascertained between performance in the chair sit to stand test (OR = 2.26; p = 0.043. Muscle strength (r = 0.72; p < 0.000 and the chair sit to stand test (r = 0.73; p < 0.000 showed excellent correlation with work ability. Conclusion: The variables for functional capacity were associated with work ability.
Approximation properties of fine hyperbolic graphs
Indian Academy of Sciences (India)
2016-08-26
Aug 26, 2016 ... In this paper, we propose a definition of approximation property which is called the metric invariant translation approximation property for a countable discrete metric space. Moreover, we use ... Department of Applied Mathematics, Shanghai Finance University, Shanghai 201209, People's Republic of China ...
Approximate and renormgroup symmetries
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, Nail H. [Blekinge Institute of Technology, Karlskrona (Sweden). Dept. of Mathematics Science; Kovalev, Vladimir F. [Russian Academy of Sciences, Moscow (Russian Federation). Inst. of Mathematical Modeling
2009-07-01
''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)
Approximate and renormgroup symmetries
International Nuclear Information System (INIS)
Ibragimov, Nail H.; Kovalev, Vladimir F.
2009-01-01
''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)
Potvin, Guy
2015-10-01
We examine how the Rytov approximation describing log-amplitude and phase fluctuations of a wave propagating through weak uniform turbulence can be generalized to the case of turbulence with a large-scale nonuniform component. We show how the large-scale refractive index field creates Fermat rays using the path integral formulation for paraxial propagation. We then show how the second-order derivatives of the Fermat ray action affect the Rytov approximation, and we discuss how a numerical algorithm would model the general Rytov approximation.
Approximate reasoning in physical systems
International Nuclear Information System (INIS)
Mutihac, R.
1991-01-01
The theory of fuzzy sets provides excellent ground to deal with fuzzy observations (uncertain or imprecise signals, wavelengths, temperatures,etc.) fuzzy functions (spectra and depth profiles) and fuzzy logic and approximate reasoning. First, the basic ideas of fuzzy set theory are briefly presented. Secondly, stress is put on application of simple fuzzy set operations for matching candidate reference spectra of a spectral library to an unknown sample spectrum (e.g. IR spectroscopy). Thirdly, approximate reasoning is applied to infer an unknown property from information available in a database (e.g. crystal systems). Finally, multi-dimensional fuzzy reasoning techniques are suggested. (Author)
Geometric approximation algorithms
Har-Peled, Sariel
2011-01-01
Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.
International Nuclear Information System (INIS)
Knobloch, A.F.
1980-01-01
A simplified cost approximation for INTOR parameter sets in a narrow parameter range is shown. Plausible constraints permit the evaluation of the consequences of parameter variations on overall cost. (orig.) [de
First-generation Students’ Underperformance at University: The Impact of the Function of Selection
Directory of Open Access Journals (Sweden)
Mickaël eJury
2015-05-01
Full Text Available According to recent research, university not only has the role to educate and train students, it also has the role to select the best students. We argue that this function of selection disadvantages first-generation students, in comparison with continuing-generation students. Thus, the mere activation of the function of selection should be sufficient to produce achievement differences between first-generation and continuing-generation students in a novel academic task. Furthermore, we propose that when the function of selection is salient, first-generation students would be more vigilant to a cue that may confirm their inferiority, which should explain their underperformance. In the present experiment, participants were asked to complete an arithmetic modular task under two conditions, which either made the function of selection salient or reduced its importance. Participants’ vigilance to a threatening cue (i.e., their performance relative to others was measured through an eye-tracking technique. The results confirmed that first-generation students performed more poorly compared to continuing-generation students only when the function of selection was salient while no differences appeared in the no-selection condition. Regarding vigilance, the results did not confirm our hypothesis; thus, mediation path could not be tested. However, results indicated that at a high level of initial performance, first-generation students looked more often at the threatening cue. In others words, these students seemed more concerned about whether they were performing more poorly than others compared to their continuing-generation counterparts. Some methodological issues are discussed, notably regarding the measure of vigilance.
Strength, functionality and beauty of university buildings in earthquake-prone countries
WADA, Akira
2018-01-01
Strength, functionality and beauty are the three qualities identifying well-designed architecture. For buildings in earthquake-prone countries such as Japan, emphasis on seismic safety frequently leads to the sacrifice of functionality and beauty. Therefore, it is important to develop new structural technologies that can ensure the seismic performance of a building without hampering the pursuit of functionality and beauty. The moment-resisting frame structures widely used for buildings in Japan are likely to experience weak-story collapse. Pin-supported walls, which can effectively enhance the structural story-by-story integrity of a building, were introduced to prevent such an unfavorable failure pattern in the seismic retrofit of an eleven-story building on a university campus in Tokyo, while also greatly aesthetically enhancing the façade of the building. The slight damage observed and monitoring records of the retrofitted building during the 2011 Tohoku earthquake in Japan demonstrate that the pin-supported walls worked as intended, protecting the building and guaranteeing the safety of its occupants during the earthquake. PMID:29434079
Hang, Tian; Chen, Hui-Jiuan; Wang, Ji; Lin, Di-an; Wu, Jiangming; Liu, Di; Cao, Yuhong; Yang, Chengduan; Liu, Chenglin; Xiao, Shuai; Gu, Meilin; Pan, Shuolin; Wu, Mei X.; Xie, Xi
2018-05-01
Dispersion of hydrophilic particles in non-polar media has many important applications yet remains difficult. Surfactant or amphiphilic functionalization was conventionally applied to disperse particles but is highly dependent on the particle/solvent system and may induce unfavorable effects and impact particle hydrophilic nature. Recently 2 μm size polystyrene microbeads coated with ZnO nanospikes have been reported to display anomalous dispersity in phobic media without using surfactant or amphiphilic functionalization. However, due to the lack of understanding whether this phenomenon was applicable to a wider range of conditions, little application has been derived from it. Here the anomalous dispersity phenomenons of hydrophilic microparticles covered with nanospikes were systematically assessed at various conditions including different particle sizes, material compositions, particle morphologies, solvent hydrophobicities, and surface polar groups. Microparticles were functionalized with nanospikes through hydrothermal route, followed by dispersity test in hydrophobic media. The results suggest nanospikes consistently prevent particle aggregation in various particle or solvent conditions, indicating the universal applicability of the anomalous dispersion phenomenons. This work provides insight on the anomalous dispersity of hydrophilic particles in various systems and offers potential application to use this method for surfactant-free dispersions.
Gautschi, Walter; Rassias, Themistocles M
2011-01-01
Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovia, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational alg
Approximate kernel competitive learning.
Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang
2015-03-01
Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches. Copyright © 2014 Elsevier Ltd. All rights reserved.
Shearlets and Optimally Sparse Approximations
DEFF Research Database (Denmark)
Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q
2012-01-01
Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations...... optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction...... to and a survey about sparse approximations of cartoon-like images by band-limited and also compactly supported shearlet frames as well as a reference for the state-of-the-art of this research field....
Rational approximations for tomographic reconstructions
International Nuclear Information System (INIS)
Reynolds, Matthew; Beylkin, Gregory; Monzón, Lucas
2013-01-01
We use optimal rational approximations of projection data collected in x-ray tomography to improve image resolution. Under the assumption that the object of interest is described by functions with jump discontinuities, for each projection we construct its rational approximation with a small (near optimal) number of terms for a given accuracy threshold. This allows us to augment the measured data, i.e., double the number of available samples in each projection or, equivalently, extend (double) the domain of their Fourier transform. We also develop a new, fast, polar coordinate Fourier domain algorithm which uses our nonlinear approximation of projection data in a natural way. Using augmented projections of the Shepp–Logan phantom, we provide a comparison between the new algorithm and the standard filtered back-projection algorithm. We demonstrate that the reconstructed image has improved resolution without additional artifacts near sharp transitions in the image. (paper)
Approximation methods in probability theory
Čekanavičius, Vydas
2016-01-01
This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.
Ma, Jin-Gang; Zhang, Cai-Rong; Gong, Ji-Jun; Wu, You-Zhi; Kou, Sheng-Zhong; Yang, Hua; Chen, Yu-Hong; Liu, Zi-Jiang; Chen, Hong-Shan
2015-08-24
Alkaline-earth metallic dopant can improve the performance of anatase TiO2 in photocatalysis and solar cells. Aiming to understand doping mechanisms, the dopant formation energies, electronic structures, and optical properties for Be, Mg, Ca, Sr, and Ba doped anatase TiO2 are investigated by using density functional theory calculations with the HSE06 and PBE functionals. By combining our results with those of previous studies, the HSE06 functional provides a better description of electronic structures. The calculated formation energies indicate that the substitution of a lattice Ti with an AEM atom is energetically favorable under O-rich growth conditions. The electronic structures suggest that, AEM dopants shift the valence bands (VBs) to higher energy, and the dopant-state energies for the cases of Ca, Sr, and Ba are quite higher than Fermi levels, while the Be and Mg dopants result into the spin polarized gap states near the top of VBs. The components of VBs and dopant-states support that the AEM dopants are active in inter-band transitions with lower energy excitations. As to optical properties, Ca/Sr/Ba are more effective than Be/Mg to enhance absorbance in visible region, but the Be/Mg are superior to Ca/Sr/Ba for the absorbance improvement in near-IR region.
Directory of Open Access Journals (Sweden)
Jin-Gang Ma
2015-08-01
Full Text Available Alkaline-earth metallic dopant can improve the performance of anatase TiO2 in photocatalysis and solar cells. Aiming to understand doping mechanisms, the dopant formation energies, electronic structures, and optical properties for Be, Mg, Ca, Sr, and Ba doped anatase TiO2 are investigated by using density functional theory calculations with the HSE06 and PBE functionals. By combining our results with those of previous studies, the HSE06 functional provides a better description of electronic structures. The calculated formation energies indicate that the substitution of a lattice Ti with an AEM atom is energetically favorable under O-rich growth conditions. The electronic structures suggest that, AEM dopants shift the valence bands (VBs to higher energy, and the dopant-state energies for the cases of Ca, Sr, and Ba are quite higher than Fermi levels, while the Be and Mg dopants result into the spin polarized gap states near the top of VBs. The components of VBs and dopant-states support that the AEM dopants are active in inter-band transitions with lower energy excitations. As to optical properties, Ca/Sr/Ba are more effective than Be/Mg to enhance absorbance in visible region, but the Be/Mg are superior to Ca/Sr/Ba for the absorbance improvement in near-IR region.
COMPUTERIZATION OF EDUCATION AS A TOOL OF UNIVERSITY TEACHER’S BASIC FUNCTIONS SUPPORT
Directory of Open Access Journals (Sweden)
V. V. Denysenko
2014-04-01
Full Text Available The intensive process of education computerization confronts modern educators a number of economic, technical, social, psychological and educational problems that need to be solved. The use of computer technology in educational process opens enormous opportunities for the development of cognitive abilities – from sensory and perceptual to speech and mental forms. In broad dissemination and use of technical aids, optical and acoustic techniques, programmed education, cinema, television, computer, the modern scientists and researchers see one of the main factors to enhance education and upbringing level both at regular and higher education institutions. Unfortunately, the process of the organic combination of technical and pedagogical sciences in terms of theory and practice introducing computer (multimedia teaching aids is not as powerful as expected; and as it has been dictated by the needs of the modern society. The slow pace of computerization’s implementation of the learning process at high school has been caused by the reasons of different nature and scale. The main objective of the article is to highlight the problems of computer teaching aids using in teaching process at higher education institutions. The conducted analysis of studying computerization allowed us determining the impact and role in providing the university teacher’s basic functions. It has been established that the teacher is one of the management leading objects of educational and cognitive students’ activity and all its functions practically may have computer support.
Directory of Open Access Journals (Sweden)
Rosalinda M. Comia
2017-11-01
Full Text Available The study focused on the extent of utilization of the educational innovations and technology in research and extension functions of SUs. The descriptive design, triangulation method, and purposive sampling were applied in this study. The findings revealed that majority of the respondents are married adults and master’s degree graduates with education as their area of specialization. They are permanent in status and have considerable years in the University serving as research or extension officer. Research of SUs have common research thrusts in terms of environment and natural resources management but differ in their own respective agenda; similarly the SUs share common extension thrusts and concerns but differ in their programs, activities and projects related to community services. Commonly encountered problems concern inadequate funds and inability to access the available technology. Officers utilized educational innovations on research and extension to a moderate extent but software and hardware were utilized to a great extent; likewise internet-based communication was utilized to a great extent for research but used moderately for extension. This implies that compared to research, most of the extension functions do not require the use of internet-based communication. From the results of the study, it was recommended that review of the existing allocation of funds for technology development may be done to improve the existing hardware, software and communication facilities.
Directory of Open Access Journals (Sweden)
Osvaldo Costa Moreira
Full Text Available AbstractObjective To verify the behavior of anthropometric, cardiovascular and functional variables as indicators of health-related physical fitness in university professors and perform a comparison of these variables between sexes.Materials and methods We conducted an observational epidemiological cross-sectional study in 145 professors (45.86 ± 9.7 years, 103 men (71.03%, which were evaluated by measuring heart rate (HR and systolic (SBP and diastolic (DBP pressure at rest, body weight, height, body mass index (BMI, body fat percentage (BF%, handgrip strength (HGS, flexibility and cardiorespiratory fitness (CRF. We proceeded to the descriptive analysis, Student t-test for comparison between sexes and multiple regression analysis to verify the association between the variables analyzed. It was adopted a significance level of p < 0.05.Results The sex affected all variables. Women had better levels of BMI, flexibility, SBP and DBP. The BF% and CRF were associated with SBP and BMI in both sexes.Conclusion The behavior of anthropometric, cardiovascular and functional variables indicated unsatisfactory values for flexibility, HGS and BMI, with the worst levels among men. Furthermore, the variables that showed better association with HRPF were BF% and CRF.
Establishment of hybridized focus measure functions as a universal method for autofocusing
Shah, Mohammad Imran; Mishra, Smriti; Rout, Chittaranjan
2017-12-01
Exact focusing is essential for any automatic image capturing system. Performances of focus measure functions (FMFs) used for autofocusing are sensitive to image contents and imaging systems. Therefore, identification of universal FMF assumes a lot of significance. Eight FMFs were hybridized in pairs of two and implemented simultaneously on a single stack to calculate the hybrid focus measure. In total, 28 hybrid FMFs (HFMFs) and eight FMFs were implemented on stacks of images from three different imaging modalities. Performance of FMFs was found to the best at 50% region sampling. Accuracy, focus error, and false maxima were calculated to evaluate the performance of each FMF. Nineteen HFMFs provided >90% accuracy. Image distortion (noise, contrast, saturation, illumination, etc.) was performed to evaluate robustness of HFMFs. Hybrid of tenengrad variance and steerable filter-based (VGRnSFB) FMFs was identified as the most robust and accurate function with an accuracy of ≥90% and a relatively lower focus error and false maxima rate. Sharpness of focus curve of VGRnSFB along with eight individual FMFs was also computed to determine the efficacy of HFMF for the optimization process. VGRnSFB HFMF may be implemented for automated capturing of an image for any imaging system.
On Covering Approximation Subspaces
Directory of Open Access Journals (Sweden)
Xun Ge
2009-06-01
Full Text Available Let (U';C' be a subspace of a covering approximation space (U;C and X⊂U'. In this paper, we show that and B'(X⊂B(X∩U'. Also, iff (U;C has Property Multiplication. Furthermore, some connections between outer (resp. inner definable subsets in (U;C and outer (resp. inner definable subsets in (U';C' are established. These results answer a question on covering approximation subspace posed by J. Li, and are helpful to obtain further applications of Pawlak rough set theory in pattern recognition and artificial intelligence.
Beyond the random phase approximation
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian S.
2013-01-01
We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for ab initio calculations of electronic correlation energies in solids and molecules. The method is an extension of the random phase approximation (RPA) derived from time-dependent density...... functional theory and the adiabatic connection fluctuation-dissipation theorem and contains no fitted parameters. The new kernel is shown to preserve the accurate description of dispersive interactions from RPA while significantly improving the description of short-range correlation in molecules, insulators......, and metals. For molecular atomization energies, the rALDA is a factor of 7 better than RPA and a factor of 4 better than the Perdew-Burke-Ernzerhof (PBE) functional when compared to experiments, and a factor of 3 (1.5) better than RPA (PBE) for cohesive energies of solids. For transition metals...
Lekala, M. L.; Chakrabarti, B.; Das, T. K.; Rampho, G. J.; Sofianos, S. A.; Adam, R. M.; Haldar, S. K.
2017-05-01
We study the ground-state and the low-lying excitations of a trapped Bose gas in an isotropic harmonic potential for very small (˜ 3) to very large (˜ 10^7) particle numbers. We use the two-body correlated basis functions and the shape-dependent van der Waals interaction in our many-body calculations. We present an exhaustive study of the effect of inter-atomic correlations and the accuracy of the mean-field equations considering a wide range of particle numbers. We calculate the ground-state energy and the one-body density for different values of the van der Waals parameter C6. We compare our results with those of the modified Gross-Pitaevskii results, the correlated Hartree hypernetted-chain equations (which also utilize the two-body correlated basis functions), as well as of the diffusion Monte Carlo for hard sphere interactions. We observe the effect of the attractive tail of the van der Waals potential in the calculations of the one-body density over the truly repulsive zero-range potential as used in the Gross-Pitaevskii equation and discuss the finite-size effects. We also present the low-lying collective excitations which are well described by a hydrodynamic model in the large particle limit.
International Nuclear Information System (INIS)
Niksic, T.; Vretenar, D.; Ring, P.
2006-01-01
The framework of relativistic self-consistent mean-field models is extended to include correlations related to the restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to perform configuration mixing of angular-momentum and particle-number projected relativistic wave functions. The geometry is restricted to axially symmetric shapes, and the intrinsic wave functions are generated from the solutions of the relativistic mean-field+Lipkin-Nogami BCS equations, with a constraint on the mass quadrupole moment. The model employs a relativistic point-coupling (contact) nucleon-nucleon effective interaction in the particle-hole channel, and a density-independent δ-interaction in the pairing channel. Illustrative calculations are performed for 24 Mg, 32 S, and 36 Ar, and compared with results obtained employing the model developed in the first part of this work, i.e., without particle-number projection, as well as with the corresponding nonrelativistic models based on Skyrme and Gogny effective interactions
Directory of Open Access Journals (Sweden)
Pollard Beth
2012-12-01
Full Text Available Abstract Background The Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC is a widely used patient reported outcome in osteoarthritis. An important, but frequently overlooked, aspect of validating health outcome measures is to establish if items exhibit differential item functioning (DIF. That is, if respondents have the same underlying level of an attribute, does the item give the same score in different subgroups or is it biased towards one subgroup or another. The aim of the study was to explore DIF in the Likert format WOMAC for the first time in a UK osteoarthritis population with respect to demographic, social, clinical and psychological factors. Methods The sample comprised a community sample of 763 people with osteoarthritis who participated in the Somerset and Avon Survey of Health. The WOMAC was explored for DIF by gender, age, social deprivation, social class, employment status, distress, body mass index and clinical factors. Ordinal regression models were used to identify DIF items. Results After adjusting for age, two items were identified for the physical functioning subscale as having DIF with age identified as the DIF factor for 2 items, gender for 1 item and body mass index for 1 item. For the WOMAC pain subscale, for people with hip osteoarthritis one item was identified with age-related DIF. The impact of the DIF items rarely had a significant effect on the conclusions of group comparisons. Conclusions Overall, the WOMAC performed well with only a small number of DIF items identified. However, as DIF items were identified in for the WOMAC physical functioning subscale it would be advisable to analyse data taking into account the possible impact of the DIF items when weight, gender or especially age effects, are the focus of interest in UK-based osteoarthritis studies. Similarly for the WOMAC pain subscale in people with hip osteoarthritis it would be worthwhile to analyse data taking into account the
DEFF Research Database (Denmark)
Madsen, Rasmus Elsborg
2005-01-01
The Dirichlet compound multinomial (DCM), which has recently been shown to be well suited for modeling for word burstiness in documents, is here investigated. A number of conceptual explanations that account for these recent results, are provided. An exponential family approximation of the DCM...
Approximation by Cylinder Surfaces
DEFF Research Database (Denmark)
Randrup, Thomas
1997-01-01
We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...
Analytical approximation of neutron physics data
International Nuclear Information System (INIS)
Badikov, S.A.; Vinogradov, V.A.; Gaj, E.V.; Rabotnov, N.S.
1984-01-01
The method for experimental neutron-physical data analytical approximation by rational functions based on the Pade approximation is suggested. It is shown that the existence of the Pade approximation specific properties in polar zones is an extremely favourable analytical property essentially extending the convergence range and increasing its rate as compared with polynomial approximation. The Pade approximation is the particularly natural instrument for resonance curve processing as the resonances conform to the complex poles of the approximant. But even in a general case analytical representation of the data in this form is convenient and compact. Thus representation of the data on the neutron threshold reaction cross sections (BOSPOR constant library) in the form of rational functions lead to approximately twenty fold reduction of the storaged numerical information as compared with the by-point calculation at the same accWracy
Optimal Piecewise-Linear Approximation of the Quadratic Chaotic Dynamics
Directory of Open Access Journals (Sweden)
J. Petrzela
2012-04-01
Full Text Available This paper shows the influence of piecewise-linear approximation on the global dynamics associated with autonomous third-order dynamical systems with the quadratic vector fields. The novel method for optimal nonlinear function approximation preserving the system behavior is proposed and experimentally verified. This approach is based on the calculation of the state attractor metric dimension inside a stochastic optimization routine. The approximated systems are compared to the original by means of the numerical integration. Real electronic circuits representing individual dynamical systems are derived using classical as well as integrator-based synthesis and verified by time-domain analysis in Orcad Pspice simulator. The universality of the proposed method is briefly discussed, especially from the viewpoint of the higher-order dynamical systems. Future topics and perspectives are also provided
Cosmological applications of Padé approximant
International Nuclear Information System (INIS)
Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan
2014-01-01
As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation
Cosmological applications of Padé approximant
Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan
2014-01-01
As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation.
Vasić, M.; Radojević, Z.
2017-08-01
One of the main disadvantages of the recently reported method, for setting up the drying regime based on the theory of moisture migration during drying, lies in a fact that it is based on a large number of isothermal experiments. In addition each isothermal experiment requires the use of different drying air parameters. The main goal of this paper was to find a way how to reduce the number of isothermal experiments without affecting the quality of the previously proposed calculation method. The first task was to define the lower and upper inputs as well as the output of the “black box” which will be used in the Box-Wilkinson’s orthogonal multi-factorial experimental design. Three inputs (drying air temperature, humidity and velocity) were used within the experimental design. The output parameter of the model represents the time interval between any two chosen characteristic points presented on the Deff - t. The second task was to calculate the output parameter for each planed experiments. The final output of the model is the equation which can predict the time interval between any two chosen characteristic points as a function of the drying air parameters. This equation is valid for any value of the drying air parameters which are within the defined area designated with lower and upper limiting values.
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2011-01-01
Most prestack traveltime relations we tend work with are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multi-focusing or double square-root (DSR) and the common reflection stack (CRS) equations. Using the DSR equation, I analyze the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I derive expansion based solutions of this eikonal based on polynomial expansions in terms of the reflection and dip angles in a generally inhomogenous background medium. These approximate solutions are free of singularities and can be used to estimate travetimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. A Marmousi example demonstrates the usefulness of the approach. © 2011 Society of Exploration Geophysicists.
Topology, calculus and approximation
Komornik, Vilmos
2017-01-01
Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...
Approximate Bayesian recursive estimation
Czech Academy of Sciences Publication Activity Database
Kárný, Miroslav
2014-01-01
Roč. 285, č. 1 (2014), s. 100-111 ISSN 0020-0255 R&D Projects: GA ČR GA13-13502S Institutional support: RVO:67985556 Keywords : Approximate parameter estimation * Bayesian recursive estimation * Kullback–Leibler divergence * Forgetting Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.038, year: 2014 http://library.utia.cas.cz/separaty/2014/AS/karny-0425539.pdf
Approximating Preemptive Stochastic Scheduling
Megow Nicole; Vredeveld Tjark
2009-01-01
We present constant approximative policies for preemptive stochastic scheduling. We derive policies with a guaranteed performance ratio of 2 for scheduling jobs with release dates on identical parallel machines subject to minimizing the sum of weighted completion times. Our policies as well as their analysis apply also to the recently introduced more general model of stochastic online scheduling. The performance guarantee we give matches the best result known for the corresponding determinist...
Optimization and approximation
Pedregal, Pablo
2017-01-01
This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.
Henderson, Saras; Kendall, Elizabeth; Forday, Peter; Cowan, Debbie
2013-01-01
Culturally and linguistically diverse (CALD) communities in Queensland, Australia, do not access health services, contributing to poor health outcomes. To improve health in CALD communities, a partnership was formed between the state government, two nongovernment CALD-specific organizations (NGOs), and a university to develop a service that could facilitate health service use. This qualitative research explored the partners' perspectives on how the partnership functioned and its outcomes. We sought to (1) explore how participants engaged with the principles of partnership, the processes they used, and their beliefs about the facilitators and barriers to intersectoral collaboration and (2) gain insights into how the partners perceived the development and functioning of the partnership. Qualitative, semistructured interviews were conducted with each of the key stakeholders in the partnership (n = 4). A focus group was also conducted with those working within the two NGO partners in the delivery of the service (n = 8). Open-ended questions drawn from the literature on partnership principles were used to guide the interviews and focus group data collection. The data were transcribed and analyzed using thematic principles. The four themes identified were: (1) Perceived benefits of the partnership outweighed organizational differences; (2) respectful relationships sustained the partnership; (3) mitigating conflict enabled the purpose of the partnership to be fulfilled; and (4) a neutral interpersonal space enabled the partnership to be enacted. Our study showed how contextual pressures created within the system can damage tenuous connections that have been developed between otherwise competitive organizations, leading to dissolution of partnerships. However, the study has also shown that partnerships may be purpose and time bound, not necessarily with respect to longevity. Through strategic negotiations, partnerships can be sustained until the goal of the partnership is
Necci, Marco; Piovesan, Damiano; Tosatto, Silvio C E
2016-12-01
Intrinsic disorder (ID) in proteins has been extensively described for the last decade; a large-scale classification of ID in proteins is mostly missing. Here, we provide an extensive analysis of ID in the protein universe on the UniProt database derived from sequence-based predictions in MobiDB. Almost half the sequences contain an ID region of at least five residues. About 9% of proteins have a long ID region of over 20 residues which are more abundant in Eukaryotic organisms and most frequently cover less than 20% of the sequence. A small subset of about 67,000 (out of over 80 million) proteins is fully disordered and mostly found in Viruses. Most proteins have only one ID, with short ID evenly distributed along the sequence and long ID overrepresented in the center. The charged residue composition of Das and Pappu was used to classify ID proteins by structural propensities and corresponding functional enrichment. Swollen Coils seem to be used mainly as structural components and in biosynthesis in both Prokaryotes and Eukaryotes. In Bacteria, they are confined in the nucleoid and in Viruses provide DNA binding function. Coils & Hairpins seem to be specialized in ribosome binding and methylation activities. Globules & Tadpoles bind antigens in Eukaryotes but are involved in killing other organisms and cytolysis in Bacteria. The Undefined class is used by Bacteria to bind toxic substances and mediate transport and movement between and within organisms in Viruses. Fully disordered proteins behave similarly, but are enriched for glycine residues and extracellular structures. © 2016 The Protein Society.
Cdc42 and Tks5: a minimal and universal molecular signature for functional invadosomes.
Di Martino, Julie; Paysan, Lisa; Gest, Caroline; Lagrée, Valérie; Juin, Amélie; Saltel, Frédéric; Moreau, Violaine
2014-01-01
Invadosomes are actin-based structures involved in extracellular-matrix degradation. Invadosomes, either known as podosomes or invadopodia, are found in an increasing number of cell types. Moreover, their overall organization and molecular composition may vary from one cell type to the other. Some are constitutive such as podosomes in hematopoietic cells whereas others are inducible. However, they share the same feature, their ability to interact and to degrade the extracellular matrix. Based on the literature and our own experiments, the aim of this study was to establish a minimal molecular definition of active invadosomes. We first highlighted that Cdc42 is the key RhoGTPase involved in invadosome formation in all described models. Using different cellular models, such as NIH-3T3, HeLa, and endothelial cells, we demonstrated that overexpression of an active form of Cdc42 is sufficient to form invadosome actin cores. Therefore, active Cdc42 must be considered not only as an inducer of filopodia, but also as an inducer of invadosomes. Depending on the expression level of Tks5, these Cdc42-dependent actin cores were endowed or not with a proteolytic activity. In fact, Tks5 overexpression rescued this activity in Tks5 low expressing cells. We thus described the adaptor protein Tks5 as a major actor of the invadosome degradation function. Surprisingly, we found that Src kinases are not always required for invadosome formation and function. These data suggest that even if Src family members are the principal kinases involved in the majority of invadosomes, it cannot be considered as a common element for all invadosome structures. We thus define a minimal and universal molecular signature of invadosome that includes Cdc42 activity and Tks5 presence in order to drive the actin machinery and the proteolytic activity of these invasive structures.
Directory of Open Access Journals (Sweden)
Yan Li
2017-11-01
Full Text Available Due to the volatile and correlated nature of wind speed, a high share of wind power penetration poses challenges to power system production simulation. Existing power system probabilistic production simulation approaches are in short of considering the time-varying characteristics of wind power and load, as well as the correlation between wind speeds at the same time, which brings about some problems in planning and analysis for the power system with high wind power penetration. Based on universal generating function (UGF, this paper proposes a novel probabilistic production simulation approach considering wind speed correlation. UGF is utilized to develop the chronological models of wind power that characterizes wind speed correlation simultaneously, as well as the chronological models of conventional generation sources and load. The supply and demand are matched chronologically to not only obtain generation schedules, but also reliability indices both at each simulation interval and the whole period. The proposed approach has been tested on the improved IEEE-RTS 79 test system and is compared with the Monte Carlo approach and the sequence operation theory approach. The results verified the proposed approach with the merits of computation simplicity and accuracy.
Do light nuclei display a universal γ-ray strength function?
Directory of Open Access Journals (Sweden)
Voinov A.
2012-02-01
Full Text Available In this work we focus on properties in the quasi-continuum of light nuclei. Generally, both level density and γ-ray strength function (γ-SF differ from nucleus to nucleus. In order to investigate this closer, we have performed particle-γ coincidences using the reactions (p, p', (p, d and (p, t on a 46Ti target. In particular, the very rich data set of the 46Ti(p, p'46Ti inelastic scattering reaction allows analysis of the coincidence data for many independent data sets. Using the Oslo method, we find one common level density for all data sets. If transitions to well-separated low-energy levels are included, the deduced γ-SF may change by a factor of 2 – 3, due strong to Porter-Thomas fluctuations. However, a universal γ-SF with small fluctuations is found provided that only excitation energies above 3 MeV are taken into account. The nuclear structure of the titaniums is discussed within a combinatorial quasi-particle model, showing that only few Nilsson orbitals participate in building up the level density for these light nuclei.
Universal failure model for multi-unit systems with shared functionality
International Nuclear Information System (INIS)
Volovoi, Vitali
2013-01-01
A Universal Failure Model (UFM) is proposed for complex systems that rely on a large number of entities for performing a common function. Economy of scale or other considerations may dictate the need to pool resources for common purpose, but the resulting strong coupling precludes the grouping of those components into modules. Existing system-level failure models rely on modularity for reducing modeling complexity, so the UFM will fill an important gap in constructing efficient system-level models. Conceptually, the UFM resembles cellular automata (CA) infused with realistic failure mechanisms. Components’ behavior is determined based on the balance between their strength (capacity) and their load (demand) share. If the load exceeds the components’ capacity, the component fails and its load share is distributed among its neighbors (possibly with a time delay and load losses). The strength of components can degrade with time if the load exceeds an elastic threshold. The global load (demand) carried by the system can vary over time, with the peak values providing shocks to the system (e.g., wind loads in civil structures, electricity demand, stressful activities to human bodies, or drought in an ecosystem). Unlike the models traditionally studied by CA, the focus of the presented model is on the system reliability, and specifically on the study of time-to-failure distributions, rather than steady-state patterns and average time-to-failure characteristics. In this context, the relationships between the types of failure distributions and the parameters of the failure model are discussed
Cyclic approximation to stasis
Directory of Open Access Journals (Sweden)
Stewart D. Johnson
2009-06-01
Full Text Available Neighborhoods of points in $mathbb{R}^n$ where a positive linear combination of $C^1$ vector fields sum to zero contain, generically, cyclic trajectories that switch between the vector fields. Such points are called stasis points, and the approximating switching cycle can be chosen so that the timing of the switches exactly matches the positive linear weighting. In the case of two vector fields, the stasis points form one-dimensional $C^1$ manifolds containing nearby families of two-cycles. The generic case of two flows in $mathbb{R}^3$ can be diffeomorphed to a standard form with cubic curves as trajectories.
International Nuclear Information System (INIS)
El Sawi, M.
1983-07-01
A simple approach employing properties of solutions of differential equations is adopted to derive an appropriate extension of the WKBJ method. Some of the earlier techniques that are commonly in use are unified, whereby the general approximate solution to a second-order homogeneous linear differential equation is presented in a standard form that is valid for all orders. In comparison to other methods, the present one is shown to be leading in the order of iteration, and thus possibly has the ability of accelerating the convergence of the solution. The method is also extended for the solution of inhomogeneous equations. (author)
The relaxation time approximation
International Nuclear Information System (INIS)
Gairola, R.P.; Indu, B.D.
1991-01-01
A plausible approximation has been made to estimate the relaxation time from a knowledge of the transition probability of phonons from one state (r vector, q vector) to other state (r' vector, q' vector), as a result of collision. The relaxation time, thus obtained, shows a strong dependence on temperature and weak dependence on the wave vector. In view of this dependence, relaxation time has been expressed in terms of a temperature Taylor's series in the first Brillouin zone. Consequently, a simple model for estimating the thermal conductivity is suggested. the calculations become much easier than the Callaway model. (author). 14 refs
Methods of approximation theory
National Research Council Canada - National Science Library
Stepane︠t︡s, A. I
2005-01-01
.... Korneichuk, Α. V. Efimov, S. A. Telyakovskii, etc. In the same years, the concept of (φ, β) -derivative defined for a given function / by a given sequence of numbers ψ = ψ (k), k = 1 , 2 , . . . , and numbers β was formed. The ordinary rth derivative, r = 1 , 2 , . . . , of a periodic function is a particular case of the (φ, /3)-derivative for y(k...
Directory of Open Access Journals (Sweden)
John H. Summerfield
2015-01-01
Full Text Available This work investigates a one-dimensional model for the solid-state diffusion in a LiC6/LiMnO2 rechargeable cell. This cell is used in hybrid electric vehicles. In this environment the cell experiences low frequency electrical pulses that degrade the electrodes. The model’s starting point is Fick’s second law of diffusion. The Laplace transform is used to move from time as the independent variable to frequency as the independent variable. To better understand the effect of frequency changes on the cell, a transfer function is constructed. The transfer function is a transcendental function so a Padé approximant is found to better describe the model at the origin. Consider ∂c(r,t/∂t=D∂2c(r/∂2r+(2/r(∂c(r/∂r.
Directory of Open Access Journals (Sweden)
Usenko L.V.
2017-04-01
Full Text Available Progressive aging of the population is accompanied by age-related changes in the body, primarily from the central nervous system, which causes a decline in the cognitive health of man and society as a whole. The emergence of cognitive deficits leads to a decrease in a person's ability to think, learn, actively perceive information, make decisions, worsen other psycho-physiological functions. The aim of our study was to assess the state of cognitive functions of the elderly people, the dynamics of their changes, depending on the age stage of life, as well as under the influence of program exercises and specially designed trainings aimed at activating mental and physical activity. 165 students of the university aged 55-85 years took part in the study. Two groups of subjects were identified. The first one numbering 100 people we divided into 3 subgroups in order to identify phased age-related changes in cognitive functions and, depending on this definition, the need for preventive or corrective measures: 1 subgroup - 55-65 years, 2 subgroup - 66-75 years and 3 subgroup - 76 years and older. The study of their cognitive functions was determined upon admission to the university. The second group consisted of 65 people, whose indicators of cognitive functions were determined in dynamics: at admission to the university and at the completion of training. To assess the level of cognitive functions, we used a formalized screening technique - the Montreal Scale. The established dynamics of the components of cognitive functions, depending on age, makes it possible to differentially approach the choice of preventive or corrective measures aimed at activating cognitive functions, in each age group with an emphasis on those of them that have been changed to a greater extent. The effectiveness of the proposed structure of studies at the university for the elderly was shown.
Plasma Physics Approximations in Ares
International Nuclear Information System (INIS)
Managan, R. A.
2015-01-01
Lee & More derived analytic forms for the transport properties of a plasma. Many hydro-codes use their formulae for electrical and thermal conductivity. The coefficients are complex functions of Fermi-Dirac integrals, Fn( μ/θ ), the chemical potential, μ or ζ = ln(1+e μ/θ ), and the temperature, θ = kT. Since these formulae are expensive to compute, rational function approximations were fit to them. Approximations are also used to find the chemical potential, either μ or ζ . The fits use ζ as the independent variable instead of μ/θ . New fits are provided for A α (ζ ),A β (ζ ), ζ, f(ζ ) = (1 + e -μ/θ )F 1/2 (μ/θ), F 1/2 '/F 1/2 , F c α , and F c β . In each case the relative error of the fit is minimized since the functions can vary by many orders of magnitude. The new fits are designed to exactly preserve the limiting values in the non-degenerate and highly degenerate limits or as ζ→ 0 or ∞. The original fits due to Lee & More and George Zimmerman are presented for comparison.
Braxton, John M.
2010-01-01
In this article, I assert that the work of colleges and universities forms a social action system. I array the critical positions represented in this issue according to the four functional imperatives of social action systems: adaptation, goal attainment, integration, and pattern maintenance. I discuss the role of normative structures for these…
Uniform analytic approximation of Wigner rotation matrices
Hoffmann, Scott E.
2018-02-01
We derive the leading asymptotic approximation, for low angle θ, of the Wigner rotation matrix elements, dm1m2 j(θ ) , uniform in j, m1, and m2. The result is in terms of a Bessel function of integer order. We numerically investigate the error for a variety of cases and find that the approximation can be useful over a significant range of angles. This approximation has application in the partial wave analysis of wavepacket scattering.
Exposing the Mathematical Wizard: Approximating Trigonometric Functions
Gordon, Sheldon P.
2011-01-01
For almost all students, what happens when they push buttons on their calculators is essentially magic, and the techniques used are seemingly pure wizardry. In this article, the author draws back the curtain to expose some of the mathematics behind computational wizardry and introduces some fundamental ideas that are accessible to precalculus…
Distributed Approximating Functional Approach to Burgers' Equation ...
African Journals Online (AJOL)
This equation is similar to, but simpler than, the Navier-Stokes equation in fluid dynamics. To verify this advantage through some comparison studies, an exact series solution are also obtained. In addition, the presented scheme has numerically stable behavior. After demonstrating the convergence and accuracy of the ...
Rational Approximations of the Inverse Gaussian Function.
Byars, Jackson A.; Roscoe, John T.
There are at least two situations in which the behavioral scientist wishes to transform uniformly distributed data into normally distributed data: (1) In studies of sampling distributions where uniformly distributed pseudo-random numbers are generated by a computer but normally distributed numbers are desired; and (2) In measurement applications…
The random phase approximation
International Nuclear Information System (INIS)
Schuck, P.
1985-01-01
RPA is the adequate theory to describe vibrations of the nucleus of very small amplitudes. These vibrations can either be forced by an external electromagnetic field or can be eigenmodes of the nucleus. In a one dimensional analogue the potential corresponding to such eigenmodes of very small amplitude should be rather stiff otherwise the motion risks to be a large amplitude one and to enter a region where the approximation is not valid. This means that nuclei which are supposedly well described by RPA must have a very stable groundstate configuration (must e.g. be very stiff against deformation). This is usually the case for doubly magic nuclei or close to magic nuclei which are in the middle of proton and neutron shells which develop a very stable groundstate deformation; we take the deformation as an example but there are many other possible degrees of freedom as, for example, compression modes, isovector degrees of freedom, spin degrees of freedom, and many more
The quasilocalized charge approximation
International Nuclear Information System (INIS)
Kalman, G J; Golden, K I; Donko, Z; Hartmann, P
2005-01-01
The quasilocalized charge approximation (QLCA) has been used for some time as a formalism for the calculation of the dielectric response and for determining the collective mode dispersion in strongly coupled Coulomb and Yukawa liquids. The approach is based on a microscopic model in which the charges are quasilocalized on a short-time scale in local potential fluctuations. We review the conceptual basis and theoretical structure of the QLC approach and together with recent results from molecular dynamics simulations that corroborate and quantify the theoretical concepts. We also summarize the major applications of the QLCA to various physical systems, combined with the corresponding results of the molecular dynamics simulations and point out the general agreement and instances of disagreement between the two
Nonlinear approximation with general wave packets
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete...
Energy Technology Data Exchange (ETDEWEB)
Bulgac, A
2013-03-27
This document is a summary of the physics research carried out by the University of Washington centered group. Attached are reports for the previous years as well as the full exit report of the entire UNEDF collaboration.
Rational approximations and quantum algorithms with postselection
Mahadev, U.; de Wolf, R.
2015-01-01
We study the close connection between rational functions that approximate a given Boolean function, and quantum algorithms that compute the same function using post-selection. We show that the minimal degree of the former equals (up to a factor of 2) the minimal query complexity of the latter. We
Padé approximations and diophantine geometry.
Chudnovsky, D V; Chudnovsky, G V
1985-04-01
Using methods of Padé approximations we prove a converse to Eisenstein's theorem on the boundedness of denominators of coefficients in the expansion of an algebraic function, for classes of functions, parametrized by meromorphic functions. This result is applied to the Tate conjecture on the effective description of isogenies for elliptic curves.
Approximate quantum Markov chains
Sutter, David
2018-01-01
This book is an introduction to quantum Markov chains and explains how this concept is connected to the question of how well a lost quantum mechanical system can be recovered from a correlated subsystem. To achieve this goal, we strengthen the data-processing inequality such that it reveals a statement about the reconstruction of lost information. The main difficulty in order to understand the behavior of quantum Markov chains arises from the fact that quantum mechanical operators do not commute in general. As a result we start by explaining two techniques of how to deal with non-commuting matrices: the spectral pinching method and complex interpolation theory. Once the reader is familiar with these techniques a novel inequality is presented that extends the celebrated Golden-Thompson inequality to arbitrarily many matrices. This inequality is the key ingredient in understanding approximate quantum Markov chains and it answers a question from matrix analysis that was open since 1973, i.e., if Lieb's triple ma...
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2012-05-01
Many of the explicit prestack traveltime relations used in practice are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multifocusing, based on the double square-root (DSR) equation, and the common reflection stack (CRS) approaches. Using the DSR equation, I constructed the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I recasted the eikonal in terms of the reflection angle, and thus, derived expansion based solutions of this eikonal in terms of the difference between the source and receiver velocities in a generally inhomogenous background medium. The zero-order term solution, corresponding to ignoring the lateral velocity variation in estimating the prestack part, is free of singularities and can be used to estimate traveltimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. The higher-order terms include limitations for horizontally traveling waves, however, we can readily enforce stability constraints to avoid such singularities. In fact, another expansion over reflection angle can help us avoid these singularities by requiring the source and receiver velocities to be different. On the other hand, expansions in terms of reflection angles result in singularity free equations. For a homogenous background medium, as a test, the solutions are reasonably accurate to large reflection and dip angles. A Marmousi example demonstrated the usefulness and versatility of the formulation. © 2012 Society of Exploration Geophysicists.
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Abstract. The general theme of this note is illustrated by the following theorem: Theorem 1. Suppose K is a compact set in the complex plane and 0 belongs to the boundary ∂K. Let A(K) denote the space of all functions f on K such that f is holo- morphic in a neighborhood of K and f(0) = 0. Also for any given positive integer ...
Directory of Open Access Journals (Sweden)
Nirachara Boonyanuwat
2008-05-01
Full Text Available A Quality Function Deployment (QFD technique is used to design a curriculum for Industrial Engineering (IE at Prince of Songkla University (PSU. This paper shows a systematical step-by-step application of the QFD. This analysis focuses both on external evaluators of the university, companies that hire graduates and students parents, and internal evaluators of the university, the student themselves and faculty. Survey data from 232 stakeholders were used in the QFD analysis in order to identify the requirements most valued by them. Results indicate that the stakeholders are looking for the graduates abilities in the area of productivity improvement, knowledge application, production planning and control, quality management and control, and manufacturing management. Further, the QFD is used to translate the key requirements into an effective curriculum. It can be concluded that the QFD is a useful tool for designing a curriculum for higher educational institutions.
Regression with Sparse Approximations of Data
DEFF Research Database (Denmark)
Noorzad, Pardis; Sturm, Bob L.
2012-01-01
We propose sparse approximation weighted regression (SPARROW), a method for local estimation of the regression function that uses sparse approximation with a dictionary of measurements. SPARROW estimates the regression function at a point with a linear combination of a few regressands selected...... by a sparse approximation of the point in terms of the regressors. We show SPARROW can be considered a variant of \\(k\\)-nearest neighbors regression (\\(k\\)-NNR), and more generally, local polynomial kernel regression. Unlike \\(k\\)-NNR, however, SPARROW can adapt the number of regressors to use based...
Approximation of the semi-infinite interval
Directory of Open Access Journals (Sweden)
A. McD. Mercer
1980-01-01
Full Text Available The approximation of a function f∈C[a,b] by Bernstein polynomials is well-known. It is based on the binomial distribution. O. Szasz has shown that there are analogous approximations on the interval [0,∞ based on the Poisson distribution. Recently R. Mohapatra has generalized Szasz' result to the case in which the approximating function is αe−ux∑k=N∞(uxkα+β−1Γ(kα+βf(kαuThe present note shows that these results are special cases of a Tauberian theorem for certain infinite series having positive coefficients.
Mathematical analysis, approximation theory and their applications
Gupta, Vijay
2016-01-01
Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.
International Nuclear Information System (INIS)
Weron, K.
1991-08-01
This paper is a continuation of our previous work, where the new probabilistic model based directly on the reaction picture of relaxation was introduced and a general relaxation equation was derived. Here we show the universal character of distributions of damping rates and waiting times used in this model. Moreover, we discuss in detail a physical significance of the response function derived as a solution of the general relaxation equation. (author). 23 refs, 4 figs
An Examination of the Effects of ADHD Coaching on University Students' Executive Functioning
Parker, David R.; Hoffman, Sharon Field; Sawilowsky, Shlomo; Rolands, Laura
2011-01-01
Seven undergraduates at a selective Midwestern university participated in a semester-long pilot study regarding the impact of ADHD coaching services on their academic experiences. Coaches in the study had extensive qualifications, including specific training to address the needs of college students with ADHD. Three major themes emerged from…
Lopez, Daniel A.; Lopez, Daniel C.; Andrade, Lorenzo I.; Lopez, Boris A.
2011-01-01
This study analyzes the coverage, organizational patterns, problems and trends of international organizations for university cooperation in Latin America and the Caribbean. More than 30 international organizations for cooperation currently operating in Latin America and the Caribbean were identified. Two groups of institutions with more than 60%…
Changes and Emerging Trends in the CE Function on University Campuses.
Einsiedel, Albert A., Jr.
1998-01-01
Reviews global changes and the following strategies changing the definition of university extension and continuing education: (1) cost-recovery entrepreneurial model; (2) emphasis on professional continuing education; (3) diminishing focus on traditional service; (4) distance education; and (5) global marketing. (SK)
Functional multilingualism at the North-West University as part of the ...
African Journals Online (AJOL)
The aim of this article is to explore the link between language management and the sociopolitical environment in which institutions of higher learning, particularly the North-West University, operate. Along the lines set by Candlin (1991: vi–vii), it is argued that language management should take due cognisance of the ...
The Functions and Problems of the Urban University: A Comparative Perspective.
City Univ. of New York, NY. Graduate School. Center for European Studies.
Issues concerning the urban university in Great Britain, France, Sweden, Japan, and West Germany are considered in the five selected conference papers that make up this document. In "Analysis in Politics: The Regionalization of Swedish Higher Education," Rune Premfors discusses how Swedish regionalization of higher education used…
Evaluation of variational approximations
International Nuclear Information System (INIS)
Trevisan, L.A.
1991-01-01
In Feynman's approach to quantum statistical mechanics, the partition function can e represented as a path integral. A recently proposed variation method of Feynman-Kleinert is able to transform the path integral into an integral in phase space, in which the quantum fluctuations have been taken care of by introducing the effective classical potential. This method has been testes with succeed for the smooth potentials and for the singular potential of delta. The method to the strong singular potentials is applied: a quadratic potential and a linear potential both with a rigid wall at the origin. By satisfying the condition that the density of the particle be vanish at the origin, and adapted method of Feynman-Kleinert in order to improve the method is introduced. (author)
Directory of Open Access Journals (Sweden)
Newman Wadesango
2017-05-01
Full Text Available Quality of financial reporting is limited to issues of compliance to statutory provisions under which state enterprises in Zimbabwe operate, usefulness of the reports produced and their impact on the national fiscus. It is thus measured by way of compliance to these expectations and is indicated by way of a disclosure index signifying the presence of each of the expected aspects. This study therefore sought to establish the contribution of enterprise risk management and internal audit function towards the quality of financial reporting in universities in Zimbabwe. The study adopted a desktop analysis where relevant literature was reviewed. Quality of internal audit function was found to influence quality of financial reporting in that the strength, or quality, of the IAF will contribute to a distinctly different control environment depending on the strength of the good corporate governance in the university. Findings of this desktop research have undoubtedly revealed the gaps in the governance processes in state universities and it is envisaged that a careful analysis of these lacunas will provide a guide in the development of strategies and policy that strengthen state enterprise governance processes. It is hoped that this will help the parent ministry in charge of state enterprises, and, the relevant management of specific state enterprises to determine the magnitude of resources and efforts for implementation of efficient and effective enterprise risk management, internal audit function and corporate governance systems
Spline approximation, Part 1: Basic methodology
Ezhov, Nikolaj; Neitzel, Frank; Petrovic, Svetozar
2018-04-01
In engineering geodesy point clouds derived from terrestrial laser scanning or from photogrammetric approaches are almost never used as final results. For further processing and analysis a curve or surface approximation with a continuous mathematical function is required. In this paper the approximation of 2D curves by means of splines is treated. Splines offer quite flexible and elegant solutions for interpolation or approximation of "irregularly" distributed data. Depending on the problem they can be expressed as a function or as a set of equations that depend on some parameter. Many different types of splines can be used for spline approximation and all of them have certain advantages and disadvantages depending on the approximation problem. In a series of three articles spline approximation is presented from a geodetic point of view. In this paper (Part 1) the basic methodology of spline approximation is demonstrated using splines constructed from ordinary polynomials and splines constructed from truncated polynomials. In the forthcoming Part 2 the notion of B-spline will be explained in a unique way, namely by using the concept of convex combinations. The numerical stability of all spline approximation approaches as well as the utilization of splines for deformation detection will be investigated on numerical examples in Part 3.
Energy Technology Data Exchange (ETDEWEB)
Cavinato, M.; Marangoni, M.; Saruis, A.M.
1990-10-01
This report describes the COINCIDENCE code written for the IBM 3090/300E computer in Fortran 77 language. The output data of this code are the (e, e'x) threefold differential cross-sections, the nuclear structure functions, the polarization asymmetry and the angular correlation coefficients. In the real photon limit, the output data are the angular distributions for plane polarized incident photons. The code reads from tape the transition matrix elements previously calculated, by in continuum self-consistent RPA (random phase approximation) theory with Skyrme interactions. This code has been used to perform a numerical analysis of coincidence (e, e'x) reactions with polarized electrons on the /sup 16/O nucleous.
The correlation function for density perturbations in an expanding universe. II - Nonlinear theory
Mcclelland, J.; Silk, J.
1977-01-01
A formalism is developed to find the two-point and higher-order correlation functions for a given distribution of sizes and shapes of perturbations which are randomly placed in three-dimensional space. The perturbations are described by two parameters such as central density and size, and the two-point correlation function is explicitly related to the luminosity function of groups and clusters of galaxies
Unambiguous results from variational matrix Pade approximants
International Nuclear Information System (INIS)
Pindor, Maciej.
1979-10-01
Variational Matrix Pade Approximants are studied as a nonlinear variational problem. It is shown that although a stationary value of the Schwinger functional is a stationary value of VMPA, the latter has also another stationary value. It is therefore proposed that instead of looking for a stationary point of VMPA, one minimizes some non-negative functional and then one calculates VMPA at the point where the former has the absolute minimum. This approach, which we call the Method of the Variational Gradient (MVG) gives unambiguous results and is also shown to minimize a distance between the approximate and the exact stationary values of the Schwinger functional
Pade approximant calculations for neutron escape probability
International Nuclear Information System (INIS)
El Wakil, S.A.; Saad, E.A.; Hendi, A.A.
1984-07-01
The neutron escape probability from a non-multiplying slab containing internal source is defined in terms of a functional relation for the scattering function for the diffuse reflection problem. The Pade approximant technique is used to get numerical results which compare with exact results. (author)
Li, Weiwei; Yang, Wenjing; Li, Wenfu; Li, Yadan; Wei, Dongtao; Li, Huimin; Qiu, Jiang; Zhang, Qinglin
2015-01-01
Creative persons play an important role in technical innovation and social progress. There is little research on the neural correlates with researchers with high academic achievement. We used a combined structural (regional gray matter volume, rGMV) and functional (resting-state functional connectivity analysis, rsFC) approach to examine the…
Improved Dutch Roll Approximation for Hypersonic Vehicle
Directory of Open Access Journals (Sweden)
Liang-Liang Yin
2014-06-01
Full Text Available An improved dutch roll approximation for hypersonic vehicle is presented. From the new approximations, the dutch roll frequency is shown to be a function of the stability axis yaw stability and the dutch roll damping is mainly effected by the roll damping ratio. In additional, an important parameter called roll-to-yaw ratio is obtained to describe the dutch roll mode. Solution shows that large-roll-to-yaw ratio is the generate character of hypersonic vehicle, which results the large error for the practical approximation. Predictions from the literal approximations derived in this paper are compared with actual numerical values for s example hypersonic vehicle, results show the approximations work well and the error is below 10 %.
Directory of Open Access Journals (Sweden)
Dell’Osso L
2014-07-01
Full Text Available Liliana Dell’Osso,1 Marianna Abelli,1 Stefano Pini,1 Marina Carlini,1 Barbara Carpita,1 Elisabetta Macchi,2 Federica Gorrasi,2 Francesco Mengali,1 Rosalba Tognetti,2 Gabriele Massimetti1 1Department of Clinical and Experimental Medicine, Section of Psychiatry, 2Prorectorate to Students Affairs and Right to Education, University of Pisa, Pisa, Italy Abstract: Social anxiety disorder is a common condition often associated with severe impairment in educational career. The aim of this paper was to evaluate prevalence rates and correlates of mild, moderate, and severe forms of social anxiety spectrum in a large sample of university students. Overall, 717 university students were assessed with the Social Anxiety Spectrum Self-Report questionnaire. Using two cut-off scores, 61.4% of subjects were classified as low scorers, 10% as medium scorers, and 28.6% as high scorers. Both high and medium scorers reported fears related to social situations. Interpersonal sensitivity and specific phobias were more common among women with low scores. Childhood/adolescence social anxiety features were more common among males with medium scores. Behavioral inhibition was more common among males with high scores. Functional impairment was severe among high scorers and, to a lesser extent, among medium scorers. Social anxiety spectrum is largely represented among university students. Future studies should investigate whether sufferers of social phobia underachieve or end their professional objectives prematurely. Keywords: social anxiety spectrum, behavioral inhibition, gender, subthreshold, self-rating, DSM-5
Directory of Open Access Journals (Sweden)
Ali akbar Farhangi
2018-06-01
Full Text Available Currently, ICT and educational processes are experiencing development and innovation. This new trend will help promote educational technology and enhance innovations regarding educational planning. E-learning is considered as one of the most prominent ICT applications across the world. Advantages of virtual learning have entailed daily usage in various universities. Learning management systems are specific web-based systems to manage, track students, define courses, and evaluate the learners. However, these systems may involve inefficiencies and disadvantages as well. This paper attempts to identify the LMS functional areas in University of Tehran based on a specific conceptual framework and to present the relevant issues and problems for each dimension. The data for the present study were collected using focused group interviews, system observations. The researchers also compared the documents and the university system with that of other universities. The results of the theme analysis indicated that “communication” and “system cooperation” dimensions are involved with more important problems and issues. The researchers believe that the main issues are due to the test modules, evaluations, and systemic and underlying databases.
Square well approximation to the optical potential
International Nuclear Information System (INIS)
Jain, A.K.; Gupta, M.C.; Marwadi, P.R.
1976-01-01
Approximations for obtaining T-matrix elements for a sum of several potentials in terms of T-matrices for individual potentials are studied. Based on model calculations for S-wave for a sum of two separable non-local potentials of Yukawa type form factors and a sum of two delta function potentials, it is shown that the T-matrix for a sum of several potentials can be approximated satisfactorily over all the energy regions by the sum of T-matrices for individual potentials. Based on this, an approximate method for finding T-matrix for any local potential by approximating it by a sum of suitable number of square wells is presented. This provides an interesting way to calculate the T-matrix for any arbitary potential in terms of Bessel functions to a good degree of accuracy. The method is applied to the Saxon-Wood potentials and good agreement with exact results is found. (author)
Directory of Open Access Journals (Sweden)
Jingyu Shi
2017-05-01
Full Text Available This study examines the association between family function and self-esteem of Chinese university students with grandparenting experience, and explores the moderating effects of social support in this link. Two thousand five hundred thirty university students (1372 males and 1158 females from a Chinese university completed the Perceived Social Support Scale, the Rosenberg’s Self-esteem Scale, and the Family Assessment Device (FAD. Six hundred and forty-five (25.69% students reported grandparenting experience and they reported lower scores on self-esteem and social support than the students raised only by their parents. The grandparenting group scored higher on such dimensions of family functioning as Communication, Role, Affective Involvement, Affective Responsiveness, and General Family Function (GF than their counterpart group. For both groups, self-esteem scores were positively correlated with social support scores, while negatively correlated with FAD all sub-scale scores. Hierarchical regression analysis showed that for the students with grandparenting experience the social support moderated the relationship between GF and self-esteem. When students reported a high level of social support, those with low GF score reported higher scores in self-esteem than those with low self-esteem. However, in case of low social support, there were no differences in self-esteem between groups with high and low GF scores. These findings suggest that social support plays a positive role to relieve the adverse impact of poor family function on self-esteem of the adolescents with grandparenting experience. In addition, the significance and limitations of the results will be discussed.
Shi, Jingyu; Wang, Lu; Yao, Yuhong; Su, Na; Zhao, Xudong; Zhan, Chenyu
2017-01-01
This study examines the association between family function and self-esteem of Chinese university students with grandparenting experience, and explores the moderating effects of social support in this link. Two thousand five hundred thirty university students (1372 males and 1158 females) from a Chinese university completed the Perceived Social Support Scale, the Rosenberg's Self-esteem Scale, and the Family Assessment Device (FAD). Six hundred and forty-five (25.69%) students reported grandparenting experience and they reported lower scores on self-esteem and social support than the students raised only by their parents. The grandparenting group scored higher on such dimensions of family functioning as Communication, Role, Affective Involvement, Affective Responsiveness, and General Family Function (GF) than their counterpart group. For both groups, self-esteem scores were positively correlated with social support scores, while negatively correlated with FAD all sub-scale scores. Hierarchical regression analysis showed that for the students with grandparenting experience the social support moderated the relationship between GF and self-esteem. When students reported a high level of social support, those with low GF score reported higher scores in self-esteem than those with low self-esteem. However, in case of low social support, there were no differences in self-esteem between groups with high and low GF scores. These findings suggest that social support plays a positive role to relieve the adverse impact of poor family function on self-esteem of the adolescents with grandparenting experience. In addition, the significance and limitations of the results will be discussed.
Shi, Jingyu; Wang, Lu; Yao, Yuhong; Su, Na; Zhao, Xudong; Zhan, Chenyu
2017-01-01
This study examines the association between family function and self-esteem of Chinese university students with grandparenting experience, and explores the moderating effects of social support in this link. Two thousand five hundred thirty university students (1372 males and 1158 females) from a Chinese university completed the Perceived Social Support Scale, the Rosenberg’s Self-esteem Scale, and the Family Assessment Device (FAD). Six hundred and forty-five (25.69%) students reported grandparenting experience and they reported lower scores on self-esteem and social support than the students raised only by their parents. The grandparenting group scored higher on such dimensions of family functioning as Communication, Role, Affective Involvement, Affective Responsiveness, and General Family Function (GF) than their counterpart group. For both groups, self-esteem scores were positively correlated with social support scores, while negatively correlated with FAD all sub-scale scores. Hierarchical regression analysis showed that for the students with grandparenting experience the social support moderated the relationship between GF and self-esteem. When students reported a high level of social support, those with low GF score reported higher scores in self-esteem than those with low self-esteem. However, in case of low social support, there were no differences in self-esteem between groups with high and low GF scores. These findings suggest that social support plays a positive role to relieve the adverse impact of poor family function on self-esteem of the adolescents with grandparenting experience. In addition, the significance and limitations of the results will be discussed. PMID:28611720
THE MOTIVATION IN THE PERFORMANCE OF THE INSPECTION FUNCTIONS: INSPECTION SERVICE AT THE UNIVERSITY
Directory of Open Access Journals (Sweden)
Andrés Falcón Armas
2014-06-01
Full Text Available A summary of Hackman and Oldham job characteristics model (1976, 1980 is presented as follows. The five cores job dimensions and their relationships with the critical psychological states and with the personal and organisational outcomes are also defined. Likewise, observed is the modulatory role of self-efficiency variables, intensity of the personal development and self-satisfaction needs with the context. The predictive theoretical relationship model is related to the post of inspector of education in the field of educational organisations, including universities.
Forms of Approximate Radiation Transport
Brunner, G
2002-01-01
Photon radiation transport is described by the Boltzmann equation. Because this equation is difficult to solve, many different approximate forms have been implemented in computer codes. Several of the most common approximations are reviewed, and test problems illustrate the characteristics of each of the approximations. This document is designed as a tutorial so that code users can make an educated choice about which form of approximate radiation transport to use for their particular simulation.
Approximation by planar elastic curves
DEFF Research Database (Denmark)
Brander, David; Gravesen, Jens; Nørbjerg, Toke Bjerge
2016-01-01
We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient......-driven optimization is then used to find the approximating elastic curve....
Function of Attachment Hierarchies in Young Adults Experiencing the Transition From University
Directory of Open Access Journals (Sweden)
Elaine Scharfe
2017-10-01
Full Text Available An important cornerstone of Bowlby’s attachment theory (1969/1997 is the proposal that moving away from parents and toward peers is an indication of healthy development. In this study, we explored the benefit of the shift, not the shift itself, in a sample of emerging adults experiencing a stressful life event (i.e., the transition from university. Although the shift from parents to peers is an important cornerstone of Bowlby’s theory, this study is one of the first to test the differential effects of parent and peer networks on adjustment. In this longitudinal study, 73 participants completed surveys to assess attachment, social networks, and distress one month before completing their undergraduate degree and 6 months later. We found that participants experiencing the transition from university, who chose a peer as the first person in their network, tended to report stable scores over time whereas participants who chose a family member reported more variable scores. Interestingly, the direction of change was not different for the groups, just the magnitude of change. Furthermore, the difference in adjustment was not found when we compared the groups using the percent hierarchy method highlighting that there is a benefit of exploring primary attachment relationships when examining the influence of networks on adjustment.
International Nuclear Information System (INIS)
Blum, Daniel B; Voth, Greg A; Bewley, Gregory P; Bodenschatz, Eberhard; Gibert, Mathieu; Xu Haitao; Gylfason, Ármann; Mydlarski, Laurent; Yeung, P K
2011-01-01
We present a systematic comparison of conditional structure functions in nine turbulent flows. The flows studied include forced isotropic turbulence simulated on a periodic domain, passive grid wind tunnel turbulence in air and in pressurized SF 6 , active grid wind tunnel turbulence (in both synchronous and random driving modes), the flow between counter-rotating discs, oscillating grid turbulence and the flow in the Lagrangian exploration module (in both constant and random driving modes). We compare longitudinal Eulerian second-order structure functions conditioned on the instantaneous large-scale velocity in each flow to assess the ways in which the large scales affect the small scales in a variety of turbulent flows. Structure functions are shown to have larger values when the large-scale velocity significantly deviates from the mean in most flows, suggesting that dependence on the large scales is typical in many turbulent flows. The effects of the large-scale velocity on the structure functions can be quite strong, with the structure function varying by up to a factor of 2 when the large-scale velocity deviates from the mean by ±2 standard deviations. In several flows, the effects of the large-scale velocity are similar at all the length scales we measured, indicating that the large-scale effects are scale independent. In a few flows, the effects of the large-scale velocity are larger on the smallest length scales. (paper)
DEFF Research Database (Denmark)
Sadegh, Payman; Spall, J. C.
1998-01-01
simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo...
International Conference Approximation Theory XIV
Schumaker, Larry
2014-01-01
This volume developed from papers presented at the international conference Approximation Theory XIV, held April 7–10, 2013 in San Antonio, Texas. The proceedings contains surveys by invited speakers, covering topics such as splines on non-tensor-product meshes, Wachspress and mean value coordinates, curvelets and shearlets, barycentric interpolation, and polynomial approximation on spheres and balls. Other contributed papers address a variety of current topics in approximation theory, including eigenvalue sequences of positive integral operators, image registration, and support vector machines. This book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.
Dynamical rescaling, the EMC effect and universality of hadron structure functions
International Nuclear Information System (INIS)
Close, F.E.
1984-04-01
Data are compared on the EMC effect, with the hypothesis that the quark confinement size increases in going from a free nucleon to a nucleus. In QCD a dynamical rescaling is predicted: Q 2 variation of the distribution function in a given target parallels the dependence on confinement size, R, at fixed Q 2 . Thus a dynamical scale invariance obtains when both R and Q 2 are varied, yielding the dynamical rescaling relation F 2 sup(A)(x, Q 2 ) = F 2 sup(N)(x, zetaQ 2 ) where zeta > 1 is predicted for any nucleus and is a function of the confinement size. Data on 12 nuclei agree with this, implying that confinement size is governed by nuclear density. The formalism is tested by relating the pion and nucleon structure functions. (author)
DEFF Research Database (Denmark)
DING, YI; Wang, Peng; Goel, Lalit
2010-01-01
from long term planning point of view utilizing universal generating function (UGF) methods. The reliability models of wind farms and conventional generators are represented as the correspondin UGFs and the special operators for these UGFs are defined to evaluate the customer and the system...... reliabilities. The effect of transmission network on customer reliabilities is also considered in the system UGF. The power output models of wind turbine generators in a wind farm considering wind speed correlation and un-correlation are developed, respectively. A reliability-based reserve expansion method...
Conductance of Sidewall-Functionalized Carbon Nanotubes: Universal Dependence on Adsorption Sites
DEFF Research Database (Denmark)
García-Lastra, J.M.; Thygesen, Kristian Sommer; Strange, Mikkel
2008-01-01
We use density functional theory to study the effect of molecular adsorbates on the conductance of metallic carbon nanotubes (CNT). The five molecules considered (NO2, NH2, H, COOH, OH) lead to very similar scattering of the electrons. The adsorption of a single molecule suppresses one of the two...
DEFF Research Database (Denmark)
Sadegh, Payman
1997-01-01
This paper deals with a projection algorithm for stochastic approximation using simultaneous perturbation gradient approximation for optimization under inequality constraints where no direct gradient of the loss function is available and the inequality constraints are given as explicit functions...... of the optimization parameters. It is shown that, under application of the projection algorithm, the parameter iterate converges almost surely to a Kuhn-Tucker point, The procedure is illustrated by a numerical example, (C) 1997 Elsevier Science Ltd....
Dell'Osso, Liliana; Abelli, Marianna; Pini, Stefano; Carlini, Marina; Carpita, Barbara; Macchi, Elisabetta; Gorrasi, Federica; Mengali, Francesco; Tognetti, Rosalba; Massimetti, Gabriele
2014-01-01
Social anxiety disorder is a common condition often associated with severe impairment in educational career. The aim of this paper was to evaluate prevalence rates and correlates of mild, moderate, and severe forms of social anxiety spectrum in a large sample of university students. Overall, 717 university students were assessed with the Social Anxiety Spectrum Self-Report questionnaire. Using two cut-off scores, 61.4% of subjects were classified as low scorers, 10% as medium scorers, and 28.6% as high scorers. Both high and medium scorers reported fears related to social situations. Interpersonal sensitivity and specific phobias were more common among women with low scores. Childhood/adolescence social anxiety features were more common among males with medium scores. Behavioral inhibition was more common among males with high scores. Functional impairment was severe among high scorers and, to a lesser extent, among medium scorers. Social anxiety spectrum is largely represented among university students. Future studies should investigate whether sufferers of social phobia underachieve or end their professional objectives prematurely.
The RNAi Universe in Fungi: A Varied Landscape of Small RNAs and Biological Functions.
Torres-Martínez, Santiago; Ruiz-Vázquez, Rosa M
2017-09-08
RNA interference (RNAi) is a conserved eukaryotic mechanism that uses small RNA molecules to suppress gene expression through sequence-specific messenger RNA degradation, translational repression, or transcriptional inhibition. In filamentous fungi, the protective function of RNAi in the maintenance of genome integrity is well known. However, knowledge of the regulatory role of RNAi in fungi has had to wait until the recent identification of different endogenous small RNA classes, which are generated by distinct RNAi pathways. In addition, RNAi research on new fungal models has uncovered the role of small RNAs and RNAi pathways in the regulation of diverse biological functions. In this review, we give an up-to-date overview of the different classes of small RNAs and RNAi pathways in fungi and their roles in the defense of genome integrity and regulation of fungal physiology and development, as well as in the interaction of fungi with biotic and abiotic environments.
Tanaka, Shoji; Kirino, Eiji
2016-01-01
Conceiving concrete mental imagery is critical for skillful musical expression and performance. The precuneus, a core component of the default mode network (DMN), is a hub of mental image processing that participates in functions such as episodic memory retrieval and imagining future events. The precuneus connects with many brain regions in the frontal, parietal, temporal, and occipital cortices. The aim of this study was to examine the effects of long-term musical training on the resting-sta...
Functioning of the students business-incubators on the base of leading Ukrainian universities
S.A. Tulchinska
2015-01-01
The aim of the article. The aim of the article is the research of business-incubators functioning in Ukraine as a component of innovative infrastructure in general and student business-incubators in particular and developing criteria for evaluating their activity. The results of the analysis. It was determined that purpose of student innovation business incubator should be protection and representation of students interests through innovative transformation of students ideas, projects in t...
Directory of Open Access Journals (Sweden)
A.I. Bosenco
2013-11-01
Full Text Available A study of the functional capacity of the organism lower division students. The study involved 85 students of 1-2 courses, 14 of which were engaged and were part of the team of the University of volleyball. As a student of muscular work performed pedaling on bicycle. The energy level was determined by performing metered loads with changing facilities for closed cycle. The data characterizing the physiological "cost" of adaptation, the level of stress the body of students in different phases of muscular work. Developed and presented model characteristics of the energy level of the body of girls. Reviewed degree of mobilization of functional reserves under load for closed loop five-point scale. Defined physical condition of students during the first year. The recommendations of the evaluation and prediction of the actual state of the physical health of students and improve physical education in high school.
A universal Model-R Coupler to facilitate the use of R functions for model calibration and analysis
Wu, Yiping; Liu, Shuguang; Yan, Wende
2014-01-01
Mathematical models are useful in various fields of science and engineering. However, it is a challenge to make a model utilize the open and growing functions (e.g., model inversion) on the R platform due to the requirement of accessing and revising the model's source code. To overcome this barrier, we developed a universal tool that aims to convert a model developed in any computer language to an R function using the template and instruction concept of the Parameter ESTimation program (PEST) and the operational structure of the R-Soil and Water Assessment Tool (R-SWAT). The developed tool (Model-R Coupler) is promising because users of any model can connect an external algorithm (written in R) with their model to implement various model behavior analyses (e.g., parameter optimization, sensitivity and uncertainty analysis, performance evaluation, and visualization) without accessing or modifying the model's source code.
Methods of Fourier analysis and approximation theory
Tikhonov, Sergey
2016-01-01
Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.
Prescod-Weinstein, Chanda; Afshordi, Niayesh
2011-01-01
Structure formation provides a strong test of any cosmic acceleration model because a successful dark energy model must not inhibit or overpredict the development of observed large-scale structures. Traditional approaches to studies of structure formation in the presence of dark energy or a modified gravity implement a modified Press-Schechter formalism, which relates the linear overdensities to the abundance of dark matter haloes at the same time. We critically examine the universality of the Press-Schechter formalism for different cosmologies, and show that the halo abundance is best correlated with spherical linear overdensity at 94% of collapse (or observation) time. We then extend this argument to ellipsoidal collapse (which decreases the fractional time of best correlation for small haloes), and show that our results agree with deviations from modified Press-Schechter formalism seen in simulated mass functions. This provides a novel universal prescription to measure linear density evolution, based on current and future observations of cluster (or dark matter) halo mass function. In particular, even observations of cluster abundance in a single epoch will constrain the entire history of linear growth of cosmological of perturbations.
Schachner, Adena; Zhu, Liqi; Li, Jing; Kelemen, Deborah
2017-01-01
Young children in Western cultures tend to endorse teleological (function-based) explanations broadly across many domains, even when scientifically unwarranted. For instance, in contrast to Western adults, they explicitly endorse the idea that mountains were created for climbing, just like hats were created for warmth. Is this bias a product of culture, or a product of universal aspects of human cognition? In two studies, we explored whether adults and children in Mainland China, a highly secular, non-Western culture, show a bias for teleological explanations. When explaining both object properties (Exp. 1) and origins (Exp. 2), we found evidence that they do. While Chinese adults restricted teleological explanations to scientifically warranted cases, Chinese children endorsed them more broadly, extending them across different kinds of natural phenomena. This bias decreased with rising grade level across first, second and fourth grade. Overall, these data provide evidence that children’s bias for teleological explanations is not solely a product of Western Abrahamic cultures. Instead, it extends to other cultures including the East Asian secular culture of modern-day China. This suggests that the bias for function-based explanations may be driven by universal aspects of human cognition. PMID:28110152
Density functionals from deep learning
McMahon, Jeffrey M.
2016-01-01
Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional are required. In this work, a model based on deep learning is developed to approximate this functional. Deep learning allows computational models that are capable of naturally discovering intricate structure in large and/or high-dimensional data sets, with multiple levels of abstraction. As no assumptions are ...
Some results in Diophantine approximation
DEFF Research Database (Denmark)
Pedersen, Steffen Højris
the basic concepts on which the papers build. Among other it introduces metric Diophantine approximation, Mahler’s approach on algebraic approximation, the Hausdorff measure, and properties of the formal Laurent series over Fq. The introduction ends with a discussion on Mahler’s problem when considered......This thesis consists of three papers in Diophantine approximation, a subbranch of number theory. Preceding these papers is an introduction to various aspects of Diophantine approximation and formal Laurent series over Fq and a summary of each of the three papers. The introduction introduces...
International Nuclear Information System (INIS)
Freidel, L.; Maillet, J.M.
1992-09-01
Using a geometrical approach to the quantum Yang-Baxter equation, the quantum algebra U h (sl 2 ) and its universal quantum R-matrix are explicitly constructed as functionals of the associated classical r-matrix. In this framework, the quantum algebra U h (sl 2 ) is naturally imbedded in the universal enveloping algebra of the sl 2 current algebra. (author) 13 refs
The universal existence of myodural bridge in mammals: an indication of a necessary function.
Zheng, Nan; Yuan, Xiao-Ying; Chi, Yan-Yan; Liu, Pei; Wang, Bing; Sui, Jia-Ying; Han, Seung-Ho; Yu, Sheng-Bo; Sui, Hong-Jin
2017-08-15
The "myodural bridge" was described in literatures as a dense fibrous tissue connecting the sub-occipital musculature with the spinal dura mater in human studies. Now the concept of "myodural bridge" was perceived as an exact anatomical structure presumably essential for critical physiological functions in human body, and might exist in other mammals as well. To determine the existence of the "myodural bridge" in other mammals and to lay a foundation for the functional study, we examined representatives in five different mammalian orders. Based on the anatomical dissections, P45 plastinated sections and histological sections, we found that a dense fibrous tissue connected the rectus capitisdorsalis minor and the spinal dura mater through the dorsal atlanto-occipital interspace with or without the medium of the posterior atlanto-occipital membrane. These observed connective tissues were very similar to the "myodural bridge" previously described in humans. We proposed that the "myodural bridge", as an evolutionally conserved structure, presents in many other mammals. Moreover, we believed that the "myodural bridge" might be a homologous organ in mammals. Thus, this study could provide an insight for our understanding the physiological significance of the "myodural bridge", especially in human.