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)
Traveling cluster approximation for uncorrelated amorphous systems
International Nuclear Information System (INIS)
Kaplan, T.; Sen, A.K.; Gray, L.J.; Mills, R.
1985-01-01
In this paper, the authors apply the TCA concepts to spatially disordered, uncorrelated systems (e.g., fluids or amorphous metals without short-range order). This is the first approximation scheme for amorphous systems that takes cluster effects into account while preserving the Herglotz property for any amount of disorder. They have performed some computer calculations for the pair TCA, for the model case of delta-function potentials on a one-dimensional random chain. These results are compared with exact calculations (which, in principle, taken into account all cluster effects) and with the CPA, which is the single-site TCA. The density of states for the pair TCA clearly shows some improvement over the CPA, and yet, apparently, the pair approximation distorts some of the features of the exact results. They conclude that the effects of large clusters are much more important in an uncorrelated liquid metal than in a substitutional alloy. As a result, the pair TCA, which does quite a nice job for alloys, is not adequate for the liquid. Larger clusters must be treated exactly, and therefore an n-TCA with n > 2 must be used
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
Variational random phase approximation for the anharmonic oscillator
International Nuclear Information System (INIS)
Dukelsky, J.; Schuck, P.
1990-04-01
The recently derived Variational Random Phase Approximation is examined using the anharmonic oscillator model. Special attention is paid to the ground state RPA wave function and the convergence of the proposed truncation scheme to obtain the diagonal density matrix. Comparison with the standard Coupled Cluster method is made
Variational Gaussian approximation for Poisson data
Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen
2018-02-01
The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.
Analysis of the dynamical cluster approximation for the Hubbard model
Aryanpour, K.; Hettler, M. H.; Jarrell, M.
2002-01-01
We examine a central approximation of the recently introduced Dynamical Cluster Approximation (DCA) by example of the Hubbard model. By both analytical and numerical means we study non-compact and compact contributions to the thermodynamic potential. We show that approximating non-compact diagrams by their cluster analogs results in a larger systematic error as compared to the compact diagrams. Consequently, only the compact contributions should be taken from the cluster, whereas non-compact ...
APPECT: An Approximate Backbone-Based Clustering Algorithm for Tags
DEFF Research Database (Denmark)
Zong, Yu; Xu, Guandong; Jin, Pin
2011-01-01
algorithm for Tags (APPECT). The main steps of APPECT are: (1) we execute the K-means algorithm on a tag similarity matrix for M times and collect a set of tag clustering results Z={C1,C2,…,Cm}; (2) we form the approximate backbone of Z by executing a greedy search; (3) we fix the approximate backbone...... as the initial tag clustering result and then assign the rest tags into the corresponding clusters based on the similarity. Experimental results on three real world datasets namely MedWorm, MovieLens and Dmoz demonstrate the effectiveness and the superiority of the proposed method against the traditional...... Agglomerative Clustering on tagging data, which possess the inherent drawbacks, such as the sensitivity of initialization. In this paper, we instead make use of the approximate backbone of tag clustering results to find out better tag clusters. In particular, we propose an APProximate backbonE-based Clustering...
Quasi-planar elemental clusters in pair interactions approximation
Directory of Open Access Journals (Sweden)
Chkhartishvili Levan
2016-01-01
Full Text Available The pair-interactions approximation, when applied to describe elemental clusters, only takes into account bonding between neighboring atoms. According to this approach, isomers of wrapped forms of 2D clusters – nanotubular and fullerene-like structures – and truly 3D clusters, are generally expected to be more stable than their quasi-planar counterparts. This is because quasi-planar clusters contain more peripheral atoms with dangling bonds and, correspondingly, fewer atoms with saturated bonds. However, the differences in coordination numbers between central and peripheral atoms lead to the polarization of bonds. The related corrections to the molar binding energy can make small, quasi-planar clusters more stable than their 2D wrapped allotropes and 3D isomers. The present work provides a general theoretical frame for studying the relative stability of small elemental clusters within the pair interactions approximation.
Discussion of CoSA: Clustering of Sparse Approximations
Energy Technology Data Exchange (ETDEWEB)
Armstrong, Derek Elswick [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-03-07
The purpose of this talk is to discuss the possible applications of CoSA (Clustering of Sparse Approximations) to the exploitation of HSI (HyperSpectral Imagery) data. CoSA is presented by Moody et al. in the Journal of Applied Remote Sensing (“Land cover classification in multispectral imagery using clustering of sparse approximations over learned feature dictionaries”, Vol. 8, 2014) and is based on machine learning techniques.
The dilute random field Ising model by finite cluster approximation
International Nuclear Information System (INIS)
Benyoussef, A.; Saber, M.
1987-09-01
Using the finite cluster approximation, phase diagrams of bond and site diluted three-dimensional simple cubic Ising models with a random field have been determined. The resulting phase diagrams have the same general features for both bond and site dilution. (author). 7 refs, 4 figs
Traveling-cluster approximation for uncorrelated amorphous systems
International Nuclear Information System (INIS)
Sen, A.K.; Mills, R.; Kaplan, T.; Gray, L.J.
1984-01-01
We have developed a formalism for including cluster effects in the one-electron Green's function for a positionally disordered (liquid or amorphous) system without any correlation among the scattering sites. This method is an extension of the technique known as the traveling-cluster approximation (TCA) originally obtained and applied to a substitutional alloy by Mills and Ratanavararaksa. We have also proved the appropriate fixed-point theorem, which guarantees, for a bounded local potential, that the self-consistent equations always converge upon iteration to a unique, Herglotz solution. To our knowledge, this is the only analytic theory for considering cluster effects. Furthermore, we have performed some computer calculations in the pair TCA, for the model case of delta-function potentials on a one-dimensional random chain. These results have been compared with ''exact calculations'' (which, in principle, take into account all cluster effects) and with the coherent-potential approximation (CPA), which is the single-site TCA. The density of states for the pair TCA clearly shows some improvement over the CPA and yet, apparently, the pair approximation distorts some of the features of the exact results
Variation in verb cluster interruption
Hendriks, Lotte
2014-01-01
Except for finite verbs in main clauses, verbs in Standard Dutch cluster together in a clause-final position. In certain Dutch dialects, non-verbal material can occur within this verb cluster (Verhasselt 1961; Koelmans 1965, among many others). These dialects vary with respect to which types of
Kim, SungKun; Lee, Hunpyo
2017-06-01
Via a dynamical cluster approximation with N c = 4 in combination with a semiclassical approximation (DCA+SCA), we study the doped two-dimensional Hubbard model. We obtain a plaquette antiferromagnetic (AF) Mott insulator, a plaquette AF ordered metal, a pseudogap (or d-wave superconductor) and a paramagnetic metal by tuning the doping concentration. These features are similar to the behaviors observed in copper-oxide superconductors and are in qualitative agreement with the results calculated by the cluster dynamical mean field theory with the continuous-time quantum Monte Carlo (CDMFT+CTQMC) approach. The results of our DCA+SCA differ from those of the CDMFT+CTQMC approach in that the d-wave superconducting order parameters are shown even in the high doped region, unlike the results of the CDMFT+CTQMC approach. We think that the strong plaquette AF orderings in the dynamical cluster approximation (DCA) with N c = 4 suppress superconducting states with increasing doping up to strongly doped region, because frozen dynamical fluctuations in a semiclassical approximation (SCA) approach are unable to destroy those orderings. Our calculation with short-range spatial fluctuations is initial research, because the SCA can manage long-range spatial fluctuations in feasible computational times beyond the CDMFT+CTQMC tool. We believe that our future DCA+SCA calculations should supply information on the fully momentum-resolved physical properties, which could be compared with the results measured by angle-resolved photoemission spectroscopy experiments.
A cluster approximation for the transfer-matrix method
International Nuclear Information System (INIS)
Surda, A.
1990-08-01
A cluster approximation for the transfer-method is formulated. The calculation of the partition function of lattice models is transformed to a nonlinear mapping problem. The method yields the free energy, correlation functions and the phase diagrams for a large class of lattice models. The high accuracy of the method is exemplified by the calculation of the critical temperature of the Ising model. (author). 14 refs, 2 figs, 1 tab
Approximate variational solutions of the Grad-Shafranov equation
International Nuclear Information System (INIS)
Ludwig, G.O.
2001-01-01
Approximate solutions of the Grad-Schlueter-Shafranov equation based on variational methods are developed. The power series solutions of the Euler-Lagrange equations for equilibrium are compared with direct variational results for a low aspect ratio tokamak equilibrium. (author)
Space-angle approximations in the variational nodal method
International Nuclear Information System (INIS)
Lewis, E. E.; Palmiotti, G.; Taiwo, T.
1999-01-01
The variational nodal method is formulated such that the angular and spatial approximations maybe examined separately. Spherical harmonic, simplified spherical harmonic, and discrete ordinate approximations are coupled to the primal hybrid finite element treatment of the spatial variables. Within this framework, two classes of spatial trial functions are presented: (1) orthogonal polynomials for the treatment of homogeneous nodes and (2) bilinear finite subelement trial functions for the treatment of fuel assembly sized nodes in which fuel-pin cell cross sections are represented explicitly. Polynomial and subelement trial functions are applied to benchmark water-reactor problems containing MOX fuel using spherical harmonic and simplified spherical harmonic approximations. The resulting accuracy and computing costs are compared
Sparse linear models: Variational approximate inference and Bayesian experimental design
International Nuclear Information System (INIS)
Seeger, Matthias W
2009-01-01
A wide range of problems such as signal reconstruction, denoising, source separation, feature selection, and graphical model search are addressed today by posterior maximization for linear models with sparsity-favouring prior distributions. The Bayesian posterior contains useful information far beyond its mode, which can be used to drive methods for sampling optimization (active learning), feature relevance ranking, or hyperparameter estimation, if only this representation of uncertainty can be approximated in a tractable manner. In this paper, we review recent results for variational sparse inference, and show that they share underlying computational primitives. We discuss how sampling optimization can be implemented as sequential Bayesian experimental design. While there has been tremendous recent activity to develop sparse estimation, little attendance has been given to sparse approximate inference. In this paper, we argue that many problems in practice, such as compressive sensing for real-world image reconstruction, are served much better by proper uncertainty approximations than by ever more aggressive sparse estimation algorithms. Moreover, since some variational inference methods have been given strong convex optimization characterizations recently, theoretical analysis may become possible, promising new insights into nonlinear experimental design.
Sparse linear models: Variational approximate inference and Bayesian experimental design
Energy Technology Data Exchange (ETDEWEB)
Seeger, Matthias W [Saarland University and Max Planck Institute for Informatics, Campus E1.4, 66123 Saarbruecken (Germany)
2009-12-01
A wide range of problems such as signal reconstruction, denoising, source separation, feature selection, and graphical model search are addressed today by posterior maximization for linear models with sparsity-favouring prior distributions. The Bayesian posterior contains useful information far beyond its mode, which can be used to drive methods for sampling optimization (active learning), feature relevance ranking, or hyperparameter estimation, if only this representation of uncertainty can be approximated in a tractable manner. In this paper, we review recent results for variational sparse inference, and show that they share underlying computational primitives. We discuss how sampling optimization can be implemented as sequential Bayesian experimental design. While there has been tremendous recent activity to develop sparse estimation, little attendance has been given to sparse approximate inference. In this paper, we argue that many problems in practice, such as compressive sensing for real-world image reconstruction, are served much better by proper uncertainty approximations than by ever more aggressive sparse estimation algorithms. Moreover, since some variational inference methods have been given strong convex optimization characterizations recently, theoretical analysis may become possible, promising new insights into nonlinear experimental design.
A test of the adhesion approximation for gravitational clustering
Melott, Adrian L.; Shandarin, Sergei; Weinberg, David H.
1993-01-01
We quantitatively compare a particle implementation of the adhesion approximation to fully non-linear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel-dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel-dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate than that from ZA or TZA, (b) the error in the phase angle of Fourier components is worse than that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.
Approximate solutions: ramps and periodic variations. Chapter 5
International Nuclear Information System (INIS)
1998-01-01
The aim of reactor regulation is generally to maintain reactor power at the demand power, or to vary it slowly to attain a new demand power. On the other hand, the purpose of reactor shutdown systems (SDS) is to insert rapidly, on actuation, a large negative reactivity in order to minimize an overpower, or limit the energy released during a transient, so that fuel failure is improbable. Control mechanisms are therefore characterized by: their reactivity worth (mk), which must exceed the reactivity effect which the mechanism is designed to compensate; and their insertion rate (mk/s), which must be at least as fast as the effect to be controlled. Table 5.1 gives a summary of the various control mechanisms in a CANDU 6 reactor. The reactivity worth shown for each mechanism is the static reactivity change associated with full movement of the device. In reality, the dynamic reactivity will vary in a continuous manner, not suddenly, as assumed in the previous chapter. The realistic simulation of a reactivity insertion in the reactor must then take into account the rate of insertion of reactivity, which is governed by the insertion speed of the mechanism. We have seen in the previous chapter that it is possible to solved analytically the point-kinetics equations for constant reactivity. We could generalize these solutions to step-wise reactivity variations by linking together the analytic solutions to for a sequence of step changes. This approach is not necessarily the best from a numerical point of view. By introducing one or more simplifying assumptions, it will be possible to obtain an analytical solution of arbitrary variations in reactivity or in the external source. These assumptions will undoubtedly limit the applicability of the results, but the approximate solutions obtained will allow us to describe the reactor behaviour analytically. (author)
Essays on variational approximation techniques for stochastic optimization problems
Deride Silva, Julio A.
This dissertation presents five essays on approximation and modeling techniques, based on variational analysis, applied to stochastic optimization problems. It is divided into two parts, where the first is devoted to equilibrium problems and maxinf optimization, and the second corresponds to two essays in statistics and uncertainty modeling. Stochastic optimization lies at the core of this research as we were interested in relevant equilibrium applications that contain an uncertain component, and the design of a solution strategy. In addition, every stochastic optimization problem relies heavily on the underlying probability distribution that models the uncertainty. We studied these distributions, in particular, their design process and theoretical properties such as their convergence. Finally, the last aspect of stochastic optimization that we covered is the scenario creation problem, in which we described a procedure based on a probabilistic model to create scenarios for the applied problem of power estimation of renewable energies. In the first part, Equilibrium problems and maxinf optimization, we considered three Walrasian equilibrium problems: from economics, we studied a stochastic general equilibrium problem in a pure exchange economy, described in Chapter 3, and a stochastic general equilibrium with financial contracts, in Chapter 4; finally from engineering, we studied an infrastructure planning problem in Chapter 5. We stated these problems as belonging to the maxinf optimization class and, in each instance, we provided an approximation scheme based on the notion of lopsided convergence and non-concave duality. This strategy is the foundation of the augmented Walrasian algorithm, whose convergence is guaranteed by lopsided convergence, that was implemented computationally, obtaining numerical results for relevant examples. The second part, Essays about statistics and uncertainty modeling, contains two essays covering a convergence problem for a sequence
Variational, projection methods and Pade approximants in scattering theory
International Nuclear Information System (INIS)
Turchetti, G.
1980-12-01
Several aspects on the scattering theory are discussed in a perturbative scheme. The Pade approximant method plays an important role in such a scheme. Solitons solutions are also discussed in this same scheme. (L.C.) [pt
Variation Iteration Method for The Approximate Solution of Nonlinear ...
African Journals Online (AJOL)
In this study, we considered the numerical solution of the nonlinear Burgers equation using the Variational Iteration Method (VIM). The method seeks to examine the convergence of solutions of the Burgers equation at the expense of the parameters x and t of which the amount of errors depends. Numerical experimentation ...
International Nuclear Information System (INIS)
Mery, P.
1977-01-01
The operator and matrix Pade approximation are defined. The fact that these approximants can be derived from the Schwinger variational principle is emphasized. In potential theory, using this variational aspect it is shown that the matrix Pade approximation allow to reproduce the exact solution of the Lippman-Schwinger equation with any required accuracy taking only into account the knowledge of the first two coefficients in the Born expansion. The deep analytic structure of this variational matrix Pade approximation (hyper Pade approximation) is discussed
Maitra, Rahul; Nakajima, Takahito
2017-11-28
We present an accurate single reference coupled cluster theory in which the conventional Fock operator matrix is suitably dressed to simulate the effect of triple and higher excitations within a singles and doubles framework. The dressing thus invoked originates from a second-order perturbative approximation of a similarity transformed Hamiltonian and induces higher rank excitations through local renormalization of individual occupied and unoccupied orbital lines. Such a dressing is able to recover a significant amount of correlation effects beyond singles and doubles approximation, but only with an economic n 5 additional cost. Due to the inclusion of higher rank excitations via the Fock matrix dressing, this method is a natural improvement over conventional coupled cluster theory with singles and doubles approximation, and this method would be demonstrated via applications on some challenging systems. This highly promising scheme has a conceptually simple structure which is also easily generalizable to a multi-reference coupled cluster scheme for treating strong degeneracy. We shall demonstrate that this method is a natural lowest order perturbative approximation to the recently developed iterative n-body excitation inclusive coupled cluster singles and doubles scheme [R. Maitra et al., J. Chem. Phys. 147, 074103 (2017)].
Variational cluster perturbation theory for Bose-Hubbard models
International Nuclear Information System (INIS)
Koller, W; Dupuis, N
2006-01-01
We discuss the application of the variational cluster perturbation theory (VCPT) to the Mott-insulator-to-superfluid transition in the Bose-Hubbard model. We show how the VCPT can be formulated in such a way that it gives a translation invariant excitation spectrum-free of spurious gaps-despite the fact that it formally breaks translation invariance. The phase diagram and the single-particle Green function in the insulating phase are obtained for one-dimensional systems. When the chemical potential of the cluster is taken as a variational parameter, the VCPT reproduces the dimensional dependence of the phase diagram even for one-site clusters. We find a good quantitative agreement with the results of the density-matrix renormalization group when the number of sites in the cluster becomes of order 10. The extension of the method to the superfluid phase is discussed
Chen, Zhenhua; Hoffmann, Mark R
2012-07-07
A unitary wave operator, exp (G), G(+) = -G, is considered to transform a multiconfigurational reference wave function Φ to the potentially exact, within basis set limit, wave function Ψ = exp (G)Φ. To obtain a useful approximation, the Hausdorff expansion of the similarity transformed effective Hamiltonian, exp (-G)Hexp (G), is truncated at second order and the excitation manifold is limited; an additional separate perturbation approximation can also be made. In the perturbation approximation, which we refer to as multireference unitary second-order perturbation theory (MRUPT2), the Hamiltonian operator in the highest order commutator is approximated by a Mo̸ller-Plesset-type one-body zero-order Hamiltonian. If a complete active space self-consistent field wave function is used as reference, then the energy is invariant under orbital rotations within the inactive, active, and virtual orbital subspaces for both the second-order unitary coupled cluster method and its perturbative approximation. Furthermore, the redundancies of the excitation operators are addressed in a novel way, which is potentially more efficient compared to the usual full diagonalization of the metric of the excited configurations. Despite the loss of rigorous size-extensivity possibly due to the use of a variational approach rather than a projective one in the solution of the amplitudes, test calculations show that the size-extensivity errors are very small. Compared to other internally contracted multireference perturbation theories, MRUPT2 only needs reduced density matrices up to three-body even with a non-complete active space reference wave function when two-body excitations within the active orbital subspace are involved in the wave operator, exp (G). Both the coupled cluster and perturbation theory variants are amenable to large, incomplete model spaces. Applications to some widely studied model systems that can be problematic because of geometry dependent quasidegeneracy, H4, P4
Approximate fuzzy C-means (AFCM) cluster analysis of medical magnetic resonance image (MRI) data
International Nuclear Information System (INIS)
DelaPaz, R.L.; Chang, P.J.; Bernstein, R.; Dave, J.V.
1987-01-01
The authors describe the application of an approximate fuzzy C-means (AFCM) clustering algorithm as a data dimension reduction approach to medical magnetic resonance images (MRI). Image data consisted of one T1-weighted, two T2-weighted, and one T2*-weighted (magnetic susceptibility) image for each cranial study and a matrix of 10 images generated from 10 combinations of TE and TR for each body lymphoma study. All images were obtained with a 1.5 Tesla imaging system (GE Signa). Analyses were performed on over 100 MR image sets with a variety of pathologies. The cluster analysis was operated in an unsupervised mode and computational overhead was minimized by utilizing a table look-up approach without adversely affecting accuracy. Image data were first segmented into 2 coarse clusters, each of which was then subdivided into 16 fine clusters. The final tissue classifications were presented as color-coded anatomically-mapped images and as two and three dimensional displays of cluster center data in selected feature space (minimum spanning tree). Fuzzy cluster analysis appears to be a clinically useful dimension reduction technique which results in improved diagnostic specificity of medical magnetic resonance images
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.
International Nuclear Information System (INIS)
Skorupski, Krzysztof; Hellmers, Jens; Feng, Wen; Mroczka, Janusz; Wriedt, Thomas; Mädler, Lutz
2015-01-01
In this paper we study the spectral behaviour of indium tin oxide (ITO) nanoparticle clusters using different sinter neck models for the connections between the primary particles. The investigations include light scattering calculations based on the Discrete Dipole Approximation (DDA). The corresponding clusters are generated using the Cluster–Cluster algorithm proposed by Filippov et al. Different sintering neck models led to significantly different spectral features. A spectral neck factor that reveals the thickness of the necks connecting the primary particles with a simple measurement method is introduced. - Highlights: • We investigate the necking phenomenon in ITO fractal-like aggregates. • Extinction diagrams are sensitive to changes of the neck size. • We propose a simple procedure for measuring the neck size in ITO aggregates
Approximate first collision probabilities for neutrons in cylindrical and cluster lattices
International Nuclear Information System (INIS)
Robinson, G.S.
1979-05-01
Methods for calculating approximate first collision probabilities for neutrons in cylindrical and cluster lattices are presented and compared with numerical solution methods. The methods differ from those of other authors in the inclusion of anisotropic boundary conditions for both geometries. The methods, which are fast enough for routine use in multigroup and resonance subgroup calculations, have been coded in FORTRAN and included in modules of the AUS scheme for reactor neutronics calculations
Independent center, independent electron approximation for dynamics of molecules and clusters
International Nuclear Information System (INIS)
McGuire, J.H.; Straton, J.C.; Wang, J.; Wang, Y.D.; Weaver, O.L.; Corchs, S.E.; Rivarola, R.D.
1996-01-01
A formalism is developed for evaluating probabilities and cross sections for multiple-electron transitions in scattering of molecules and clusters by charged collision partners. First, the molecule is divided into subclusters each made up of identical centers (atoms). Within each subcluster coherent scattering from identical centers may lead to observable phase terms and a geometrical structure factor. Then, using a mean field approximation to describe the interactions between centers we obtain A I ∼ summation k product ke iδ k I A Ik . Second, the independent electron approximation for each center may be obtained by neglecting the correlation between electrons in each center. The probability amplitude for each center is then a product of single electron transition probability amplitudes, a Ik i , i.e. A Ik ≅ product iaik i . Finally, the independent subcluster approximation is introduced by neglecting the interactions between different subclusters in the molecule or cluster. The total probability amplitude then reduces to a simple product of amplitudes for each subcluster, A≅ product IAI . Limitations of this simple approximation are discussed. copyright 1996 American Institute of Physics
Energy Technology Data Exchange (ETDEWEB)
Yoo, J.; Shin, H. S.; Song, T. Y.; Park, W. S. [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1997-12-31
Previous our numerical results in computing point kinetics equations show a possibility in developing approximations to estimate sensitivity responses of nuclear reactor. We recalculate sensitivity responses by maintaining the corrections with first order of sensitivity parameter. We present a method for computing sensitivity responses of nuclear reactor based on an approximation derived from point kinetics equations. Exploiting this approximation, we found that the first order approximation works to estimate variations in the time to reach peak power because of their linear dependence on a sensitivity parameter, and that there are errors in estimating the peak power in the first order approximation for larger sensitivity parameters. To confirm legitimacy of out approximation, these approximate results are compared with exact results obtained from out previous numerical study. 4 refs., 2 figs., 3 tabs. (Author)
Energy Technology Data Exchange (ETDEWEB)
Yoo, J; Shin, H S; Song, T Y; Park, W S [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1998-12-31
Previous our numerical results in computing point kinetics equations show a possibility in developing approximations to estimate sensitivity responses of nuclear reactor. We recalculate sensitivity responses by maintaining the corrections with first order of sensitivity parameter. We present a method for computing sensitivity responses of nuclear reactor based on an approximation derived from point kinetics equations. Exploiting this approximation, we found that the first order approximation works to estimate variations in the time to reach peak power because of their linear dependence on a sensitivity parameter, and that there are errors in estimating the peak power in the first order approximation for larger sensitivity parameters. To confirm legitimacy of out approximation, these approximate results are compared with exact results obtained from out previous numerical study. 4 refs., 2 figs., 3 tabs. (Author)
Collective-field-corrected strong field approximation for laser-irradiated metal clusters
International Nuclear Information System (INIS)
Keil, Th; Bauer, D
2014-01-01
The strong field approximation (SFA) formulated in terms of so-called ‘quantum orbits’ led to much insight into intense-laser driven ionization dynamics. In plain SFA, the emitted electron is treated as a free electron in the laser field alone. However, with improving experimental techniques and more advanced numerical simulations, it becomes more and more obvious that the plain SFA misses interesting effects even on a qualitative level. Examples are holographic side lobes, the low-energy structure, radial patterns in photoelectron spectra at low kinetic energies and strongly rotated angular distributions. For this reason, increasing efforts have been recently devoted to Coulomb corrections of the SFA. In the current paper, we follow a similar line but consider ionization of metal clusters. It is known that photoelectrons from clusters can be much more energetic than those emitted from atoms or small molecules, especially if the Mie resonance of the expanding cluster is evoked. We develop a SFA that takes the collective field inside the cluster via the simple rigid-sphere model into account. Our approach is based on field-corrected quantum orbits so that the acceleration process (or any other spectral feature of interest) can be investigated in detail. (paper)
Approximate treatment of semicore states in GW calculations with application to Au clusters.
Xian, Jiawei; Baroni, Stefano; Umari, P
2014-03-28
We address the treatment of transition metal atoms in GW electronic-structure calculations within the plane-wave pseudo-potential formalism. The contributions of s and p semi-core electrons to the self-energy, which are essential to grant an acceptable accuracy, are dealt with using a recently proposed scheme whereby the exchange components are treated exactly at the G0W0 level, whereas a suitable approximation to the correlation components is devised. This scheme is benchmarked for small gold nano-clusters, resulting in ionization potentials, electron affinities, and density of states in very good agreement with those obtained from calculations where s and p semicore states are treated as valence orbitals, and allowing us to apply this same scheme to clusters of intermediate size, Au20 and Au32, that would be otherwise very difficult to deal with.
Approximate treatment of semicore states in GW calculations with application to Au clusters
Energy Technology Data Exchange (ETDEWEB)
Xian, Jiawei [SISSA – Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, I-34136 Trieste (Italy); Baroni, Stefano [SISSA – Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, I-34136 Trieste (Italy); CNR-IOM Democritos, Theory-Elettra group, Trieste (Italy); Umari, P., E-mail: paolo.umari@unipd.it [CNR-IOM Democritos, Theory-Elettra group, Trieste (Italy); Dipartimento di Fisica e Astronomia, Università di Padova, Via Marzolo 8, I-35131 Padova (Italy)
2014-03-28
We address the treatment of transition metal atoms in GW electronic-structure calculations within the plane-wave pseudo-potential formalism. The contributions of s and p semi-core electrons to the self-energy, which are essential to grant an acceptable accuracy, are dealt with using a recently proposed scheme whereby the exchange components are treated exactly at the G{sub 0}W{sub 0} level, whereas a suitable approximation to the correlation components is devised. This scheme is benchmarked for small gold nano-clusters, resulting in ionization potentials, electron affinities, and density of states in very good agreement with those obtained from calculations where s and p semicore states are treated as valence orbitals, and allowing us to apply this same scheme to clusters of intermediate size, Au{sub 20} and Au{sub 32}, that would be otherwise very difficult to deal with.
Approximate treatment of semicore states in GW calculations with application to Au clusters
International Nuclear Information System (INIS)
Xian, Jiawei; Baroni, Stefano; Umari, P.
2014-01-01
We address the treatment of transition metal atoms in GW electronic-structure calculations within the plane-wave pseudo-potential formalism. The contributions of s and p semi-core electrons to the self-energy, which are essential to grant an acceptable accuracy, are dealt with using a recently proposed scheme whereby the exchange components are treated exactly at the G 0 W 0 level, whereas a suitable approximation to the correlation components is devised. This scheme is benchmarked for small gold nano-clusters, resulting in ionization potentials, electron affinities, and density of states in very good agreement with those obtained from calculations where s and p semicore states are treated as valence orbitals, and allowing us to apply this same scheme to clusters of intermediate size, Au 20 and Au 32 , that would be otherwise very difficult to deal with
Accelerating the coupled-cluster singles and doubles method using the chain-of-sphere approximation
Dutta, Achintya Kumar; Neese, Frank; Izsák, Róbert
2018-06-01
In this paper, we present a chain-of-sphere implementation of the external exchange term, the computational bottleneck of coupled-cluster calculations at the singles and doubles level. This implementation is compared to standard molecular orbital, atomic orbital and resolution of identity implementations of the same term within the ORCA package and turns out to be the most efficient one for larger molecules, with a better accuracy than the resolution-of-identity approximation. Furthermore, it becomes possible to perform a canonical CC calculation on a tetramer of nucleobases in 17 days, 20 hours.
Laplace transform homotopy perturbation method for the approximation of variational problems.
Filobello-Nino, U; Vazquez-Leal, H; Rashidi, M M; Sedighi, H M; Perez-Sesma, A; Sandoval-Hernandez, M; Sarmiento-Reyes, A; Contreras-Hernandez, A D; Pereyra-Diaz, D; Hoyos-Reyes, C; Jimenez-Fernandez, V M; Huerta-Chua, J; Castro-Gonzalez, F; Laguna-Camacho, J R
2016-01-01
This article proposes the application of Laplace Transform-Homotopy Perturbation Method and some of its modifications in order to find analytical approximate solutions for the linear and nonlinear differential equations which arise from some variational problems. As case study we will solve four ordinary differential equations, and we will show that the proposed solutions have good accuracy, even we will obtain an exact solution. In the sequel, we will see that the square residual error for the approximate solutions, belongs to the interval [0.001918936920, 0.06334882582], which confirms the accuracy of the proposed methods, taking into account the complexity and difficulty of variational problems.
Directory of Open Access Journals (Sweden)
Klin-eam Chakkrid
2009-01-01
Full Text Available Abstract A new approximation method for solving variational inequalities and fixed points of nonexpansive mappings is introduced and studied. We prove strong convergence theorem of the new iterative scheme to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the variational inequality for the inverse-strongly monotone mapping which solves some variational inequalities. Moreover, we apply our main result to obtain strong convergence to a common fixed point of nonexpansive mapping and strictly pseudocontractive mapping in a Hilbert space.
Diagnostic quality and observer variation in radiographic diagnoses of approximal caries
International Nuclear Information System (INIS)
Espelid, I.; Tveit, A.B.
1986-01-01
The aim of the study was to compare observer variations, observer strategy, and diagnostic quality with regard to radiographic caries diagnoses made at different depth levels. Qualitative assessment of approximal carious lesions on the basis of radiographs were made for sound (n=28) and carious (n=123) lesions by seven dentists. The inter- and intra-observer variations were lowest when lesions were diagnosed as being in the outermost parts of the teeth. The frequency of false positive scores was lower when dentin was examined as compared with enamel. The quality of radiographic diagnoses showed small variations (p>0.05) when different levels of pulpal depths were interpreted
Variational Multi-Scale method with spectral approximation of the sub-scales.
Dia, Ben Mansour; Chá con-Rebollo, Tomas
2015-01-01
A variational multi-scale method where the sub-grid scales are computed by spectral approximations is presented. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base
International Nuclear Information System (INIS)
Amaral, N.C.; Maffeo, B.; Guenzburger, D.J.R.
1982-01-01
Molecular orbitals calculations were performed for clusters representing the CaF 2 , SrF 2 and BaF 2 ionic crystals. The discrete variational method was employed, with the Xα approximation for the exchange interaction; a detailed investigation of different models for embedding the clusters in the solids led to a realistic description of the effect of neighbour ions in the infinite crystal. The results obtained were used to interpret optical and photoelectron data reported in the literature. In the case of CaF 2 , comparisons were made with existing band structure calculations. (Author) [pt
Microscopic Electron Variations Measured Simultaneously By The Cluster Spacecraft
Buckley, A. M.; Carozzi, T. D.; Gough, M. P.; Beloff, N.
Data is used from the Particle Correlator experiments running on each of the four Cluster spacecraft so as to determine common microscopic behaviour in the elec- tron population observed over the macroscopic Cluster separations. The Cluster par- ticle correlator experiments operate by forming on board Auto Correlation Functions (ACFs) generated from short time series of electron counts obtained, as a function of electron energy, from the PEACE HEEA sensor. The information on the microscopic variation of the electron flux covers the frequency range DC up to 41 kHz (encom- passing typical electron plasma frequencies and electron gyro frequencies and their harmonics), the electron energy range is that covered by the PEACE HEEA sensor (within the range 1 eV to 26 keV). Results are presented of coherent electron struc- tures observed simultaneously by the four spacecraft in the differing plasma interac- tion regions and boundaries encountered by Cluster. As an aid to understanding the plasma interactions, use is made of numerical simulations which model both the un- derlying statistical properties of the electrons and also the manner in which particle correlator experiments operate.
International Nuclear Information System (INIS)
Mookerjee, A.; Prasad, R.
1993-09-01
We present a method for calculating the electronic structure of disordered alloys with short range order (SRO) which guarantees positive density of states for all values of the SRO parameter. The method is based on the generalized augmented space theorem which is valid for alloys with SRO. This theorem is applied to alloys with SRO in the tight-binding linear muffin-tin orbital (TB-LMTO) framework. This is done by using the augmented space formulation of Mookerjee and cluster coherent potential approximation. As an illustration, the method is applied to a single band mode TB-LMTO Hamiltonian. We find that the SRO can induce substantial changes in the density of states. (author). 22 refs, 2 figs
Bronstein, Leo; Koeppl, Heinz
2018-01-01
Approximate solutions of the chemical master equation and the chemical Fokker-Planck equation are an important tool in the analysis of biomolecular reaction networks. Previous studies have highlighted a number of problems with the moment-closure approach used to obtain such approximations, calling it an ad hoc method. In this article, we give a new variational derivation of moment-closure equations which provides us with an intuitive understanding of their properties and failure modes and allows us to correct some of these problems. We use mixtures of product-Poisson distributions to obtain a flexible parametric family which solves the commonly observed problem of divergences at low system sizes. We also extend the recently introduced entropic matching approach to arbitrary ansatz distributions and Markov processes, demonstrating that it is a special case of variational moment closure. This provides us with a particularly principled approximation method. Finally, we extend the above approaches to cover the approximation of multi-time joint distributions, resulting in a viable alternative to process-level approximations which are often intractable.
Variational Multi-Scale method with spectral approximation of the sub-scales.
Dia, Ben Mansour
2015-01-07
A variational multi-scale method where the sub-grid scales are computed by spectral approximations is presented. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base of eigenfunctions which are orthonormal in weighted L2 spaces. We propose a feasible VMS-spectral method by truncation of this spectral expansion to a nite number of modes.
Variational P1 approximations of general-geometry multigroup transport problems
International Nuclear Information System (INIS)
Rulko, R.P.; Tomasevic, D.; Larsen, E.W.
1995-01-01
A variational approximation is developed for general-geometry multigroup transport problems with arbitrary anisotropic scattering. The variational principle is based on a functional that approximates a reaction rate in a subdomain of the system. In principle, approximations that result from this functional ''optimally'' determine such reaction rates. The functional contains an arbitrary parameter α and requires the approximate solutions of a forward and an adjoint transport problem. If the basis functions for the forward and adjoint solutions are chosen to be linear functions of the angular variable Ω, the functional yields the familiar multigroup P 1 equations for all values of α. However, the boundary conditions that result from the functional depend on α. In particular, for problems with vacuum boundaries, one obtains the conventional mixed boundary condition, but with an extrapolation distance that depends continuously on α. The choice α = 0 yields a generalization of boundary conditions derived earlier by Federighi and Pomraning for a more limited class of problems. The choice α = 1 yields a generalization of boundary conditions derived previously by Davis for monoenergetic problems. Other boundary conditions are obtained by choosing different values of α. The authors discuss this indeterminancy of α in conjunction with numerical experiments
Speeding up equation of motion coupled cluster theory with the chain of spheres approximation
International Nuclear Information System (INIS)
Dutta, Achintya Kumar; Neese, Frank; Izsák, Róbert
2016-01-01
In the present paper, the chain of spheres exchange (COSX) approximation is applied to the highest scaling terms in the equation of motion (EOM) coupled cluster equations with single and double excitations, in particular, the terms involving integrals with four virtual labels. It is found that even the acceleration of this single term yields significant computational gains without compromising the desired accuracy of the method. For an excitation energy calculation on a cluster of five water molecules using 585 basis functions, the four virtual term is 9.4 times faster using COSX with a loose grid than using the canonical implementation, which yields a 2.6 fold acceleration for the whole of the EOM calculation. For electron attachment calculations, the four virtual term is 15 times and the total EOM calculation is 10 times faster than the canonical calculation for the same system. The accuracy of the new method was tested using Thiel’s test set for excited states using the same settings and the maximum absolute deviation over the whole test set was found to be 12.945 cm −1 (59 μHartree) for excitation energies and 6.799 cm −1 (31 μHartree) for electron attachments. Using MP2 amplitudes for the ground state in combination with the parallel evaluation of the full EOM equations in the manner discussed in this paper enabled us to perform calculations for large systems. Electron affinity values for the two lowest states of a Zn protoporphyrine model compound (224 correlated electrons and 1120 basis functions) were obtained in 3 days 19 h using 4 cores of a Xeon E5-2670 processor allocating 10 GB memory per core. Calculating the lowest two excitation energies for trans-retinal (114 correlated electrons and 539 basis functions) took 1 day 21 h using eight cores of the same processor and identical memory allocation per core
Speeding up equation of motion coupled cluster theory with the chain of spheres approximation
Energy Technology Data Exchange (ETDEWEB)
Dutta, Achintya Kumar; Neese, Frank, E-mail: frank.neese@cec.mpg.de; Izsák, Róbert, E-mail: robert.izsak@cec.mpg.de [Max-Planck-Institut für Chemische Energiekonversion, Stiftstr. 34-36, 45470 Mülheim an der Ruhr (Germany)
2016-01-21
In the present paper, the chain of spheres exchange (COSX) approximation is applied to the highest scaling terms in the equation of motion (EOM) coupled cluster equations with single and double excitations, in particular, the terms involving integrals with four virtual labels. It is found that even the acceleration of this single term yields significant computational gains without compromising the desired accuracy of the method. For an excitation energy calculation on a cluster of five water molecules using 585 basis functions, the four virtual term is 9.4 times faster using COSX with a loose grid than using the canonical implementation, which yields a 2.6 fold acceleration for the whole of the EOM calculation. For electron attachment calculations, the four virtual term is 15 times and the total EOM calculation is 10 times faster than the canonical calculation for the same system. The accuracy of the new method was tested using Thiel’s test set for excited states using the same settings and the maximum absolute deviation over the whole test set was found to be 12.945 cm{sup −1} (59 μHartree) for excitation energies and 6.799 cm{sup −1} (31 μHartree) for electron attachments. Using MP2 amplitudes for the ground state in combination with the parallel evaluation of the full EOM equations in the manner discussed in this paper enabled us to perform calculations for large systems. Electron affinity values for the two lowest states of a Zn protoporphyrine model compound (224 correlated electrons and 1120 basis functions) were obtained in 3 days 19 h using 4 cores of a Xeon E5-2670 processor allocating 10 GB memory per core. Calculating the lowest two excitation energies for trans-retinal (114 correlated electrons and 539 basis functions) took 1 day 21 h using eight cores of the same processor and identical memory allocation per core.
Projection after variation in the finite-temperature Hartree-Fock-Bogoliubov approximation
Fanto, P.
2017-11-01
The finite-temperature Hartree-Fock-Bogoliubov (HFB) approximation often breaks symmetries of the underlying many-body Hamiltonian. Restricting the calculation of the HFB partition function to a subspace with good quantum numbers through projection after variation restores some of the correlations lost in breaking these symmetries, although effects of the broken symmetries such as sharp kinks at phase transitions remain. However, the most general projection after variation formula in the finite-temperature HFB approximation is limited by a sign ambiguity. Here, I extend the Pfaffian formula for the many-body traces of HFB density operators introduced by Robledo [L. M. Robledo, Phys. Rev. C. 79, 021302(R) (2009), 10.1103/PhysRevC.79.021302] to eliminate this sign ambiguity and evaluate the more complicated many-body traces required in projection after variation in the most general HFB case. The method is validated through a proof-of-principle calculation of the particle-number-projected HFB thermal energy in a simple model.
Variational calculations in gauge theories with approximate projection on gauge invariant states
International Nuclear Information System (INIS)
Heinemann, C.; Martin, C.; Vautherin, D.; Iancu, E.
1999-01-01
Variational calculations using Gaussian wave functionals combined with an approximate projection on gauge invariant states are presented. The minimization with respect to the kernel and center of the Gaussian leads to a gap type equation which is free of the difficulties generally encountered with negative modes. We show that the divergences in the expectation value of the energy density are only logarithmic and can be removed by a renormalization of the coupling constant. The renormalized energy density has a minimum which corresponds to a vanishing background magnetic field. We obtain an estimate for the gluon condensate. (authors)
The Cluster Variation Method: A Primer for Neuroscientists.
Maren, Alianna J
2016-09-30
Effective Brain-Computer Interfaces (BCIs) require that the time-varying activation patterns of 2-D neural ensembles be modelled. The cluster variation method (CVM) offers a means for the characterization of 2-D local pattern distributions. This paper provides neuroscientists and BCI researchers with a CVM tutorial that will help them to understand how the CVM statistical thermodynamics formulation can model 2-D pattern distributions expressing structural and functional dynamics in the brain. The premise is that local-in-time free energy minimization works alongside neural connectivity adaptation, supporting the development and stabilization of consistent stimulus-specific responsive activation patterns. The equilibrium distribution of local patterns, or configuration variables , is defined in terms of a single interaction enthalpy parameter ( h ) for the case of an equiprobable distribution of bistate (neural/neural ensemble) units. Thus, either one enthalpy parameter (or two, for the case of non-equiprobable distribution) yields equilibrium configuration variable values. Modeling 2-D neural activation distribution patterns with the representational layer of a computational engine, we can thus correlate variational free energy minimization with specific configuration variable distributions. The CVM triplet configuration variables also map well to the notion of a M = 3 functional motif. This paper addresses the special case of an equiprobable unit distribution, for which an analytic solution can be found.
The Cluster Variation Method: A Primer for Neuroscientists
Directory of Open Access Journals (Sweden)
Alianna J. Maren
2016-09-01
Full Text Available Effective Brain–Computer Interfaces (BCIs require that the time-varying activation patterns of 2-D neural ensembles be modelled. The cluster variation method (CVM offers a means for the characterization of 2-D local pattern distributions. This paper provides neuroscientists and BCI researchers with a CVM tutorial that will help them to understand how the CVM statistical thermodynamics formulation can model 2-D pattern distributions expressing structural and functional dynamics in the brain. The premise is that local-in-time free energy minimization works alongside neural connectivity adaptation, supporting the development and stabilization of consistent stimulus-specific responsive activation patterns. The equilibrium distribution of local patterns, or configuration variables, is defined in terms of a single interaction enthalpy parameter (h for the case of an equiprobable distribution of bistate (neural/neural ensemble units. Thus, either one enthalpy parameter (or two, for the case of non-equiprobable distribution yields equilibrium configuration variable values. Modeling 2-D neural activation distribution patterns with the representational layer of a computational engine, we can thus correlate variational free energy minimization with specific configuration variable distributions. The CVM triplet configuration variables also map well to the notion of a M = 3 functional motif. This paper addresses the special case of an equiprobable unit distribution, for which an analytic solution can be found.
Metallicity Variations in the Type II Globular Cluster NGC 6934
Marino, A. F.; Yong, D.; Milone, A. P.; Piotto, G.; Lundquist, M.; Bedin, L. R.; Chené, A.-N.; Da Costa, G.; Asplund, M.; Jerjen, H.
2018-06-01
The Hubble Space Telescope photometric survey of Galactic globular clusters (GCs) has revealed a peculiar “chromosome map” for NGC 6934. In addition to a typical sequence, similar to that observed in Type I GCs, NGC 6934 displays additional stars on the red side, analogous to the anomalous Type II GCs, as defined in our previous work. We present a chemical abundance analysis of four red giants in this GC. Two stars are located on the chromosome map sequence common to all GCs, and another two lie on the additional sequence. We find (i) star-to-star Fe variations, with the two anomalous stars being enriched by ∼0.2 dex. Because of our small-size sample, this difference is at the ∼2.5σ level. (ii) There is no evidence for variations in the slow neutron-capture abundances over Fe, at odds with what is often observed in anomalous Type II GCs, e.g., M 22 and ω Centauri (iii) no large variations in light elements C, O, and Na, compatible with locations of the targets on the lower part of the chromosome map where such variations are not expected. Since the analyzed stars are homogeneous in light elements, the only way to reproduce the photometric splits on the sub-giant (SGB) and the red giant (RGB) branches is to assume that red RGB/faint SGB stars are enhanced in [Fe/H] by ∼0.2. This fact corroborates the spectroscopic evidence of a metallicity variation in NGC 6934. The observed chemical pattern resembles only partially the other Type II GCs, suggesting that NGC 6934 might belong either to a third class of GCs, or be a link between normal Type I and anomalous Type II GCs. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555. This paper includes data gathered with the 6.5 m Magellan Telescopes located at Las Campanas Observatory, Chile, and Gemini Telescope at Canada–France–Hawaii Telescope.
Generating the patterns of variation with GeoGebra: the case of polynomial approximations
Attorps, Iiris; Björk, Kjell; Radic, Mirko
2016-01-01
In this paper, we report a teaching experiment regarding the theory of polynomial approximations at the university mathematics teaching in Sweden. The experiment was designed by applying Variation theory and by using the free dynamic mathematics software GeoGebra. The aim of this study was to investigate if the technology-assisted teaching of Taylor polynomials compared with traditional way of work at the university level can support the teaching and learning of mathematical concepts and ideas. An engineering student group (n = 19) was taught Taylor polynomials with the assistance of GeoGebra while a control group (n = 18) was taught in a traditional way. The data were gathered by video recording of the lectures, by doing a post-test concerning Taylor polynomials in both groups and by giving one question regarding Taylor polynomials at the final exam for the course in Real Analysis in one variable. In the analysis of the lectures, we found Variation theory combined with GeoGebra to be a potentially powerful tool for revealing some critical aspects of Taylor Polynomials. Furthermore, the research results indicated that applying Variation theory, when planning the technology-assisted teaching, supported and enriched students' learning opportunities in the study group compared with the control group.
International Nuclear Information System (INIS)
Moradian, Rostam
2006-01-01
We develop a generalized real-space effective medium super-cell approximation (EMSCA) method to treat the electronic states of interacting disordered systems. This method is general and allows randomness both in the on-site energies and in the hopping integrals. For a non-interacting disordered system, in the special case of randomness in the on-site energies, this method is equivalent to the non-local coherent potential approximation (NLCPA) derived previously. Also, for an interacting system the EMSCA method leads to the real-space derivation of the generalized dynamical cluster approximation (DCA) for a general lattice structure. We found that the original DCA and the NLCPA are two simple cases of this technique, so the EMSCA is equivalent to the generalized DCA where there is included interaction and randomness in the on-site energies and in the hopping integrals. All of the equations of this formalism are derived by using the effective medium theory in real space
Directory of Open Access Journals (Sweden)
Hayashi Takeshi
2013-01-01
Full Text Available Abstract Background Genomic selection is an effective tool for animal and plant breeding, allowing effective individual selection without phenotypic records through the prediction of genomic breeding value (GBV. To date, genomic selection has focused on a single trait. However, actual breeding often targets multiple correlated traits, and, therefore, joint analysis taking into consideration the correlation between traits, which might result in more accurate GBV prediction than analyzing each trait separately, is suitable for multi-trait genomic selection. This would require an extension of the prediction model for single-trait GBV to multi-trait case. As the computational burden of multi-trait analysis is even higher than that of single-trait analysis, an effective computational method for constructing a multi-trait prediction model is also needed. Results We described a Bayesian regression model incorporating variable selection for jointly predicting GBVs of multiple traits and devised both an MCMC iteration and variational approximation for Bayesian estimation of parameters in this multi-trait model. The proposed Bayesian procedures with MCMC iteration and variational approximation were referred to as MCBayes and varBayes, respectively. Using simulated datasets of SNP genotypes and phenotypes for three traits with high and low heritabilities, we compared the accuracy in predicting GBVs between multi-trait and single-trait analyses as well as between MCBayes and varBayes. The results showed that, compared to single-trait analysis, multi-trait analysis enabled much more accurate GBV prediction for low-heritability traits correlated with high-heritability traits, by utilizing the correlation structure between traits, while the prediction accuracy for uncorrelated low-heritability traits was comparable or less with multi-trait analysis in comparison with single-trait analysis depending on the setting for prior probability that a SNP has zero
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.
Hyperbolic tangent variational approximation for interfacial profiles of binary polymer blends
International Nuclear Information System (INIS)
Lifschitz, M.; Freed, K.F.; Tang, H.
1995-01-01
Contemporary theories of binary polymer blend interfaces incorporate such features of real polymer blends as compressibility, local correlations, monomer structure, etc. However, these theories require complicated numerical schemes, and their solutions often cannot be interpreted in a physically clear fashion. We develop a variational formalism for computing interfacial properties of binary polymer blends based on a hyperbolic tangent representation for the interfaces. While such an analysis is straightforward in the incompressible limit, the extension to compressible binary blends requires two distinct width parameters and nontrivial analysis. When the profile width parameters are chosen to minimize the excess free energy of a phase separated binary blend, then the interfacial properties computed from our simplified interfacial theory closely match those computed with the much more sophisticated (and computationally intensive) treatments. Significant attention is devoted to describing the interfacial properties of blends in the regime intermediate between the strong and the weak segregation limits as well as to extrapolating between these limits. The extension of the square gradient theory to the Tang--Freed quartic approximation provides a more precise definition of the weak segregation limit, but the treatment is found to overestimate both the interfacial tension and width in the strong segregation limit. The width parameters for the different components of a strongly asymmetric compressible blend vary to a lesser extent than an asymptotic analysis in the bulk suggests. This finding indicates that the central portion of the profile contributes the most in the minimization of the excess free energy with respect to the variational width parameters. copyright 1995 American Institute of Physics
International Nuclear Information System (INIS)
Kleinig, W.; Nesterenko, V.O.; Reinhard, P.-G.; Serra, Ll.
1998-01-01
The systematics of the plasmon response in spherical K, Na and Li clusters in a wide size region (8≤N≤440) is studied. We have considered two simplifying approximations whose validity has been established previously. First, a separable approach to the random-phase approximation is used. This involves an expansion of the residual interaction into a sum of separable terms until convergence is reached. Second, the electron-ion interaction is modelled by using the pseudo-Hamiltonian jellium model (MHJM) which includes nonlocal effects by means of realistic atomic pseudo-Hamiltonians. In cases where nonlocal effects are negligible the Structure Averaged Jellium Model (SAJM) has been used. Good agreement with available experimental data is achieved for K, Na (using the SAJM) and small Li clusters (invoking the PHJM). The trends for peak position and width are generally well reproduced, even up to details of the Landau fragmentation in several clusters. Less good agreement, however, is found for large Li clusters. This remains an open question
Application of the cluster variation method to ordering in an interstitital solid solution
DEFF Research Database (Denmark)
Pekelharing, Marjon I.; Böttger, Amarante; Somers, Marcel A. J.
1999-01-01
The tetrahedron approximation of the cluster variation method (CVM) was applied to describe the ordering on the fcc interstitial sublattice of gamma-Fe[N] and gamma'-Fe4N1-x. A Lennard-Jones potential was used to describe the dominantly strain-induced interactions, caused by misfitting of the N...... atoms in the interstitial octahedral sites. The gamma-Fe[N]/gamma'-Fe4N1-x miscibility gap, short range ordering (SRO), and long-range ordering (LRO) of nitrogen in gamma-Fe[N] and gamma'-Fe4N1-x, respectively, and lattice parameters of gamma and gamm' were calculated. For the first time, N distribution...... parameters,as calculated by CVM, were compared directly to Mössbauer data for specific surroundings of Fe atoms....
Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations
Verde, Licia; Heavens, Alan F; Jimenez, Raul; Matarrese, Sabino
2013-01-01
We provide an exact expression for the multi-variate joint probability distribution function of non-Gaussian fields primordially arising from local transformations of a Gaussian field. This kind of non-Gaussianity is generated in many models of inflation. We apply our expression to the non- Gaussianity estimation from Cosmic Microwave Background maps and the halo mass function where we obtain analytical expressions. We also provide analytic approximations and their range of validity. For the Cosmic Microwave Background we give a fast way to compute the PDF which is valid up to 7{\\sigma} for fNL values (both true and sampled) not ruled out by current observations, which consists of expressing the PDF as a combination of bispectrum and trispectrum of the temperature maps. The resulting expression is valid for any kind of non-Gaussianity and is not limited to the local type. The above results may serve as the basis for a fully Bayesian analysis of the non-Gaussianity parameter.
International Nuclear Information System (INIS)
Kabulov, A.B.
2003-01-01
Atomic nuclei display different kinds of collective motion. The well known example - is the collective model arising from valent nucleons motion. The other a special kind of collective motion is cluster mode. If a collective model has quadrupole character, then cluster one has dipole character. In the boson formalism this model is describing by dynamic symmetry U(6) direct X U(4). The common Hamiltonian symmetrical to U(6) direct X U(4) group has a form H=H d +H p +V pd . In the paper the asymptotical wave function for dipole states connected with (N-1) bosons of s- and d-types is presented. In this case the problem for Hamiltonian eigenvalues is solving by analytical way. With use Elliot method and wave functions asymptotical form the operators for matrix elements of E2-, E1-, M1-transitions are cited
A Variational Level Set Model Combined with FCMS for Image Clustering Segmentation
Directory of Open Access Journals (Sweden)
Liming Tang
2014-01-01
Full Text Available The fuzzy C means clustering algorithm with spatial constraint (FCMS is effective for image segmentation. However, it lacks essential smoothing constraints to the cluster boundaries and enough robustness to the noise. Samson et al. proposed a variational level set model for image clustering segmentation, which can get the smooth cluster boundaries and closed cluster regions due to the use of level set scheme. However it is very sensitive to the noise since it is actually a hard C means clustering model. In this paper, based on Samson’s work, we propose a new variational level set model combined with FCMS for image clustering segmentation. Compared with FCMS clustering, the proposed model can get smooth cluster boundaries and closed cluster regions due to the use of level set scheme. In addition, a block-based energy is incorporated into the energy functional, which enables the proposed model to be more robust to the noise than FCMS clustering and Samson’s model. Some experiments on the synthetic and real images are performed to assess the performance of the proposed model. Compared with some classical image segmentation models, the proposed model has a better performance for the images contaminated by different noise levels.
Tian, Fuyang; Cao, Dong; Dong, Xiaoning; Zhao, Xinqiang; Li, Fade; Wang, Zhonghua
2017-06-01
Behavioral features recognition was an important effect to detect oestrus and sickness in dairy herds and there is a need for heat detection aid. The detection method was based on the measure of the individual behavioural activity, standing time, and temperature of dairy using vibrational sensor and temperature sensor in this paper. The data of behavioural activity index, standing time, lying time and walking time were sent to computer by lower power consumption wireless communication system. The fast approximate K-means algorithm (FAKM) was proposed to deal the data of the sensor for behavioral features recognition. As a result of technical progress in monitoring cows using computers, automatic oestrus detection has become possible.
International Nuclear Information System (INIS)
Franca, L.P.; Stenberg, R.
1989-06-01
Stability conditions are described to analyze a variational formulation emanating from a variational principle for linear isotropic elasticity. The variational principle is based on four dependent variables (namely, the strain tensor, augmented stress, pressure and displacement) and is shown to be valid for any compressibility including the incompressible limit. An improved convergence error analysis is established for a Galerkin-least-squares method based upon these four variables. The analysis presented establishes convergence for a wide choice of combinations of finite element interpolations. (author) [pt
Directory of Open Access Journals (Sweden)
Rosemary M McCloskey
2017-11-01
Full Text Available Clustering infections by genetic similarity is a popular technique for identifying potential outbreaks of infectious disease, in part because sequences are now routinely collected for clinical management of many infections. A diverse number of nonparametric clustering methods have been developed for this purpose. These methods are generally intuitive, rapid to compute, and readily scale with large data sets. However, we have found that nonparametric clustering methods can be biased towards identifying clusters of diagnosis-where individuals are sampled sooner post-infection-rather than the clusters of rapid transmission that are meant to be potential foci for public health efforts. We develop a fundamentally new approach to genetic clustering based on fitting a Markov-modulated Poisson process (MMPP, which represents the evolution of transmission rates along the tree relating different infections. We evaluated this model-based method alongside five nonparametric clustering methods using both simulated and actual HIV sequence data sets. For simulated clusters of rapid transmission, the MMPP clustering method obtained higher mean sensitivity (85% and specificity (91% than the nonparametric methods. When we applied these clustering methods to published sequences from a study of HIV-1 genetic clusters in Seattle, USA, we found that the MMPP method categorized about half (46% as many individuals to clusters compared to the other methods. Furthermore, the mean internal branch lengths that approximate transmission rates were significantly shorter in clusters extracted using MMPP, but not by other methods. We determined that the computing time for the MMPP method scaled linearly with the size of trees, requiring about 30 seconds for a tree of 1,000 tips and about 20 minutes for 50,000 tips on a single computer. This new approach to genetic clustering has significant implications for the application of pathogen sequence analysis to public health, where
An Experimental Observation of Axial Variation of Average Size of Methane Clusters in a Gas Jet
International Nuclear Information System (INIS)
Ji-Feng, Han; Chao-Wen, Yang; Jing-Wei, Miao; Jian-Feng, Lu; Meng, Liu; Xiao-Bing, Luo; Mian-Gong, Shi
2010-01-01
Axial variation of average size of methane clusters in a gas jet produced by supersonic expansion of methane through a cylindrical nozzle of 0.8 mm in diameter is observed using a Rayleigh scattering method. The scattered light intensity exhibits a power scaling on the backing pressure ranging from 16 to 50 bar, and the power is strongly Z dependent varying from 8.4 (Z = 3 mm) to 5.4 (Z = 11 mm), which is much larger than that of the argon cluster. The scattered light intensity versus axial position shows that the position of 5 mm has the maximum signal intensity. The estimation of the average cluster size on axial position Z indicates that the cluster growth process goes forward until the maximum average cluster size is reached at Z = 9 mm, and the average cluster size will decrease gradually for Z > 9 mm
Approximation of Fixed Points of Nonexpansive Mappings and Solutions of Variational Inequalities
Directory of Open Access Journals (Sweden)
Chidume CO
2008-01-01
Full Text Available Abstract Let be a real -uniformly smooth Banach space with constant , . Let and be a nonexpansive map and an -strongly accretive map which is also -Lipschitzian, respectively. Let be a real sequence in that satisfies the following condition: and . For and , define a sequence iteratively in by , , . Then, converges strongly to the unique solution of the variational inequality problem (search for such that for all , where . A convergence theorem related to finite family of nonexpansive maps is also proved.
New Constraints on Spatial Variations of the Fine Structure Constant from Clusters of Galaxies
Directory of Open Access Journals (Sweden)
Ivan De Martino
2016-12-01
Full Text Available We have constrained the spatial variation of the fine structure constant using multi-frequency measurements of the thermal Sunyaev-Zeldovich effect of 618 X-ray selected clusters. Although our results are not competitive with the ones from quasar absorption lines, we improved by a factor 10 and ∼2.5 previous results from Cosmic Microwave Background power spectrum and from galaxy clusters, respectively.
Black, Joshua A.; Knowles, Peter J.
2018-06-01
The performance of quasi-variational coupled-cluster (QV) theory applied to the calculation of activation and reaction energies has been investigated. A statistical analysis of results obtained for six different sets of reactions has been carried out, and the results have been compared to those from standard single-reference methods. In general, the QV methods lead to increased activation energies and larger absolute reaction energies compared to those obtained with traditional coupled-cluster theory.
Iterative approximation of a solution of a general variational-like inclusion in Banach spaces
International Nuclear Information System (INIS)
Chidume, C.E.; Kazmi, K.R.; Zegeye, H.
2002-07-01
In this paper, we introduce a class of η-accretive mappings in a real Banach space, and show that the η-proximal point mapping for η-m-accretive mapping is Lipschitz continuous. Further we develop an iterative algorithm for a class of general variational-like inclusions involving η-accretive mappings in real Banach space, and discuss its convergence criteria. The class of η-accretive mappings includes several important classes of operators that have been studied by various authors. (author)
International Nuclear Information System (INIS)
Nikolova, I.; Johanson, K.J.
1999-01-01
Fruitbodies of Cantharellus tubaeformis grown in clusters were collected from a normal Swedish coniferous forest. In the laboratory, individual fruitbodies were transferred into plastic vials and the 137 Cs activity concentrations were determined and expressed as Bq kg -1 fresh weight. After drying at 55 o , the 137 CS levels were recalculated and expressed as Bq kg -1 dry weight. Large variations of 137 Cs activity concentrations between individual fruitbodies within the clusters were observed. In 1995, the range in the 137 CS levels of individual fruitbodies in one cluster were from 9,194 to 164,811 and in another cluster from 2,338 to 38,377 Bq kg -1 . The mean values for these two clusters were 90,294 and 13,556 Bq kg -1 respectively. In 1998, the mean value for eight clusters showed a range from 26,373 to 67,281 Bq kg -1 . The largest variations between individual fruitbodies within a cluster were from 11,875 to 107,160 Bq kg -1 . Refs. 10 (author)
Photon energy dependent intensity variations observed in Auger spectra of free argon clusters
International Nuclear Information System (INIS)
Lundwall, M; Lindblad, A; Bergersen, H; Rander, T; Oehrwall, G; Tchaplyguine, M; Peredkov, S; Svensson, S; Bjoerneholm, O
2006-01-01
Photon energy dependent intensity variations are experimentally observed in the L 2,3 M 2,3 M 2,3 Auger spectra of argon clusters. Two cluster sizes are examined in the present study. Extrinsic scattering effects, both elastic and inelastic, involving the photoelectron are discussed and suggested as the explanation of the variations in the Auger signal. The atoms in the first few coordination shells surrounding the core-ionized atom are proposed to be the main targets for the scattering processes
Quantum theory of anharmonic oscillators - a variational and systematic general approximation method
International Nuclear Information System (INIS)
Yamazaki, K.; Kyoto Univ.
1984-01-01
The paper investigates the energy levels and wavefunctions of an anharmonic oscillator characterised by the potential 1/2ω 2 q 2 +lambdaq 4 . As a lowest-order approximation an extremely simple formula for energy levels, Esub(i)sup(0) = (i+1/2)1/4(3/αsub(i)+αsub(i)), is derived (i being the quantum number of the energy level). This formula reproduces the exact energy levels within an error of about 1%. Systematically higher orders of the present perturbation theory are developed. The present second-order perturbation theory reduces the errors of the lowest-order results by a factor of about 1/5 in general. Various ranges (large, intermediate, small) of (i, lambda) are investigated and compared with the exact values obtained by other workers. For i = 0, 1, even the fourth-order perturbation calculation can be elaborated explicitly, which reduces the error to about 0.01% for any lambda. For small lambda it gives correct numerical coefficients up to lambda 4 terms, as it should. (author)
EVIDENCE FOR CLUSTER TO CLUSTER VARIATIONS IN LOW-MASS STELLAR ROTATIONAL EVOLUTION
International Nuclear Information System (INIS)
Coker, Carl T.; Pinsonneault, Marc; Terndrup, Donald M.
2016-01-01
The concordance model for angular momentum evolution postulates that star-forming regions and clusters are an evolutionary sequence that can be modeled with assumptions about protostar–disk coupling, angular momentum loss from magnetized winds that saturates in a mass-dependent fashion at high rotation rates, and core-envelope decoupling for solar analogs. We test this approach by combining established data with the large h Per data set from the MONITOR project and new low-mass Pleiades data. We confirm prior results that young low-mass stars can be used to test star–disk coupling and angular momentum loss independent of the treatment of internal angular momentum transport. For slow rotators, we confirm the need for star–disk interactions to evolve the ONC to older systems, using h Per (age 13 Myr) as our natural post-disk case. There is no evidence for extremely long-lived disks as an alternative to core-envelope decoupling. However, our wind models cannot evolve rapid rotators from h Per to older systems consistently, and we find that this result is robust with respect to the choice of angular momentum loss prescription. We outline two possible solutions: either there is cosmic variance in the distribution of stellar rotation rates in different clusters or there are substantially enhanced torques in low-mass rapid rotators. We favor the former explanation and discuss observational tests that could be used to distinguish them. If the distribution of initial conditions depends on environment, models that test parameters by assuming a universal underlying distribution of initial conditions will need to be re-evaluated.
EVIDENCE FOR CLUSTER TO CLUSTER VARIATIONS IN LOW-MASS STELLAR ROTATIONAL EVOLUTION
Energy Technology Data Exchange (ETDEWEB)
Coker, Carl T.; Pinsonneault, Marc; Terndrup, Donald M., E-mail: coker@astronomy.ohio-state.edu, E-mail: pinsono@astronomy.ohio-state.edu, E-mail: terndrup@astronomy.ohio-state.edu [Department of Astronomy, The Ohio State University, Columbus, OH 43210 (United States)
2016-12-10
The concordance model for angular momentum evolution postulates that star-forming regions and clusters are an evolutionary sequence that can be modeled with assumptions about protostar–disk coupling, angular momentum loss from magnetized winds that saturates in a mass-dependent fashion at high rotation rates, and core-envelope decoupling for solar analogs. We test this approach by combining established data with the large h Per data set from the MONITOR project and new low-mass Pleiades data. We confirm prior results that young low-mass stars can be used to test star–disk coupling and angular momentum loss independent of the treatment of internal angular momentum transport. For slow rotators, we confirm the need for star–disk interactions to evolve the ONC to older systems, using h Per (age 13 Myr) as our natural post-disk case. There is no evidence for extremely long-lived disks as an alternative to core-envelope decoupling. However, our wind models cannot evolve rapid rotators from h Per to older systems consistently, and we find that this result is robust with respect to the choice of angular momentum loss prescription. We outline two possible solutions: either there is cosmic variance in the distribution of stellar rotation rates in different clusters or there are substantially enhanced torques in low-mass rapid rotators. We favor the former explanation and discuss observational tests that could be used to distinguish them. If the distribution of initial conditions depends on environment, models that test parameters by assuming a universal underlying distribution of initial conditions will need to be re-evaluated.
Hao, Dapeng; Ren, Cong; Li, Chuanxing
2012-05-01
A central idea in biology is the hierarchical organization of cellular processes. A commonly used method to identify the hierarchical modular organization of network relies on detecting a global signature known as variation of clustering coefficient (so-called modularity scaling). Although several studies have suggested other possible origins of this signature, it is still widely used nowadays to identify hierarchical modularity, especially in the analysis of biological networks. Therefore, a further and systematical investigation of this signature for different types of biological networks is necessary. We analyzed a variety of biological networks and found that the commonly used signature of hierarchical modularity is actually the reflection of spoke-like topology, suggesting a different view of network architecture. We proved that the existence of super-hubs is the origin that the clustering coefficient of a node follows a particular scaling law with degree k in metabolic networks. To study the modularity of biological networks, we systematically investigated the relationship between repulsion of hubs and variation of clustering coefficient. We provided direct evidences for repulsion between hubs being the underlying origin of the variation of clustering coefficient, and found that for biological networks having no anti-correlation between hubs, such as gene co-expression network, the clustering coefficient doesn't show dependence of degree. Here we have shown that the variation of clustering coefficient is neither sufficient nor exclusive for a network to be hierarchical. Our results suggest the existence of spoke-like modules as opposed to "deterministic model" of hierarchical modularity, and suggest the need to reconsider the organizational principle of biological hierarchy.
Directory of Open Access Journals (Sweden)
Hao Dapeng
2012-05-01
Full Text Available Abstract Background A central idea in biology is the hierarchical organization of cellular processes. A commonly used method to identify the hierarchical modular organization of network relies on detecting a global signature known as variation of clustering coefficient (so-called modularity scaling. Although several studies have suggested other possible origins of this signature, it is still widely used nowadays to identify hierarchical modularity, especially in the analysis of biological networks. Therefore, a further and systematical investigation of this signature for different types of biological networks is necessary. Results We analyzed a variety of biological networks and found that the commonly used signature of hierarchical modularity is actually the reflection of spoke-like topology, suggesting a different view of network architecture. We proved that the existence of super-hubs is the origin that the clustering coefficient of a node follows a particular scaling law with degree k in metabolic networks. To study the modularity of biological networks, we systematically investigated the relationship between repulsion of hubs and variation of clustering coefficient. We provided direct evidences for repulsion between hubs being the underlying origin of the variation of clustering coefficient, and found that for biological networks having no anti-correlation between hubs, such as gene co-expression network, the clustering coefficient doesn’t show dependence of degree. Conclusions Here we have shown that the variation of clustering coefficient is neither sufficient nor exclusive for a network to be hierarchical. Our results suggest the existence of spoke-like modules as opposed to “deterministic model” of hierarchical modularity, and suggest the need to reconsider the organizational principle of biological hierarchy.
Energy Technology Data Exchange (ETDEWEB)
Zinenko, V. I., E-mail: zvi@iph.krasn.ru; Pavlovskii, M. S. [Russian Academy of Sciences, Kirensky Institute of Physics, Siberian Branch (Russian Federation)
2017-02-15
We have analyzed the low-temperature thermodynamic properties of spin ice in the staggered and direct (acting along the [111] axis) fields for rare-earth oxides with the chalcolamprite structure and general formula Re{sub 2}{sup 3+}Me{sub 2}{sup 4+}O{sub 7}{sup 2-}. Calculations have been performed in the cluster approximation. The results have been compared with experimental temperature dependences of heat capacity and entropy for Dy{sub 2}Ti{sub 2}O{sub 7} compound for different values of the external field in the [111] direction. The experimental data and calculated results have also been compared for the Pr{sub 2}Ru{sub 2}O{sub 7} compound with the antiferromagnetic ordering of magnetic moments of ruthenium ions, which gives rise to the staggered field acting on the system of rare-earth ions. The calculated temperature dependences of heat capacity and entropy are in good agreement with experimental data.
Caricato, Marco
2018-04-01
We report the theory and the implementation of the linear response function of the coupled cluster (CC) with the single and double excitations method combined with the polarizable continuum model of solvation, where the correlation solvent response is approximated with the perturbation theory with energy and singles density (PTES) scheme. The singles name is derived from retaining only the contribution of the CC single excitation amplitudes to the correlation density. We compare the PTES working equations with those of the full-density (PTED) method. We then test the PTES scheme on the evaluation of excitation energies and transition dipoles of solvated molecules, as well as of the isotropic polarizability and specific rotation. Our results show a negligible difference between the PTED and PTES schemes, while the latter affords a significantly reduced computational cost. This scheme is general and can be applied to any solvation model that includes mutual solute-solvent polarization, including explicit models. Therefore, the PTES scheme is a competitive approach to compute response properties of solvated systems using CC methods.
International Nuclear Information System (INIS)
Bozkaya, Uğur; Sherrill, C. David
2016-01-01
An efficient implementation is presented for analytic gradients of the coupled-cluster singles and doubles (CCSD) method with the density-fitting approximation, denoted DF-CCSD. Frozen core terms are also included. When applied to a set of alkanes, the DF-CCSD analytic gradients are significantly accelerated compared to conventional CCSD for larger molecules. The efficiency of our DF-CCSD algorithm arises from the acceleration of several different terms, which are designated as the “gradient terms”: computation of particle density matrices (PDMs), generalized Fock-matrix (GFM), solution of the Z-vector equation, formation of the relaxed PDMs and GFM, back-transformation of PDMs and GFM to the atomic orbital (AO) basis, and evaluation of gradients in the AO basis. For the largest member of the alkane set (C 10 H 22 ), the computational times for the gradient terms (with the cc-pVTZ basis set) are 2582.6 (CCSD) and 310.7 (DF-CCSD) min, respectively, a speed up of more than 8-folds. For gradient related terms, the DF approach avoids the usage of four-index electron repulsion integrals. Based on our previous study [U. Bozkaya, J. Chem. Phys. 141, 124108 (2014)], our formalism completely avoids construction or storage of the 4-index two-particle density matrix (TPDM), using instead 2- and 3-index TPDMs. The DF approach introduces negligible errors for equilibrium bond lengths and harmonic vibrational frequencies.
Population clustering based on copy number variations detected from next generation sequencing data.
Duan, Junbo; Zhang, Ji-Gang; Wan, Mingxi; Deng, Hong-Wen; Wang, Yu-Ping
2014-08-01
Copy number variations (CNVs) can be used as significant bio-markers and next generation sequencing (NGS) provides a high resolution detection of these CNVs. But how to extract features from CNVs and further apply them to genomic studies such as population clustering have become a big challenge. In this paper, we propose a novel method for population clustering based on CNVs from NGS. First, CNVs are extracted from each sample to form a feature matrix. Then, this feature matrix is decomposed into the source matrix and weight matrix with non-negative matrix factorization (NMF). The source matrix consists of common CNVs that are shared by all the samples from the same group, and the weight matrix indicates the corresponding level of CNVs from each sample. Therefore, using NMF of CNVs one can differentiate samples from different ethnic groups, i.e. population clustering. To validate the approach, we applied it to the analysis of both simulation data and two real data set from the 1000 Genomes Project. The results on simulation data demonstrate that the proposed method can recover the true common CNVs with high quality. The results on the first real data analysis show that the proposed method can cluster two family trio with different ancestries into two ethnic groups and the results on the second real data analysis show that the proposed method can be applied to the whole-genome with large sample size consisting of multiple groups. Both results demonstrate the potential of the proposed method for population clustering.
Energy Technology Data Exchange (ETDEWEB)
Mészáros, Szabolcs [ELTE Gothard Astrophysical Observatory, H-9704 Szombathely, Szent Imre Herceg st. 112 (Hungary); Martell, Sarah L. [Department of Astrophysics, School of Physics, University of New South Wales, Sydney, NSW 2052 (Australia); Shetrone, Matthew [University of Texas at Austin, McDonald Observatory, Fort Davis, TX 79734 (United States); Lucatello, Sara [INAF-Osservatorio Astronomico di Padova, vicolo dell Osservatorio 5, I-35122 Padova (Italy); Troup, Nicholas W.; Pérez, Ana E. García; Majewski, Steven R. [Department of Astronomy, University of Virginia, Charlottesville, VA 22904-4325 (United States); Bovy, Jo [Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540 (United States); Cunha, Katia [University of Arizona, Tucson, AZ 85719 (United States); García-Hernández, Domingo A.; Prieto, Carlos Allende [Instituto de Astrofísica de Canarias (IAC), E-38200 La Laguna, Tenerife (Spain); Overbeek, Jamie C. [Department of Astronomy, Indiana University, Bloomington, IN 47405 (United States); Beers, Timothy C. [Department of Physics and JINA Center for the Evolution of the Elements, University of Notre Dame, Notre Dame, IN 46556 (United States); Frinchaboy, Peter M. [Texas Christian University, Fort Worth, TX 76129 (United States); Hearty, Fred R.; Schneider, Donald P. [Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, PA 16802 (United States); Holtzman, Jon [New Mexico State University, Las Cruces, NM 88003 (United States); Nidever, David L. [Department of Astronomy, University of Michigan, Ann Arbor, MI 48109 (United States); Schiavon, Ricardo P. [Astrophysics Research Institute, IC2, Liverpool Science Park, Liverpool John Moores University, 146 Brownlow Hill, Liverpool, L3 5RF (United Kingdom); and others
2015-05-15
We investigate the light-element behavior of red giant stars in northern globular clusters (GCs) observed by the SDSS-III Apache Point Observatory Galactic Evolution Experiment. We derive abundances of 9 elements (Fe, C, N, O, Mg, Al, Si, Ca, and Ti) for 428 red giant stars in 10 GCs. The intrinsic abundance range relative to measurement errors is examined, and the well-known C–N and Mg–Al anticorrelations are explored using an extreme-deconvolution code for the first time in a consistent way. We find that Mg and Al drive the population membership in most clusters, except in M107 and M71, the two most metal-rich clusters in our study, where the grouping is most sensitive to N. We also find a diversity in the abundance distributions, with some clusters exhibiting clear abundance bimodalities (for example M3 and M53) while others show extended distributions. The spread of Al abundances increases significantly as cluster average metallicity decreases as previously found by other works, which we take as evidence that low metallicity, intermediate mass AGB polluters were more common in the more metal-poor clusters. The statistically significant correlation of [Al/Fe] with [Si/Fe] in M15 suggests that {sup 28}Si leakage has occurred in this cluster. We also present C, N, and O abundances for stars cooler than 4500 K and examine the behavior of A(C+N+O) in each cluster as a function of temperature and [Al/Fe]. The scatter of A(C+N+O) is close to its estimated uncertainty in all clusters and independent of stellar temperature. A(C+N+O) exhibits small correlations and anticorrelations with [Al/Fe] in M3 and M13, but we cannot be certain about these relations given the size of our abundance uncertainties. Star-to-star variations of α-element (Si, Ca, Ti) abundances are comparable to our estimated errors in all clusters.
3D variational brain tumor segmentation using Dirichlet priors on a clustered feature set.
Popuri, Karteek; Cobzas, Dana; Murtha, Albert; Jägersand, Martin
2012-07-01
Brain tumor segmentation is a required step before any radiation treatment or surgery. When performed manually, segmentation is time consuming and prone to human errors. Therefore, there have been significant efforts to automate the process. But, automatic tumor segmentation from MRI data is a particularly challenging task. Tumors have a large diversity in shape and appearance with intensities overlapping the normal brain tissues. In addition, an expanding tumor can also deflect and deform nearby tissue. In our work, we propose an automatic brain tumor segmentation method that addresses these last two difficult problems. We use the available MRI modalities (T1, T1c, T2) and their texture characteristics to construct a multidimensional feature set. Then, we extract clusters which provide a compact representation of the essential information in these features. The main idea in this work is to incorporate these clustered features into the 3D variational segmentation framework. In contrast to previous variational approaches, we propose a segmentation method that evolves the contour in a supervised fashion. The segmentation boundary is driven by the learned region statistics in the cluster space. We incorporate prior knowledge about the normal brain tissue appearance during the estimation of these region statistics. In particular, we use a Dirichlet prior that discourages the clusters from the normal brain region to be in the tumor region. This leads to a better disambiguation of the tumor from brain tissue. We evaluated the performance of our automatic segmentation method on 15 real MRI scans of brain tumor patients, with tumors that are inhomogeneous in appearance, small in size and in proximity to the major structures in the brain. Validation with the expert segmentation labels yielded encouraging results: Jaccard (58%), Precision (81%), Recall (67%), Hausdorff distance (24 mm). Using priors on the brain/tumor appearance, our proposed automatic 3D variational
Constraints on a possible variation of the fine structure constant from galaxy cluster data
Energy Technology Data Exchange (ETDEWEB)
Holanda, R.F.L. [Departamento de Física, Universidade Estadual da Paraíba, 58429-500, Campina Grande – PB (Brazil); Landau, S.J.; Sánchez G, I.E. [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, and IFIBA, CONICET, Ciudad Universitaria – PabI, Buenos Aires 1428 (Argentina); Alcaniz, J.S. [Departamento de Astronomia, Observatório Nacional, 20921-400, Rio de Janeiro – RJ (Brazil); Busti, V.C., E-mail: holanda@uepb.edu.br, E-mail: slandau@df.uba.ar, E-mail: alcaniz@on.br, E-mail: isg.cos@gmail.com, E-mail: vinicius.busti@astro.iag.usp.br [Departamento de Física Matemática, Instituto de Física, Universidade de São Paulo, CP 66318, 05508-090, São Paulo – SP (Brazil)
2016-05-01
We propose a new method to probe a possible time evolution of the fine structure constant α from X-ray and Sunyaev-Zel'dovich measurements of the gas mass fraction ( f {sub gas}) in galaxy clusters. Taking into account a direct relation between variations of α and violations of the distance-duality relation, we discuss constraints on α for a class of dilaton runaway models. Although not yet competitive with bounds from high- z quasar absorption systems, our constraints, considering a sample of 29 measurements of f {sub gas}, in the redshift interval 0.14 < z < 0.89, provide an independent estimate of α variation at low and intermediate redshifts. Furthermore, current and planned surveys will provide a larger amount of data and thus allow to improve the limits on α variation obtained in the present analysis.
No Evidence of Chemical Abundance Variations in the Intermediate-age Cluster NGC 1783
Zhang, Hao; de Grijs, Richard; Li, Chengyuan; Wu, Xiaohan
2018-02-01
We have analyzed multi-passband photometric observations, obtained with the Hubble Space Telescope, of the massive (1.8 × 105 M ⊙), intermediate-age (1.8 Gyr-old) Large Magellanic Cloud star cluster NGC 1783. The morphology of the cluster’s red giant branch does not exhibit a clear broadening beyond its intrinsic width; the observed width is consistent with that owing to photometric uncertainties alone and independent of the photometric selection boundaries we applied to obtain our sample of red giant stars. The color dispersion of the cluster’s red giant stars around the best-fitting ridgeline is 0.062 ± 0.009 mag, which is equivalent to the width of 0.080 ± 0.001 mag derived from artificial simple stellar population tests, that is, tests based on single-age, single-metallicity stellar populations. NGC 1783 is comparably as massive as other star clusters that show clear evidence of multiple stellar populations. After incorporating mass-loss recipes from its current age of 1.8 Gyr to an age of 6 Gyr, NGC 1783 is expected to remain as massive as some other clusters that host clear multiple populations at these intermediate ages. If we were to assume that mass is an important driver of multiple population formation, then NGC 1783 should have exhibited clear evidence of chemical abundance variations. However, our results support the absence of any chemical abundance variations in NGC 1783.
Hudes, Mark L; McCann, Joyce C; Ames, Bruce N
2009-03-01
A simple statistical method is described to test whether data are consistent with minimum statistical variability expected in a biological experiment. The method is applied to data presented in data tables in a subset of 84 articles among more than 200 published by 3 investigators in a small medical biochemistry department at a major university in India and to 29 "control" articles selected by key word PubMed searches. Major conclusions include: 1) unusual clustering of coefficients of variation (CVs) was observed for data from the majority of articles analyzed that were published by the 3 investigators from 2000-2007; unusual clustering was not observed for data from any of their articles examined that were published between 1992 and 1999; and 2) among a group of 29 control articles retrieved by PubMed key word, title, or title/abstract searches, unusually clustered CVs were observed in 3 articles. Two of these articles were coauthored by 1 of the 3 investigators, and 1 was from the same university but a different department. We are unable to offer a statistical or biological explanation for the unusual clustering observed.
Moody, Daniela; Wohlberg, Brendt
2018-01-02
An approach for land cover classification, seasonal and yearly change detection and monitoring, and identification of changes in man-made features may use a clustering of sparse approximations (CoSA) on sparse representations in learned dictionaries. The learned dictionaries may be derived using efficient convolutional sparse coding to build multispectral or hyperspectral, multiresolution dictionaries that are adapted to regional satellite image data. Sparse image representations of images over the learned dictionaries may be used to perform unsupervised k-means clustering into land cover categories. The clustering process behaves as a classifier in detecting real variability. This approach may combine spectral and spatial textural characteristics to detect geologic, vegetative, hydrologic, and man-made features, as well as changes in these features over time.
Energy Technology Data Exchange (ETDEWEB)
Jacquier, Sandra [Ecole Nationale Superieure des Mines de Saint-Etienne, 158 Cours Fauriel, 42023 F-St. Etienne (France); Gruy, Frederic [Ecole Nationale Superieure des Mines de Saint-Etienne, 158 Cours Fauriel, 42023 F-St. Etienne (France)], E-mail: fgruy@emse.fr
2008-11-15
We previously [Jacquier S, Gruy F. Approximation of the light scattering cross-section for aggregated spherical non-absorbent particles. JQSRT 2008;109:789-810] reformulated the anomalous diffraction (AD) approximation to calculate the light scattering cross section of aggregates by introducing their chord length distribution (CLD). It was applied to several ordered aggregates. This new method is entitled ADr, with the r for rapid because this one is at least 100 times faster than the standard AD method. In this article, we are searching for an approximated expression for CLD suitable all at once for ordered and disordered aggregates. The corresponding scattering cross-section values are compared to the ones coming from the standard AD approximation.
International Nuclear Information System (INIS)
Jacquier, Sandra; Gruy, Frederic
2008-01-01
We previously [Jacquier S, Gruy F. Approximation of the light scattering cross-section for aggregated spherical non-absorbent particles. JQSRT 2008;109:789-810] reformulated the anomalous diffraction (AD) approximation to calculate the light scattering cross section of aggregates by introducing their chord length distribution (CLD). It was applied to several ordered aggregates. This new method is entitled ADr, with the r for rapid because this one is at least 100 times faster than the standard AD method. In this article, we are searching for an approximated expression for CLD suitable all at once for ordered and disordered aggregates. The corresponding scattering cross-section values are compared to the ones coming from the standard AD approximation
First-principles cluster variation calculations of tetragonal-cubic transition in ZrO2
International Nuclear Information System (INIS)
Mohri, Tetsuo; Chen, Ying; Kiyokane, Naoya
2013-01-01
Highlights: ► Cluster variation method is extended to study displacive transition. ► Electronic structure total energy calculations are performed on ZrO2. ► Tetragonal-cubic transition is studied within the framework of order -disorder transition. -- Abstract: It is attempted to extend the basic idea of continuous displacement cluster variation method (CDCVM) to the study of a displacive phase transition. As a preliminary study, we focus on cubic to tetragonal transition in ZrO 2 in which oxygen atoms on the cubic lattice are displaced alternatively in the opposite direction (upward and downward) along the tetragonal axis. Within the CDCVM, displaced atoms are regarded as different atomic species, and two distinguished atoms, A-oxygen (upward shifting) and B-oxygen (downward shifting), are introduced in the description of the free energy. FLAPW electronic structure total energy calculations are performed to extract effective interaction energies among displaced oxygen atoms, and by combing them with CDCVM, the transition temperature is calculated from the first-principles
International Nuclear Information System (INIS)
Arnold, Alexander; Bruhns, Otto T; Reichling, Stefan; Mosler, Joern
2010-01-01
This paper is concerned with an efficient implementation suitable for the elastography inverse problem. More precisely, the novel algorithm allows us to compute the unknown stiffness distribution in soft tissue by means of the measured displacement field by considerably reducing the numerical cost compared to previous approaches. This is realized by combining and further elaborating variational mesh adaption with a clustering technique similar to those known from digital image compression. Within the variational mesh adaption, the underlying finite element discretization is only locally refined if this leads to a considerable improvement of the numerical solution. Additionally, the numerical complexity is reduced by the aforementioned clustering technique, in which the parameters describing the stiffness of the respective soft tissue are sorted according to a predefined number of intervals. By doing so, the number of unknowns associated with the elastography inverse problem can be chosen explicitly. A positive side effect of this method is the reduction of artificial noise in the data (smoothing of the solution). The performance and the rate of convergence of the resulting numerical formulation are critically analyzed by numerical examples.
Kesharwani, Manoj K.; Sylvetsky, Nitai; Martin, Jan M. L.
2017-11-01
We show that the DCSD (distinguishable clusters with all singles and doubles) correlation method permits the calculation of vibrational spectra at near-CCSD(T) quality but at no more than CCSD cost, and with comparatively inexpensive analytical gradients. For systems dominated by a single reference configuration, even MP2.5 is a viable alternative, at MP3 cost. MP2.5 performance for vibrational frequencies is comparable to double hybrids such as DSD-PBEP86-D3BJ, but without resorting to empirical parameters. DCSD is also quite suitable for computing zero-point vibrational energies in computational thermochemistry.
Kesharwani, Manoj K.; Sylvetsky, Nitai; Martin, Jan M. L.
2017-01-01
We show that the DCSD (distinguishable clusters with all singles and doubles) correlation method permits the calculation of vibrational spectra at near-CCSD(T) quality but at no more than CCSD cost, and with comparatively inexpensive analytical gradients. For systems dominated by a single reference configuration, even MP2.5 is a viable alternative, at MP3 cost. MP2.5 performance for vibrational frequencies is comparable to double hybrids such as DSD-PBEP86-D3BJ, but without resorting to empir...
Excitonic Order and Superconductivity in the Two-Orbital Hubbard Model: Variational Cluster Approach
Fujiuchi, Ryo; Sugimoto, Koudai; Ohta, Yukinori
2018-06-01
Using the variational cluster approach based on the self-energy functional theory, we study the possible occurrence of excitonic order and superconductivity in the two-orbital Hubbard model with intra- and inter-orbital Coulomb interactions. It is known that an antiferromagnetic Mott insulator state appears in the regime of strong intra-orbital interaction, a band insulator state appears in the regime of strong inter-orbital interaction, and an excitonic insulator state appears between them. In addition to these states, we find that the s±-wave superconducting state appears in the small-correlation regime, and the dx2 - y2-wave superconducting state appears on the boundary of the antiferromagnetic Mott insulator state. We calculate the single-particle spectral function of the model and compare the band gap formation due to the superconducting and excitonic orders.
LIGHT-ELEMENT ABUNDANCE VARIATIONS AT LOW METALLICITY: THE GLOBULAR CLUSTER NGC 5466
International Nuclear Information System (INIS)
Shetrone, Matthew; Martell, Sarah L.; Wilkerson, Rachel; Adams, Joshua; Siegel, Michael H.; Smith, Graeme H.; Bond, Howard E.
2010-01-01
We present low-resolution (R ≅850) spectra for 67 asymptotic giant branch (AGB), horizontal branch, and red giant branch (RGB) stars in the low-metallicity globular cluster NGC 5466, taken with the VIRUS-P integral-field spectrograph at the 2.7 m Harlan J. Smith telescope at McDonald Observatory. Sixty-six stars are confirmed, and one rejected, as cluster members based on radial velocity, which we measure to an accuracy of 16 km s -1 via template-matching techniques. CN and CH band strengths have been measured for 29 RGB and AGB stars in NGC 5466, and the band-strength indices measured from VIRUS-P data show close agreement with those measured from Keck/LRIS spectra previously taken for five of our target stars. We also determine carbon abundances from comparisons with synthetic spectra. The RGB stars in our data set cover a range in absolute V magnitude from +2 to -3, which permits us to study the rate of carbon depletion on the giant branch as well as the point of its onset. The data show a clear decline in carbon abundance with rising luminosity above the luminosity function 'bump' on the giant branch, and also a subdued range in CN band strength, suggesting ongoing internal mixing in individual stars but minor or no primordial star-to-star variation in light-element abundances.
Ancestral Variations of the PCDHG Gene Cluster Predispose to Dyslexia in a Multiplex Family
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Teesta Naskar
2018-02-01
Full Text Available Dyslexia is a heritable neurodevelopmental disorder characterized by difficulties in reading and writing. In this study, we describe the identification of a set of 17 polymorphisms located across 1.9 Mb region on chromosome 5q31.3, encompassing genes of the PCDHG cluster, TAF7, PCDH1 and ARHGAP26, dominantly inherited with dyslexia in a multi-incident family. Strikingly, the non-risk form of seven variations of the PCDHG cluster, are preponderant in the human lineage, while risk alleles are ancestral and conserved across Neanderthals to non-human primates. Four of these seven ancestral variations (c.460A > C [p.Ile154Leu], c.541G > A [p.Ala181Thr], c.2036G > C [p.Arg679Pro] and c.2059A > G [p.Lys687Glu] result in amino acid alterations. p.Ile154Leu and p.Ala181Thr are present at EC2: EC3 interacting interface of γA3-PCDH and γA4-PCDH respectively might affect trans-homophilic interaction and hence neuronal connectivity. p.Arg679Pro and p.Lys687Glu are present within the linker region connecting trans-membrane to extracellular domain. Sequence analysis indicated the importance of p.Ile154, p.Arg679 and p.Lys687 in maintaining class specificity. Thus the observed association of PCDHG genes encoding neural adhesion proteins reinforces the hypothesis of aberrant neuronal connectivity in the pathophysiology of dyslexia. Additionally, the striking conservation of the identified variants indicates a role of PCDHG in the evolution of highly specialized cognitive skills critical to reading.
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
DEFF Research Database (Denmark)
Veraart, Almut
and present a new estimator for the asymptotic ‘variance’ of the centered realised variance in the presence of jumps. Next, we compare the finite sample performance of the various estimators by means of detailed Monte Carlo studies where we study the impact of the jump activity, the jump size of the jumps......This paper studies the impact of jumps on volatility estimation and inference based on various realised variation measures such as realised variance, realised multipower variation and truncated realised multipower variation. We review the asymptotic theory of those realised variation measures...... in the price and the presence of additional independent or dependent jumps in the volatility on the finite sample performance of the various estimators. We find that the finite sample performance of realised variance, and in particular of the log–transformed realised variance, is generally good, whereas...
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Veloso Germany Gonçalves
2001-01-01
Full Text Available Episodic paroxysmal hemicrania (EPH is a rare disorder characterized by frequent, daily attacks of short-lived, unilateral headache with accompanying ipsilateral autonomic features. EPH has attack periods which last weeks to months separated by remission intervals lasting months to years, however, a seasonal variation has never been reported in EPH. We report a new case of EPH with a clear seasonal pattern: a 32-year-old woman with a right-sided headache for 17 years. Pain occurred with a seasonal variation, with bouts lasting one month (usually in the first months of the year and remission periods lasting around 11 months. During these periods she had headache from three to five times per day, lasting from 15 to 30 minutes, without any particular period preference. There were no precipitating or aggravating factors. Tearing and conjunctival injection accompanied ipsilaterally the pain. Previous treatments provided no pain relief. She completely responded to indomethacin 75 mg daily. After three years, the pain recurred with longer attack duration and was just relieved with prednisone. We also propose a new hypothesis: the EPH-cluster headache continuum.
Exploring gravitational lensing model variations in the Frontier Fields galaxy clusters
Harris James, Nicholas John; Raney, Catie; Brennan, Sean; Keeton, Charles
2018-01-01
Multiple groups have been working on modeling the mass distributions of the six lensing galaxy clusters in the Hubble Space Telescope Frontier Fields data set. The magnification maps produced from these mass models will be important for the future study of the lensed background galaxies, but there exists significant variation in the different groups’ models and magnification maps. We explore the use of two-dimensional histograms as a tool for visualizing these magnification map variations. Using a number of simple, one- or two-halo singular isothermal sphere models, we explore the features that are produced in 2D histogram model comparisons when parameters such as halo mass, ellipticity, and location are allowed to vary. Our analysis demonstrates the potential of 2D histograms as a means of observing the full range of differences between the Frontier Fields groups’ models.This work has been supported by funding from National Science Foundation grants PHY-1560077 and AST-1211385, and from the Space Telescope Science Institute.
International Nuclear Information System (INIS)
Nakatsuji, H.; Hirao, K.
1978-01-01
The symmetry-adapted-cluster (SAC) expansion of an exact wavefunction is given. It is constructed from the generators of the symmetry-adapted excited configurations having the symmetry under consideration, and includes their higher-order effect and self-consistency effect. It is different from the conventional cluster expansions in several important points, and is suitable for applications to open-shell systems as well as closed-shell systems. The variational equation for the SAC wavefunction has a form similar to the generalized Brillouin theorem in accordance with the inclusion of the higher-order effect and the self-consistency effect. We have expressed some existing open-shell orbital theories equivalently in the conventional cluster expansion formulas, and on this basis, we have given the pseudo-orbital theory which is an extension of open-shell orbital theory in the SAC expansion formula
International Nuclear Information System (INIS)
Simmerer, Jennifer; Ivans, Inese I.; Filler, Dan; Francois, Patrick; Charbonnel, Corinne; Monier, Richard; James, Gaël
2013-01-01
We present the metallicity as traced by the abundance of iron in the retrograde globular cluster NGC 3201, measured from high-resolution, high signal-to-noise spectra of 24 red giant branch stars. A spectroscopic analysis reveals a spread in [Fe/H] in the cluster stars at least as large as 0.4 dex. Star-to-star metallicity variations are supported both through photometry and through a detailed examination of spectra. We find no correlation between iron abundance and distance from the cluster core, as might be inferred from recent photometric studies. NGC 3201 is the lowest mass halo cluster to date to contain stars with significantly different [Fe/H] values.
Simmerer, Jennifer; Ivans, Inese I.; Filler, Dan; Francois, Patrick; Charbonnel, Corinne; Monier, Richard; James, Gaël
2013-02-01
We present the metallicity as traced by the abundance of iron in the retrograde globular cluster NGC 3201, measured from high-resolution, high signal-to-noise spectra of 24 red giant branch stars. A spectroscopic analysis reveals a spread in [Fe/H] in the cluster stars at least as large as 0.4 dex. Star-to-star metallicity variations are supported both through photometry and through a detailed examination of spectra. We find no correlation between iron abundance and distance from the cluster core, as might be inferred from recent photometric studies. NGC 3201 is the lowest mass halo cluster to date to contain stars with significantly different [Fe/H] values.
Automated assessment and tracking of human body thermal variations using unsupervised clustering.
Yousefi, Bardia; Fleuret, Julien; Zhang, Hai; Maldague, Xavier P V; Watt, Raymond; Klein, Matthieu
2016-12-01
The presented approach addresses a review of the overheating that occurs during radiological examinations, such as magnetic resonance imaging, and a series of thermal experiments to determine a thermally suitable fabric material that should be used for radiological gowns. Moreover, an automatic system for detecting and tracking of the thermal fluctuation is presented. It applies hue-saturated-value-based kernelled k-means clustering, which initializes and controls the points that lie on the region-of-interest (ROI) boundary. Afterward, a particle filter tracks the targeted ROI during the video sequence independently of previous locations of overheating spots. The proposed approach was tested during experiments and under conditions very similar to those used during real radiology exams. Six subjects have voluntarily participated in these experiments. To simulate the hot spots occurring during radiology, a controllable heat source was utilized near the subject's body. The results indicate promising accuracy for the proposed approach to track hot spots. Some approximations were used regarding the transmittance of the atmosphere, and emissivity of the fabric could be neglected because of the independence of the proposed approach for these parameters. The approach can track the heating spots continuously and correctly, even for moving subjects, and provides considerable robustness against motion artifact, which occurs during most medical radiology procedures.
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.
Fumagalli, Ivan; Parolini, Nicola; Verani, Marco
2018-02-01
We analyze a free-surface problem described by time-dependent Navier-Stokes equations. Surface tension, capillary effects and wall friction are taken into account in the evolution of the system, influencing the motion of the contact line - where the free surface hits the wall - and of the dynamics of the contact angle. The differential equations governing the phenomenon are first derived from the variational principle of minimum reduced dissipation, and then discretized by means of the ALE approach. The numerical properties of the resulting scheme are investigated, drawing a parallel with the physical properties holding at the continuous level. Some instability issues are addressed in detail, in the case of an explicit treatment of the geometry, and novel additional terms are introduced in the discrete formulation in order to damp the instabilities. Numerical tests assess the suitability of the approach, the influence of the parameters, and the effectiveness of the new stabilizing terms.
Indian Academy of Sciences (India)
2017-09-27
Sep 27, 2017 ... Author for correspondence (zh4403701@126.com). MS received 15 ... lic clusters using density functional theory (DFT)-GGA of the DMOL3 package. ... In the process of geometric optimization, con- vergence thresholds ..... and Postgraduate Research & Practice Innovation Program of. Jiangsu Province ...
Indian Academy of Sciences (India)
environmental as well as technical problems during fuel gas utilization. ... adsorption on some alloys of Pd, namely PdAu, PdAg ... ried out on small neutral and charged Au24,26,27, Cu,28 ... study of Zanti et al.29 on Pdn (n = 1–9) clusters.
Variations in CCL3L gene cluster sequence and non-specific gene copy numbers
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Edberg Jeffrey C
2010-03-01
Full Text Available Abstract Background Copy number variations (CNVs of the gene CC chemokine ligand 3-like1 (CCL3L1 have been implicated in HIV-1 susceptibility, but the association has been inconsistent. CCL3L1 shares homology with a cluster of genes localized to chromosome 17q12, namely CCL3, CCL3L2, and, CCL3L3. These genes are involved in host defense and inflammatory processes. Several CNV assays have been developed for the CCL3L1 gene. Findings Through pairwise and multiple alignments of these genes, we have shown that the homology between these genes ranges from 50% to 99% in complete gene sequences and from 70-100% in the exonic regions, with CCL3L1 and CCL3L3 being identical. By use of MEGA 4 and BioEdit, we aligned sense primers, anti-sense primers, and probes used in several previously described assays against pre-multiple alignments of all four chemokine genes. Each set of probes and primers aligned and matched with overlapping sequences in at least two of the four genes, indicating that previously utilized RT-PCR based CNV assays are not specific for only CCL3L1. The four available assays measured median copies of 2 and 3-4 in European and African American, respectively. The concordance between the assays ranged from 0.44-0.83 suggesting individual discordant calls and inconsistencies with the assays from the expected gene coverage from the known sequence. Conclusions This indicates that some of the inconsistencies in the association studies could be due to assays that provide heterogenous results. Sequence information to determine CNV of the three genes separately would allow to test whether their association with the pathogenesis of a human disease or phenotype is affected by an individual gene or by a combination of these genes.
Variation in sequence and location of the fumonisin mycotoxin niosynthetic gene cluster in Fusarium
Proctor, R.H.; Hove, van F.; Susca, A.; Stea, A.; Busman, M.; Lee, van der T.A.J.; Waalwijk, C.; Moretti, A.
2010-01-01
In Fusarium, the ability to produce fumonisins is governed by a 17-gene fumonisin biosynthetic gene (FUM) cluster. Here, we examined the cluster in F. oxysporum strain O-1890 and nine other species selected to represent a wide range of the genetic diversity within the GFSC.
Susca, Antonia; Proctor, Robert H; Butchko, Robert A E; Haidukowski, Miriam; Stea, Gaetano; Logrieco, Antonio; Moretti, Antonio
2014-12-01
The ability to produce fumonisin mycotoxins varies among members of the black aspergilli. Previously, analyses of selected genes in the fumonisin biosynthetic gene (fum) cluster in black aspergilli from California grapes indicated that fumonisin-nonproducing isolates of Aspergillus welwitschiae lack six fum genes, but nonproducing isolates of Aspergillus niger do not. In the current study, analyses of black aspergilli from grapes from the Mediterranean Basin indicate that the genomic context of the fum cluster is the same in isolates of A. niger and A. welwitschiae regardless of fumonisin-production ability and that full-length clusters occur in producing isolates of both species and nonproducing isolates of A. niger. In contrast, the cluster has undergone an eight-gene deletion in fumonisin-nonproducing isolates of A. welwitschiae. Phylogenetic analyses suggest each species consists of a mixed population of fumonisin-producing and nonproducing individuals, and that existence of both production phenotypes may provide a selective advantage to these species. Differences in gene content of fum cluster homologues and phylogenetic relationships of fum genes suggest that the mutation(s) responsible for the nonproduction phenotype differs, and therefore arose independently, in the two species. Partial fum cluster homologues were also identified in genome sequences of four other black Aspergillus species. Gene content of these partial clusters and phylogenetic relationships of fum sequences indicate that non-random partial deletion of the cluster has occurred multiple times among the species. This in turn suggests that an intact cluster and fumonisin production were once more widespread among black aspergilli. Copyright © 2014 Elsevier Inc. All rights reserved.
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Guo Junqiao
2008-09-01
Full Text Available Abstract Background The effects of climate variations on bacillary dysentery incidence have gained more recent concern. However, the multi-collinearity among meteorological factors affects the accuracy of correlation with bacillary dysentery incidence. Methods As a remedy, a modified method to combine ridge regression and hierarchical cluster analysis was proposed for investigating the effects of climate variations on bacillary dysentery incidence in northeast China. Results All weather indicators, temperatures, precipitation, evaporation and relative humidity have shown positive correlation with the monthly incidence of bacillary dysentery, while air pressure had a negative correlation with the incidence. Ridge regression and hierarchical cluster analysis showed that during 1987–1996, relative humidity, temperatures and air pressure affected the transmission of the bacillary dysentery. During this period, all meteorological factors were divided into three categories. Relative humidity and precipitation belonged to one class, temperature indexes and evaporation belonged to another class, and air pressure was the third class. Conclusion Meteorological factors have affected the transmission of bacillary dysentery in northeast China. Bacillary dysentery prevention and control would benefit from by giving more consideration to local climate variations.
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.
Leveraging long sequencing reads to investigate R-gene clustering and variation in sugar beet
Host-pathogen interactions are of prime importance to modern agriculture. Plants utilize various types of resistance genes to mitigate pathogen damage. Identification of the specific gene responsible for a specific resistance can be difficult due to duplication and clustering within R-gene families....
Chacó n Rebollo, Tomá s; Dia, Ben Mansour
2015-01-01
This paper introduces a variational multi-scale method where the sub-grid scales are computed by spectral approximations. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base of eigenfunctions which are orthonormal in weighted L2 spaces. This allows to element-wise calculate the sub-grid scales by means of the associated spectral expansion. We propose a feasible VMS-spectral method by truncation of this spectral expansion to a finite number of modes. We apply this general framework to the convection-diffusion equation, by analytically computing the family of eigenfunctions. We perform a convergence and error analysis. We also present some numerical tests that show the stability of the method for an odd number of spectral modes, and an improvement of accuracy in the large resolved scales, due to the adding of the sub-grid spectral scales.
Chacón Rebollo, Tomás
2015-03-01
This paper introduces a variational multi-scale method where the sub-grid scales are computed by spectral approximations. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base of eigenfunctions which are orthonormal in weighted L2 spaces. This allows to element-wise calculate the sub-grid scales by means of the associated spectral expansion. We propose a feasible VMS-spectral method by truncation of this spectral expansion to a finite number of modes. We apply this general framework to the convection-diffusion equation, by analytically computing the family of eigenfunctions. We perform a convergence and error analysis. We also present some numerical tests that show the stability of the method for an odd number of spectral modes, and an improvement of accuracy in the large resolved scales, due to the adding of the sub-grid spectral scales.
Genetic variations and haplotype diversity of the UGT1 gene cluster in the Chinese population.
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Jing Yang
Full Text Available Vertebrates require tremendous molecular diversity to defend against numerous small hydrophobic chemicals. UDP-glucuronosyltransferases (UGTs are a large family of detoxification enzymes that glucuronidate xenobiotics and endobiotics, facilitating their excretion from the body. The UGT1 gene cluster contains a tandem array of variable first exons, each preceded by a specific promoter, and a common set of downstream constant exons, similar to the genomic organization of the protocadherin (Pcdh, immunoglobulin, and T-cell receptor gene clusters. To assist pharmacogenomics studies in Chinese, we sequenced nine first exons, promoter and intronic regions, and five common exons of the UGT1 gene cluster in a population sample of 253 unrelated Chinese individuals. We identified 101 polymorphisms and found 15 novel SNPs. We then computed allele frequencies for each polymorphism and reconstructed their linkage disequilibrium (LD map. The UGT1 cluster can be divided into five linkage blocks: Block 9 (UGT1A9, Block 9/7/6 (UGT1A9, UGT1A7, and UGT1A6, Block 5 (UGT1A5, Block 4/3 (UGT1A4 and UGT1A3, and Block 3' UTR. Furthermore, we inferred haplotypes and selected their tagSNPs. Finally, comparing our data with those of three other populations of the HapMap project revealed ethnic specificity of the UGT1 genetic diversity in Chinese. These findings have important implications for future molecular genetic studies of the UGT1 gene cluster as well as for personalized medical therapies in Chinese.
Arnup, Sarah J; McKenzie, Joanne E; Hemming, Karla; Pilcher, David; Forbes, Andrew B
2017-08-15
In a cluster randomised crossover (CRXO) design, a sequence of interventions is assigned to a group, or 'cluster' of individuals. Each cluster receives each intervention in a separate period of time, forming 'cluster-periods'. Sample size calculations for CRXO trials need to account for both the cluster randomisation and crossover aspects of the design. Formulae are available for the two-period, two-intervention, cross-sectional CRXO design, however implementation of these formulae is known to be suboptimal. The aims of this tutorial are to illustrate the intuition behind the design; and provide guidance on performing sample size calculations. Graphical illustrations are used to describe the effect of the cluster randomisation and crossover aspects of the design on the correlation between individual responses in a CRXO trial. Sample size calculations for binary and continuous outcomes are illustrated using parameters estimated from the Australia and New Zealand Intensive Care Society - Adult Patient Database (ANZICS-APD) for patient mortality and length(s) of stay (LOS). The similarity between individual responses in a CRXO trial can be understood in terms of three components of variation: variation in cluster mean response; variation in the cluster-period mean response; and variation between individual responses within a cluster-period; or equivalently in terms of the correlation between individual responses in the same cluster-period (within-cluster within-period correlation, WPC), and between individual responses in the same cluster, but in different periods (within-cluster between-period correlation, BPC). The BPC lies between zero and the WPC. When the WPC and BPC are equal the precision gained by crossover aspect of the CRXO design equals the precision lost by cluster randomisation. When the BPC is zero there is no advantage in a CRXO over a parallel-group cluster randomised trial. Sample size calculations illustrate that small changes in the specification of
Benchmark Applications of Variations of Multireference Equation of Motion Coupled-Cluster Theory
Czech Academy of Sciences Publication Activity Database
Huntington, L. M.; Demel, Ondřej; Nooijen, M.
2016-01-01
Roč. 12, č. 1 (2016), s. 114-132 ISSN 1549-9618 R&D Projects: GA ČR GJ15-00058Y Institutional support: RVO:61388955 Keywords : MR-EOM * Benchmark applications * variations Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 5.245, year: 2016
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
International Nuclear Information System (INIS)
Boudreault, S.; Bailer-Jones, C. A. L.
2009-01-01
We present the stellar and substellar mass function (MF) of the open cluster IC 2391, plus its radial dependence, and use this to put constraints on the formation mechanism of brown dwarfs (BDs). Our multi-band optical and infrared photometric survey with spectroscopic follow-up covers 11 deg 2 , making it the largest survey of this cluster to date. We observe a radial variation in the MF over the range 0.072-0.3 M sun , but no significant variation in the MF below the substellar boundary at the three cluster radius intervals is analyzed. This lack of radial variation for low masses is what we would expect with the ejection scenario for BD formation, although considering that IC 2391 has an age about three times older than its crossing time, we expect that BDs with a velocity greater than the escape velocity have already escaped the cluster. Alternatively, the variation in the MF of the stellar objects could be an indication that they have undergone mass segregation via dynamical evolution. We also observe a significant variation across the cluster in the color of the (background) field star locus in color-magnitude diagrams and conclude that this is due to variable background extinction in the Galactic plane. From our preliminary spectroscopic follow-up, to confirm BD status and cluster membership, we find that all candidates are M dwarfs (in either the field or the cluster), demonstrating the efficiency of our photometric selection method in avoiding contaminants (e.g., red giants). About half of our photometric candidates for which we have spectra are spectroscopically confirmed as cluster members; two are new spectroscopically confirmed BD members of IC 2391.
Variations in Decision-Making Profiles by Age and Gender: A Cluster-Analytic Approach
Delaney, Rebecca; Strough, JoNell; Parker, Andrew M.; de Bruin, Wandi Bruine
2015-01-01
Using cluster-analysis, we investigated whether rational, intuitive, spontaneous, dependent, and avoidant styles of decision making (Scott & Bruce, 1995) combined to form distinct decision-making profiles that differed by age and gender. Self-report survey data were collected from 1,075 members of RAND’s American Life Panel (56.2% female, 18–93 years, Mage = 53.49). Three decision-making profiles were identified: affective/experiential, independent/self-controlled, and an interpersonally-oriented dependent profile. Older people were less likely to be in the affective/experiential profile and more likely to be in the independent/self-controlled profile. Women were less likely to be in the affective/experiential profile and more likely to be in the interpersonally-oriented dependent profile. Interpersonally-oriented profiles are discussed as an overlooked but important dimension of how people make important decisions. PMID:26005238
Variations in Decision-Making Profiles by Age and Gender: A Cluster-Analytic Approach.
Delaney, Rebecca; Strough, JoNell; Parker, Andrew M; de Bruin, Wandi Bruine
2015-10-01
Using cluster-analysis, we investigated whether rational, intuitive, spontaneous, dependent, and avoidant styles of decision making (Scott & Bruce, 1995) combined to form distinct decision-making profiles that differed by age and gender. Self-report survey data were collected from 1,075 members of RAND's American Life Panel (56.2% female, 18-93 years, M age = 53.49). Three decision-making profiles were identified: affective/experiential, independent/self-controlled, and an interpersonally-oriented dependent profile. Older people were less likely to be in the affective/experiential profile and more likely to be in the independent/self-controlled profile. Women were less likely to be in the affective/experiential profile and more likely to be in the interpersonally-oriented dependent profile. Interpersonally-oriented profiles are discussed as an overlooked but important dimension of how people make important decisions.
Engineering practice variation through provider agreement: a cluster-randomized feasibility trial.
McCarren, Madeline; Twedt, Elaine L; Mansuri, Faizmohamed M; Nelson, Philip R; Peek, Brian T
2014-01-01
Minimal-risk randomized trials that can be embedded in practice could facilitate learning health-care systems. A cluster-randomized design was proposed to compare treatment strategies by assigning clusters (eg, providers) to "favor" a particular drug, with providers retaining autonomy for specific patients. Patient informed consent might be waived, broadening inclusion. However, it is not known if providers will adhere to the assignment or whether institutional review boards will waive consent. We evaluated the feasibility of this trial design. Agreeable providers were randomized to "favor" either hydrochlorothiazide or chlorthalidone when starting patients on thiazide-type therapy for hypertension. The assignment applied when the provider had already decided to start a thiazide, and providers could deviate from the strategy as needed. Prescriptions were aggregated to produce a provider strategy-adherence rate. All four institutional review boards waived documentation of patient consent. Providers (n=18) followed their assigned strategy for most of their new thiazide prescriptions (n=138 patients). In the "favor hydrochlorothiazide" group, there was 99% adherence to that strategy. In the "favor chlorthalidone" group, chlorthalidone comprised 77% of new thiazide starts, up from 1% in the pre-study period. When the assigned strategy was followed, dosing in the recommended range was 48% for hydrochlorothiazide (25-50 mg/day) and 100% for chlorthalidone (12.5-25.0 mg/day). Providers were motivated to participate by a desire to contribute to a comparative effectiveness study. A study promotional mug, provider information letter, and interactions with the site investigator were identified as most helpful in reminding providers of their study drug strategy. Providers prescribed according to an assigned drug-choice strategy most of the time for the purpose of a comparative effectiveness study. This simple design could facilitate research participation and behavior change
Bhattacharya, Anindya; De, Rajat K
2010-08-01
Distance based clustering algorithms can group genes that show similar expression values under multiple experimental conditions. They are unable to identify a group of genes that have similar pattern of variation in their expression values. Previously we developed an algorithm called divisive correlation clustering algorithm (DCCA) to tackle this situation, which is based on the concept of correlation clustering. But this algorithm may also fail for certain cases. In order to overcome these situations, we propose a new clustering algorithm, called average correlation clustering algorithm (ACCA), which is able to produce better clustering solution than that produced by some others. ACCA is able to find groups of genes having more common transcription factors and similar pattern of variation in their expression values. Moreover, ACCA is more efficient than DCCA with respect to the time of execution. Like DCCA, we use the concept of correlation clustering concept introduced by Bansal et al. ACCA uses the correlation matrix in such a way that all genes in a cluster have the highest average correlation values with the genes in that cluster. We have applied ACCA and some well-known conventional methods including DCCA to two artificial and nine gene expression datasets, and compared the performance of the algorithms. The clustering results of ACCA are found to be more significantly relevant to the biological annotations than those of the other methods. Analysis of the results show the superiority of ACCA over some others in determining a group of genes having more common transcription factors and with similar pattern of variation in their expression profiles. Availability of the software: The software has been developed using C and Visual Basic languages, and can be executed on the Microsoft Windows platforms. The software may be downloaded as a zip file from http://www.isical.ac.in/~rajat. Then it needs to be installed. Two word files (included in the zip file) need to
Electronic states in clusters of H forms of zeolites with variation of the Si/Al ratio
International Nuclear Information System (INIS)
Gun'ko, V.M.
1987-01-01
Fragments of H forms of zeolites of the faujasite type including up to 12 silicon- and aluminum-oxygen tetrahedrons and having different Si/Al ratios have been calculated in the cluster approximation by the MINDO/3 and CNDO/2 methods. The dependence of the integral and orbital densities of electronic states in the clusters on the aluminum content has been investigated. It has been shown that the profiles of the s- and p-orbital density of states of Al remain practically unchanged as the Si/Al ratio is lowered and that the maxima of the orbital density of states of Si broaden, and new maxima appear at the bottom and top of the valence band. When the acidity of the structural OH groups is lowered, the maxima of the orbital density of states of the H atoms are displaced appreciably only in the deep valence band, while in the upper valence band the positions of the peaks of the s-orbital density of states of the H atoms remain constant. Satisfactory agreement of the calculated orbital densities of states of Si, Al, and O with the corresponding x-ray photoelectron spectra has been obtained. In the deep valence band the data from the MINDO/3 method are better than those from the CNDO/2 method and reproduce the positions of the maxima in the x-ray photoelectron spectra
Directory of Open Access Journals (Sweden)
Yaolong Li
2017-01-01
Full Text Available By focusing on the issue of rolling element bearing (REB performance degradation assessment (PDA, a solution based on variational mode decomposition (VMD and Gath-Geva clustering time series segmentation (GGCTSS has been proposed. VMD is a new decomposition method. Since it is different from the recursive decomposition method, for example, empirical mode decomposition (EMD, local mean decomposition (LMD, and local characteristic-scale decomposition (LCD, VMD needs a priori parameters. In this paper, we will propose a method to optimize the parameters in VMD, namely, the number of decomposition modes and moderate bandwidth constraint, based on genetic algorithm. Executing VMD with the acquired parameters, the BLIMFs are obtained. By taking the envelope of the BLIMFs, the sensitive BLIMFs are selected. And then we take the amplitude of the defect frequency (ADF as a degradative feature. To get the performance degradation assessment, we are going to use the method called Gath-Geva clustering time series segmentation. Afterwards, the method is carried out by two pieces of run-to-failure data. The results indicate that the extracted feature could depict the process of degradation precisely.
Cycle-Based Cluster Variational Method for Direct and Inverse Inference
Furtlehner, Cyril; Decelle, Aurélien
2016-08-01
Large scale inference problems of practical interest can often be addressed with help of Markov random fields. This requires to solve in principle two related problems: the first one is to find offline the parameters of the MRF from empirical data (inverse problem); the second one (direct problem) is to set up the inference algorithm to make it as precise, robust and efficient as possible. In this work we address both the direct and inverse problem with mean-field methods of statistical physics, going beyond the Bethe approximation and associated belief propagation algorithm. We elaborate on the idea that loop corrections to belief propagation can be dealt with in a systematic way on pairwise Markov random fields, by using the elements of a cycle basis to define regions in a generalized belief propagation setting. For the direct problem, the region graph is specified in such a way as to avoid feed-back loops as much as possible by selecting a minimal cycle basis. Following this line we are led to propose a two-level algorithm, where a belief propagation algorithm is run alternatively at the level of each cycle and at the inter-region level. Next we observe that the inverse problem can be addressed region by region independently, with one small inverse problem per region to be solved. It turns out that each elementary inverse problem on the loop geometry can be solved efficiently. In particular in the random Ising context we propose two complementary methods based respectively on fixed point equations and on a one-parameter log likelihood function minimization. Numerical experiments confirm the effectiveness of this approach both for the direct and inverse MRF inference. Heterogeneous problems of size up to 10^5 are addressed in a reasonable computational time, notably with better convergence properties than ordinary belief propagation.
Czech Academy of Sciences Publication Activity Database
Janeček, Ivan; Naar, P.; Stachoň, M.; Gadéa, F. X.; Kalus, R.
2017-01-01
Roč. 19, č. 4 (2017), s. 2778-2790 ISSN 1463-9076 R&D Projects: GA MŠk ED2.1.00/03.0082; GA MŠk(CZ) LO1406 Institutional support: RVO:68145535 Keywords : atom ic clusters * molecular physics * computer simulations Subject RIV: CF - Physical ; Theoretical Chemistry OBOR OECD: Atom ic, molecular and chemical physics (physics of atom s and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 4.123, year: 2016 http://pubs.rsc.org/en/content/articlelanding/2017/cp/c6cp07479k#!divAbstract
Czech Academy of Sciences Publication Activity Database
Janeček, Ivan; Naar, P.; Stachoň, M.; Gadéa, F. X.; Kalus, R.
2017-01-01
Roč. 19, č. 4 (2017), s. 2778-2790 ISSN 1463-9076 R&D Projects: GA MŠk ED2.1.00/03.0082; GA MŠk(CZ) LO1406 Institutional support: RVO:68145535 Keywords : atomic clusters * molecular physics * computer simulations Subject RIV: CF - Physical ; Theoretical Chemistry OBOR OECD: Atomic, molecular and chemical physics ( physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 4.123, year: 2016 http://pubs.rsc.org/en/content/articlelanding/2017/cp/c6cp07479k#!divAbstract
Energy Technology Data Exchange (ETDEWEB)
Popescu, Bogdan; Hanson, M. M., E-mail: bogdan.popescu@uc.edu, E-mail: margaret.hanson@uc.edu [Department of Physics, University of Cincinnati, P.O. Box 210011, Cincinnati, OH 45221-0011 (United States)
2014-01-01
A growing fraction of simple stellar population models, in an aim to create more realistic simulations capable of including stochastic variation in their outputs, begin their simulations with a distribution of discrete stars following a power-law function of masses. Careful attention is needed to create a correctly sampled initial mass function (IMF), and here we provide a solid mathematical method, called MASSCLEAN IMF Sampling, for doing so. We use our method to perform 10 million MASSCLEAN Monte Carlo stellar cluster simulations to determine the most massive star in a mass distribution as a function of the total mass of the cluster. We find that a maximum mass range is predicted, not a single maximum mass. This range is (1) dependent on the total mass of the cluster and (2) independent of an upper stellar mass limit, M{sub limit} , for unsaturated clusters and emerges naturally from our IMF sampling method. We then turn our analysis around, starting with our new database of 25 million simulated clusters, to constrain the highest mass star from the observed integrated colors of a sample of 40 low-mass Large Magellanic Cloud stellar clusters of known age and mass. Finally, we present an analytical description of the maximum mass range of the most massive star as a function of the cluster's total mass and present a new M{sub max} -M{sub cluster} relation.
International Nuclear Information System (INIS)
Popescu, Bogdan; Hanson, M. M.
2014-01-01
A growing fraction of simple stellar population models, in an aim to create more realistic simulations capable of including stochastic variation in their outputs, begin their simulations with a distribution of discrete stars following a power-law function of masses. Careful attention is needed to create a correctly sampled initial mass function (IMF), and here we provide a solid mathematical method, called MASSCLEAN IMF Sampling, for doing so. We use our method to perform 10 million MASSCLEAN Monte Carlo stellar cluster simulations to determine the most massive star in a mass distribution as a function of the total mass of the cluster. We find that a maximum mass range is predicted, not a single maximum mass. This range is (1) dependent on the total mass of the cluster and (2) independent of an upper stellar mass limit, M limit , for unsaturated clusters and emerges naturally from our IMF sampling method. We then turn our analysis around, starting with our new database of 25 million simulated clusters, to constrain the highest mass star from the observed integrated colors of a sample of 40 low-mass Large Magellanic Cloud stellar clusters of known age and mass. Finally, we present an analytical description of the maximum mass range of the most massive star as a function of the cluster's total mass and present a new M max -M cluster relation.
Directory of Open Access Journals (Sweden)
Byungwan Jo
2017-03-01
Full Text Available In the present case study, the use of an advanced, efficient and low-cost technique for monitoring an urban stream was reported. Physicochemical parameters (PcPs of Jungnangcheon stream (Seoul, South Korea were assessed using an Internet of Things (IoT platform. Temperature, dissolved oxygen (DO, and pH parameters were monitored for the three summer months and the first fall month at a fixed location. Analysis was performed using clustering techniques (CTs, such as K-means clustering, agglomerative hierarchical clustering (AHC, and density-based spatial clustering of applications with noise (DBSCAN. An IoT-based Arduino sensor module (ASM network with a 99.99% efficient communication platform was developed to allow collection of stream data with user-friendly software and hardware and facilitated data analysis by interested individuals using their smartphones. Clustering was used to formulate relationships among physicochemical parameters. K-means clustering was used to identify natural clusters using the silhouette coefficient based on cluster compactness and looseness. AHC grouped all data into two clusters as well as temperature, DO and pH into four, eight, and four clusters, respectively. DBSCAN analysis was also performed to evaluate yearly variations in physicochemical parameters. Noise points (NOISE of temperature in 2016 were border points (ƥ, whereas in 2014 and 2015 they remained core points (ɋ, indicating a trend toward increasing stream temperature. We found the stream parameters were within the permissible limits set by the Water Quality Standards for River Water, South Korea.
International Nuclear Information System (INIS)
Barnes, J.; Dekel, A.; Efstathiou, G.; Frenk, C.S.; Yale Univ., New Haven, CT; California Univ., Santa Barbara; Cambridge Univ., England; Sussex Univ., Brighton, England)
1985-01-01
The cluster correlation function xi sub c(r) is compared with the particle correlation function, xi(r) in cosmological N-body simulations with a wide range of initial conditions. The experiments include scale-free initial conditions, pancake models with a coherence length in the initial density field, and hybrid models. Three N-body techniques and two cluster-finding algorithms are used. In scale-free models with white noise initial conditions, xi sub c and xi are essentially identical. In scale-free models with more power on large scales, it is found that the amplitude of xi sub c increases with cluster richness; in this case the clusters give a biased estimate of the particle correlations. In the pancake and hybrid models (with n = 0 or 1), xi sub c is steeper than xi, but the cluster correlation length exceeds that of the points by less than a factor of 2, independent of cluster richness. Thus the high amplitude of xi sub c found in studies of rich clusters of galaxies is inconsistent with white noise and pancake models and may indicate a primordial fluctuation spectrum with substantial power on large scales. 30 references
The mathematical structure of the approximate linear response relation
International Nuclear Information System (INIS)
Yasuda, Muneki; Tanaka, Kazuyuki
2007-01-01
In this paper, we study the mathematical structures of the linear response relation based on Plefka's expansion and the cluster variation method in terms of the perturbation expansion, and we show how this linear response relation approximates the correlation functions of the specified system. Moreover, by comparing the perturbation expansions of the correlation functions estimated by the linear response relation based on these approximation methods with exact perturbative forms of the correlation functions, we are able to explain why the approximate techniques using the linear response relation work well
DEFF Research Database (Denmark)
Veraart, Almut
2011-01-01
and present a new estimator for the asymptotic "variance" of the centered realised variance in the presence of jumps. Next, we compare the finite sample performance of the various estimators by means of detailed Monte Carlo studies. Here we study the impact of the jump activity, of the jump size of the jumps......This paper studies the impact of jumps on volatility estimation and inference based on various realised variation measures such as realised variance, realised multipower variation and truncated realised multipower variation. We review the asymptotic theory of those realised variation measures...... in the price and of the presence of additional independent or dependent jumps in the volatility. We find that the finite sample performance of realised variance and, in particular, of log--transformed realised variance is generally good, whereas the jump--robust statistics tend to struggle in the presence...
Directory of Open Access Journals (Sweden)
Ronny Kellner
Full Text Available The maintenance of an intimate interaction between plant-biotrophic fungi and their hosts over evolutionary times involves strong selection and adaptative evolution of virulence-related genes. The highly specialised maize pathogen Ustilago maydis is assigned with a high evolutionary capability to overcome host resistances due to its high rates of sexual recombination, large population sizes and long distance dispersal. Unlike most studied fungus-plant interactions, the U. maydis - Zea mays pathosystem lacks a typical gene-for-gene interaction. It exerts a large set of secreted fungal virulence factors that are mostly organised in gene clusters. Their contribution to virulence has been experimentally demonstrated but their genetic diversity within U. maydis remains poorly understood. Here, we report on the intraspecific diversity of 34 potential virulence factor genes of U. maydis. We analysed their sequence polymorphisms in 17 isolates of U. maydis from Europe, North and Latin America. We focused on gene cluster 2A, associated with virulence attenuation, cluster 19A that is crucial for virulence, and the cluster-independent effector gene pep1. Although higher compared to four house-keeping genes, the overall levels of intraspecific genetic variation of virulence clusters 2A and 19A, and pep1 are remarkably low and commensurate to the levels of 14 studied non-virulence genes. In addition, each gene is present in all studied isolates and synteny in cluster 2A is conserved. Furthermore, 7 out of 34 virulence genes contain either no polymorphisms or only synonymous substitutions among all isolates. However, genetic variation of clusters 2A and 19A each resolve the large scale population structure of U. maydis indicating subpopulations with decreased gene flow. Hence, the genetic diversity of these virulence-related genes largely reflect the demographic history of U. maydis populations.
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)
DEFF Research Database (Denmark)
Harris, Abigail K P; Williamson, Neil R; Slater, Holly
2004-01-01
The prodigiosin biosynthesis gene cluster (pig cluster) from two strains of Serratia (S. marcescens ATCC 274 and Serratia sp. ATCC 39006) has been cloned, sequenced and expressed in heterologous hosts. Sequence analysis of the respective pig clusters revealed 14 ORFs in S. marcescens ATCC 274...... and 15 ORFs in Serratia sp. ATCC 39006. In each Serratia species, predicted gene products showed similarity to polyketide synthases (PKSs), non-ribosomal peptide synthases (NRPSs) and the Red proteins of Streptomyces coelicolor A3(2). Comparisons between the two Serratia pig clusters and the red cluster...... from Str. coelicolor A3(2) revealed some important differences. A modified scheme for the biosynthesis of prodigiosin, based on the pathway recently suggested for the synthesis of undecylprodigiosin, is proposed. The distribution of the pig cluster within several Serratia sp. isolates is demonstrated...
International Nuclear Information System (INIS)
Telesca, Luciano
2011-01-01
Research highlights: → Time-clustering behaviour in seismicity can be detected by applying the Allan Factor. → The reservoir-induced seismicity at Koyna-Warna (India) is time-clusterized. → Pre- and co-seismic increases of the time-clustering degree are revealed. - Abstract: The time-clustering behavior of the 1996-2005 seismicity of Koyna-Warna region (India), a unique site where reservoir-triggered earthquakes have been continuously occurring over the last about 50 year, has been analyzed. The scaling exponent α, estimated by using the Allan Factor method, a powerful tool to investigate clusterization in point processes, shows co-seismic and pre-seismic enhancements associated with the occurrence of the major events.
Isobe, H; Shoji, M; Yamanaka, S; Mino, H; Umena, Y; Kawakami, K; Kamiya, N; Shen, J-R; Yamaguchi, K
2014-06-28
Full geometry optimizations followed by the vibrational analysis were performed for eight spin configurations of the CaMn4O4X(H2O)3Y (X = O, OH; Y = H2O, OH) cluster in the S1 and S3 states of the oxygen evolution complex (OEC) of photosystem II (PSII). The energy gaps among these configurations obtained by vertical, adiabatic and adiabatic plus zero-point-energy (ZPE) correction procedures have been used for computation of the effective exchange integrals (J) in the spin Hamiltonian model. The J values are calculated by the (1) analytical method and the (2) generalized approximate spin projection (AP) method that eliminates the spin contamination errors of UB3LYP solutions. Using J values derived from these methods, exact diagonalization of the spin Hamiltonian matrix was carried out, yielding excitation energies and spin densities of the ground and lower-excited states of the cluster. The obtained results for the right (R)- and left (L)-opened structures in the S1 and S3 states are found to be consistent with available optical and magnetic experimental results. Implications of the computational results are discussed in relation to (a) the necessity of the exact diagonalization for computations of reliable energy levels, (b) magneto-structural correlations in the CaMn4O5 cluster of the OEC of PSII, (c) structural symmetry breaking in the S1 and S3 states, and (d) the right- and left-handed scenarios for the O-O bond formation for water oxidation.
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.
Clustering in the Zel'dovich approximation
International Nuclear Information System (INIS)
Martinez-Gonzalez, E.; Sanz, J.L.
1991-01-01
We study the evolution of the spatial correlation function using the Zel'dovich solution. The calculations for two different scale-free spectra filtered with a Gaussian window function lead to the conclusions that first zero-crossing occurs at a larger scale compared to linear theory, and the amplitude and slope are slightly greater when non-linear effects are included, although the differences are small for relevant scales where the amplitude is above 0.1. (author)
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.
Directory of Open Access Journals (Sweden)
Yichong Li
Full Text Available BACKGROUND: Chronic diseases have become the leading causes of mortality in China and related behavioral risk factors (BRFs changed dramatically in past decades. We aimed to examine the prevalence, co-variations, clustering and the independent correlates of five BRFs at the national level. METHODOLOGY/PRINCIPAL FINDINGS: We used data from the 2007 China Chronic Disease and Risk Factor Surveillance, in which multistage clustering sampling was adopted to collect a nationally representative sample of 49,247 Chinese aged 15 to 69 years. We estimated the prevalence and clustering (mean number of BRFs of five BRFs: tobacco use, excessive alcohol drinking, insufficient intake of vegetable and fruit, physical inactivity, and overweight or obesity. We conducted binary logistic regression models to examine the co-variations among five BRFs with adjustment of demographic and socioeconomic factors, chronic conditions and other BRFs. Ordinal logistic regression was constructed to investigate the independent associations between each covariate and the clustering of BRFs within individuals. Overall, 57.0% of Chinese population had at least two BRFs and the mean number of BRFs is 1.80 (95% confidence interval: 1.78-1.83. Eight of the ten pairs of bivariate associations between the five BRFs were found statistically significant. Chinese with older age, being a male, living in rural areas, having lower education level and lower yearly household income experienced increased likelihood of having more BRFs. CONCLUSIONS/SIGNIFICANCE: Current BRFs place the majority of Chinese aged 15 to 69 years at risk for the future development of chronic disease, which calls for urgent public health programs to reduce these risk factors. Prominent correlations between BRFs imply that a combined package of interventions targeting multiple BRFs might be appropriate. These interventions should target elder population, men, and rural residents, especially those with lower SES.
Energy Technology Data Exchange (ETDEWEB)
Keskin, Mustafa [Department of Physics, Erciyes University, 38039 Kayseri (Turkey)], E-mail: keskin@erciyes.edu.tr; Canko, Osman [Department of Physics, Erciyes University, 38039 Kayseri (Turkey)
2008-01-15
We study the thermal variations of the ferromagnetic spin-3/2 Blume-Emery-Griffiths (BEG) model with repulsive biquadratic coupling by using the lowest approximation of the cluster variation method (LACVM) in the absence and presence of the external magnetic field. We obtain metastable and unstable branches of the order parameters besides the stable branches and phase transitions of these branches are investigated extensively. The classification of the stable, metastable and unstable states is made by comparing the free energy values of these states. We also study the dynamics of the model by using the path probability method (PPM) with the point distribution in order to make sure that we find and define the metastable and unstable branches of the order parameters completely and correctly. We present the metastable phase diagrams in addition to the equilibrium phase diagrams in the (kT/J, K/J) and (kT/J, D/J) planes. It is found that the metastable phase diagrams always exist at the low temperatures, which are consistent with experimental and theoretical works.
International Nuclear Information System (INIS)
Keskin, Mustafa; Canko, Osman
2008-01-01
We study the thermal variations of the ferromagnetic spin-3/2 Blume-Emery-Griffiths (BEG) model with repulsive biquadratic coupling by using the lowest approximation of the cluster variation method (LACVM) in the absence and presence of the external magnetic field. We obtain metastable and unstable branches of the order parameters besides the stable branches and phase transitions of these branches are investigated extensively. The classification of the stable, metastable and unstable states is made by comparing the free energy values of these states. We also study the dynamics of the model by using the path probability method (PPM) with the point distribution in order to make sure that we find and define the metastable and unstable branches of the order parameters completely and correctly. We present the metastable phase diagrams in addition to the equilibrium phase diagrams in the (kT/J, K/J) and (kT/J, D/J) planes. It is found that the metastable phase diagrams always exist at the low temperatures, which are consistent with experimental and theoretical works
Directory of Open Access Journals (Sweden)
Zhang Xinmin
2011-05-01
Full Text Available Abstract Background In highly copy number variable (CNV regions such as the human defensin gene locus, comprehensive assessment of sequence variations is challenging. PCR approaches are practically restricted to tiny fractions, and next-generation sequencing (NGS approaches of whole individual genomes e.g. by the 1000 Genomes Project is confined by an affordable sequence depth. Combining target enrichment with NGS may represent a feasible approach. Results As a proof of principle, we enriched a ~850 kb section comprising the CNV defensin gene cluster DEFB, the invariable DEFA part and 11 control regions from two genomes by sequence capture and sequenced it by 454 technology. 6,651 differences to the human reference genome were found. Comparison to HapMap genotypes revealed sensitivities and specificities in the range of 94% to 99% for the identification of variations. Using error probabilities for rigorous filtering revealed 2,886 unique single nucleotide variations (SNVs including 358 putative novel ones. DEFB CN determinations by haplotype ratios were in agreement with alternative methods. Conclusion Although currently labor extensive and having high costs, target enriched NGS provides a powerful tool for the comprehensive assessment of SNVs in highly polymorphic CNV regions of individual genomes. Furthermore, it reveals considerable amounts of putative novel variations and simultaneously allows CN estimation.
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.
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...
Energy Technology Data Exchange (ETDEWEB)
Nair, S.S. [Department of Physics, Cochin University of Science and Technology, Cochin 682 022 (India)]. E-mail: swapna@cusat.ac.in; Rajesh, S. [Department of Physics, Cochin University of Science and Technology, Cochin 682 022 (India); Abraham, V.S. [School of Engineering and Sciences, International University of Bremen, 28759 (Germany); Anantharaman, M.R. [Department of Physics, Cochin University of Science and Technology, Cochin 682 022 (India)]. E-mail: mraiyer@yahoo.com; Nampoori, V.P.N. [International School of Photonics, Cochin University of Science and Technology, Cochin-22 (India)
2006-10-15
Fine magnetic particles (size{approx_equal}100 A) belonging to the series Zn {sub x} Fe{sub 1-} {sub x} Fe{sub 2}O{sub 4} were synthesized by cold co-precipitation methods and their structural properties were evaluated using X-ray diffraction. Magnetization studies have been carried out using vibrating sample magnetometry (VSM) showing near-zero loss loop characteristics. Ferrofluids were then prepared employing these fine magnetic powders using oleic acid as surfactant and kerosene as carrier liquid by modifying the usually reported synthesis technique in order to induce anisotropy and enhance the magneto-optical signals. Liquid thin films of these fluids were prepared and field-induced laser transmission through these films was studied. The transmitted light intensity decreases at the centre with applied magnetic field in a linear fashion when subjected to low magnetic fields and saturate at higher fields. This is in accordance with the saturation in cluster formation. The pattern exhibited by these films in the presence of different magnetic fields was observed with the help of a CCD camera and was recorded photographically.
Venkatakrishnan, Balasubramanian; Palii, Miorel-Lucian; Agbandje-McKenna, Mavis; McKenna, Robert
2012-03-01
The Protein Data Bank (PDB) contains over 71,000 structures. Extensively studied proteins have hundreds of submissions available, including mutations, different complexes, and space groups, allowing for application of data-mining algorithms to analyze an array of static structures and gain insight about a protein's structural variation and possibly its dynamics. This investigation is a case study of HIV protease (PR) using in-house algorithms for data mining and structure superposition through generalized formulæ that account for multiple conformations and fractional occupancies. Temperature factors (B-factors) are compared with spatial displacement from the mean structure over the entire study set and separately over bound and ligand-free structures, to assess the significance of structural deviation in a statistical context. Space group differences are also examined.
Impact and spreading behavior of cluster atoms bombarding substrates
Energy Technology Data Exchange (ETDEWEB)
Fang, Te-Hua, E-mail: fang.tehua@msa.hinet.net [Institute of Mechanical and Electromechanical Engineering, National Formosa University, Yunlin 632, Taiwan (China); Kang, Shao-Hui; Liao, Jia-Hung [Institute of Mechanical and Electromechanical Engineering, National Formosa University, Yunlin 632, Taiwan (China)
2009-12-15
The purpose of this study is to investigate the behavior of copper cluster atoms bombarding a substrate using molecule dynamics based on tight-binding second moment approximation (TB-SMA) potential. The simulated results show that a crater on the substrate surface was created by the impact of the clusters. The variations of kinetic energy of cluster bombardments can be divided into three stages. At the initial impact level, the kinetic energies of the clusters and the substrate were constant. Then, the system went into a sluggish stage of energy variation, in which the kinetic energy of the clusters reduced. In the final stage, the kinetic energy of the system became stable. The high slip vector region around the crater had a disorder damage zone. The symmetry-like cross-slip occurred beneath the top layer of the substrate along the <1 1 0> orientations. The spreading index, temperature, and potential functions that affect the bombardments are also discussed.
Impact and spreading behavior of cluster atoms bombarding substrates
International Nuclear Information System (INIS)
Fang, Te-Hua; Kang, Shao-Hui; Liao, Jia-Hung
2009-01-01
The purpose of this study is to investigate the behavior of copper cluster atoms bombarding a substrate using molecule dynamics based on tight-binding second moment approximation (TB-SMA) potential. The simulated results show that a crater on the substrate surface was created by the impact of the clusters. The variations of kinetic energy of cluster bombardments can be divided into three stages. At the initial impact level, the kinetic energies of the clusters and the substrate were constant. Then, the system went into a sluggish stage of energy variation, in which the kinetic energy of the clusters reduced. In the final stage, the kinetic energy of the system became stable. The high slip vector region around the crater had a disorder damage zone. The symmetry-like cross-slip occurred beneath the top layer of the substrate along the orientations. The spreading index, temperature, and potential functions that affect the bombardments are also discussed.
Clustering of near clusters versus cluster compactness
International Nuclear Information System (INIS)
Yu Gao; Yipeng Jing
1989-01-01
The clustering properties of near Zwicky clusters are studied by using the two-point angular correlation function. The angular correlation functions for compact and medium compact clusters, for open clusters, and for all near Zwicky clusters are estimated. The results show much stronger clustering for compact and medium compact clusters than for open clusters, and that open clusters have nearly the same clustering strength as galaxies. A detailed study of the compactness-dependence of correlation function strength is worth investigating. (author)
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.
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)
Cluster size selectivity in the product distribution of ethene dehydrogenation on niobium clusters.
Parnis, J Mark; Escobar-Cabrera, Eric; Thompson, Matthew G K; Jacula, J Paul; Lafleur, Rick D; Guevara-García, Alfredo; Martínez, Ana; Rayner, David M
2005-08-18
Ethene reactions with niobium atoms and clusters containing up to 25 constituent atoms have been studied in a fast-flow metal cluster reactor. The clusters react with ethene at about the gas-kinetic collision rate, indicating a barrierless association process as the cluster removal step. Exceptions are Nb8 and Nb10, for which a significantly diminished rate is observed, reflecting some cluster size selectivity. Analysis of the experimental primary product masses indicates dehydrogenation of ethene for all clusters save Nb10, yielding either Nb(n)C2H2 or Nb(n)C2. Over the range Nb-Nb6, the extent of dehydrogenation increases with cluster size, then decreases for larger clusters. For many clusters, secondary and tertiary product masses are also observed, showing varying degrees of dehydrogenation corresponding to net addition of C2H4, C2H2, or C2. With Nb atoms and several small clusters, formal addition of at least six ethene molecules is observed, suggesting a polymerization process may be active. Kinetic analysis of the Nb atom and several Nb(n) cluster reactions with ethene shows that the process is consistent with sequential addition of ethene units at rates corresponding approximately to the gas-kinetic collision frequency for several consecutive reacting ethene molecules. Some variation in the rate of ethene pick up is found, which likely reflects small energy barriers or steric constraints associated with individual mechanistic steps. Density functional calculations of structures of Nb clusters up to Nb(6), and the reaction products Nb(n)C2H2 and Nb(n)C2 (n = 1...6) are presented. Investigation of the thermochemistry for the dehydrogenation of ethene to form molecular hydrogen, for the Nb atom and clusters up to Nb6, demonstrates that the exergonicity of the formation of Nb(n)C2 species increases with cluster size over this range, which supports the proposal that the extent of dehydrogenation is determined primarily by thermodynamic constraints. Analysis of
APPROXIMATION OF PROBABILITY DISTRIBUTIONS IN QUEUEING MODELS
Directory of Open Access Journals (Sweden)
T. I. Aliev
2013-03-01
Full Text Available For probability distributions with variation coefficient, not equal to unity, mathematical dependences for approximating distributions on the basis of first two moments are derived by making use of multi exponential distributions. It is proposed to approximate distributions with coefficient of variation less than unity by using hypoexponential distribution, which makes it possible to generate random variables with coefficient of variation, taking any value in a range (0; 1, as opposed to Erlang distribution, having only discrete values of coefficient of variation.
Sparse approximation with bases
2015-01-01
This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...
Approximate 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.
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.
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)
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.
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...
Ordered cones and approximation
Keimel, Klaus
1992-01-01
This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.
Approximate 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.)
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
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.
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.
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
A unified approach to the Darwin approximation
International Nuclear Information System (INIS)
Krause, Todd B.; Apte, A.; Morrison, P. J.
2007-01-01
There are two basic approaches to the Darwin approximation. The first involves solving the Maxwell equations in Coulomb gauge and then approximating the vector potential to remove retardation effects. The second approach approximates the Coulomb gauge equations themselves, then solves these exactly for the vector potential. There is no a priori reason that these should result in the same approximation. Here, the equivalence of these two approaches is investigated and a unified framework is provided in which to view the Darwin approximation. Darwin's original treatment is variational in nature, but subsequent applications of his ideas in the context of Vlasov's theory are not. We present here action principles for the Darwin approximation in the Vlasov context, and this serves as a consistency check on the use of the approximation in this setting
PREFACE: Nuclear Cluster Conference; Cluster'07
Freer, Martin
2008-05-01
The Cluster Conference is a long-running conference series dating back to the 1960's, the first being initiated by Wildermuth in Bochum, Germany, in 1969. The most recent meeting was held in Nara, Japan, in 2003, and in 2007 the 9th Cluster Conference was held in Stratford-upon-Avon, UK. As the name suggests the town of Stratford lies upon the River Avon, and shortly before the conference, due to unprecedented rainfall in the area (approximately 10 cm within half a day), lay in the River Avon! Stratford is the birthplace of the `Bard of Avon' William Shakespeare, and this formed an intriguing conference backdrop. The meeting was attended by some 90 delegates and the programme contained 65 70 oral presentations, and was opened by a historical perspective presented by Professor Brink (Oxford) and closed by Professor Horiuchi (RCNP) with an overview of the conference and future perspectives. In between, the conference covered aspects of clustering in exotic nuclei (both neutron and proton-rich), molecular structures in which valence neutrons are exchanged between cluster cores, condensates in nuclei, neutron-clusters, superheavy nuclei, clusters in nuclear astrophysical processes and exotic cluster decays such as 2p and ternary cluster decay. The field of nuclear clustering has become strongly influenced by the physics of radioactive beam facilities (reflected in the programme), and by the excitement that clustering may have an important impact on the structure of nuclei at the neutron drip-line. It was clear that since Nara the field had progressed substantially and that new themes had emerged and others had crystallized. Two particular topics resonated strongly condensates and nuclear molecules. These topics are thus likely to be central in the next cluster conference which will be held in 2011 in the Hungarian city of Debrechen. Martin Freer Participants and Cluster'07
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.
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
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.
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...
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.
Histamine headache; Headache - histamine; Migrainous neuralgia; Headache - cluster; Horton's headache; Vascular headache - cluster ... Doctors do not know exactly what causes cluster headaches. They ... (chemical in the body released during an allergic response) or ...
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.
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...
Electronic and magnetic properties of small rhodium clusters
Energy Technology Data Exchange (ETDEWEB)
Soon, Yee Yeen; Yoon, Tiem Leong [School of Physics, Universiti Sains Malaysia, 11800 USM, Penang (Malaysia); Lim, Thong Leng [Faculty of Engineering and Technology, Multimedia University, Melaka Campus, 75450 Melaka (Malaysia)
2015-04-24
We report a theoretical study of the electronic and magnetic properties of rhodium-atomic clusters. The lowest energy structures at the semi-empirical level of rhodium clusters are first obtained from a novel global-minimum search algorithm, known as PTMBHGA, where Gupta potential is used to describe the atomic interaction among the rhodium atoms. The structures are then re-optimized at the density functional theory (DFT) level with exchange-correlation energy approximated by Perdew-Burke-Ernzerhof generalized gradient approximation. For the purpose of calculating the magnetic moment of a given cluster, we calculate the optimized structure as a function of the spin multiplicity within the DFT framework. The resultant magnetic moments with the lowest energies so obtained allow us to work out the magnetic moment as a function of cluster size. Rhodium atomic clusters are found to display a unique variation in the magnetic moment as the cluster size varies. However, Rh{sub 4} and Rh{sub 6} are found to be nonmagnetic. Electronic structures of the magnetic ground-state structures are also investigated within the DFT framework. The results are compared against those based on different theoretical approaches available in the literature.
Leimar, Olof; Doebeli, Michael; Dieckmann, Ulf
2008-04-01
We have analyzed the evolution of a quantitative trait in populations that are spatially extended along an environmental gradient, with gene flow between nearby locations. In the absence of competition, there is stabilizing selection toward a locally best-adapted trait that changes gradually along the gradient. According to traditional ideas, gradual spatial variation in environmental conditions is expected to lead to gradual variation in the evolved trait. A contrasting possibility is that the trait distribution instead breaks up into discrete clusters. Doebeli and Dieckmann (2003) argued that competition acting locally in trait space and geographical space can promote such clustering. We have investigated this possibility using deterministic population dynamics for asexual populations, analyzing our model numerically and through an analytical approximation. We examined how the evolution of clusters is affected by the shape of competition kernels, by the presence of Allee effects, and by the strength of gene flow along the gradient. For certain parameter ranges clustering was a robust outcome, and for other ranges there was no clustering. Our analysis shows that the shape of competition kernels is important for clustering: the sign structure of the Fourier transform of a competition kernel determines whether the kernel promotes clustering. Also, we found that Allee effects promote clustering, whereas gene flow can have a counteracting influence. In line with earlier findings, we could demonstrate that phenotypic clustering was favored by gradients of intermediate slope.
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
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.
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
Mathematical classification and clustering
Mirkin, Boris
1996-01-01
I am very happy to have this opportunity to present the work of Boris Mirkin, a distinguished Russian scholar in the areas of data analysis and decision making methodologies. The monograph is devoted entirely to clustering, a discipline dispersed through many theoretical and application areas, from mathematical statistics and combina torial optimization to biology, sociology and organizational structures. It compiles an immense amount of research done to date, including many original Russian de velopments never presented to the international community before (for instance, cluster-by-cluster versions of the K-Means method in Chapter 4 or uniform par titioning in Chapter 5). The author's approach, approximation clustering, allows him both to systematize a great part of the discipline and to develop many in novative methods in the framework of optimization problems. The optimization methods considered are proved to be meaningful in the contexts of data analysis and clustering. The material presented in ...
International Nuclear Information System (INIS)
Moeller, R.; Tschoeke, H.
1978-01-01
If spacer grids are used to keep the fuel rods in their places - as in the fuel elements of the SNR series, exact tests are necessary to find out whether and to what extent temperature peaks near the supporting points affect cladding tube design. To clarify this special problem, experimental investigations have been carried out for the first time in a rod cluster model of the SNR-300 fuel element cross-flowed with sodium. The investigations and findings so far are reported on. (orig./RW) [de
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.
Approximate Solutions of Interactive Dynamic Influence Diagrams Using Model Clustering
DEFF Research Database (Denmark)
Zeng, Yifeng; Doshi, Prashant; Qiongyu, Cheng
2007-01-01
Interactive dynamic influence diagrams (I-DIDs) offer a transparent and semantically clear representation for the sequential decision-making problem over multiple time steps in the presence of other interacting agents. Solving I-DIDs exactly involves knowing the solutions of possible models...
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
DEFF Research Database (Denmark)
Ackerman, Margareta; Ben-David, Shai; Branzei, Simina
2012-01-01
We investigate a natural generalization of the classical clustering problem, considering clustering tasks in which different instances may have different weights.We conduct the first extensive theoretical analysis on the influence of weighted data on standard clustering algorithms in both...... the partitional and hierarchical settings, characterizing the conditions under which algorithms react to weights. Extending a recent framework for clustering algorithm selection, we propose intuitive properties that would allow users to choose between clustering algorithms in the weighted setting and classify...
Boland, Melinde R S; Kruis, Annemarije L; Huygens, Simone A; Tsiachristas, Apostolos; Assendelft, Willem J J; Gussekloo, Jacobijn; Blom, Coert M G; Chavannes, Niels H; Rutten-van Mölken, Maureen P M H
2015-12-17
This study aims to (1) examine the variation in implementation of a 2-year chronic obstructive pulmonary disease (COPD) management programme called RECODE, (2) analyse the facilitators and barriers to implementation and (3) investigate the influence of this variation on health outcomes. Implementation variation among the 20 primary-care teams was measured directly using a self-developed scale and indirectly through the level of care integration as measured with the Patient Assessment of Chronic Illness Care (PACIC) and the Assessment of Chronic Illness Care (ACIC). Interviews were held to obtain detailed information regarding the facilitators and barriers to implementation. Multilevel models were used to investigate the association between variation in implementation and change in outcomes. The teams implemented, on average, eight of the 19 interventions, and the specific package of interventions varied widely. Important barriers and facilitators of implementation were (in)sufficient motivation of healthcare provider and patient, the high starting level of COPD care, the small size of the COPD population per team, the mild COPD population, practicalities of the information and communication technology (ICT) system, and hurdles in reimbursement. Level of implementation as measured with our own scale and the ACIC was not associated with health outcomes. A higher level of implementation measured with the PACIC was positively associated with improved self-management capabilities, but this association was not found for other outcomes. There was a wide variety in the implementation of RECODE, associated with barriers at individual, social, organisational and societal level. There was little association between extent of implementation and health outcomes.
Boland, Melinde R S; Kruis, Annemarije L; Huygens, Simone A; Tsiachristas, Apostolos; Assendelft, Willem J J; Gussekloo, Jacobijn; Blom, Coert M G; Chavannes, Niels H; Rutten-van Mölken, Maureen P M H
2015-01-01
This study aims to (1) examine the variation in implementation of a 2-year chronic obstructive pulmonary disease (COPD) management programme called RECODE, (2) analyse the facilitators and barriers to implementation and (3) investigate the influence of this variation on health outcomes. Implementation variation among the 20 primary-care teams was measured directly using a self-developed scale and indirectly through the level of care integration as measured with the Patient Assessment of Chronic Illness Care (PACIC) and the Assessment of Chronic Illness Care (ACIC). Interviews were held to obtain detailed information regarding the facilitators and barriers to implementation. Multilevel models were used to investigate the association between variation in implementation and change in outcomes. The teams implemented, on average, eight of the 19 interventions, and the specific package of interventions varied widely. Important barriers and facilitators of implementation were (in)sufficient motivation of healthcare provider and patient, the high starting level of COPD care, the small size of the COPD population per team, the mild COPD population, practicalities of the information and communication technology (ICT) system, and hurdles in reimbursement. Level of implementation as measured with our own scale and the ACIC was not associated with health outcomes. A higher level of implementation measured with the PACIC was positively associated with improved self-management capabilities, but this association was not found for other outcomes. There was a wide variety in the implementation of RECODE, associated with barriers at individual, social, organisational and societal level. There was little association between extent of implementation and health outcomes. PMID:26677770
Structure and bonding in clusters
International Nuclear Information System (INIS)
Kumar, V.
1991-10-01
We review here the recent progress made in the understanding of the electronic and atomic structure of small clusters of s-p bonded materials using the density functional molecular dynamics technique within the local density approximation. Starting with a brief description of the method, results are presented for alkali metal clusters, clusters of divalent metals such as Mg and Be which show a transition from van der Waals or weak chemical bonding to metallic behaviour as the cluster size grows and clusters of Al, Sn and Sb. In the case of semiconductors, we discuss results for Si, Ge and GaAs clusters. Clusters of other materials such as P, C, S, and Se are also briefly discussed. From these and other available results we suggest the possibility of unique structures for the magic clusters. (author). 69 refs, 7 figs, 1 tab
Structural properties of small rhodium clusters
Energy Technology Data Exchange (ETDEWEB)
Soon, Yee Yeen; Yoon, Tiem Leong [School of Physics, Universiti Sains Malaysia, 11800 USM, Penang (Malaysia); Lim, Thong Leng [Faculty of Engineering and Technology, Multimedia University, Melaka Campus, 75450 Melaka (Malaysia)
2015-04-24
We report a systematic study of the structural properties of rhodium clusters at the atomistic level. A novel global-minimum search algorithm, known as parallel tempering multicanonical basin hopping plus genetic algorithm (PTMBHGA), is used to obtain the geometrical structures with lowest minima at the semi-empirical level where Gupta potential is used to describe the atomic interaction among the rhodium atoms. These structures are then re-optimized at the density functional theory (DFT) level with exchange-correlation energy approximated by Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA). The structures are optimized for different spin multiplicities. The ones with lowest energies will be taken as ground-state structures. In most cases, we observe only minor changes in the geometry and bond length of the clusters as a result of DFT-level re-optimization. Only in some limited cases, the initial geometries obtained from the PTMBHGA are modified by the re-optimization. The variation of structural properties, such as ground-state geometry, symmetry and binding energy, with respect to the cluster size is studied and agreed well with other results available in the literature.
Katz, R
1992-11-01
Cluster management is a management model that fosters decentralization of management, develops leadership potential of staff, and creates ownership of unit-based goals. Unlike shared governance models, there is no formal structure created by committees and it is less threatening for managers. There are two parts to the cluster management model. One is the formation of cluster groups, consisting of all staff and facilitated by a cluster leader. The cluster groups function for communication and problem-solving. The second part of the cluster management model is the creation of task forces. These task forces are designed to work on short-term goals, usually in response to solving one of the unit's goals. Sometimes the task forces are used for quality improvement or system problems. Clusters are groups of not more than five or six staff members, facilitated by a cluster leader. A cluster is made up of individuals who work the same shift. For example, people with job titles who work days would be in a cluster. There would be registered nurses, licensed practical nurses, nursing assistants, and unit clerks in the cluster. The cluster leader is chosen by the manager based on certain criteria and is trained for this specialized role. The concept of cluster management, criteria for choosing leaders, training for leaders, using cluster groups to solve quality improvement issues, and the learning process necessary for manager support are described.
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...
Indian Academy of Sciences (India)
First page Back Continue Last page Overview Graphics. Hardness of Clustering. Both k-means and k-medians intractable (when n and d are both inputs even for k =2). The best known deterministic algorithms. are based on Voronoi partitioning that. takes about time. Need for approximation – “close” to optimal.
Wang, Ningning; Zhang, Di; Wang, Zhenhui; Xun, Hongwei; Ma, Jian; Wang, Hui; Huang, Wei; Liu, Ying; Lin, Xiuyun; Li, Ning; Ou, Xiufang; Zhang, Chunyu; Wang, Ming-Bo; Liu, Bao
2014-06-30
Endogenous small (sm) RNAs (primarily si- and miRNAs) are important trans/cis-acting regulators involved in diverse cellular functions. In plants, the RNA-dependent RNA polymerases (RDRs) are essential for smRNA biogenesis. It has been established that RDR2 is involved in the 24 nt siRNA-dependent RNA-directed DNA methylation (RdDM) pathway. Recent studies have suggested that RDR1 is involved in a second RdDM pathway that relies mostly on 21 nt smRNAs and functions to silence a subset of genomic loci that are usually refractory to the normal RdDM pathway in Arabidopsis. Whether and to what extent the homologs of RDR1 may have similar functions in other plants remained unknown. We characterized a loss-of-function mutant (Osrdr1) of the OsRDR1 gene in rice (Oryza sativa L.) derived from a retrotransposon Tos17 insertion. Microarray analysis identified 1,175 differentially expressed genes (5.2% of all expressed genes in the shoot-tip tissue of rice) between Osrdr1 and WT, of which 896 and 279 genes were up- and down-regulated, respectively, in Osrdr1. smRNA sequencing revealed regional alterations in smRNA clusters across the rice genome. Some of the regions with altered smRNA clusters were associated with changes in DNA methylation. In addition, altered expression of several miRNAs was detected in Osrdr1, and at least some of which were associated with altered expression of predicted miRNA target genes. Despite these changes, no phenotypic difference was identified in Osrdr1 relative to WT under normal condition; however, ephemeral phenotypic fluctuations occurred under some abiotic stress conditions. Our results showed that OsRDR1 plays a role in regulating a substantial number of endogenous genes with diverse functions in rice through smRNA-mediated pathways involving DNA methylation, and which participates in abiotic stress response.
International Nuclear Information System (INIS)
Geraedts, J.M.P.
1983-01-01
Spectra of isotopically mixed clusters (dimers of SF 6 ) are calculated as well as transition frequencies. The result leads to speculations about the suitability of the laser-cluster fragmentation process for isotope separation. (Auth.)
... a role. Unlike migraine and tension headache, cluster headache generally isn't associated with triggers, such as foods, hormonal changes or stress. Once a cluster period begins, however, drinking alcohol ...
African Journals Online (AJOL)
Background: The importance of local variations in patterns of health and disease are increasingly recognised, but, particularly in the case of tropical infections, available methods and resources for characterising disease clusters in time and space are limited. Whilst the Global Positioning System. (GPS) allows accurate and ...
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
Pearce, Iris
1985-01-01
Cluster headache is the most severe primary headache with recurrent pain attacks described as worse than giving birth. The aim of this paper was to make an overview of current knowledge on cluster headache with a focus on pathophysiology and treatment. This paper presents hypotheses of cluster headache pathophysiology, current treatment options and possible future therapy approaches. For years, the hypothalamus was regarded as the key structure in cluster headache, but is now thought to be pa...
Queiroz, Dayane Andrade
2015-01-01
Neste trabalho apresentamos as categorias cluster, que foram introduzidas por Aslak Bakke Buan, Robert Marsh, Markus Reineke, Idun Reiten e Gordana Todorov, com o objetivo de categoriíicar as algebras cluster criadas em 2002 por Sergey Fomin e Andrei Zelevinsky. Os autores acima, em [4], mostraram que existe uma estreita relação entre algebras cluster e categorias cluster para quivers cujo grafo subjacente é um diagrama de Dynkin. Para isto desenvolveram uma teoria tilting na estrutura triang...
International Nuclear Information System (INIS)
Teller, E.
1985-01-01
In the following, a few simple remarks on the evolution and properties of stellar clusters will be collected. In particular, globular clusters will be considered. Though details of such clusters are often not known, a few questions can be clarified with the help of primitive arguments. These are:- why are spherical clusters spherical, why do they have high densities, why do they consist of approximately a million stars, how may a black hole of great mass form within them, may they be the origin of gamma-ray bursts, may their invisible remnants account for the missing mass of our galaxy. The available data do not warrant a detailed evaluation. However, it is remarkable that exceedingly simple models can shed some light on the questions enumerated above. (author)
White, S
1994-01-01
Galaxy clusters are the largest coherent objects in Universe. It has been known since 1933 that their dynamical properties require either a modification of the theory of gravity, or the presence of a dominant component of unseen material of unknown nature. Clusters still provide the best laboratories for studying the amount and distribution of this dark matter relative to the material which can be observed directly -- the galaxies themselves and the hot,X-ray-emitting gas which lies between them.Imaging and spectroscopy of clusters by satellite-borne X -ray telescopes has greatly improved our knowledge of the structure and composition of this intergalactic medium. The results permit a number of new approaches to some fundamental cosmological questions,but current indications from the data are contradictory. The observed irregularity of real clusters seems to imply recent formation epochs which would require a universe with approximately the critical density. On the other hand, the large baryon fraction observ...
Energy Technology Data Exchange (ETDEWEB)
Sanfilippo, Antonio P.; Calapristi, Augustin J.; Crow, Vernon L.; Hetzler, Elizabeth G.; Turner, Alan E.
2004-05-26
We present an approach to the disambiguation of cluster labels that capitalizes on the notion of semantic similarity to assign WordNet senses to cluster labels. The approach provides interesting insights on how document clustering can provide the basis for developing a novel approach to word sense disambiguation.
SHERSTIUK S.V.; POSYLAYEVA K.I.
2013-01-01
In the article there are the theoretical and methodological approaches to the nature and existence of the cluster. The cluster differences from other kinds of cooperative and integration associations. Was develop by scientific-practical recommendations for forming a competitive horticultur cluster.
On the dipole approximation with error estimates
Boßmann, Lea; Grummt, Robert; Kolb, Martin
2018-01-01
The dipole approximation is employed to describe interactions between atoms and radiation. It essentially consists of neglecting the spatial variation of the external field over the atom. Heuristically, this is justified by arguing that the wavelength is considerably larger than the atomic length scale, which holds under usual experimental conditions. We prove the dipole approximation in the limit of infinite wavelengths compared to the atomic length scale and estimate the rate of convergence. Our results include N-body Coulomb potentials and experimentally relevant electromagnetic fields such as plane waves and laser pulses.
DEFF Research Database (Denmark)
Gulati, Mukesh; Lund-Thomsen, Peter; Suresh, Sangeetha
2018-01-01
sell their products successfully in international markets, but there is also an increasingly large consumer base within India. Indeed, Indian industrial clusters have contributed to a substantial part of this growth process, and there are several hundred registered clusters within the country...... of this handbook, which focuses on the role of CSR in MSMEs. Hence we contribute to the literature on CSR in industrial clusters and specifically CSR in Indian industrial clusters by investigating the drivers of CSR in India’s industrial clusters....
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...
Variation Iteration Method for The Approximate Solution of Nonlinear ...
African Journals Online (AJOL)
Tonistar
Nigerian Journal of Basic and Applied Science (June, 2016, 24(1): 70-75 ... 1 Department of Mathematics, University of Ilorin, P.M.B 1515, Ilorin, Nigeria ... All computational framework of the research were performed with the aid of Maple 18 ...
Sampling Polya-Gamma random variates: alternate and approximate techniques
Windle, Jesse; Polson, Nicholas G.; Scott, James G.
2014-01-01
Efficiently sampling from the P\\'olya-Gamma distribution, ${PG}(b,z)$, is an essential element of P\\'olya-Gamma data augmentation. Polson et. al (2013) show how to efficiently sample from the ${PG}(1,z)$ distribution. We build two new samplers that offer improved performance when sampling from the ${PG}(b,z)$ distribution and $b$ is not unity.
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.
THE ASSEMBLY OF GALAXY CLUSTERS
International Nuclear Information System (INIS)
Berrier, Joel C.; Stewart, Kyle R.; Bullock, James S.; Purcell, Chris W.; Barton, Elizabeth J.; Wechsler, Risa H.
2009-01-01
We study the formation of 53 galaxy cluster-size dark matter halos (M = 10 14.0-14.76 M sun ) formed within a pair of cosmological Λ cold dark matter N-body simulations, and track the accretion histories of cluster subhalos with masses large enough to host ∼0.3 L * galaxies. By associating subhalos with cluster galaxies, we find the majority of galaxies in clusters experience no 'preprocessing' in the group environment prior to their accretion into the cluster. On average, 70% of cluster galaxies fall into the cluster potential directly from the field, with no luminous companions in their host halos at the time of accretion; less than 12% are accreted as members of groups with five or more galaxies. Moreover, we find that cluster galaxies are significantly less likely to have experienced a merger in the recent past (∼<6 Gyr) than a field halo of the same mass. These results suggest that local cluster processes such as ram pressure stripping, galaxy harassment, or strangulation play the dominant role in explaining the difference between cluster and field populations at a fixed stellar mass, and that pre-evolution or past merging in the group environment is of secondary importance for setting cluster galaxy properties for most clusters. The accretion times for z = 0 cluster members are quite extended, with ∼20% incorporated into the cluster halo more than 7 Gyr ago and ∼20% within the last 2 Gyr. By comparing the observed morphological fractions in cluster and field populations, we estimate an approximate timescale for late-type to early-type transformation within the cluster environment to be ∼6 Gyr.
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....
Wagstaff, Kiri L.
2012-03-01
On obtaining a new data set, the researcher is immediately faced with the challenge of obtaining a high-level understanding from the observations. What does a typical item look like? What are the dominant trends? How many distinct groups are included in the data set, and how is each one characterized? Which observable values are common, and which rarely occur? Which items stand out as anomalies or outliers from the rest of the data? This challenge is exacerbated by the steady growth in data set size [11] as new instruments push into new frontiers of parameter space, via improvements in temporal, spatial, and spectral resolution, or by the desire to "fuse" observations from different modalities and instruments into a larger-picture understanding of the same underlying phenomenon. Data clustering algorithms provide a variety of solutions for this task. They can generate summaries, locate outliers, compress data, identify dense or sparse regions of feature space, and build data models. It is useful to note up front that "clusters" in this context refer to groups of items within some descriptive feature space, not (necessarily) to "galaxy clusters" which are dense regions in physical space. The goal of this chapter is to survey a variety of data clustering methods, with an eye toward their applicability to astronomical data analysis. In addition to improving the individual researcher’s understanding of a given data set, clustering has led directly to scientific advances, such as the discovery of new subclasses of stars [14] and gamma-ray bursts (GRBs) [38]. All clustering algorithms seek to identify groups within a data set that reflect some observed, quantifiable structure. Clustering is traditionally an unsupervised approach to data analysis, in the sense that it operates without any direct guidance about which items should be assigned to which clusters. There has been a recent trend in the clustering literature toward supporting semisupervised or constrained
Approximated solutions to the Schroedinger equation
International Nuclear Information System (INIS)
Rico, J.F.; Fernandez-Alonso, J.I.
1977-01-01
The authors are currently working on a couple of the well-known deficiencies of the variation method and present here some of the results that have been obtained so far. The variation method does not give information a priori on the trial functions best suited for a particular problem nor does it give information a posteriori on the degree of precision attained. In order to clarify the origin of both difficulties, a geometric interpretation of the variation method is presented. This geometric interpretation is the starting point for the exact formal solution to the fundamental state and for the step-by-step approximations to the exact solution which are also given. Some comments on these results are included. (Auth.)
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
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.
International Nuclear Information System (INIS)
Schaeffer, R.
1987-01-01
The galaxy and cluster luminosity functions are constructed from a model of the mass distribution based on hierarchical clustering at an epoch where the matter distribution is non-linear. These luminosity functions are seen to reproduce the present distribution of objects as can be inferred from the observations. They can be used to deduce the redshift dependence of the cluster distribution and to extrapolate the observations towards the past. The predicted evolution of the cluster distribution is quite strong, although somewhat less rapid than predicted by the linear theory
Measuring Gravitational Flexion in ACS Clusters
Goldberg, David
2005-07-01
We propose measurement of the gravitational "Flexion" signal in ACS cluster images. The flexion, or "arciness" of a lensed background galaxy arises from variations in the lensing field. As a result, it is extremely sensitive to small scale perturbations in the field, and thus, to substructure in clusters. Moreover, because flexion represents gravitationally induced asymmetries in the lensed image, it is completely separable from traditional measurements of shear, which focus on the induced ellipticity of the image, and thus, the two signals may be extracted simultaneously. Since typical galaxies are roughly symmetric upon 180 degree rotation, even a small induced flexion can potentially produce a noticeable effect {Goldberg & Bacon, 2005}. We propose the measurement of substructure within approximately 4 clusters with high-quality ACS data, and will further apply a test of a new tomographic technique whereby comparisons of lensed arcs at different redshifts may be used to estimate the background cosmology, and thus place constraints on the equation of state of dark energy.
International Nuclear Information System (INIS)
Pen'kov, F.M.
1998-01-01
The Born-Oppenheimer approximation is used to obtain an equation for the effective interaction in three atoms bound by a single electron. For low binding energies in an 'electron + atom' pair, long-range forces arise between the atoms, leading to bound states when the size of the three-atom cluster is a few tens of angstrom. A system made of alkali-metal atoms is considered as an example
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...
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.
Error Estimates for the Approximation of the Effective Hamiltonian
International Nuclear Information System (INIS)
Camilli, Fabio; Capuzzo Dolcetta, Italo; Gomes, Diogo A.
2008-01-01
We study approximation schemes for the cell problem arising in homogenization of Hamilton-Jacobi equations. We prove several error estimates concerning the rate of convergence of the approximation scheme to the effective Hamiltonian, both in the optimal control setting and as well as in the calculus of variations setting
A new analytical approximation to the Duffing-harmonic oscillator
International Nuclear Information System (INIS)
Fesanghary, M.; Pirbodaghi, T.; Asghari, M.; Sojoudi, H.
2009-01-01
In this paper, a novel analytical approximation to the nonlinear Duffing-harmonic oscillator is presented. The variational iteration method (VIM) is used to obtain some accurate analytical results for frequency. The accuracy of the results is excellent in the whole range of oscillation amplitude variations.
DISRUPTION OF STAR CLUSTERS IN THE INTERACTING ANTENNAE GALAXIES
International Nuclear Information System (INIS)
Karl, Simon J.; Naab, Thorsten; Fall, S. Michael
2011-01-01
We re-examine the age distribution of star clusters in the Antennae in the context of N-body+hydrodynamical simulations of these interacting galaxies. All of the simulations that account for the observed morphology and other properties of the Antennae have star formation rates that vary relatively slowly with time, by factors of only 1.3-2.5 in the past 10 8 yr. In contrast, the observed age distribution of the clusters declines approximately as a power law, dN/dτ∝τ γ with γ = -1.0, for ages 10 6 yr ∼ 9 yr. These two facts can only be reconciled if the clusters are disrupted progressively for at least ∼10 8 yr and possibly ∼10 9 yr. When we combine the simulated formation rates with a power-law model, f surv ∝τ δ , for the fraction of clusters that survive to each age τ, we match the observed age distribution with exponents in the range -0.9 ∼< δ ∼< -0.6 (with a slightly different δ for each simulation). The similarity between δ and γ indicates that dN/dτ is shaped mainly by the disruption of clusters rather than variations in their formation rate. Thus, the situation in the interacting Antennae resembles that in relatively quiescent galaxies such as the Milky Way and the Magellanic Clouds.
Minku, Leandro L.
2017-10-06
Background: Software Effort Estimation (SEE) can be formulated as an online learning problem, where new projects are completed over time and may become available for training. In this scenario, a Cross-Company (CC) SEE approach called Dycom can drastically reduce the number of Within-Company (WC) projects needed for training, saving the high cost of collecting such training projects. However, Dycom relies on splitting CC projects into different subsets in order to create its CC models. Such splitting can have a significant impact on Dycom\\'s predictive performance. Aims: This paper investigates whether clustering methods can be used to help finding good CC splits for Dycom. Method: Dycom is extended to use clustering methods for creating the CC subsets. Three different clustering methods are investigated, namely Hierarchical Clustering, K-Means, and Expectation-Maximisation. Clustering Dycom is compared against the original Dycom with CC subsets of different sizes, based on four SEE databases. A baseline WC model is also included in the analysis. Results: Clustering Dycom with K-Means can potentially help to split the CC projects, managing to achieve similar or better predictive performance than Dycom. However, K-Means still requires the number of CC subsets to be pre-defined, and a poor choice can negatively affect predictive performance. EM enables Dycom to automatically set the number of CC subsets while still maintaining or improving predictive performance with respect to the baseline WC model. Clustering Dycom with Hierarchical Clustering did not offer significant advantage in terms of predictive performance. Conclusion: Clustering methods can be an effective way to automatically generate Dycom\\'s CC subsets.
Global survey of star clusters in the Milky Way. VI. Age distribution and cluster formation history
Piskunov, A. E.; Just, A.; Kharchenko, N. V.; Berczik, P.; Scholz, R.-D.; Reffert, S.; Yen, S. X.
2018-06-01
Context. The all-sky Milky Way Star Clusters (MWSC) survey provides uniform and precise ages, along with other relevant parameters, for a wide variety of clusters in the extended solar neighbourhood. Aims: In this study we aim to construct the cluster age distribution, investigate its spatial variations, and discuss constraints on cluster formation scenarios of the Galactic disk during the last 5 Gyrs. Methods: Due to the spatial extent of the MWSC, we have considered spatial variations of the age distribution along galactocentric radius RG, and along Z-axis. For the analysis of the age distribution we used 2242 clusters, which all lie within roughly 2.5 kpc of the Sun. To connect the observed age distribution to the cluster formation history we built an analytical model based on simple assumptions on the cluster initial mass function and on the cluster mass-lifetime relation, fit it to the observations, and determined the parameters of the cluster formation law. Results: Comparison with the literature shows that earlier results strongly underestimated the number of evolved clusters with ages t ≳ 100 Myr. Recent studies based on all-sky catalogues agree better with our data, but still lack the oldest clusters with ages t ≳ 1 Gyr. We do not observe a strong variation in the age distribution along RG, though we find an enhanced fraction of older clusters (t > 1 Gyr) in the inner disk. In contrast, the distribution strongly varies along Z. The high altitude distribution practically does not contain clusters with t < 1 Gyr. With simple assumptions on the cluster formation history, the cluster initial mass function and the cluster lifetime we can reproduce the observations. The cluster formation rate and the cluster lifetime are strongly degenerate, which does not allow us to disentangle different formation scenarios. In all cases the cluster formation rate is strongly declining with time, and the cluster initial mass function is very shallow at the high mass end.
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.
The cluster bootstrap consistency in generalized estimating equations
Cheng, Guang
2013-03-01
The cluster bootstrap resamples clusters or subjects instead of individual observations in order to preserve the dependence within each cluster or subject. In this paper, we provide a theoretical justification of using the cluster bootstrap for the inferences of the generalized estimating equations (GEE) for clustered/longitudinal data. Under the general exchangeable bootstrap weights, we show that the cluster bootstrap yields a consistent approximation of the distribution of the regression estimate, and a consistent approximation of the confidence sets. We also show that a computationally more efficient one-step version of the cluster bootstrap provides asymptotically equivalent inference. © 2012.
International Nuclear Information System (INIS)
Romli
1997-01-01
Cluster analysis is the name of group of multivariate techniques whose principal purpose is to distinguish similar entities from the characteristics they process.To study this analysis, there are several algorithms that can be used. Therefore, this topic focuses to discuss the algorithms, such as, similarity measures, and hierarchical clustering which includes single linkage, complete linkage and average linkage method. also, non-hierarchical clustering method, which is popular name K -mean method ' will be discussed. Finally, this paper will be described the advantages and disadvantages of every methods
Everitt, Brian S; Leese, Morven; Stahl, Daniel
2011-01-01
Cluster analysis comprises a range of methods for classifying multivariate data into subgroups. By organizing multivariate data into such subgroups, clustering can help reveal the characteristics of any structure or patterns present. These techniques have proven useful in a wide range of areas such as medicine, psychology, market research and bioinformatics.This fifth edition of the highly successful Cluster Analysis includes coverage of the latest developments in the field and a new chapter dealing with finite mixture models for structured data.Real life examples are used throughout to demons
DEFF Research Database (Denmark)
Böcker, S.; Baumbach, Jan
2013-01-01
. The problem has been the inspiration for numerous algorithms in bioinformatics, aiming at clustering entities such as genes, proteins, phenotypes, or patients. In this paper, we review exact and heuristic methods that have been proposed for the Cluster Editing problem, and also applications......The Cluster Editing problem asks to transform a graph into a disjoint union of cliques using a minimum number of edge modifications. Although the problem has been proven NP-complete several times, it has nevertheless attracted much research both from the theoretical and the applied side...
Approximate circuits for increased reliability
Hamlet, Jason R.; Mayo, Jackson R.
2015-08-18
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
Projected coupled cluster theory.
Qiu, Yiheng; Henderson, Thomas M; Zhao, Jinmo; Scuseria, Gustavo E
2017-08-14
Coupled cluster theory is the method of choice for weakly correlated systems. But in the strongly correlated regime, it faces a symmetry dilemma, where it either completely fails to describe the system or has to artificially break certain symmetries. On the other hand, projected Hartree-Fock theory captures the essential physics of many kinds of strong correlations via symmetry breaking and restoration. In this work, we combine and try to retain the merits of these two methods by applying symmetry projection to broken symmetry coupled cluster wave functions. The non-orthogonal nature of states resulting from the application of symmetry projection operators furnishes particle-hole excitations to all orders, thus creating an obstacle for the exact evaluation of overlaps. Here we provide a solution via a disentanglement framework theory that can be approximated rigorously and systematically. Results of projected coupled cluster theory are presented for molecules and the Hubbard model, showing that spin projection significantly improves unrestricted coupled cluster theory while restoring good quantum numbers. The energy of projected coupled cluster theory reduces to the unprojected one in the thermodynamic limit, albeit at a much slower rate than projected Hartree-Fock.
Lithium in old open clusters - NGC 188
International Nuclear Information System (INIS)
Hobbs, L.M.; Pilachowski, C.
1988-01-01
Echelle spectra which include the Li I line at 6707 A are reported for seven main-sequence stars and one subgiant in NGC 188. The Li I line is detected in five of the six dwarfs which are highly probable cluster members. The derived atmospheric Li/H ratios exceed the solar value by factors ranging approximately from 10 to 40, although these apparently closely solarlike stars are about twice as old as the sun. The variation of the lithium abundance with stellar mass along the main sequences of the Pleiades, the Hyades, NGC 752, and NGC 188 are compared. The resulting evolutionary pattern indicates that the lithium fraction in the Galactic gas has shown no appreciable change from Li/H of roughly 10 to the -9th since the birth of NGC 188 about 10 Gyr ago, except that the abundance could have been higher by an uncertain but possibly appreciable factor at the beginning of that epoch. 51 references
Pottawattamie County School System, Council Bluffs, IA.
The 15 occupational clusters (transportation, fine arts and humanities, communications and media, personal service occupations, construction, hospitality and recreation, health occupations, marine science occupations, consumer and homemaking-related occupations, agribusiness and natural resources, environment, public service, business and office…
DEFF Research Database (Denmark)
Berks, G.; Keyserlingk, Diedrich Graf von; Jantzen, Jan
2000-01-01
A symptom is a condition indicating the presence of a disease, especially, when regarded as an aid in diagnosis.Symptoms are the smallest units indicating the existence of a disease. A syndrome on the other hand is an aggregate, set or cluster of concurrent symptoms which together indicate...... and clustering are the basic concerns in medicine. Classification depends on definitions of the classes and their required degree of participant of the elements in the cases' symptoms. In medicine imprecise conditions are the rule and therefore fuzzy methods are much more suitable than crisp ones. Fuzzy c......-mean clustering is an easy and well improved tool, which has been applied in many medical fields. We used c-mean fuzzy clustering after feature extraction from an aphasia database. Factor analysis was applied on a correlation matrix of 26 symptoms of language disorders and led to five factors. The factors...
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.
The Hartree-Fock seniority approximation
International Nuclear Information System (INIS)
Gomez, J.M.G.; Prieto, C.
1986-01-01
A new self-consistent method is used to take into account the mean-field and the pairing correlations in nuclei at the same time. We call it the Hartree-Fock seniority approximation, because the long-range and short-range correlations are treated in the frameworks of Hartree-Fock theory and the seniority scheme. The method is developed in detail for a minimum-seniority variational wave function in the coordinate representation for an effective interaction of the Skyrme type. An advantage of the present approach over the Hartree-Fock-Bogoliubov theory is the exact conservation of angular momentum and particle number. Furthermore, the computational effort required in the Hartree-Fock seniority approximation is similar to that ofthe pure Hartree-Fock picture. Some numerical calculations for Ca isotopes are presented. (orig.)
Time development of cascades by the binary collision approximation code
International Nuclear Information System (INIS)
Fukumura, A.; Ishino, S.; Sekimura, N.
1991-01-01
To link a molecular dynamic calculation to binary collision approximation codes to explore high energy cascade damage, time between consecutive collisions is introduced into the binary collision MARLOWE code. Calculated results for gold by the modified code show formation of sub-cascades and their spatial and time overlapping, which can affect formation of defect clusters. (orig.)
Donchev, Todor I [Urbana, IL; Petrov, Ivan G [Champaign, IL
2011-05-31
Described herein is an apparatus and a method for producing atom clusters based on a gas discharge within a hollow cathode. The hollow cathode includes one or more walls. The one or more walls define a sputtering chamber within the hollow cathode and include a material to be sputtered. A hollow anode is positioned at an end of the sputtering chamber, and atom clusters are formed when a gas discharge is generated between the hollow anode and the hollow cathode.
Massey, Richard; Kitching, Thomas; Nagai, Daisuke
2010-01-01
The unique properties of dark matter are revealed during collisions between clusters of galaxies, such as the bullet cluster (1E 0657−56) and baby bullet (MACS J0025−12). These systems provide evidence for an additional, invisible mass in the separation between the distributions of their total mass, measured via gravitational lensing, and their ordinary ‘baryonic’ matter, measured via its X-ray emission. Unfortunately, the information available from these systems is limited by their rarity. C...
Leroux, Elizabeth; Ducros, Anne
2008-01-01
Abstract Cluster headache (CH) is a primary headache disease characterized by recurrent short-lasting attacks (15 to 180 minutes) of excruciating unilateral periorbital pain accompanied by ipsilateral autonomic signs (lacrimation, nasal congestion, ptosis, miosis, lid edema, redness of the eye). It affects young adults, predominantly males. Prevalence is estimated at 0.5–1.0/1,000. CH has a circannual and circadian periodicity, attacks being clustered (hence the name) in bouts that can occur ...
Gene cluster statistics with gene families.
Raghupathy, Narayanan; Durand, Dannie
2009-05-01
Identifying genomic regions that descended from a common ancestor is important for understanding the function and evolution of genomes. In distantly related genomes, clusters of homologous gene pairs are evidence of candidate homologous regions. Demonstrating the statistical significance of such "gene clusters" is an essential component of comparative genomic analyses. However, currently there are no practical statistical tests for gene clusters that model the influence of the number of homologs in each gene family on cluster significance. In this work, we demonstrate empirically that failure to incorporate gene family size in gene cluster statistics results in overestimation of significance, leading to incorrect conclusions. We further present novel analytical methods for estimating gene cluster significance that take gene family size into account. Our methods do not require complete genome data and are suitable for testing individual clusters found in local regions, such as contigs in an unfinished assembly. We consider pairs of regions drawn from the same genome (paralogous clusters), as well as regions drawn from two different genomes (orthologous clusters). Determining cluster significance under general models of gene family size is computationally intractable. By assuming that all gene families are of equal size, we obtain analytical expressions that allow fast approximation of cluster probabilities. We evaluate the accuracy of this approximation by comparing the resulting gene cluster probabilities with cluster probabilities obtained by simulating a realistic, power-law distributed model of gene family size, with parameters inferred from genomic data. Surprisingly, despite the simplicity of the underlying assumption, our method accurately approximates the true cluster probabilities. It slightly overestimates these probabilities, yielding a conservative test. We present additional simulation results indicating the best choice of parameter values for data
The efficiency of Flory approximation
International Nuclear Information System (INIS)
Obukhov, S.P.
1984-01-01
The Flory approximation for the self-avoiding chain problem is compared with a conventional perturbation theory expansion. While in perturbation theory each term is averaged over the unperturbed set of configurations, the Flory approximation is equivalent to the perturbation theory with the averaging over the stretched set of configurations. This imposes restrictions on the integration domain in higher order terms and they can be treated self-consistently. The accuracy δν/ν of Flory approximation for self-avoiding chain problems is estimated to be 2-5% for 1 < d < 4. (orig.)
Searching for multiple stellar populations in the massive, old open cluster Berkeley 39
Bragaglia, A.; Gratton, R. G.; Carretta, E.; D'Orazi, V.; Sneden, C.; Lucatello, S.
2012-12-01
The most massive star clusters include several generations of stars with a different chemical composition (mainly revealed by an Na-O anti-correlation) while low-mass star clusters appear to be chemically homogeneous. We are investigating the chemical composition of several clusters with masses of a few 104 M⊙ to establish the lower mass limit for the multiple stellar population phenomenon. Using VLT/FLAMES spectra we determine abundances of Fe, O, Na, and several other elements (α, Fe-peak, and neutron-capture elements) in the old open cluster Berkeley 39. This is a massive open cluster: M ~ 104 M⊙, approximately at the border between small globular clusters and large open clusters. Our sample size of about 30 stars is one of the largest studied for abundances in any open cluster to date, and will be useful to determine improved cluster parameters, such as age, distance, and reddening when coupled with precise, well-calibrated photometry. We find that Berkeley 39 is slightly metal-poor, ⟨[Fe/H]⟩ = -0.20, in agreement with previous studies of this cluster. More importantly, we do not detect any star-to-star variation in the abundances of Fe, O, and Na within quite stringent upper limits. The rms scatter is 0.04, 0.10, and 0.05 dex for Fe, O, and Na, respectively. This small spread can be entirely explained by the noise in the spectra and by uncertainties in the atmospheric parameters. We conclude that Berkeley 39 is a single-population cluster. Based on observations collected at ESO telescopes under programme 386.B-0009.Tables 2 and 3 are available in electronic form at http://www.aanda.org
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.
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
Weighted approximation with varying weight
Totik, Vilmos
1994-01-01
A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.
Framework for sequential approximate optimization
Jacobs, J.H.; Etman, L.F.P.; Keulen, van F.; Rooda, J.E.
2004-01-01
An object-oriented framework for Sequential Approximate Optimization (SAO) isproposed. The framework aims to provide an open environment for thespecification and implementation of SAO strategies. The framework is based onthe Python programming language and contains a toolbox of Python
Statistical Significance for Hierarchical Clustering
Kimes, Patrick K.; Liu, Yufeng; Hayes, D. Neil; Marron, J. S.
2017-01-01
Summary Cluster analysis has proved to be an invaluable tool for the exploratory and unsupervised analysis of high dimensional datasets. Among methods for clustering, hierarchical approaches have enjoyed substantial popularity in genomics and other fields for their ability to simultaneously uncover multiple layers of clustering structure. A critical and challenging question in cluster analysis is whether the identified clusters represent important underlying structure or are artifacts of natural sampling variation. Few approaches have been proposed for addressing this problem in the context of hierarchical clustering, for which the problem is further complicated by the natural tree structure of the partition, and the multiplicity of tests required to parse the layers of nested clusters. In this paper, we propose a Monte Carlo based approach for testing statistical significance in hierarchical clustering which addresses these issues. The approach is implemented as a sequential testing procedure guaranteeing control of the family-wise error rate. Theoretical justification is provided for our approach, and its power to detect true clustering structure is illustrated through several simulation studies and applications to two cancer gene expression datasets. PMID:28099990
Analyzing the errors of DFT approximations for compressed water systems
International Nuclear Information System (INIS)
Alfè, D.; Bartók, A. P.; Csányi, G.; Gillan, M. J.
2014-01-01
We report an extensive study of the errors of density functional theory (DFT) approximations for compressed water systems. The approximations studied are based on the widely used PBE and BLYP exchange-correlation functionals, and we characterize their errors before and after correction for 1- and 2-body errors, the corrections being performed using the methods of Gaussian approximation potentials. The errors of the uncorrected and corrected approximations are investigated for two related types of water system: first, the compressed liquid at temperature 420 K and density 1.245 g/cm 3 where the experimental pressure is 15 kilobars; second, thermal samples of compressed water clusters from the trimer to the 27-mer. For the liquid, we report four first-principles molecular dynamics simulations, two generated with the uncorrected PBE and BLYP approximations and a further two with their 1- and 2-body corrected counterparts. The errors of the simulations are characterized by comparing with experimental data for the pressure, with neutron-diffraction data for the three radial distribution functions, and with quantum Monte Carlo (QMC) benchmarks for the energies of sets of configurations of the liquid in periodic boundary conditions. The DFT errors of the configuration samples of compressed water clusters are computed using QMC benchmarks. We find that the 2-body and beyond-2-body errors in the liquid are closely related to similar errors exhibited by the clusters. For both the liquid and the clusters, beyond-2-body errors of DFT make a substantial contribution to the overall errors, so that correction for 1- and 2-body errors does not suffice to give a satisfactory description. For BLYP, a recent representation of 3-body energies due to Medders, Babin, and Paesani [J. Chem. Theory Comput. 9, 1103 (2013)] gives a reasonably good way of correcting for beyond-2-body errors, after which the remaining errors are typically 0.5 mE h ≃ 15 meV/monomer for the liquid and the
Self-consistent approximations beyond the CPA: Part II
International Nuclear Information System (INIS)
Kaplan, T.; Gray, L.J.
1982-01-01
This paper concentrates on a self-consistent approximation for random alloys developed by Kaplan, Leath, Gray, and Diehl. The construction of the augmented space formalism for a binary alloy is sketched, and the notation to be used derived. Using the operator methods of the augmented space, the self-consistent approximation is derived for the average Green's function, and for evaluating the self-energy, taking into account the scattering by clusters of excitations. The particular cluster approximation desired is derived by treating the scattering by the excitations with S /SUB T/ exactly. Fourier transforms on the disorder-space clustersite labels solve the self-consistent set of equations. Expansion to short range order in the alloy is also discussed. A method to reduce the problem to a computationally tractable form is described
Quantum annealing for combinatorial clustering
Kumar, Vaibhaw; Bass, Gideon; Tomlin, Casey; Dulny, Joseph
2018-02-01
Clustering is a powerful machine learning technique that groups "similar" data points based on their characteristics. Many clustering algorithms work by approximating the minimization of an objective function, namely the sum of within-the-cluster distances between points. The straightforward approach involves examining all the possible assignments of points to each of the clusters. This approach guarantees the solution will be a global minimum; however, the number of possible assignments scales quickly with the number of data points and becomes computationally intractable even for very small datasets. In order to circumvent this issue, cost function minima are found using popular local search-based heuristic approaches such as k-means and hierarchical clustering. Due to their greedy nature, such techniques do not guarantee that a global minimum will be found and can lead to sub-optimal clustering assignments. Other classes of global search-based techniques, such as simulated annealing, tabu search, and genetic algorithms, may offer better quality results but can be too time-consuming to implement. In this work, we describe how quantum annealing can be used to carry out clustering. We map the clustering objective to a quadratic binary optimization problem and discuss two clustering algorithms which are then implemented on commercially available quantum annealing hardware, as well as on a purely classical solver "qbsolv." The first algorithm assigns N data points to K clusters, and the second one can be used to perform binary clustering in a hierarchical manner. We present our results in the form of benchmarks against well-known k-means clustering and discuss the advantages and disadvantages of the proposed techniques.
The VMC survey. XI. Radial stellar population gradients in the galactic globular cluster 47 Tucanae
Energy Technology Data Exchange (ETDEWEB)
Li, Chengyuan; De Grijs, Richard [Kavli Institute for Astronomy and Astrophysics, Peking University, Yi He Yuan Lu 5, Hai Dian District, Beijing 100871 (China); Deng, Licai [Key Laboratory for Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing 100012 (China); Rubele, Stefano; Girardi, Leo; Gullieuszik, Marco [INAF-Osservatorio Astronomico di Padova, vicolo dell' Osservatorio 5, I-35122 Padova (Italy); Wang, Chuchu [Department of Astronomy, Peking University, Yi He Yuan Lu 5, Hai Dian District, Beijing 100871 (China); Bekki, Kenji; For, Bi-Qing [ICRAR M468, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009 (Australia); Cioni, Maria-Rosa L. [Department of Physics, Astronomy, and Mathematics, University of Hertfordshire, Hatfield AL10 9AB (United Kingdom); Clementini, Gisella [INAF-Osservatorio Astronomico di Bologna, Via Ranzani 1, I-40127 Bologna (Italy); Emerson, Jim [Astronomy Unit, School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS (United Kingdom); Groenewegen, Martin A. T. [Royal Observatory of Belgium, Ringlaan 3, 1180 Ukkel (Belgium); Guandalini, Roald [Instituut voor Sterrenkunde, KU Leuven, Celestijnenlaan 200D 2401, 3001 Leuven (Belgium); Marconi, Marcella; Ripepi, Vincenzo [INAF-Osservatorio Astronomico di Capodimonte, via Moiariello 16, I-80131 Naples (Italy); Piatti, Andrés E. [Observatorio Astrońomico, Universidad Nacional de Córdoba, Laprida 854, 5000 Córdoba (Argentina); Van Loon, Jacco Th., E-mail: joshuali@pku.edu.cn, E-mail: grijs@pku.edu.cn [Astrophysics Group, Lennard-Jones Laboratories, Keele University, Staffordshire ST5 5BG (United Kingdom)
2014-07-20
We present a deep near-infrared color-magnitude diagram of the Galactic globular cluster 47 Tucanae, obtained with the Visible and Infrared Survey Telescope for Astronomy (VISTA) as part of the VISTA near-infrared Y, J, K{sub s} survey of the Magellanic System (VMC). The cluster stars comprising both the subgiant and red giant branches exhibit apparent, continuous variations in color-magnitude space as a function of radius. Subgiant branch stars at larger radii are systematically brighter than their counterparts closer to the cluster core; similarly, red-giant-branch stars in the cluster's periphery are bluer than their more centrally located cousins. The observations can very well be described by adopting an age spread of ∼0.5 Gyr as well as radial gradients in both the cluster's helium abundance (Y) and metallicity (Z), which change gradually from (Y = 0.28, Z = 0.005) in the cluster core to (Y = 0.25, Z = 0.003) in its periphery. We conclude that the cluster's inner regions host a significant fraction of second-generation stars, which decreases with increasing radius; the stellar population in the 47 Tuc periphery is well approximated by a simple stellar population.
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
Variational treatment of the centre-of-mass motion
International Nuclear Information System (INIS)
Cornelissens, T.
1986-01-01
The weightfunction in Lipkin's general expression for eliminating the centre-of-mass coordinate from nuclear wavefunctions has been approximated by a gaussian function exp (-lambdaR 2 ) with one parameter lambda to be determined by a variational calculation. This variational calculation has been carried out for the ground state of 6 Li, first using a wavefunction with different oscillator parameters for the s and p nucleons, second using oscillator functions which are also axially deformed. In both cases the centre-of-mass treatment leads to a remarkable energy gain. The lowest energies are obtained for a negative value of lambda. This surprising result can be explained on the basis of a cluster model for the internal wavefunction of 6 Li : the negative value of lambda increases the separation between the alpha and deuteron cluster. As a further test for our centre-of-mass corrected internal wavefunctions we have calculated the charge formfactor of 6 Li. At low momentum transfer we obtain an excellent agreement with the experimental results. At higher momentum transfers we obtain a diffraction dip, but not yet at the right position and height. Finally we have compared our results for the ground state energy with different cluster model results in the literature. We can conclude that, even without using a generator coordinate method, our centre-of-mass corrected wavefunctions lead to equally good results as the most sophisticated cluster models
Statistical trajectory of an approximate EM algorithm for probabilistic image processing
International Nuclear Information System (INIS)
Tanaka, Kazuyuki; Titterington, D M
2007-01-01
We calculate analytically a statistical average of trajectories of an approximate expectation-maximization (EM) algorithm with generalized belief propagation (GBP) and a Gaussian graphical model for the estimation of hyperparameters from observable data in probabilistic image processing. A statistical average with respect to observed data corresponds to a configuration average for the random-field Ising model in spin glass theory. In the present paper, hyperparameters which correspond to interactions and external fields of spin systems are estimated by an approximate EM algorithm. A practical algorithm is described for gray-level image restoration based on a Gaussian graphical model and GBP. The GBP approach corresponds to the cluster variation method in statistical mechanics. Our main result in the present paper is to obtain the statistical average of the trajectory in the approximate EM algorithm by using loopy belief propagation and GBP with respect to degraded images generated from a probability density function with true values of hyperparameters. The statistical average of the trajectory can be expressed in terms of recursion formulas derived from some analytical calculations
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....
Diophantine approximation and Dirichlet series
Queffélec, Hervé
2013-01-01
This self-contained book will benefit beginners as well as researchers. It is devoted to Diophantine approximation, the analytic theory of Dirichlet series, and some connections between these two domains, which often occur through the Kronecker approximation theorem. Accordingly, the book is divided into seven chapters, the first three of which present tools from commutative harmonic analysis, including a sharp form of the uncertainty principle, ergodic theory and Diophantine approximation to be used in the sequel. A presentation of continued fraction expansions, including the mixing property of the Gauss map, is given. Chapters four and five present the general theory of Dirichlet series, with classes of examples connected to continued fractions, the famous Bohr point of view, and then the use of random Dirichlet series to produce non-trivial extremal examples, including sharp forms of the Bohnenblust-Hille theorem. Chapter six deals with Hardy-Dirichlet spaces, which are new and useful Banach spaces of anal...
Approximations to camera sensor noise
Jin, Xiaodan; Hirakawa, Keigo
2013-02-01
Noise is present in all image sensor data. Poisson distribution is said to model the stochastic nature of the photon arrival process, while it is common to approximate readout/thermal noise by additive white Gaussian noise (AWGN). Other sources of signal-dependent noise such as Fano and quantization also contribute to the overall noise profile. Question remains, however, about how best to model the combined sensor noise. Though additive Gaussian noise with signal-dependent noise variance (SD-AWGN) and Poisson corruption are two widely used models to approximate the actual sensor noise distribution, the justification given to these types of models are based on limited evidence. The goal of this paper is to provide a more comprehensive characterization of random noise. We concluded by presenting concrete evidence that Poisson model is a better approximation to real camera model than SD-AWGN. We suggest further modification to Poisson that may improve the noise model.
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.
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)
Face Recognition using Approximate Arithmetic
DEFF Research Database (Denmark)
Marso, Karol
Face recognition is image processing technique which aims to identify human faces and found its use in various diﬀerent ﬁelds for example in security. Throughout the years this ﬁeld evolved and there are many approaches and many diﬀerent algorithms which aim to make the face recognition as eﬀective...... processing applications the results do not need to be completely precise and use of the approximate arithmetic can lead to reduction in terms of delay, space and power consumption. In this paper we examine possible use of approximate arithmetic in face recognition using Eigenfaces algorithm....
Approximate particle number projection in hot nuclei
International Nuclear Information System (INIS)
Kosov, D.S.; Vdovin, A.I.
1995-01-01
Heated finite systems like, e.g., hot atomic nuclei have to be described by the canonical partition function. But this is a quite difficult technical problem and, as a rule, the grand canonical partition function is used in the studies. As a result, some shortcomings of the theoretical description appear because of the thermal fluctuations of the number of particles. Moreover, in nuclei with pairing correlations the quantum number fluctuations are introduced by some approximate methods (e.g., by the standard BCS method). The exact particle number projection is very cumbersome and an approximate number projection method for T ≠ 0 basing on the formalism of thermo field dynamics is proposed. The idea of the Lipkin-Nogami method to perform any operator as a series in the number operator powers is used. The system of equations for the coefficients of this expansion is written and the solution of the system in the next approximation after the BCS one is obtained. The method which is of the 'projection after variation' type is applied to a degenerate single j-shell model. 14 refs., 1 tab
Evaluation of Fresnel's corrections to the eikonal approximation by the separabilization method
International Nuclear Information System (INIS)
Musakhanov, M.M.; Zubarev, A.L.
1975-01-01
Method of separabilization of potential over the Schroedinger approximate solutions, leading to Schwinger's variational principle for scattering amplitude, is suggested. The results are applied to calculation of the Fresnel corrections to the Glauber approximation
Minku, Leandro L.; Hou, Siqing
2017-01-01
baseline WC model is also included in the analysis. Results: Clustering Dycom with K-Means can potentially help to split the CC projects, managing to achieve similar or better predictive performance than Dycom. However, K-Means still requires the number
Approximate Reanalysis in Topology Optimization
DEFF Research Database (Denmark)
Amir, Oded; Bendsøe, Martin P.; Sigmund, Ole
2009-01-01
In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, the integration of an approximate reanalysis procedure into the framework of topology optimization of continuum structures...
Approximate Matching of Hierarchial Data
DEFF Research Database (Denmark)
Augsten, Nikolaus
-grams of a tree are all its subtrees of a particular shape. Intuitively, two trees are similar if they have many pq-grams in common. The pq-gram distance is an efficient and effective approximation of the tree edit distance. We analyze the properties of the pq-gram distance and compare it with the tree edit...
Approximation of Surfaces by Cylinders
DEFF Research Database (Denmark)
Randrup, Thomas
1998-01-01
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...
Approximation properties of haplotype tagging
Directory of Open Access Journals (Sweden)
Dreiseitl Stephan
2006-01-01
Full Text Available Abstract Background Single nucleotide polymorphisms (SNPs are locations at which the genomic sequences of population members differ. Since these differences are known to follow patterns, disease association studies are facilitated by identifying SNPs that allow the unique identification of such patterns. This process, known as haplotype tagging, is formulated as a combinatorial optimization problem and analyzed in terms of complexity and approximation properties. Results It is shown that the tagging problem is NP-hard but approximable within 1 + ln((n2 - n/2 for n haplotypes but not approximable within (1 - ε ln(n/2 for any ε > 0 unless NP ⊂ DTIME(nlog log n. A simple, very easily implementable algorithm that exhibits the above upper bound on solution quality is presented. This algorithm has running time O((2m - p + 1 ≤ O(m(n2 - n/2 where p ≤ min(n, m for n haplotypes of size m. As we show that the approximation bound is asymptotically tight, the algorithm presented is optimal with respect to this asymptotic bound. Conclusion The haplotype tagging problem is hard, but approachable with a fast, practical, and surprisingly simple algorithm that cannot be significantly improved upon on a single processor machine. Hence, significant improvement in computatational efforts expended can only be expected if the computational effort is distributed and done in parallel.
All-Norm Approximation Algorithms
Azar, Yossi; Epstein, Leah; Richter, Yossi; Woeginger, Gerhard J.; Penttonen, Martti; Meineche Schmidt, Erik
2002-01-01
A major drawback in optimization problems and in particular in scheduling problems is that for every measure there may be a different optimal solution. In many cases the various measures are different ℓ p norms. We address this problem by introducing the concept of an All-norm ρ-approximation
Truthful approximations to range voting
DEFF Research Database (Denmark)
Filos-Ratsika, Aris; Miltersen, Peter Bro
We consider the fundamental mechanism design problem of approximate social welfare maximization under general cardinal preferences on a finite number of alternatives and without money. The well-known range voting scheme can be thought of as a non-truthful mechanism for exact social welfare...
On badly approximable complex numbers
DEFF Research Database (Denmark)
Esdahl-Schou, Rune; Kristensen, S.
We show that the set of complex numbers which are badly approximable by ratios of elements of , where has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably...
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.
Pythagorean Approximations and Continued Fractions
Peralta, Javier
2008-01-01
In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers…
Ultrafast Approximation for Phylogenetic Bootstrap
Bui Quang Minh, [No Value; Nguyen, Thi; von Haeseler, Arndt
Nonparametric bootstrap has been a widely used tool in phylogenetic analysis to assess the clade support of phylogenetic trees. However, with the rapidly growing amount of data, this task remains a computational bottleneck. Recently, approximation methods such as the RAxML rapid bootstrap (RBS) and
Beyond the Point Ps Approximation
Stepanov, Sergey V.; Zvezhinskiy, Dmitry S.; Byakov, Vsevolod M.
2012-01-01
In application to positron annihilation spectroscopy, Ps atom is considered not as a point particle, but as a finite size e+ e- pair localized in a bubble-state in a medium. Variation of the internal Coulombic e+ -e- attraction vs. the bubble radius is estimated.
Clustering User Behavior in Scientific Collections
Blixhavn, Øystein Hoel
2014-01-01
This master thesis looks at how clustering techniques can be appliedto a collection of scientific documents. Approximately one year of serverlogs from the CERN Document Server (CDS) are analyzed and preprocessed.Based on the findings of this analysis, and a review of thecurrent state of the art, three different clustering methods are selectedfor further work: Simple k-Means, Hierarchical Agglomerative Clustering(HAC) and Graph Partitioning. In addition, a custom, agglomerativeclustering algor...
Electricity Consumption Clustering Using Smart Meter Data
Directory of Open Access Journals (Sweden)
Alexander Tureczek
2018-04-01
Full Text Available Electricity smart meter consumption data is enabling utilities to analyze consumption information at unprecedented granularity. Much focus has been directed towards consumption clustering for diversifying tariffs; through modern clustering methods, cluster analyses have been performed. However, the clusters developed exhibit a large variation with resulting shadow clusters, making it impossible to truly identify the individual clusters. Using clearly defined dwelling types, this paper will present methods to improve clustering by harvesting inherent structure from the smart meter data. This paper clusters domestic electricity consumption using smart meter data from the Danish city of Esbjerg. Methods from time series analysis and wavelets are applied to enable the K-Means clustering method to account for autocorrelation in data and thereby improve the clustering performance. The results show the importance of data knowledge and we identify sub-clusters of consumption within the dwelling types and enable K-Means to produce satisfactory clustering by accounting for a temporal component. Furthermore our study shows that careful preprocessing of the data to account for intrinsic structure enables better clustering performance by the K-Means method.
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
Compound Poisson Approximations for Sums of Random Variables
Serfozo, Richard F.
1986-01-01
We show that a sum of dependent random variables is approximately compound Poisson when the variables are rarely nonzero and, given they are nonzero, their conditional distributions are nearly identical. We give several upper bounds on the total-variation distance between the distribution of such a sum and a compound Poisson distribution. Included is an example for Markovian occurrences of a rare event. Our bounds are consistent with those that are known for Poisson approximations for sums of...
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...
Hydrogen: Beyond the Classic Approximation
International Nuclear Information System (INIS)
Scivetti, Ivan
2003-01-01
The classical nucleus approximation is the most frequently used approach for the resolution of problems in condensed matter physics.However, there are systems in nature where it is necessary to introduce the nuclear degrees of freedom to obtain a correct description of the properties.Examples of this, are the systems with containing hydrogen.In this work, we have studied the resolution of the quantum nuclear problem for the particular case of the water molecule.The Hartree approximation has been used, i.e. we have considered that the nuclei are distinguishable particles.In addition, we have proposed a model to solve the tunneling process, which involves the resolution of the nuclear problem for configurations of the system away from its equilibrium position
Approximation errors during variance propagation
International Nuclear Information System (INIS)
Dinsmore, Stephen
1986-01-01
Risk and reliability analyses are often performed by constructing and quantifying large fault trees. The inputs to these models are component failure events whose probability of occuring are best represented as random variables. This paper examines the errors inherent in two approximation techniques used to calculate the top event's variance from the inputs' variance. Two sample fault trees are evaluated and several three dimensional plots illustrating the magnitude of the error over a wide range of input means and variances are given
WKB approximation in atomic physics
International Nuclear Information System (INIS)
Karnakov, Boris Mikhailovich
2013-01-01
Provides extensive coverage of the Wentzel-Kramers-Brillouin approximation and its applications. Presented as a sequence of problems with highly detailed solutions. Gives a concise introduction for calculating Rydberg states, potential barriers and quasistationary systems. This book has evolved from lectures devoted to applications of the Wentzel-Kramers-Brillouin- (WKB or quasi-classical) approximation and of the method of 1/N -expansion for solving various problems in atomic and nuclear physics. The intent of this book is to help students and investigators in this field to extend their knowledge of these important calculation methods in quantum mechanics. Much material is contained herein that is not to be found elsewhere. WKB approximation, while constituting a fundamental area in atomic physics, has not been the focus of many books. A novel method has been adopted for the presentation of the subject matter, the material is presented as a succession of problems, followed by a detailed way of solving them. The methods introduced are then used to calculate Rydberg states in atomic systems and to evaluate potential barriers and quasistationary states. Finally, adiabatic transition and ionization of quantum systems are covered.
DEFF Research Database (Denmark)
Christensen, Thomas Budde
The cluster theory attributed to Michael Porter has significantly influenced industrial policies in countries across Europe and North America since the beginning of the 1990s. Institutions such as the EU, OECD and the World Bank and governments in countries such as the UK, France, The Netherlands...... or management. Both the Accelerate Wales and the Accelerate Cluster programmes target this issue by trying to establish networks between companies that can be used to supply knowledge from research institutions to manufacturing companies. The paper concludes that public sector interventions can make...... businesses. The universities were not considered by the participating companies to be important parts of the local business environment and inputs from universities did not appear to be an important source to access knowledge about new product development or new techniques in production, distribution...
Small Business Administration — The Regional Innovation Clusters serve a diverse group of sectors and geographies. Three of the initial pilot clusters, termed Advanced Defense Technology clusters,...
Mucha, Hans-Joachim; Sofyan, Hizir
2000-01-01
As an explorative technique, duster analysis provides a description or a reduction in the dimension of the data. It classifies a set of observations into two or more mutually exclusive unknown groups based on combinations of many variables. Its aim is to construct groups in such a way that the profiles of objects in the same groups are relatively homogenous whereas the profiles of objects in different groups are relatively heterogeneous. Clustering is distinct from classification techniques, ...
Lexical preferences in Dutch verbal cluster ordering
Bloem, J.; Bellamy, K.; Karvovskaya, E.; Kohlberger, M.; Saad, G.
2016-01-01
This study discusses lexical preferences as a factor affecting the word order variation in Dutch verbal clusters. There are two grammatical word orders for Dutch two-verb clusters, with no clear meaning difference. Using the method of collostructional analysis, I find significant associations
Approximate simulation of Hawkes processes
DEFF Research Database (Denmark)
Møller, Jesper; Rasmussen, Jakob Gulddahl
2006-01-01
Hawkes processes are important in point process theory and its applications, and simulation of such processes are often needed for various statistical purposes. This article concerns a simulation algorithm for unmarked and marked Hawkes processes, exploiting that the process can be constructed...... as a Poisson cluster process. The algorithm suffers from edge effects but is much faster than the perfect simulation algorithm introduced in our previous work Møller and Rasmussen (2004). We derive various useful measures for the error committed when using the algorithm, and we discuss various empirical...... results for the algorithm compared with perfect simulations. Extensions of the algorithm and the results to more general types of marked point processes are also discussed....
An approximation to the interference term using Frobenius Method
Energy Technology Data Exchange (ETDEWEB)
Palma, Daniel A.P.; Martinez, Aquilino S.; Silva, Fernando C. da [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
2007-07-01
An analytical approximation of the interference term {chi}(x,{xi}) is proposed. The approximation is based on the differential equation to {chi}(x,{xi}) using the Frobenius method and the parameter variation. The analytical expression of the {chi}(x,{xi}) obtained in terms of the elementary functions is very simple and precise. In this work one applies the approximations to the Doppler broadening functions and to the interference term in determining the neutron cross sections. Results were validated for the resonances of the U{sup 238} isotope for different energies and temperature ranges. (author)
An approximation to the interference term using Frobenius Method
International Nuclear Information System (INIS)
Palma, Daniel A.P.; Martinez, Aquilino S.; Silva, Fernando C. da
2007-01-01
An analytical approximation of the interference term χ(x,ξ) is proposed. The approximation is based on the differential equation to χ(x,ξ) using the Frobenius method and the parameter variation. The analytical expression of the χ(x,ξ) obtained in terms of the elementary functions is very simple and precise. In this work one applies the approximations to the Doppler broadening functions and to the interference term in determining the neutron cross sections. Results were validated for the resonances of the U 238 isotope for different energies and temperature ranges. (author)
Clustering Millions of Faces by Identity.
Otto, Charles; Wang, Dayong; Jain, Anil K
2018-02-01
Given a large collection of unlabeled face images, we address the problem of clustering faces into an unknown number of identities. This problem is of interest in social media, law enforcement, and other applications, where the number of faces can be of the order of hundreds of million, while the number of identities (clusters) can range from a few thousand to millions. To address the challenges of run-time complexity and cluster quality, we present an approximate Rank-Order clustering algorithm that performs better than popular clustering algorithms (k-Means and Spectral). Our experiments include clustering up to 123 million face images into over 10 million clusters. Clustering results are analyzed in terms of external (known face labels) and internal (unknown face labels) quality measures, and run-time. Our algorithm achieves an F-measure of 0.87 on the LFW benchmark (13 K faces of 5,749 individuals), which drops to 0.27 on the largest dataset considered (13 K faces in LFW + 123M distractor images). Additionally, we show that frames in the YouTube benchmark can be clustered with an F-measure of 0.71. An internal per-cluster quality measure is developed to rank individual clusters for manual exploration of high quality clusters that are compact and isolated.
Approximate solutions to Mathieu's equation
Wilkinson, Samuel A.; Vogt, Nicolas; Golubev, Dmitry S.; Cole, Jared H.
2018-06-01
Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrödinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as to be of use to the broader physics community.
Approximate Inference for Wireless Communications
DEFF Research Database (Denmark)
Hansen, Morten
This thesis investigates signal processing techniques for wireless communication receivers. The aim is to improve the performance or reduce the computationally complexity of these, where the primary focus area is cellular systems such as Global System for Mobile communications (GSM) (and extensions...... to the optimal one, which usually requires an unacceptable high complexity. Some of the treated approximate methods are based on QL-factorization of the channel matrix. In the work presented in this thesis it is proven how the QL-factorization of frequency-selective channels asymptotically provides the minimum...
Quantum tunneling beyond semiclassical approximation
International Nuclear Information System (INIS)
Banerjee, Rabin; Majhi, Bibhas Ranjan
2008-01-01
Hawking radiation as tunneling by Hamilton-Jacobi method beyond semiclassical approximation is analysed. We compute all quantum corrections in the single particle action revealing that these are proportional to the usual semiclassical contribution. We show that a simple choice of the proportionality constants reproduces the one loop back reaction effect in the spacetime, found by conformal field theory methods, which modifies the Hawking temperature of the black hole. Using the law of black hole mechanics we give the corrections to the Bekenstein-Hawking area law following from the modified Hawking temperature. Some examples are explicitly worked out.
Generalized Gradient Approximation Made Simple
International Nuclear Information System (INIS)
Perdew, J.P.; Burke, K.; Ernzerhof, M.
1996-01-01
Generalized gradient approximations (GGA close-quote s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. copyright 1996 The American Physical Society
Impulse approximation in solid helium
International Nuclear Information System (INIS)
Glyde, H.R.
1985-01-01
The incoherent dynamic form factor S/sub i/(Q, ω) is evaluated in solid helium for comparison with the impulse approximation (IA). The purpose is to determine the Q values for which the IA is valid for systems such a helium where the atoms interact via a potential having a steeply repulsive but not infinite hard core. For 3 He, S/sub i/(Q, ω) is evaluated from first principles, beginning with the pair potential. The density of states g(ω) is evaluated using the self-consistent phonon theory and S/sub i/(Q,ω) is expressed in terms of g(ω). For solid 4 He resonable models of g(ω) using observed input parameters are used to evaluate S/sub i/(Q,ω). In both cases S/sub i/(Q, ω) is found to approach the impulse approximation S/sub IA/(Q, ω) closely for wave vector transfers Q> or approx. =20 A -1 . The difference between S/sub i/ and S/sub IA/, which is due to final state interactions of the scattering atom with the remainder of the atoms in the solid, is also predominantly antisymmetric in (ω-ω/sub R/), where ω/sub R/ is the recoil frequency. This suggests that the symmetrization procedure proposed by Sears to eliminate final state contributions should work well in solid helium
Finite approximations in fluid mechanics
International Nuclear Information System (INIS)
Hirschel, E.H.
1986-01-01
This book contains twenty papers on work which was conducted between 1983 and 1985 in the Priority Research Program ''Finite Approximations in Fluid Mechanics'' of the German Research Society (Deutsche Forschungsgemeinschaft). Scientists from numerical mathematics, fluid mechanics, and aerodynamics present their research on boundary-element methods, factorization methods, higher-order panel methods, multigrid methods for elliptical and parabolic problems, two-step schemes for the Euler equations, etc. Applications are made to channel flows, gas dynamical problems, large eddy simulation of turbulence, non-Newtonian flow, turbomachine flow, zonal solutions for viscous flow problems, etc. The contents include: multigrid methods for problems from fluid dynamics, development of a 2D-Transonic Potential Flow Solver; a boundary element spectral method for nonstationary viscous flows in 3 dimensions; navier-stokes computations of two-dimensional laminar flows in a channel with a backward facing step; calculations and experimental investigations of the laminar unsteady flow in a pipe expansion; calculation of the flow-field caused by shock wave and deflagration interaction; a multi-level discretization and solution method for potential flow problems in three dimensions; solutions of the conservation equations with the approximate factorization method; inviscid and viscous flow through rotating meridional contours; zonal solutions for viscous flow problems
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.
Dynamical Vertex Approximation for the Hubbard Model
Toschi, Alessandro
A full understanding of correlated electron systems in the physically relevant situations of three and two dimensions represents a challenge for the contemporary condensed matter theory. However, in the last years considerable progress has been achieved by means of increasingly more powerful quantum many-body algorithms, applied to the basic model for correlated electrons, the Hubbard Hamiltonian. Here, I will review the physics emerging from studies performed with the dynamical vertex approximation, which includes diagrammatic corrections to the local description of the dynamical mean field theory (DMFT). In particular, I will first discuss the phase diagram in three dimensions with a special focus on the commensurate and incommensurate magnetic phases, their (quantum) critical properties, and the impact of fluctuations on electronic lifetimes and spectral functions. In two dimensions, the effects of non-local fluctuations beyond DMFT grow enormously, determining the appearance of a low-temperature insulating behavior for all values of the interaction in the unfrustrated model: Here the prototypical features of the Mott-Hubbard metal-insulator transition, as well as the existence of magnetically ordered phases, are completely overwhelmed by antiferromagnetic fluctuations of exponentially large extension, in accordance with the Mermin-Wagner theorem. Eventually, by a fluctuation diagnostics analysis of cluster DMFT self-energies, the same magnetic fluctuations are identified as responsible for the pseudogap regime in the holed-doped frustrated case, with important implications for the theoretical modeling of the cuprate physics.
International Nuclear Information System (INIS)
Song, Jeeseon; Mohr, Joseph J.; Barkhouse, Wayne A.; Rude, Cody; Warren, Michael S.; Dolag, Klaus
2012-01-01
We present a galaxy catalog simulator that converts N-body simulations with halo and subhalo catalogs into mock, multiband photometric catalogs. The simulator assigns galaxy properties to each subhalo in a way that reproduces the observed cluster galaxy halo occupation distribution, the radial and mass-dependent variation in fractions of blue galaxies, the luminosity functions in the cluster and the field, and the color-magnitude relation in clusters. Moreover, the evolution of these parameters is tuned to match existing observational constraints. Parameterizing an ensemble of cluster galaxy properties enables us to create mock catalogs with variations in those properties, which in turn allows us to quantify the sensitivity of cluster finding to current observational uncertainties in these properties. Field galaxies are sampled from existing multiband photometric surveys of similar depth. We present an application of the catalog simulator to characterize the selection function and contamination of a galaxy cluster finder that utilizes the cluster red sequence together with galaxy clustering on the sky. We estimate systematic uncertainties in the selection to be at the ≤15% level with current observational constraints on cluster galaxy populations and their evolution. We find the contamination in this cluster finder to be ∼35% to redshift z ∼ 0.6. In addition, we use the mock galaxy catalogs to test the optical mass indicator B gc and a red-sequence redshift estimator. We measure the intrinsic scatter of the B gc -mass relation to be approximately log normal with σ log10M ∼0.25 and we demonstrate photometric redshift accuracies for massive clusters at the ∼3% level out to z ∼ 0.7.
Cost versus precision for approximate typing for Python
Fritz, Levin; Hage, J.
2017-01-01
In this paper we describe a variation of monotone frameworks that enables us to perform approximate typing of Python, in particular for dealing with some of its more dynamic features such as first-class functions and Python's dynamic class system. We additionally introduce a substantial number of
Cost versus Precision for Approximate Typing for Python
Fritz, Levin; Hage, J
2014-01-01
In this paper we describe a variation of monotone frameworks that enables us to perform approximate typing of Python, in particular for dealing with some of its more dynamic features such as first-class functions and Python’s dynamic class system. We additionally introduce a substantial number of
A Statistical Mechanics Approach to Approximate Analytical Bootstrap Averages
DEFF Research Database (Denmark)
Malzahn, Dorthe; Opper, Manfred
2003-01-01
We apply the replica method of Statistical Physics combined with a variational method to the approximate analytical computation of bootstrap averages for estimating the generalization error. We demonstrate our approach on regression with Gaussian processes and compare our results with averages...
Variational transition state theory
International Nuclear Information System (INIS)
Truhlar, D.G.
1986-01-01
This project is concerned with the development and applications of generalized transition state theory and multidimensional tunneling approximations to chemical reaction rates. They have developed and implemented several practical versions of variational transition state theory (VTST), namely canonical variational theory (CVT), improved canonical variational theory (ICVT), and microcanonical variational theory (μVT). They have also developed and implemented several accurate multidimensional semiclassical tunneling approximations, the most accurate of which are the small-curvature semiclassical adiabatic (SCSA), large-curvature version-3 (LC3), and least-action (LA) approximations. They have applied the methods to thermal rate constants, using transmission coefficients based on ground-state tunneling, and they have also presented and applied adiabatic and diabatic extensions to calculated rate constants for vibrationally excited reactants. Their general goal is to develop accurate methods for calculating chemical reaction rate constants that remain practical even for reasonably complicated molecules. The approximations mentioned above yield rate constants for systems whose potential energy surface is known or assumed. Thus a second, equally important aspect of their work is the determination or modeling, semi-empirically and/or from electronic structure calculations, of potential energy surfaces
Maximum-entropy clustering algorithm and its global convergence analysis
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Constructing a batch of differentiable entropy functions touniformly approximate an objective function by means of the maximum-entropy principle, a new clustering algorithm, called maximum-entropy clustering algorithm, is proposed based on optimization theory. This algorithm is a soft generalization of the hard C-means algorithm and possesses global convergence. Its relations with other clustering algorithms are discussed.
Cluster Characteristics in a MIMO Indoor Propagation Environment
DEFF Research Database (Denmark)
Czink, Nicolai; Yin, Xuefeng; Ozcelik, Huseyin
2007-01-01
, strong (obstructed-)line-of-sight clusters show Rician fading, corresponding to few dominant propagation paths, whereas most clusters exhibit Rayleigh fading, corresponding to many paths with approximately equal powers and uncorrelated phases. Root-mean-square cluster azimuth spreads (CASs) were...
Approximating the minimum cycle mean
Directory of Open Access Journals (Sweden)
Krishnendu Chatterjee
2013-07-01
Full Text Available We consider directed graphs where each edge is labeled with an integer weight and study the fundamental algorithmic question of computing the value of a cycle with minimum mean weight. Our contributions are twofold: (1 First we show that the algorithmic question is reducible in O(n^2 time to the problem of a logarithmic number of min-plus matrix multiplications of n-by-n matrices, where n is the number of vertices of the graph. (2 Second, when the weights are nonnegative, we present the first (1 + ε-approximation algorithm for the problem and the running time of our algorithm is ilde(O(n^ω log^3(nW/ε / ε, where O(n^ω is the time required for the classic n-by-n matrix multiplication and W is the maximum value of the weights.
Nonlinear approximation with dictionaries I. Direct estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
2004-01-01
We study various approximation classes associated with m-term approximation by elements from a (possibly) redundant dictionary in a Banach space. The standard approximation class associated with the best m-term approximation is compared to new classes defined by considering m-term approximation w...
Approximate cohomology in Banach algebras | Pourabbas ...
African Journals Online (AJOL)
We introduce the notions of approximate cohomology and approximate homotopy in Banach algebras and we study the relation between them. We show that the approximate homotopically equivalent cochain complexes give the same approximate cohomologies. As a special case, approximate Hochschild cohomology is ...
Low-temperature excitations within the Bethe approximation
International Nuclear Information System (INIS)
Biazzo, I; Ramezanpour, A
2013-01-01
We propose the variational quantum cavity method to construct a minimal energy subspace of wavevectors that are used to obtain some upper bounds for the energy cost of the low-temperature excitations. Given a trial wavefunction we use the cavity method of statistical physics to estimate the Hamiltonian expectation and to find the optimal variational parameters in the subspace of wavevectors orthogonal to the lower-energy wavefunctions. To this end, we write the overlap between two wavefunctions within the Bethe approximation, which allows us to replace the global orthogonality constraint with some local constraints on the variational parameters. The method is applied to the transverse Ising model and different levels of approximations are compared with the exact numerical solutions for small systems. (paper)
Nuclear clustering - a cluster core model study
International Nuclear Information System (INIS)
Paul Selvi, G.; Nandhini, N.; Balasubramaniam, M.
2015-01-01
Nuclear clustering, similar to other clustering phenomenon in nature is a much warranted study, since it would help us in understanding the nature of binding of the nucleons inside the nucleus, closed shell behaviour when the system is highly deformed, dynamics and structure at extremes. Several models account for the clustering phenomenon of nuclei. We present in this work, a cluster core model study of nuclear clustering in light mass nuclei
Electronic shell structure in multiply charged silver clusters
International Nuclear Information System (INIS)
Kandler, O.; Athanassenas, K.; Echt, O.; Kreisle, D.; Leisner, T.; Recknagel, E.
1991-01-01
Silver clusters are generated by standard laser vaporization technique and ionized via multiphoton ionization. Time-of-flight mass spectrometry reveals singly, doubly and triply charged clusters, Ag n z+ (z=1, 2, 3). The spectra show, for all charge states, intensity variations, indicating enhanced stabilities for cluster sizes with closed electronic configurations in accord with the spherical jellium model. (orig.)
THE LIFETIME AND POWERS OF FR IIs IN GALAXY CLUSTERS
International Nuclear Information System (INIS)
Antognini, Joe; Bird, Jonathan; Martini, Paul
2012-01-01
We have identified and studied a sample of 151 FR IIs found in brightest cluster galaxies (BCGs) in the MaxBCG cluster catalog with data from FIRST and NVSS. We have compared the radio luminosities and projected lengths of these FR IIs to the projected length distribution of a range of mock catalogs generated by an FR II model and estimate the FR II lifetime to be 1.9 × 10 8 yr. The uncertainty in the lifetime calculation is a factor of two, primarily due to uncertainties in the intracluster medium (ICM) density and the FR II axial ratio. We furthermore measure the jet power distribution of FR IIs in BCGs and find that it is well described by a log-normal distribution with a median power of 1.1 × 10 37 W and a coefficient of variation of 2.2. These jet powers are nearly linearly related to the observed luminosities, and this relation is steeper than many other estimates, although it is dependent on the jet model. We investigate correlations between FR II and cluster properties and find that galaxy luminosity is correlated with jet power. This implies that jet power is also correlated with black hole mass, as the stellar luminosity of a BCG should be a good proxy for its spheroid mass and therefore the black hole mass. Jet power, however, is not correlated with cluster richness, nor is FR II lifetime strongly correlated with any cluster properties. We calculate the enthalpy of the lobes to examine the impact of the FR IIs on the ICM and find that heating due to adiabatic expansion is too small to offset radiative cooling by a factor of at least six. In contrast, the jet power is approximately an order of magnitude larger than required to counteract cooling. We conclude that if feedback from FR IIs offsets cooling of the ICM, then heating must be primarily due to another mechanism associated with FR II expansion.
A local search for a graph clustering problem
Navrotskaya, Anna; Il'ev, Victor
2016-10-01
In the clustering problems one has to partition a given set of objects (a data set) into some subsets (called clusters) taking into consideration only similarity of the objects. One of most visual formalizations of clustering is graph clustering, that is grouping the vertices of a graph into clusters taking into consideration the edge structure of the graph whose vertices are objects and edges represent similarities between the objects. In the graph k-clustering problem the number of clusters does not exceed k and the goal is to minimize the number of edges between clusters and the number of missing edges within clusters. This problem is NP-hard for any k ≥ 2. We propose a polynomial time (2k-1)-approximation algorithm for graph k-clustering. Then we apply a local search procedure to the feasible solution found by this algorithm and hold experimental research of obtained heuristics.
International Nuclear Information System (INIS)
Kaplan, T.; Gray, L.J.
1984-01-01
The self-consistent approximation of Kaplan, Leath, Gray, and Diehl is applied to models for substitutional random alloys with muffin-tin potentials. The particular advantage of this approximation is that, in addition to including cluster scattering, the muffin-tin potentials in the alloy can depend on the occupation of the surrounding sites (i.e., environmental disorder is included)
Theoretical study of the electron-cluster elastic scattering
International Nuclear Information System (INIS)
Descourt, P.; Guet, C.; Farine, M.
1997-01-01
The properties of the clusters consisting of some tens to several hundreds of alkali atoms are generally quite well described in the jellium approximation. This approximation treats the cluster as a charged Fermi liquid of finite size. The optical response predicted by this approximation and taking into account the electron-electron correlations of the Hartree-Fock mean field agrees rather well with the experiment. The objective of this work was to obtain a quantal many-body formalism, within jellium approximation, applicable to elastic scattering of electrons from an alkali-metal-cluster. Influence of correlations on the phase shifts was also taken into account
Absence of missing mass in clusters
Energy Technology Data Exchange (ETDEWEB)
Fesenko, B.I.
1981-01-01
The evaluation of the radial-velocity dispersion in clusters of galaxies is considered by using order statistics to reduce the distortions introduced by foreground and background galaxies and by large errors in velocity measurement. For four nearby clusters of galaxies, including the Coma cluster, velocity dispersions are obtained which are approximately four times lower than previously reported values. It is found that more remote galaxies exhibit the same tendency to a reduction in missing mass. A detailed examination of the statistical properties of galaxies in the Virgo cluster reveals that the cluster might not actually exist, but may be just a large excess in the number density of bright galaxies, possibly the result of an increase in the visibility of objects in the appropriate directions. It is concluded that the presence of a large amount of missing mass in clusters of galaxies is yet to be proven.
Accurate density-functional calculations on large systems: Fullerenes and magnetic clusters
International Nuclear Information System (INIS)
Dunlap, B.I.
1996-01-01
Efforts to accurately compute all-electron density-functional energies for large molecules and clusters using Gaussian basis sets will be reviewed. The foundation of this effort, variational fitting, will be described and followed by three applications of the method. The first application concerns fullerenes. When first discovered, C 60 is quite unstable relative to the higher fullerenes. In addition, to raising questions about the relative abundance of the various fullerenes, this work conflicted with the then state-of-the art density-funcitonal calculations on crystalline graphite. Now high accuracy molecular and band structure calculations are in fairly good agreement. Second, we have used these methods to design transition metal clusters having the highest magnetic moment by maximizing the symmetry-required degeneracy of the one-electron orbitals. Most recently, we have developed accurate, variational generalized-gradient approximation (GGA) forces for use in geometry optimization of clusters and in molecular-dynamics simulations of friction. The GGA optimized geometries of a number of large clusters will be given
General strongly nonlinear variational inequalities
International Nuclear Information System (INIS)
Siddiqi, A.H.; Ansari, Q.H.
1990-07-01
In this paper we develop iterative algorithms for finding approximate solutions for new classes of variational and quasi-variational inequalities which include, as special case, some known results in this field. It is shown that the solutions of the iterative schemes converge to the exact solutions. (author). 15 refs
Directory of Open Access Journals (Sweden)
Ducros Anne
2008-07-01
Full Text Available Abstract Cluster headache (CH is a primary headache disease characterized by recurrent short-lasting attacks (15 to 180 minutes of excruciating unilateral periorbital pain accompanied by ipsilateral autonomic signs (lacrimation, nasal congestion, ptosis, miosis, lid edema, redness of the eye. It affects young adults, predominantly males. Prevalence is estimated at 0.5–1.0/1,000. CH has a circannual and circadian periodicity, attacks being clustered (hence the name in bouts that can occur during specific months of the year. Alcohol is the only dietary trigger of CH, strong odors (mainly solvents and cigarette smoke and napping may also trigger CH attacks. During bouts, attacks may happen at precise hours, especially during the night. During the attacks, patients tend to be restless. CH may be episodic or chronic, depending on the presence of remission periods. CH is associated with trigeminovascular activation and neuroendocrine and vegetative disturbances, however, the precise cautive mechanisms remain unknown. Involvement of the hypothalamus (a structure regulating endocrine function and sleep-wake rhythms has been confirmed, explaining, at least in part, the cyclic aspects of CH. The disease is familial in about 10% of cases. Genetic factors play a role in CH susceptibility, and a causative role has been suggested for the hypocretin receptor gene. Diagnosis is clinical. Differential diagnoses include other primary headache diseases such as migraine, paroxysmal hemicrania and SUNCT syndrome. At present, there is no curative treatment. There are efficient treatments to shorten the painful attacks (acute treatments and to reduce the number of daily attacks (prophylactic treatments. Acute treatment is based on subcutaneous administration of sumatriptan and high-flow oxygen. Verapamil, lithium, methysergide, prednisone, greater occipital nerve blocks and topiramate may be used for prophylaxis. In refractory cases, deep-brain stimulation of the
Confidence Intervals for Asbestos Fiber Counts: Approximate Negative Binomial Distribution.
Bartley, David; Slaven, James; Harper, Martin
2017-03-01
The negative binomial distribution is adopted for analyzing asbestos fiber counts so as to account for both the sampling errors in capturing only a finite number of fibers and the inevitable human variation in identifying and counting sampled fibers. A simple approximation to this distribution is developed for the derivation of quantiles and approximate confidence limits. The success of the approximation depends critically on the use of Stirling's expansion to sufficient order, on exact normalization of the approximating distribution, on reasonable perturbation of quantities from the normal distribution, and on accurately approximating sums by inverse-trapezoidal integration. Accuracy of the approximation developed is checked through simulation and also by comparison to traditional approximate confidence intervals in the specific case that the negative binomial distribution approaches the Poisson distribution. The resulting statistics are shown to relate directly to early research into the accuracy of asbestos sampling and analysis. Uncertainty in estimating mean asbestos fiber concentrations given only a single count is derived. Decision limits (limits of detection) and detection limits are considered for controlling false-positive and false-negative detection assertions and are compared to traditional limits computed assuming normal distributions. Published by Oxford University Press on behalf of the British Occupational Hygiene Society 2017.
Quantum adiabatic approximation and the geometric phase
International Nuclear Information System (INIS)
Mostafazadeh, A.
1997-01-01
A precise definition of an adiabaticity parameter ν of a time-dependent Hamiltonian is proposed. A variation of the time-dependent perturbation theory is presented which yields a series expansion of the evolution operator U(τ)=summation scr(l) U (scr(l)) (τ) with U (scr(l)) (τ) being at least of the order ν scr(l) . In particular, U (0) (τ) corresponds to the adiabatic approximation and yields Berry close-quote s adiabatic phase. It is shown that this series expansion has nothing to do with the 1/τ expansion of U(τ). It is also shown that the nonadiabatic part of the evolution operator is generated by a transformed Hamiltonian which is off-diagonal in the eigenbasis of the initial Hamiltonian. This suggests the introduction of an adiabatic product expansion for U(τ) which turns out to yield exact expressions for U(τ) for a large number of quantum systems. In particular, a simple application of the adiabatic product expansion is used to show that for the Hamiltonian describing the dynamics of a magnetic dipole in an arbitrarily changing magnetic field, there exists another Hamiltonian with the same eigenvectors for which the Schroedinger equation is exactly solvable. Some related issues concerning geometric phases and their physical significance are also discussed. copyright 1997 The American Physical Society
Brightest Cluster Galaxies in REXCESS Clusters
Haarsma, Deborah B.; Leisman, L.; Bruch, S.; Donahue, M.
2009-01-01
Most galaxy clusters contain a Brightest Cluster Galaxy (BCG) which is larger than the other cluster ellipticals and has a more extended profile. In the hierarchical model, the BCG forms through many galaxy mergers in the crowded center of the cluster, and thus its properties give insight into the assembly of the cluster as a whole. In this project, we are working with the Representative XMM-Newton Cluster Structure Survey (REXCESS) team (Boehringer et al 2007) to study BCGs in 33 X-ray luminous galaxy clusters, 0.055 < z < 0.183. We are imaging the BCGs in R band at the Southern Observatory for Astrophysical Research (SOAR) in Chile. In this poster, we discuss our methods and give preliminary measurements of the BCG magnitudes, morphology, and stellar mass. We compare these BCG properties with the properties of their host clusters, particularly of the X-ray emitting gas.
Partitional clustering algorithms
2015-01-01
This book summarizes the state-of-the-art in partitional clustering. Clustering, the unsupervised classification of patterns into groups, is one of the most important tasks in exploratory data analysis. Primary goals of clustering include gaining insight into, classifying, and compressing data. Clustering has a long and rich history that spans a variety of scientific disciplines including anthropology, biology, medicine, psychology, statistics, mathematics, engineering, and computer science. As a result, numerous clustering algorithms have been proposed since the early 1950s. Among these algorithms, partitional (nonhierarchical) ones have found many applications, especially in engineering and computer science. This book provides coverage of consensus clustering, constrained clustering, large scale and/or high dimensional clustering, cluster validity, cluster visualization, and applications of clustering. Examines clustering as it applies to large and/or high-dimensional data sets commonly encountered in reali...
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)
Parabolic approximation method for fast magnetosonic wave propagation in tokamaks
International Nuclear Information System (INIS)
Phillips, C.K.; Perkins, F.W.; Hwang, D.Q.
1985-07-01
Fast magnetosonic wave propagation in a cylindrical tokamak model is studied using a parabolic approximation method in which poloidal variations of the wave field are considered weak in comparison to the radial variations. Diffraction effects, which are ignored by ray tracing mthods, are included self-consistently using the parabolic method since continuous representations for the wave electromagnetic fields are computed directly. Numerical results are presented which illustrate the cylindrical convergence of the launched waves into a diffraction-limited focal spot on the cyclotron absorption layer near the magnetic axis for a wide range of plasma confinement parameters
Ladder variational autoencoders
DEFF Research Database (Denmark)
Sønderby, Casper Kaae; Raiko, Tapani; Maaløe, Lars
2016-01-01
Variational autoencoders are powerful models for unsupervised learning. However deep models with several layers of dependent stochastic variables are difficult to train which limits the improvements obtained using these highly expressive models. We propose a new inference model, the Ladder...... Variational Autoencoder, that recursively corrects the generative distribution by a data dependent approximate likelihood in a process resembling the recently proposed Ladder Network. We show that this model provides state of the art predictive log-likelihood and tighter log-likelihood lower bound compared...
Ladder Variational Autoencoder
DEFF Research Database (Denmark)
Sønderby, Casper Kaae; Raiko, Tapani; Maaløe, Lars
2016-01-01
Variational autoencoders are powerful models for unsupervised learning. However deep models with several layers of dependent stochastic variables are difficult to train which limits the improvements obtained using these highly expressive models. We propose a new inference model, the Ladder...... Variational Autoencoder, that recursively corrects the generative distribution by a data dependent approximate likelihood in a process resembling the recently proposed Ladder Network. We show that this model provides state of the art predictive log-likelihood and tighter log-likelihood lower bound compared...
Splines and variational methods
Prenter, P M
2008-01-01
One of the clearest available introductions to variational methods, this text requires only a minimal background in calculus and linear algebra. Its self-contained treatment explains the application of theoretic notions to the kinds of physical problems that engineers regularly encounter. The text's first half concerns approximation theoretic notions, exploring the theory and computation of one- and two-dimensional polynomial and other spline functions. Later chapters examine variational methods in the solution of operator equations, focusing on boundary value problems in one and two dimension
Plasmon resonances in large noble-metal clusters
International Nuclear Information System (INIS)
Soennichsen, C; Franzl, T; Wilk, T; Plessen, G von; Feldmann, J
2002-01-01
We investigate the optical properties of spherical gold and silver clusters with diameters of 20 nm and larger. The light scattering spectra of individual clusters are measured using dark-field microscopy, thus avoiding inhomogeneous broadening effects. The dipolar plasmon resonances of the clusters are found to have nearly Lorentzian line shapes. With increasing size we observe polaritonic red-shifts of the plasmon line and increased radiation damping for both gold and silver clusters. Apart from some cluster-to-cluster variations of the plasmon lines, agreement with Mie theory is reasonably good for the gold clusters. However, it is less satisfactory for the silver clusters, possibly due to cluster faceting or chemical effects
Diversity among galaxy clusters
International Nuclear Information System (INIS)
Struble, M.F.; Rood, H.J.
1988-01-01
The classification of galaxy clusters is discussed. Consideration is given to the classification scheme of Abell (1950's), Zwicky (1950's), Morgan, Matthews, and Schmidt (1964), and Morgan-Bautz (1970). Galaxies can be classified based on morphology, chemical composition, spatial distribution, and motion. The correlation between a galaxy's environment and morphology is examined. The classification scheme of Rood-Sastry (1971), which is based on clusters's morphology and galaxy population, is described. The six types of clusters they define include: (1) a cD-cluster dominated by a single large galaxy, (2) a cluster dominated by a binary, (3) a core-halo cluster, (4) a cluster dominated by several bright galaxies, (5) a cluster appearing flattened, and (6) an irregularly shaped cluster. Attention is also given to the evolution of cluster structures, which is related to initial density and cluster motion
Using Cluster Analysis and ICP-MS to Identify Groups of Ecstasy Tablets in Sao Paulo State, Brazil.
Maione, Camila; de Oliveira Souza, Vanessa Cristina; Togni, Loraine Rezende; da Costa, José Luiz; Campiglia, Andres Dobal; Barbosa, Fernando; Barbosa, Rommel Melgaço
2017-11-01
The variations found in the elemental composition in ecstasy samples result in spectral profiles with useful information for data analysis, and cluster analysis of these profiles can help uncover different categories of the drug. We provide a cluster analysis of ecstasy tablets based on their elemental composition. Twenty-five elements were determined by ICP-MS in tablets apprehended by Sao Paulo's State Police, Brazil. We employ the K-means clustering algorithm along with C4.5 decision tree to help us interpret the clustering results. We found a better number of two clusters within the data, which can refer to the approximated number of sources of the drug which supply the cities of seizures. The C4.5 model was capable of differentiating the ecstasy samples from the two clusters with high prediction accuracy using the leave-one-out cross-validation. The model used only Nd, Ni, and Pb concentration values in the classification of the samples. © 2017 American Academy of Forensic Sciences.
Random phase approximation: from Giant to Intra-doublet resonances
International Nuclear Information System (INIS)
Amusia, M.Ya.
2004-01-01
We discuss here the history and current achievements of one of the most powerful approaches of 20th century physics--the random phase approximation (RPA) that permits us to study collective or multiparticle effects in atoms, nuclei, molecules and clusters, as well as in quantum liquids. We concentrate on RPA application to studies of isolated atoms where it permits one to disclose the collective multielectron nature of so-called Giant resonances and predict a number of others, like Interference and Intra-doublet resonances. We present general theory as well as results of concrete calculations for a number of atoms
Random phase approximation: from Giant to Intra-doublet resonances
Energy Technology Data Exchange (ETDEWEB)
Amusia, M.Ya. E-mail: amusia@vms.huji.ac.il
2004-06-01
We discuss here the history and current achievements of one of the most powerful approaches of 20th century physics--the random phase approximation (RPA) that permits us to study collective or multiparticle effects in atoms, nuclei, molecules and clusters, as well as in quantum liquids. We concentrate on RPA application to studies of isolated atoms where it permits one to disclose the collective multielectron nature of so-called Giant resonances and predict a number of others, like Interference and Intra-doublet resonances. We present general theory as well as results of concrete calculations for a number of atoms.
Cluster temperature. Methods for its measurement and stabilization
International Nuclear Information System (INIS)
Makarov, G N
2008-01-01
Cluster temperature is an important material parameter essential to many physical and chemical processes involving clusters and cluster beams. Because of the diverse methods by which clusters can be produced, excited, and stabilized, and also because of the widely ranging values of atomic and molecular binding energies (approximately from 10 -5 to 10 eV) and numerous energy relaxation channels in clusters, cluster temperature (internal energy) ranges from 10 -3 to about 10 8 K. This paper reviews research on cluster temperature and describes methods for its measurement and stabilization. The role of cluster temperature in and its influence on physical and chemical processes is discussed. Results on the temperature dependence of cluster properties are presented. The way in which cluster temperature relates to cluster structure and to atomic and molecular interaction potentials in clusters is addressed. Methods for strong excitation of clusters and channels for their energy relaxation are discussed. Some applications of clusters and cluster beams are considered. (reviews of topical problems)
Adaptive ACMS: A robust localized Approximated Component Mode Synthesis Method
Madureira, Alexandre L.; Sarkis, Marcus
2017-01-01
We consider finite element methods of multiscale type to approximate solutions for two-dimensional symmetric elliptic partial differential equations with heterogeneous $L^\\infty$ coefficients. The methods are of Galerkin type and follows the Variational Multiscale and Localized Orthogonal Decomposition--LOD approaches in the sense that it decouples spaces into multiscale and fine subspaces. In a first method, the multiscale basis functions are obtained by mapping coarse basis functions, based...
The old open cluster Melotte 66
International Nuclear Information System (INIS)
Hawarden, T.G.
1976-01-01
Photoelectric and photographic photometry of the open cluster Melotte 66 is presented. The colour-magnitude (CM) diagram shows most of the characteristics of an old cluster. The giant branch is broad with its blue edge populated preferentially by stars from the outer parts of the cluster. There is no detectable horizontal subgiant sequence. The main sequence turn-off colour, two-colour diagram and the colour difference between the turn-off and the subgiants are used to estimate the age and composition. Melotte 66 appears to have reddening E(B-V) = 0sup(m).17 and ultraviolet excess delta(U-B) approximately 0sup(m).1. The cluster is probably between 6 and 7 x 10 9 yr old. A distance modulus (m-M) 0 =12sup(m).4 is derived, which implies that the cluster lies about 750 pc from the galactic plane. (author)
Trajectory averaging for stochastic approximation MCMC algorithms
Liang, Faming
2010-01-01
to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximationMCMC algorithms, for example, a stochastic
Reduction of Linear Programming to Linear Approximation
Vaserstein, Leonid N.
2006-01-01
It is well known that every Chebyshev linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to a Chebyshev linear approximation problem.
Proton-Induced Plasticity in Hydrogen Clusters
Energy Technology Data Exchange (ETDEWEB)
Stich, I. [JRCAT, Angstrom Technology Partnership, 1-1-4 Higashi, Tsukuba, Ibaraki 305 (Japan); Marx, D.; Parrinello, M. [Max-Planck-Institut fuer Festkoerperforschung, Heisenbergstrasse 1, 70569 Stuttgart (Germany); Terakura, K. [NAIR, Angstrom Technology Partnership, 1-1-4 Higashi, Tsukuba, Ibaraki 305 (Japan); Terakura, K. [CREST, Japan Science and Technology Corporation (JST), Kawaguchi, Saitama 332 (Japan)
1997-05-01
The effect of protonation of pure hydrogen clusters is investigated at low temperature using a combination of path-integral simulations and first-principles electronic structure calculations. The added proton gets trapped as a very localized H{sub 3}{sup +} impurity in the cluster core, and is surrounded by stable shells of solvating H{sub 2} molecules. These clusters are frozen with respect to the translational degrees of freedom, while the H{sub 2} ligands undergo large-amplitude rotations. The classical approximation for the nuclei fails to account for this effect which is akin to plastic behavior in crystals. {copyright} {ital 1997} {ital The American Physical Society}
Proton-Induced Plasticity in Hydrogen Clusters
International Nuclear Information System (INIS)
Stich, I.; Marx, D.; Parrinello, M.; Terakura, K.; Terakura, K.
1997-01-01
The effect of protonation of pure hydrogen clusters is investigated at low temperature using a combination of path-integral simulations and first-principles electronic structure calculations. The added proton gets trapped as a very localized H 3 + impurity in the cluster core, and is surrounded by stable shells of solvating H 2 molecules. These clusters are frozen with respect to the translational degrees of freedom, while the H 2 ligands undergo large-amplitude rotations. The classical approximation for the nuclei fails to account for this effect which is akin to plastic behavior in crystals. copyright 1997 The American Physical Society
Clusters in nonsmooth oscillator networks
Nicks, Rachel; Chambon, Lucie; Coombes, Stephen
2018-03-01
For coupled oscillator networks with Laplacian coupling, the master stability function (MSF) has proven a particularly powerful tool for assessing the stability of the synchronous state. Using tools from group theory, this approach has recently been extended to treat more general cluster states. However, the MSF and its generalizations require the determination of a set of Floquet multipliers from variational equations obtained by linearization around a periodic orbit. Since closed form solutions for periodic orbits are invariably hard to come by, the framework is often explored using numerical techniques. Here, we show that further insight into network dynamics can be obtained by focusing on piecewise linear (PWL) oscillator models. Not only do these allow for the explicit construction of periodic orbits, their variational analysis can also be explicitly performed. The price for adopting such nonsmooth systems is that many of the notions from smooth dynamical systems, and in particular linear stability, need to be modified to take into account possible jumps in the components of Jacobians. This is naturally accommodated with the use of saltation matrices. By augmenting the variational approach for studying smooth dynamical systems with such matrices we show that, for a wide variety of networks that have been used as models of biological systems, cluster states can be explicitly investigated. By way of illustration, we analyze an integrate-and-fire network model with event-driven synaptic coupling as well as a diffusively coupled network built from planar PWL nodes, including a reduction of the popular Morris-Lecar neuron model. We use these examples to emphasize that the stability of network cluster states can depend as much on the choice of single node dynamics as it does on the form of network structural connectivity. Importantly, the procedure that we present here, for understanding cluster synchronization in networks, is valid for a wide variety of systems in
Nonlinear ordinary differential equations analytical approximation and numerical methods
Hermann, Martin
2016-01-01
The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march...
Finite element approximation to the even-parity transport equation
International Nuclear Information System (INIS)
Lewis, E.E.
1981-01-01
This paper studies the finite element method, a procedure for reducing partial differential equations to sets of algebraic equations suitable for solution on a digital computer. The differential equation is cast into the form of a variational principle, the resulting domain then subdivided into finite elements. The dependent variable is then approximated by a simple polynomial, and these are linked across inter-element boundaries by continuity conditions. The finite element method is tailored to a variety of transport problems. Angular approximations are formulated, and the extent of ray effect mitigation is examined. Complex trial functions are introduced to enable the inclusion of buckling approximations. The ubiquitous curved interfaces of cell calculations, and coarse mesh methods are also treated. A concluding section discusses limitations of the work to date and suggests possible future directions
Clinical and radiographic assessment of approximal carious lesions
International Nuclear Information System (INIS)
Espelid, I.; Tveit, A.B.
1986-01-01
The aim of the study was to compare the radiographic diagnosis of approximal carious lesions with visual observations of the approximal surfaces and within drilled Class II cavities (made into the pulp). Sound (n=28) and carious (n=123) approximal surfaces of extracted premolars and molars were radiographed. The radiographs were studied by seven observers to diagnose caries. Lesions without cavitation were most often classified as sound (61.3%). When lesions had cavities, the rate of detection increased to 89.1%. Sound surfaces were erroneously classified as carious in 15.7% of cases. Statistically, about 6 our of every 10 qualitative assessments of lesion depth on the basis of radiographs, correctly recorded lesions as being in enamel or extending into dentin. The interexaminer variation in radiographic caries diagnosis were mostly due to difference in diagnostic criteria, whereas differences in diagnostic capability were less important
Some relations between entropy and approximation numbers
Institute of Scientific and Technical Information of China (English)
郑志明
1999-01-01
A general result is obtained which relates the entropy numbers of compact maps on Hilbert space to its approximation numbers. Compared with previous works in this area, it is particularly convenient for dealing with the cases where the approximation numbers decay rapidly. A nice estimation between entropy and approximation numbers for noncompact maps is given.
Axiomatic Characterizations of IVF Rough Approximation Operators
Directory of Open Access Journals (Sweden)
Guangji Yu
2014-01-01
Full Text Available This paper is devoted to the study of axiomatic characterizations of IVF rough approximation operators. IVF approximation spaces are investigated. The fact that different IVF operators satisfy some axioms to guarantee the existence of different types of IVF relations which produce the same operators is proved and then IVF rough approximation operators are characterized by axioms.
An approximation for kanban controlled assembly systems
Topan, E.; Avsar, Z.M.
2011-01-01
An approximation is proposed to evaluate the steady-state performance of kanban controlled two-stage assembly systems. The development of the approximation is as follows. The considered continuous-time Markov chain is aggregated keeping the model exact, and this aggregate model is approximated
Operator approximant problems arising from quantum theory
Maher, Philip J
2017-01-01
This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory. The research presented is in non-commutative operator approximation theory or, to use Halmos' terminology, in operator approximants. Focusing on the concept of approximants, this self-contained book is suitable for graduate courses.
DEFF Research Database (Denmark)
Østergaard, Christian Richter; Park, Eun Kyung
2015-01-01
Most studies on regional clusters focus on identifying factors and processes that make clusters grow. However, sometimes technologies and market conditions suddenly shift, and clusters decline. This paper analyses the process of decline of the wireless communication cluster in Denmark. The longit...... but being quick to withdraw in times of crisis....
Clustering of correlated networks
Dorogovtsev, S. N.
2003-01-01
We obtain the clustering coefficient, the degree-dependent local clustering, and the mean clustering of networks with arbitrary correlations between the degrees of the nearest-neighbor vertices. The resulting formulas allow one to determine the nature of the clustering of a network.
DEFF Research Database (Denmark)
Müller, Emmanuel; Assent, Ira; Günnemann, Stephan
2009-01-01
Subspace clustering aims at detecting clusters in any subspace projection of a high dimensional space. As the number of possible subspace projections is exponential in the number of dimensions, the result is often tremendously large. Recent approaches fail to reduce results to relevant subspace...... clusters. Their results are typically highly redundant, i.e. many clusters are detected multiple times in several projections. In this work, we propose a novel model for relevant subspace clustering (RESCU). We present a global optimization which detects the most interesting non-redundant subspace clusters...... achieves top clustering quality while competing approaches show greatly varying performance....
Theory of magnetohydrodynamic waves: The WKB approximation revisited
International Nuclear Information System (INIS)
Barnes, A.
1992-01-01
Past treatments of the eikonal or WKB theory of the propagation of magnetohydrodynamics waves have assumed a strictly isentropic background. IF in fact there is a gradient in the background entropy, then in second order in the WKB ordering, adiabatic fluctuations (in the Lagrangian sense) are not strictly isentropic in the Eulerian sense. This means that in the second order of the WKB expansion, which determines the variation of wave amplitude along rays, the violation of isentropy must be accounted for. The present paper revisits the derivation of the WKB approximation for small-amplitude magnetohydrodynamic waves, allowing for possible spatial variation of the background entropy. The equation of variation of wave amplitude is rederived; it is a bilinear equation which, it turns out, can be recast in the action conservation form. It is shown that this action conservation equation is in fact equivalent to the action conservation law obtained from Lagrangian treatments
Relative efficiency and sample size for cluster randomized trials with variable cluster sizes.
You, Zhiying; Williams, O Dale; Aban, Inmaculada; Kabagambe, Edmond Kato; Tiwari, Hemant K; Cutter, Gary
2011-02-01
The statistical power of cluster randomized trials depends on two sample size components, the number of clusters per group and the numbers of individuals within clusters (cluster size). Variable cluster sizes are common and this variation alone may have significant impact on study power. Previous approaches have taken this into account by either adjusting total sample size using a designated design effect or adjusting the number of clusters according to an assessment of the relative efficiency of unequal versus equal cluster sizes. This article defines a relative efficiency of unequal versus equal cluster sizes using noncentrality parameters, investigates properties of this measure, and proposes an approach for adjusting the required sample size accordingly. We focus on comparing two groups with normally distributed outcomes using t-test, and use the noncentrality parameter to define the relative efficiency of unequal versus equal cluster sizes and show that statistical power depends only on this parameter for a given number of clusters. We calculate the sample size required for an unequal cluster sizes trial to have the same power as one with equal cluster sizes. Relative efficiency based on the noncentrality parameter is straightforward to calculate and easy to interpret. It connects the required mean cluster size directly to the required sample size with equal cluster sizes. Consequently, our approach first determines the sample size requirements with equal cluster sizes for a pre-specified study power and then calculates the required mean cluster size while keeping the number of clusters unchanged. Our approach allows adjustment in mean cluster size alone or simultaneous adjustment in mean cluster size and number of clusters, and is a flexible alternative to and a useful complement to existing methods. Comparison indicated that we have defined a relative efficiency that is greater than the relative efficiency in the literature under some conditions. Our measure
Control of cluster ion sizes for efficient injection heating
International Nuclear Information System (INIS)
Enjoji, Hiroshi; Be, S.H.; Yano, Katsuki; Okamoto, Kosuke
1976-01-01
For heating of plasmas by injection of hydrogen cluster ions, the specific size (N/Z) approximately 10 2 molecules/charge is believed to be most desirable. A fundamental research to develop a practical method for tailoring large cluster ions into small suitable sizes has been carried out by using nitrogen cluster ions of the initial mean specific size (N/Z) 0 approximately 10 5 . The beam of neutral large clusters of total intensity 20 mAsub(eq) was led to an ionizer and then the large cluster ions are accelerated to 8.9 keV before entering the divider which disintegrates them into small fragments by multiple ionization. The mean specific size of disintegrated cluster ions (N/Z)' becomes smaller with increase in ionizing electron current of the divider. (N/Z)' becomes 10 3 approximately 10 4 at an electron current of 140 mA and an accelerating voltage of 680 V of the divider with its efficiency of 20 approximately 60%. Thus, the original large cluster ions are divided into small fragments of which the mean specific size is 1/20 approximately 1/100 of the initial value without much decrease in total intensity of the cluster ion beam
On Nash-Equilibria of Approximation-Stable Games
Awasthi, Pranjal; Balcan, Maria-Florina; Blum, Avrim; Sheffet, Or; Vempala, Santosh
One reason for wanting to compute an (approximate) Nash equilibrium of a game is to predict how players will play. However, if the game has multiple equilibria that are far apart, or ɛ-equilibria that are far in variation distance from the true Nash equilibrium strategies, then this prediction may not be possible even in principle. Motivated by this consideration, in this paper we define the notion of games that are approximation stable, meaning that all ɛ-approximate equilibria are contained inside a small ball of radius Δ around a true equilibrium, and investigate a number of their properties. Many natural small games such as matching pennies and rock-paper-scissors are indeed approximation stable. We show furthermore there exist 2-player n-by-n approximation-stable games in which the Nash equilibrium and all approximate equilibria have support Ω(log n). On the other hand, we show all (ɛ,Δ) approximation-stable games must have an ɛ-equilibrium of support O(Δ^{2-o(1)}/ɛ2{log n}), yielding an immediate n^{O(Δ^{2-o(1)}/ɛ^2log n)}-time algorithm, improving over the bound of [11] for games satisfying this condition. We in addition give a polynomial-time algorithm for the case that Δ and ɛ are sufficiently close together. We also consider an inverse property, namely that all non-approximate equilibria are far from some true equilibrium, and give an efficient algorithm for games satisfying that condition.
Analysis of corrections to the eikonal approximation
Hebborn, C.; Capel, P.
2017-11-01
Various corrections to the eikonal approximations are studied for two- and three-body nuclear collisions with the goal to extend the range of validity of this approximation to beam energies of 10 MeV/nucleon. Wallace's correction does not improve much the elastic-scattering cross sections obtained at the usual eikonal approximation. On the contrary, a semiclassical approximation that substitutes the impact parameter by a complex distance of closest approach computed with the projectile-target optical potential efficiently corrects the eikonal approximation. This opens the possibility to analyze data measured down to 10 MeV/nucleon within eikonal-like reaction models.
International Nuclear Information System (INIS)
Popok, V.N.; Prasalovich, S.V.; Odzhaev, V.B.; Campbell, E.E.B.
2001-01-01
A brief state-of-the-art review in the field of cluster-surface interactions is presented. Ionised cluster beams could become a powerful and versatile tool for the modification and processing of surfaces as an alternative to ion implantation and ion assisted deposition. The main effects of cluster-surface collisions and possible applications of cluster ion beams are discussed. The outlooks of the Cluster Implantation and Deposition Apparatus (CIDA) being developed in Guteborg University are shown
Mapping moveout approximations in TI media
Stovas, Alexey; Alkhalifah, Tariq Ali
2013-01-01
Moveout approximations play a very important role in seismic modeling, inversion, and scanning for parameters in complex media. We developed a scheme to map one-way moveout approximations for transversely isotropic media with a vertical axis of symmetry (VTI), which is widely available, to the tilted case (TTI) by introducing the effective tilt angle. As a result, we obtained highly accurate TTI moveout equations analogous with their VTI counterparts. Our analysis showed that the most accurate approximation is obtained from the mapping of generalized approximation. The new moveout approximations allow for, as the examples demonstrate, accurate description of moveout in the TTI case even for vertical heterogeneity. The proposed moveout approximations can be easily used for inversion in a layered TTI medium because the parameters of these approximations explicitly depend on corresponding effective parameters in a layered VTI medium.
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
Mapping moveout approximations in TI media
Stovas, Alexey
2013-11-21
Moveout approximations play a very important role in seismic modeling, inversion, and scanning for parameters in complex media. We developed a scheme to map one-way moveout approximations for transversely isotropic media with a vertical axis of symmetry (VTI), which is widely available, to the tilted case (TTI) by introducing the effective tilt angle. As a result, we obtained highly accurate TTI moveout equations analogous with their VTI counterparts. Our analysis showed that the most accurate approximation is obtained from the mapping of generalized approximation. The new moveout approximations allow for, as the examples demonstrate, accurate description of moveout in the TTI case even for vertical heterogeneity. The proposed moveout approximations can be easily used for inversion in a layered TTI medium because the parameters of these approximations explicitly depend on corresponding effective parameters in a layered VTI medium.
An Approximate Approach to Automatic Kernel Selection.
Ding, Lizhong; Liao, Shizhong
2016-02-02
Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.
Bounded-Degree Approximations of Stochastic Networks
Energy Technology Data Exchange (ETDEWEB)
Quinn, Christopher J.; Pinar, Ali; Kiyavash, Negar
2017-06-01
We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify optimal and near-optimal approximations in terms of Kullback-Leibler divergence. The user-chosen sparsity trades off the quality of the approximation against visual conciseness and computational tractability. One class of approximations contains graphs with speci ed in-degrees. Another class additionally requires that the graph is connected. For both classes, we propose algorithms to identify the optimal approximations and also near-optimal approximations, using a novel relaxation of submodularity. We also propose algorithms to identify the r-best approximations among these classes, enabling robust decision making.
Equilibrium structure and atomic vibrations of Nin clusters
Borisova, Svetlana D.; Rusina, Galina G.
2017-12-01
The equilibrium bond lengths and binding energy, second differences in energy and vibrational frequencies of free clusters Nin (2 ≤ n ≤ 20) were calculated with the use of the interaction potential obtained in the tight-binding approximation (TBA). The results show that the minimum vibration frequency plays a significant role in the evaluation of the dynamic stability of the clusters. A nonmonotonic dependence of the minimum vibration frequency of clusters on their size and the extreme values for the number of atoms in a cluster n = 4, 6, 13, and 19 are demonstrated. This result agrees with the theoretical and experimental data on stable structures of small metallic clusters.
Analysis of Neural Oscillations on Drosophila’s Subesophageal Ganglion Based on Approximate Entropy
Directory of Open Access Journals (Sweden)
Tian Mei
2015-10-01
Full Text Available The suboesophageal ganglion (SOG, which connects to both central and peripheral nerves, is the primary taste-processing center in the Drosophila’s brain. The neural oscillation in this center may be of great research value yet it is rarely reported. This work aims to determine the amount of unique information contained within oscillations of the SOG and describe the variability of these patterns. The approximate entropy (ApEn values of the spontaneous membrane potential (sMP of SOG neurons were calculated in this paper. The arithmetic mean (MA, standard deviation (SDA and the coefficient of variation (CVA of ApEn were proposed as the three statistical indicators to describe the irregularity and complexity of oscillations. The hierarchical clustering method was used to classify them. As a result, the oscillations in SOG were divided into five categories, including: (1 Continuous spike pattern; (2 Mixed oscillation pattern; (3 Spikelet pattern; (4 Busting pattern and (5 Sparse spike pattern. Steady oscillation state has a low level of irregularity, and vice versa. The dopamine stimulation can distinctly cut down the complexity of the mixed oscillation pattern. The current study provides a quantitative method and some critera on mining the information carried in neural oscillations.
Algorithms of maximum likelihood data clustering with applications
Giada, Lorenzo; Marsili, Matteo
2002-12-01
We address the problem of data clustering by introducing an unsupervised, parameter-free approach based on maximum likelihood principle. Starting from the observation that data sets belonging to the same cluster share a common information, we construct an expression for the likelihood of any possible cluster structure. The likelihood in turn depends only on the Pearson's coefficient of the data. We discuss clustering algorithms that provide a fast and reliable approximation to maximum likelihood configurations. Compared to standard clustering methods, our approach has the advantages that (i) it is parameter free, (ii) the number of clusters need not be fixed in advance and (iii) the interpretation of the results is transparent. In order to test our approach and compare it with standard clustering algorithms, we analyze two very different data sets: time series of financial market returns and gene expression data. We find that different maximization algorithms produce similar cluster structures whereas the outcome of standard algorithms has a much wider variability.
Testing approximate predictions of displacements of cosmological dark matter halos
Energy Technology Data Exchange (ETDEWEB)
Munari, Emiliano; Monaco, Pierluigi; Borgani, Stefano [Department of Physics, Astronomy Unit, University of Trieste, via Tiepolo 11, I-34143 Trieste (Italy); Koda, Jun [INAF – Osservatorio Astronomico di Brera, via E. Bianchi 46, I-23807 Merate (Italy); Kitaura, Francisco-Shu [Instituto de Astrofísica de Canarias, 38205 San Cristóbal de La Laguna, Santa Cruz de Tenerife (Spain); Sefusatti, Emiliano, E-mail: munari@oats.inaf.it, E-mail: monaco@oats.inaf.it, E-mail: jun.koda@brera.inaf.it, E-mail: fkitaura@iac.es, E-mail: sefusatti@oats.inaf.it, E-mail: borgani@oats.inaf.it [INAF – Osservatorio Astronomico di Trieste, via Tiepolo 11, I-34143 Trieste (Italy)
2017-07-01
We present a test to quantify how well some approximate methods, designed to reproduce the mildly non-linear evolution of perturbations, are able to reproduce the clustering of DM halos once the grouping of particles into halos is defined and kept fixed. The following methods have been considered: Lagrangian Perturbation Theory (LPT) up to third order, Truncated LPT, Augmented LPT, MUSCLE and COLA. The test runs as follows: halos are defined by applying a friends-of-friends (FoF) halo finder to the output of an N-body simulation. The approximate methods are then applied to the same initial conditions of the simulation, producing for all particles displacements from their starting position and velocities. The position and velocity of each halo are computed by averaging over the particles that belong to that halo, according to the FoF halo finder. This procedure allows us to perform a well-posed test of how clustering of the matter density and halo density fields are recovered, without asking to the approximate method an accurate reconstruction of halos. We have considered the results at z =0,0.5,1, and we have analysed power spectrum in real and redshift space, object-by-object difference in position and velocity, density Probability Distribution Function (PDF) and its moments, phase difference of Fourier modes. We find that higher LPT orders are generally able to better reproduce the clustering of halos, while little or no improvement is found for the matter density field when going to 2LPT and 3LPT. Augmentation provides some improvement when coupled with 2LPT, while its effect is limited when coupled with 3LPT. Little improvement is brought by MUSCLE with respect to Augmentation. The more expensive particle-mesh code COLA outperforms all LPT methods, and this is true even for mesh sizes as large as the inter-particle distance. This test sets an upper limit on the ability of these methods to reproduce the clustering of halos, for the cases when these objects are
Testing approximate predictions of displacements of cosmological dark matter halos
Munari, Emiliano; Monaco, Pierluigi; Koda, Jun; Kitaura, Francisco-Shu; Sefusatti, Emiliano; Borgani, Stefano
2017-07-01
We present a test to quantify how well some approximate methods, designed to reproduce the mildly non-linear evolution of perturbations, are able to reproduce the clustering of DM halos once the grouping of particles into halos is defined and kept fixed. The following methods have been considered: Lagrangian Perturbation Theory (LPT) up to third order, Truncated LPT, Augmented LPT, MUSCLE and COLA. The test runs as follows: halos are defined by applying a friends-of-friends (FoF) halo finder to the output of an N-body simulation. The approximate methods are then applied to the same initial conditions of the simulation, producing for all particles displacements from their starting position and velocities. The position and velocity of each halo are computed by averaging over the particles that belong to that halo, according to the FoF halo finder. This procedure allows us to perform a well-posed test of how clustering of the matter density and halo density fields are recovered, without asking to the approximate method an accurate reconstruction of halos. We have considered the results at z=0,0.5,1, and we have analysed power spectrum in real and redshift space, object-by-object difference in position and velocity, density Probability Distribution Function (PDF) and its moments, phase difference of Fourier modes. We find that higher LPT orders are generally able to better reproduce the clustering of halos, while little or no improvement is found for the matter density field when going to 2LPT and 3LPT. Augmentation provides some improvement when coupled with 2LPT, while its effect is limited when coupled with 3LPT. Little improvement is brought by MUSCLE with respect to Augmentation. The more expensive particle-mesh code COLA outperforms all LPT methods, and this is true even for mesh sizes as large as the inter-particle distance. This test sets an upper limit on the ability of these methods to reproduce the clustering of halos, for the cases when these objects are
Unequal cluster sizes in stepped-wedge cluster randomised trials: a systematic review.
Kristunas, Caroline; Morris, Tom; Gray, Laura
2017-11-15
To investigate the extent to which cluster sizes vary in stepped-wedge cluster randomised trials (SW-CRT) and whether any variability is accounted for during the sample size calculation and analysis of these trials. Any, not limited to healthcare settings. Any taking part in an SW-CRT published up to March 2016. The primary outcome is the variability in cluster sizes, measured by the coefficient of variation (CV) in cluster size. Secondary outcomes include the difference between the cluster sizes assumed during the sample size calculation and those observed during the trial, any reported variability in cluster sizes and whether the methods of sample size calculation and methods of analysis accounted for any variability in cluster sizes. Of the 101 included SW-CRTs, 48% mentioned that the included clusters were known to vary in size, yet only 13% of these accounted for this during the calculation of the sample size. However, 69% of the trials did use a method of analysis appropriate for when clusters vary in size. Full trial reports were available for 53 trials. The CV was calculated for 23 of these: the median CV was 0.41 (IQR: 0.22-0.52). Actual cluster sizes could be compared with those assumed during the sample size calculation for 14 (26%) of the trial reports; the cluster sizes were between 29% and 480% of that which had been assumed. Cluster sizes often vary in SW-CRTs. Reporting of SW-CRTs also remains suboptimal. The effect of unequal cluster sizes on the statistical power of SW-CRTs needs further exploration and methods appropriate to studies with unequal cluster sizes need to be employed. © Article author(s) (or their employer(s) unless otherwise stated in the text of the article) 2017. All rights reserved. No commercial use is permitted unless otherwise expressly granted.
Projection-based curve clustering
International Nuclear Information System (INIS)
Auder, Benjamin; Fischer, Aurelie
2012-01-01
This paper focuses on unsupervised curve classification in the context of nuclear industry. At the Commissariat a l'Energie Atomique (CEA), Cadarache (France), the thermal-hydraulic computer code CATHARE is used to study the reliability of reactor vessels. The code inputs are physical parameters and the outputs are time evolution curves of a few other physical quantities. As the CATHARE code is quite complex and CPU time-consuming, it has to be approximated by a regression model. This regression process involves a clustering step. In the present paper, the CATHARE output curves are clustered using a k-means scheme, with a projection onto a lower dimensional space. We study the properties of the empirically optimal cluster centres found by the clustering method based on projections, compared with the 'true' ones. The choice of the projection basis is discussed, and an algorithm is implemented to select the best projection basis among a library of orthonormal bases. The approach is illustrated on a simulated example and then applied to the industrial problem. (authors)
Girola Schneider, R.
2017-07-01
The fuzzy logic is a branch of the artificial intelligence founded on the concept that everything is a matter of degree. It intends to create mathematical approximations on the resolution of certain types of problems. In addition, it aims to produce exact results obtained from imprecise data, for which it is particularly useful for electronic and computer applications. This enables it to handle vague or unspecific information when certain parts of a system are unknown or ambiguous and, therefore, they cannot be measured in a reliable manner. Also, when the variation of a variable can produce an alteration on the others The main focus of this paper is to prove the importance of these techniques formulated from a theoretical analysis on its application on ambiguous situations in the field of the rich clusters of galaxies. The purpose is to show its applicability in the several classification systems proposed for the rich clusters, which are based on criteria such as the level of richness of the cluster, the distribution of the brightest galaxies, whether there are signs of type-cD galaxies or not or the existence of sub-clusters. Fuzzy logic enables the researcher to work with "imprecise" information implementing fuzzy sets and combining rules to define actions. The control systems based on fuzzy logic join input variables that are defined in terms of fuzzy sets through rule groups that produce one or several output values of the system under study. From this context, the application of the fuzzy logic's techniques approximates the solution of the mathematical models in abstractions about the rich galaxy cluster classification of physical properties in order to solve the obscurities that must be confronted by an investigation group in order to make a decision.
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.
Super-sample covariance approximations and partial sky coverage
Lacasa, Fabien; Lima, Marcos; Aguena, Michel
2018-04-01
Super-sample covariance (SSC) is the dominant source of statistical error on large scale structure (LSS) observables for both current and future galaxy surveys. In this work, we concentrate on the SSC of cluster counts, also known as sample variance, which is particularly useful for the self-calibration of the cluster observable-mass relation; our approach can similarly be applied to other observables, such as galaxy clustering and lensing shear. We first examined the accuracy of two analytical approximations proposed in the literature for the flat sky limit, finding that they are accurate at the 15% and 30-35% level, respectively, for covariances of counts in the same redshift bin. We then developed a harmonic expansion formalism that allows for the prediction of SSC in an arbitrary survey mask geometry, such as large sky areas of current and future surveys. We show analytically and numerically that this formalism recovers the full sky and flat sky limits present in the literature. We then present an efficient numerical implementation of the formalism, which allows fast and easy runs of covariance predictions when the survey mask is modified. We applied our method to a mask that is broadly similar to the Dark Energy Survey footprint, finding a non-negligible negative cross-z covariance, i.e. redshift bins are anti-correlated. We also examined the case of data removal from holes due to, for example bright stars, quality cuts, or systematic removals, and find that this does not have noticeable effects on the structure of the SSC matrix, only rescaling its amplitude by the effective survey area. These advances enable analytical covariances of LSS observables to be computed for current and future galaxy surveys, which cover large areas of the sky where the flat sky approximation fails.
Management of cluster headache
DEFF Research Database (Denmark)
Tfelt-Hansen, Peer C; Jensen, Rigmor H
2012-01-01
The prevalence of cluster headache is 0.1% and cluster headache is often not diagnosed or misdiagnosed as migraine or sinusitis. In cluster headache there is often a considerable diagnostic delay - an average of 7 years in a population-based survey. Cluster headache is characterized by very severe...... or severe orbital or periorbital pain with a duration of 15-180 minutes. The cluster headache attacks are accompanied by characteristic associated unilateral symptoms such as tearing, nasal congestion and/or rhinorrhoea, eyelid oedema, miosis and/or ptosis. In addition, there is a sense of restlessness...... and agitation. Patients may have up to eight attacks per day. Episodic cluster headache (ECH) occurs in clusters of weeks to months duration, whereas chronic cluster headache (CCH) attacks occur for more than 1 year without remissions. Management of cluster headache is divided into acute attack treatment...
Symmetries of cluster configurations
International Nuclear Information System (INIS)
Kramer, P.
1975-01-01
A deeper understanding of clustering phenomena in nuclei must encompass at least two interrelated aspects of the subject: (A) Given a system of A nucleons with two-body interactions, what are the relevant and persistent modes of clustering involved. What is the nature of the correlated nucleon groups which form the clusters, and what is their mutual interaction. (B) Given the cluster modes and their interaction, what systematic patterns of nuclear structure and reactions emerge from it. Are there, for example, families of states which share the same ''cluster parents''. Which cluster modes are compatible or exclude each other. What quantum numbers could characterize cluster configurations. There is no doubt that we can learn a good deal from the experimentalists who have discovered many of the features relevant to aspect (B). Symmetries specific to cluster configurations which can throw some light on both aspects of clustering are discussed
Barros, F S M; Arruda, M E; Gurgel, H C; Honório, N A
2011-12-01
Deforestation has been linked to a rise in malaria prevalence. In this paper, we studied longitudinally 20 spots, including forested and deforested portions of a temporary river in a malarigenous frontier zone. Larval habitat parameters influencing distribution of Anopheles darlingi (Diptera: Culicidae) larvae were studied. We observed that larvae were clustered in forested-deforested transitions. For the first time in the literature, it was verified that parameters determining larval distribution varied from deforested to forested areas. The proximity to human dwellings was also a significant factor determining distribution, but larvae was most importantly associated with a previously undescribed parameter, the presence of small obstructions to river flow, such as tree trunks within the river channel, which caused pooling of water during the dry season ('microdams'). In deforested areas, the most important factor determining distribution of larvae was shade (reduced luminance). Larvae were absent in the entire studied area during the wet season and present in most sites during the dry season. During the wet-dry transition, larvae were found sooner in areas with microdams, than in other areas, suggesting that flow obstruction prolongs the breeding season of An. darlingi. Adult mosquito densities and malaria incidence were higher during the dry season. Our data correlate well with the published literature, including the distribution of malaria cases near the forest fringes, and has permitted the creation of a model of An. darlingi breeding, where preference for sites with reduced luminance, human presence and microdams would interact to determine larval distribution.
Multilevel Monte Carlo in Approximate Bayesian Computation
Jasra, Ajay
2017-02-13
In the following article we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation. Several numerical examples are given.
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.
Exact and approximate multiple diffraction calculations
International Nuclear Information System (INIS)
Alexander, Y.; Wallace, S.J.; Sparrow, D.A.
1976-08-01
A three-body potential scattering problem is solved in the fixed scatterer model exactly and approximately to test the validity of commonly used assumptions of multiple scattering calculations. The model problem involves two-body amplitudes that show diffraction-like differential scattering similar to high energy hadron-nucleon amplitudes. The exact fixed scatterer calculations are compared to Glauber approximation, eikonal-expansion results and a noneikonal approximation
Cluster Decline and Resilience
DEFF Research Database (Denmark)
Østergaard, Christian Richter; Park, Eun Kyung
Most studies on regional clusters focus on identifying factors and processes that make clusters grow. However, sometimes technologies and market conditions suddenly shift, and clusters decline. This paper analyses the process of decline of the wireless communication cluster in Denmark, 1963......-2011. Our longitudinal study reveals that technological lock-in and exit of key firms have contributed to impairment of the cluster’s resilience in adapting to disruptions. Entrepreneurship has a positive effect on cluster resilience, while multinational companies have contradicting effects by bringing...... in new resources to the cluster but being quick to withdraw in times of crisis....
Bent approximations to synchrotron radiation optics
International Nuclear Information System (INIS)
Heald, S.
1981-01-01
Ideal optical elements can be approximated by bending flats or cylinders. This paper considers the applications of these approximate optics to synchrotron radiation. Analytic and raytracing studies are used to compare their optical performance with the corresponding ideal elements. It is found that for many applications the performance is adequate, with the additional advantages of lower cost and greater flexibility. Particular emphasis is placed on obtaining the practical limitations on the use of the approximate elements in typical beamline configurations. Also considered are the possibilities for approximating very long length mirrors using segmented mirrors
Local density approximations for relativistic exchange energies
International Nuclear Information System (INIS)
MacDonald, A.H.
1986-01-01
The use of local density approximations to approximate exchange interactions in relativistic electron systems is reviewed. Particular attention is paid to the physical content of these exchange energies by discussing results for the uniform relativistic electron gas from a new point of view. Work on applying these local density approximations in atoms and solids is reviewed and it is concluded that good accuracy is usually possible provided self-interaction corrections are applied. The local density approximations necessary for spin-polarized relativistic systems are discussed and some new results are presented
Approximate maximum parsimony and ancestral maximum likelihood.
Alon, Noga; Chor, Benny; Pardi, Fabio; Rapoport, Anat
2010-01-01
We explore the maximum parsimony (MP) and ancestral maximum likelihood (AML) criteria in phylogenetic tree reconstruction. Both problems are NP-hard, so we seek approximate solutions. We formulate the two problems as Steiner tree problems under appropriate distances. The gist of our approach is the succinct characterization of Steiner trees for a small number of leaves for the two distances. This enables the use of known Steiner tree approximation algorithms. The approach leads to a 16/9 approximation ratio for AML and asymptotically to a 1.55 approximation ratio for MP.
APPROXIMATIONS TO PERFORMANCE MEASURES IN QUEUING SYSTEMS
Directory of Open Access Journals (Sweden)
Kambo, N. S.
2012-11-01
Full Text Available Approximations to various performance measures in queuing systems have received considerable attention because these measures have wide applicability. In this paper we propose two methods to approximate the queuing characteristics of a GI/M/1 system. The first method is non-parametric in nature, using only the first three moments of the arrival distribution. The second method treads the known path of approximating the arrival distribution by a mixture of two exponential distributions by matching the first three moments. Numerical examples and optimal analysis of performance measures of GI/M/1 queues are provided to illustrate the efficacy of the methods, and are compared with benchmark approximations.
Coupled Cluster Theory for Large Molecules
DEFF Research Database (Denmark)
Baudin, Pablo
This thesis describes the development of local approximations to coupled cluster (CC) theory for large molecules. Two different methods are presented, the divide–expand–consolidate scheme (DEC), for the calculation of ground state energies, and a local framework denoted LoFEx, for the calculation...
Comprehensive cluster analysis with Transitivity Clustering.
Wittkop, Tobias; Emig, Dorothea; Truss, Anke; Albrecht, Mario; Böcker, Sebastian; Baumbach, Jan
2011-03-01
Transitivity Clustering is a method for the partitioning of biological data into groups of similar objects, such as genes, for instance. It provides integrated access to various functions addressing each step of a typical cluster analysis. To facilitate this, Transitivity Clustering is accessible online and offers three user-friendly interfaces: a powerful stand-alone version, a web interface, and a collection of Cytoscape plug-ins. In this paper, we describe three major workflows: (i) protein (super)family detection with Cytoscape, (ii) protein homology detection with incomplete gold standards and (iii) clustering of gene expression data. This protocol guides the user through the most important features of Transitivity Clustering and takes ∼1 h to complete.
Hierarchical modeling of cluster size in wildlife surveys
Royle, J. Andrew
2008-01-01
Clusters or groups of individuals are the fundamental unit of observation in many wildlife sampling problems, including aerial surveys of waterfowl, marine mammals, and ungulates. Explicit accounting of cluster size in models for estimating abundance is necessary because detection of individuals within clusters is not independent and detectability of clusters is likely to increase with cluster size. This induces a cluster size bias in which the average cluster size in the sample is larger than in the population at large. Thus, failure to account for the relationship between delectability and cluster size will tend to yield a positive bias in estimates of abundance or density. I describe a hierarchical modeling framework for accounting for cluster-size bias in animal sampling. The hierarchical model consists of models for the observation process conditional on the cluster size distribution and the cluster size distribution conditional on the total number of clusters. Optionally, a spatial model can be specified that describes variation in the total number of clusters per sample unit. Parameter estimation, model selection, and criticism may be carried out using conventional likelihood-based methods. An extension of the model is described for the situation where measurable covariates at the level of the sample unit are available. Several candidate models within the proposed class are evaluated for aerial survey data on mallard ducks (Anas platyrhynchos).
International Nuclear Information System (INIS)
Freeman, K.C.
1980-01-01
The young globular clusters of the LMC have ages of 10 7 -10 8 y. Their masses and structure are similar to those of the smaller galactic globular clusters. Their stellar mass functions (in the mass range 6 solar masses to 1.2 solar masses) vary greatly from cluster to cluster, although the clusters are similar in total mass, age, structure and chemical composition. It would be very interesting to know why these clusters are forming now in the LMC and not in the Galaxy. The author considers the 'young globular' or 'blue populous' clusters of the LMC. The ages of these objects are 10 7 to 10 8 y, and their masses are 10 4 to 10 5 solar masses, so they are populous enough to be really useful for studying the evolution of massive stars. The author concentrates on the structure and stellar content of these young clusters. (Auth.)
Star clusters and associations
International Nuclear Information System (INIS)
Ruprecht, J.; Palous, J.
1983-01-01
All 33 papers presented at the symposium were inputted to INIS. They dealt with open clusters, globular clusters, stellar associations and moving groups, and local kinematics and galactic structures. (E.S.)
International Nuclear Information System (INIS)
Bottiglioni, F.; Coutant, J.; Fois, M.
1978-01-01
Areas of possible applications of cluster injection are discussed. The deposition inside the plasma of molecules, issued from the dissociation of the injected clusters, has been computed. Some empirical scaling laws for the penetration are given
Diagonal Pade approximations for initial value problems
International Nuclear Information System (INIS)
Reusch, M.F.; Ratzan, L.; Pomphrey, N.; Park, W.
1987-06-01
Diagonal Pade approximations to the time evolution operator for initial value problems are applied in a novel way to the numerical solution of these problems by explicitly factoring the polynomials of the approximation. A remarkable gain over conventional methods in efficiency and accuracy of solution is obtained. 20 refs., 3 figs., 1 tab
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 ...
Approximation properties of fine hyperbolic graphs
Indian Academy of Sciences (India)
2010 Mathematics Subject Classification. 46L07. 1. Introduction. Given a countable discrete group G, some nice approximation properties for the reduced. C∗-algebras C∗ r (G) can give us the approximation properties of G. For example, Lance. [7] proved that the nuclearity of C∗ r (G) is equivalent to the amenability of G; ...
Non-Linear Approximation of Bayesian Update
Litvinenko, Alexander
2016-01-01
We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.
Simultaneous approximation in scales of Banach spaces
International Nuclear Information System (INIS)
Bramble, J.H.; Scott, R.
1978-01-01
The problem of verifying optimal approximation simultaneously in different norms in a Banach scale is reduced to verification of optimal approximation in the highest order norm. The basic tool used is the Banach space interpolation method developed by Lions and Peetre. Applications are given to several problems arising in the theory of finite element methods
Approximation algorithms for guarding holey polygons ...
African Journals Online (AJOL)
Guarding edges of polygons is a version of art gallery problem.The goal is finding the minimum number of guards to cover the edges of a polygon. This problem is NP-hard, and to our knowledge there are approximation algorithms just for simple polygons. In this paper we present two approximation algorithms for guarding ...
Efficient automata constructions and approximate automata
Watson, B.W.; Kourie, D.G.; Ngassam, E.K.; Strauss, T.; Cleophas, L.G.W.A.
2008-01-01
In this paper, we present data structures and algorithms for efficiently constructing approximate automata. An approximate automaton for a regular language L is one which accepts at least L. Such automata can be used in a variety of practical applications, including network security pattern
Efficient automata constructions and approximate automata
Watson, B.W.; Kourie, D.G.; Ngassam, E.K.; Strauss, T.; Cleophas, L.G.W.A.; Holub, J.; Zdárek, J.
2006-01-01
In this paper, we present data structures and algorithms for efficiently constructing approximate automata. An approximate automaton for a regular language L is one which accepts at least L. Such automata can be used in a variety of practical applications, including network security pattern
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.
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...
Quirks of Stirling's Approximation
Macrae, Roderick M.; Allgeier, Benjamin M.
2013-01-01
Stirling's approximation to ln "n"! is typically introduced to physical chemistry students as a step in the derivation of the statistical expression for the entropy. However, naive application of this approximation leads to incorrect conclusions. In this article, the problem is first illustrated using a familiar "toy…
Non-Linear Approximation of Bayesian Update
Litvinenko, Alexander
2016-06-23
We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.
Approximations for stop-loss reinsurance premiums
Reijnen, Rajko; Albers, Willem/Wim; Kallenberg, W.C.M.
2005-01-01
Various approximations of stop-loss reinsurance premiums are described in literature. For a wide variety of claim size distributions and retention levels, such approximations are compared in this paper to each other, as well as to a quantitative criterion. For the aggregate claims two models are
Moiseiwitsch, B L
2004-01-01
This graduate-level text's primary objective is to demonstrate the expression of the equations of the various branches of mathematical physics in the succinct and elegant form of variational principles (and thereby illuminate their interrelationship). Its related intentions are to show how variational principles may be employed to determine the discrete eigenvalues for stationary state problems and to illustrate how to find the values of quantities (such as the phase shifts) that arise in the theory of scattering. Chapter-by-chapter treatment consists of analytical dynamics; optics, wave mecha
K-means clustering versus validation measures: a data-distribution perspective.
Xiong, Hui; Wu, Junjie; Chen, Jian
2009-04-01
K-means is a well-known and widely used partitional clustering method. While there are considerable research efforts to characterize the key features of the K-means clustering algorithm, further investigation is needed to understand how data distributions can have impact on the performance of K-means clustering. To that end, in this paper, we provide a formal and organized study of the effect of skewed data distributions on K-means clustering. Along this line, we first formally illustrate that K-means tends to produce clusters of relatively uniform size, even if input data have varied "true" cluster sizes. In addition, we show that some clustering validation measures, such as the entropy measure, may not capture this uniform effect and provide misleading information on the clustering performance. Viewed in this light, we provide the coefficient of variation (CV) as a necessary criterion to validate the clustering results. Our findings reveal that K-means tends to produce clusters in which the variations of cluster sizes, as measured by CV, are in a range of about 0.3-1.0. Specifically, for data sets with large variation in "true" cluster sizes (e.g., CV > 1.0), K-means reduces variation in resultant cluster sizes to less than 1.0. In contrast, for data sets with small variation in "true" cluster sizes (e.g., CV K-means increases variation in resultant cluster sizes to greater than 0.3. In other words, for the earlier two cases, K-means produces the clustering results which are away from the "true" cluster distributions.
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 %.
Approximate error conjugation gradient minimization methods
Kallman, Jeffrey S
2013-05-21
In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems.
International Nuclear Information System (INIS)
Shaver, P.A.
1986-01-01
Evidence for clustering of and with high-redshift QSOs is discussed. QSOs of different redshifts show no clustering, but QSOs of similar redshifts appear to be clustered on a scale comparable to that of galaxies at the present epoch. In addition, spectroscopic studies of close pairs of QSOs indicate that QSOs are surrounded by a relatively high density of absorbing matter, possibly clusters of galaxies
Photometric metal abundances for twenty clusters
International Nuclear Information System (INIS)
Jennens, P.A.; Helfer, H.L.
1975-01-01
Metal abundances, colour excesses and distance moduli have been determined for individual giant stars, using UBViyz photometry, in NGC 188, 559, 752, 1245, 1342, 1907, 1912, 2099, 5139 (ω cen), 5316, 5617, 5822, 5823, 6067, IC 4651, 6819, 6940, 7142, 7261 and 7789. All six clusters with ages 3 to 8x10 9 yr have metal abundances agreeing with one another; their average value of [Fe/H]=-0.24+-0.05, agrees with the average found for the bright K-giants near the Sun. All six clusters are at least 140pc from the galactic plane. For the younger clusters less than approximately 10 9 yr old, one-third are metal deficient. The very young cluster, NGC 559, is probably very metal weak. (author)
Syakur, M. A.; Khotimah, B. K.; Rochman, E. M. S.; Satoto, B. D.
2018-04-01
Clustering is a data mining technique used to analyse data that has variations and the number of lots. Clustering was process of grouping data into a cluster, so they contained data that is as similar as possible and different from other cluster objects. SMEs Indonesia has a variety of customers, but SMEs do not have the mapping of these customers so they did not know which customers are loyal or otherwise. Customer mapping is a grouping of customer profiling to facilitate analysis and policy of SMEs in the production of goods, especially batik sales. Researchers will use a combination of K-Means method with elbow to improve efficient and effective k-means performance in processing large amounts of data. K-Means Clustering is a localized optimization method that is sensitive to the selection of the starting position from the midpoint of the cluster. So choosing the starting position from the midpoint of a bad cluster will result in K-Means Clustering algorithm resulting in high errors and poor cluster results. The K-means algorithm has problems in determining the best number of clusters. So Elbow looks for the best number of clusters on the K-means method. Based on the results obtained from the process in determining the best number of clusters with elbow method can produce the same number of clusters K on the amount of different data. The result of determining the best number of clusters with elbow method will be the default for characteristic process based on case study. Measurement of k-means value of k-means has resulted in the best clusters based on SSE values on 500 clusters of batik visitors. The result shows the cluster has a sharp decrease is at K = 3, so K as the cut-off point as the best cluster.
Cluster Physics with Merging Galaxy Clusters
Directory of Open Access Journals (Sweden)
Sandor M. Molnar
2016-02-01
Full Text Available Collisions between galaxy clusters provide a unique opportunity to study matter in a parameter space which cannot be explored in our laboratories on Earth. In the standard LCDM model, where the total density is dominated by the cosmological constant ($Lambda$ and the matter density by cold dark matter (CDM, structure formation is hierarchical, and clusters grow mostly by merging.Mergers of two massive clusters are the most energetic events in the universe after the Big Bang,hence they provide a unique laboratory to study cluster physics.The two main mass components in clusters behave differently during collisions:the dark matter is nearly collisionless, responding only to gravity, while the gas is subject to pressure forces and dissipation, and shocks and turbulenceare developed during collisions. In the present contribution we review the different methods used to derive the physical properties of merging clusters. Different physical processes leave their signatures on different wavelengths, thusour review is based on a multifrequency analysis. In principle, the best way to analyze multifrequency observations of merging clustersis to model them using N-body/HYDRO numerical simulations. We discuss the results of such detailed analyses.New high spatial and spectral resolution ground and space based telescopeswill come online in the near future. Motivated by these new opportunities,we briefly discuss methods which will be feasible in the near future in studying merging clusters.
Emergent organization of oscillator clusters in coupled self ...
Indian Academy of Sciences (India)
Additionally, the maps are coupled sequentially and unidirectionally, to their nearest neighbor, through the difference of their parametric variations. Interestingly we find that this model asymptotically yields clusters of superstable oscillators with different periods. We observe that the sizes of these oscillator clusters have a ...
Indian Academy of Sciences (India)
First page Back Continue Last page Overview Graphics. The Optical Absorption Spectra of Small Silver Clusters (5-11) ... Soft Landing and Fragmentation of Small Clusters Deposited in Noble-Gas Films. Harbich, W.; Fedrigo, S.; Buttet, J. Phys. Rev. B 1998, 58, 7428. CO combustion on supported gold clusters. Arenz M ...
DEFF Research Database (Denmark)
Lorentzen, Jochen; Robbins, Glen; Barnes, Justin
2004-01-01
The paper describes the formation of the Durban Auto Cluster in the context of trade liberalization. It argues that the improvement of operational competitiveness of firms in the cluster is prominently due to joint action. It tests this proposition by comparing the gains from cluster activities...
Marketing research cluster analysis
Directory of Open Access Journals (Sweden)
Marić Nebojša
2002-01-01
Full Text Available One area of applications of cluster analysis in marketing is identification of groups of cities and towns with similar demographic profiles. This paper considers main aspects of cluster analysis by an example of clustering 12 cities with the use of Minitab software.
Marketing research cluster analysis
Marić Nebojša
2002-01-01
One area of applications of cluster analysis in marketing is identification of groups of cities and towns with similar demographic profiles. This paper considers main aspects of cluster analysis by an example of clustering 12 cities with the use of Minitab software.
International Nuclear Information System (INIS)
Choi, Chang-Yeong; Kim, Jeong-Hyun; Kim, Seyong
2004-01-01
Using barebone PC components and NIC's, we construct a linux cluster which has 2-dimensional mesh structure. This cluster has smaller footprint, is less expensive, and use less power compared to conventional linux cluster. Here, we report our experience in building such a machine and discuss our current lattice project on the machine
Abrahamsen, M.; de Berg, M.T.; Buchin, K.A.; Mehr, M.; Mehrabi, A.D.
2017-01-01
In a geometric k -clustering problem the goal is to partition a set of points in R d into k subsets such that a certain cost function of the clustering is minimized. We present data structures for orthogonal range-clustering queries on a point set S : given a query box Q and an integer k>2 , compute
Cosmology with cluster surveys
Indian Academy of Sciences (India)
Abstract. Surveys of clusters of galaxies provide us with a powerful probe of the den- sity and nature of the dark energy. The red-shift distribution of detected clusters is highly sensitive to the dark energy equation of state parameter w. Upcoming Sunyaev–. Zel'dovich (SZ) surveys would provide us large yields of clusters to ...
The detection of clusters in rare diseases
Energy Technology Data Exchange (ETDEWEB)
Besag, J. (Washington Univ., Seattle, WA (USA) Newcastle upon Tyne Univ. (UK)); Newell, J. (Newcastle upon Tyne Univ. (UK))
1991-01-01
Tests for clustering of rare diseases investigate whether an observed pattern of cases in one or more geographical regions could reasonably have arisen by chance alone, bearing in mind the variation in background population density. In contrast, tests for the detection of clusters are concerned with screening a large region for evidence of individual 'hot spots' of disease but without any preconception about their likely locations; the results of such tests may form the basis for subsequent small area investigations, statistical or non-statistical, but will rarely be an end in themselves. The main intention of the paper is to describe and illustrate a new technique for the identification of small clusters of disease. A secondary purpose is to discuss some common pitfalls in the application of tests of clustering to epidemiological data. (author).
Numerical approximations for speeding up mcmc inference in the infinite relational model
DEFF Research Database (Denmark)
Schmidt, Mikkel Nørgaard; Albers, Kristoffer Jon
2015-01-01
The infinite relational model (IRM) is a powerful model for discovering clusters in complex networks; however, the computational speed of Markov chain Monte Carlo inference in the model can be a limiting factor when analyzing large networks. We investigate how using numerical approximations...
Analytical Evaluation of Beam Deformation Problem Using Approximate Methods
DEFF Research Database (Denmark)
Barari, Amin; Kimiaeifar, A.; Domairry, G.
2010-01-01
The beam deformation equation has very wide applications in structural engineering. As a differential equation, it has its own problem concerning existence, uniqueness and methods of solutions. Often, original forms of governing differential equations used in engineering problems are simplified......, and this process produces noise in the obtained answers. This paper deals with the solution of second order of differential equation governing beam deformation using four analytical approximate methods, namely the Perturbation, Homotopy Perturbation Method (HPM), Homotopy Analysis Method (HAM) and Variational...... Iteration Method (VIM). The comparisons of the results reveal that these methods are very effective, convenient and quite accurate for systems of non-linear differential equation....
Diffusive Wave Approximation to the Shallow Water Equations: Computational Approach
Collier, Nathan
2011-05-14
We discuss the use of time adaptivity applied to the one dimensional diffusive wave approximation to the shallow water equations. A simple and computationally economical error estimator is discussed which enables time-step size adaptivity. This robust adaptive time discretization corrects the initial time step size to achieve a user specified bound on the discretization error and allows time step size variations of several orders of magnitude. In particular, in the one dimensional results presented in this work feature a change of four orders of magnitudes for the time step over the entire simulation.
Cluster analysis for applications
Anderberg, Michael R
1973-01-01
Cluster Analysis for Applications deals with methods and various applications of cluster analysis. Topics covered range from variables and scales to measures of association among variables and among data units. Conceptual problems in cluster analysis are discussed, along with hierarchical and non-hierarchical clustering methods. The necessary elements of data analysis, statistics, cluster analysis, and computer implementation are integrated vertically to cover the complete path from raw data to a finished analysis.Comprised of 10 chapters, this book begins with an introduction to the subject o
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...
Conditional Density Approximations with Mixtures of Polynomials
DEFF Research Database (Denmark)
Varando, Gherardo; López-Cruz, Pedro L.; Nielsen, Thomas Dyhre
2015-01-01
Mixtures of polynomials (MoPs) are a non-parametric density estimation technique especially designed for hybrid Bayesian networks with continuous and discrete variables. Algorithms to learn one- and multi-dimensional (marginal) MoPs from data have recently been proposed. In this paper we introduce...... two methods for learning MoP approximations of conditional densities from data. Both approaches are based on learning MoP approximations of the joint density and the marginal density of the conditioning variables, but they differ as to how the MoP approximation of the quotient of the two densities...
Hardness and Approximation for Network Flow Interdiction
Chestnut, Stephen R.; Zenklusen, Rico
2015-01-01
In the Network Flow Interdiction problem an adversary attacks a network in order to minimize the maximum s-t-flow. Very little is known about the approximatibility of this problem despite decades of interest in it. We present the first approximation hardness, showing that Network Flow Interdiction and several of its variants cannot be much easier to approximate than Densest k-Subgraph. In particular, any $n^{o(1)}$-approximation algorithm for Network Flow Interdiction would imply an $n^{o(1)}...
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.
Schaefer, Andreas M.; Daniell, James E.; Wenzel, Friedemann
2017-07-01
Earthquake clustering is an essential part of almost any statistical analysis of spatial and temporal properties of seismic activity. The nature of earthquake clusters and subsequent declustering of earthquake catalogues plays a crucial role in determining the magnitude-dependent earthquake return period and its respective spatial variation for probabilistic seismic hazard assessment. This study introduces the Smart Cluster Method (SCM), a new methodology to identify earthquake clusters, which uses an adaptive point process for spatio-temporal cluster identification. It utilises the magnitude-dependent spatio-temporal earthquake density to adjust the search properties, subsequently analyses the identified clusters to determine directional variation and adjusts its search space with respect to directional properties. In the case of rapid subsequent ruptures like the 1992 Landers sequence or the 2010-2011 Darfield-Christchurch sequence, a reclassification procedure is applied to disassemble subsequent ruptures using near-field searches, nearest neighbour classification and temporal splitting. The method is capable of identifying and classifying earthquake clusters in space and time. It has been tested and validated using earthquake data from California and New Zealand. A total of more than 1500 clusters have been found in both regions since 1980 with M m i n = 2.0. Utilising the knowledge of cluster classification, the method has been adjusted to provide an earthquake declustering algorithm, which has been compared to existing methods. Its performance is comparable to established methodologies. The analysis of earthquake clustering statistics lead to various new and updated correlation functions, e.g. for ratios between mainshock and strongest aftershock and general aftershock activity metrics.
Interstellar Extinction in 20 Open Star Clusters
Rangwal, Geeta; Yadav, R. K. S.; Durgapal, Alok K.; Bisht, D.
2017-12-01
The interstellar extinction law in 20 open star clusters namely, Berkeley 7, Collinder 69, Hogg 10, NGC 2362, Czernik 43, NGC 6530, NGC 6871, Bochum 10, Haffner 18, IC 4996, NGC 2384, NGC 6193, NGC 6618, NGC 7160, Collinder 232, Haffner 19, NGC 2401, NGC 6231, NGC 6823, and NGC 7380 have been studied in the optical and near-IR wavelength ranges. The difference between maximum and minimum values of E(B - V) indicates the presence of non-uniform extinction in all the clusters except Collinder 69, NGC 2362, and NGC 2384. The colour excess ratios are consistent with a normal extinction law for the clusters NGC 6823, Haffner 18, Haffner 19, NGC 7160, NGC 6193, NGC 2401, NGC 2384, NGC 6871, NGC 7380, Berkeley 7, Collinder 69, and IC 4996. We have found that the differential colour-excess ΔE(B - V), which may be due to the occurrence of dust and gas inside the clusters, decreases with the age of the clusters. A spatial variation of colour excess is found in NGC 6193 in the sense that it decreases from east to west in the cluster region. For the clusters Berkeley 7, NGC 7380, and NGC 6871, a dependence of colour excess E(B - V) with spectral class and luminosity is observed. Eight stars in Collinder 232, four stars in NGC 6530, and one star in NGC 6231 have excess flux in near-IR. This indicates that these stars may have circumstellar material around them.
Taamneh, Madhar; Taamneh, Salah; Alkheder, Sharaf
2017-09-01
Artificial neural networks (ANNs) have been widely used in predicting the severity of road traffic crashes. All available information about previously occurred accidents is typically used for building a single prediction model (i.e., classifier). Too little attention has been paid to the differences between these accidents, leading, in most cases, to build less accurate predictors. Hierarchical clustering is a well-known clustering method that seeks to group data by creating a hierarchy of clusters. Using hierarchical clustering and ANNs, a clustering-based classification approach for predicting the injury severity of road traffic accidents was proposed. About 6000 road accidents occurred over a six-year period from 2008 to 2013 in Abu Dhabi were used throughout this study. In order to reduce the amount of variation in data, hierarchical clustering was applied on the data set to organize it into six different forms, each with different number of clusters (i.e., clusters from 1 to 6). Two ANN models were subsequently built for each cluster of accidents in each generated form. The first model was built and validated using all accidents (training set), whereas only 66% of the accidents were used to build the second model, and the remaining 34% were used to test it (percentage split). Finally, the weighted average accuracy was computed for each type of models in each from of data. The results show that when testing the models using the training set, clustering prior to classification achieves (11%-16%) more accuracy than without using clustering, while the percentage split achieves (2%-5%) more accuracy. The results also suggest that partitioning the accidents into six clusters achieves the best accuracy if both types of models are taken into account.
On the distortion of properties of galaxy cluster
International Nuclear Information System (INIS)
Fesenko, B.I.
1979-01-01
The supposition is substantiated that most of Abell clusters with population of 50 and more members are false clusters. Some of them may contain, as peculiar nuclei, the real clusters with the number of members from ten to 25 within the range of apparent magnitudes from m 3 to m 3 +2, where m 3 is an apparent magnitude of the galaxy which is third in brightness. The rest members of false clusters are galaxies of front and rare backgrounds. The algorithm for galaxy cluster discrimination used by Abell is shown to promote selection of the real clusters with rho < approximately 25 in which region the number of the background galaxies is considerably increased as compared to other regions of the sky. A systematic and substantial underestimation of the role of such galaxies destorts the results of the cluster structures and dynamics analysis. False clusters are surprisingly well camouflaged as real clusters: when passing to more faint galaxies, the number of the seeming members grows faster than in the ambient field; the difference in angular diameters of false clusters distinctly reflects the difference in average distances of these galaxies; dispersion in velocity of false cluster members comparatively slightly depends on the average distance to an observer, and absolute magnitudes of the brightnesses of galaxies have small dispersion, as in real clusters
Following the pioneering discovery of alpha clustering and of molecular resonances, the field of nuclear clustering is today one of those domains of heavy-ion nuclear physics that faces the greatest challenges, yet also contains the greatest opportunities. After many summer schools and workshops, in particular over the last decade, the community of nuclear molecular physicists has decided to collaborate in producing a comprehensive collection of lectures and tutorial reviews covering the field. This third volume follows the successful Lect. Notes Phys. 818 (Vol. 1) and 848 (Vol. 2), and comprises six extensive lectures covering the following topics: - Gamma Rays and Molecular Structure - Faddeev Equation Approach for Three Cluster Nuclear Reactions - Tomography of the Cluster Structure of Light Nuclei Via Relativistic Dissociation - Clustering Effects Within the Dinuclear Model : From Light to Hyper-heavy Molecules in Dynamical Mean-field Approach - Clusterization in Ternary Fission - Clusters in Light N...
Lawson, Andrew B
2002-01-01
Research has generated a number of advances in methods for spatial cluster modelling in recent years, particularly in the area of Bayesian cluster modelling. Along with these advances has come an explosion of interest in the potential applications of this work, especially in epidemiology and genome research. In one integrated volume, this book reviews the state-of-the-art in spatial clustering and spatial cluster modelling, bringing together research and applications previously scattered throughout the literature. It begins with an overview of the field, then presents a series of chapters that illuminate the nature and purpose of cluster modelling within different application areas, including astrophysics, epidemiology, ecology, and imaging. The focus then shifts to methods, with discussions on point and object process modelling, perfect sampling of cluster processes, partitioning in space and space-time, spatial and spatio-temporal process modelling, nonparametric methods for clustering, and spatio-temporal ...
Clusters and how to make it work : Cluster Strategy Toolkit
Manickam, Anu; van Berkel, Karel
2014-01-01
Clusters are the magic answer to regional economic development. Firms in clusters are more innovative; cluster policy dominates EU policy; ‘top-sectors’ and excellence are the choice of national policy makers; clusters are ‘in’. But, clusters are complex, clusters are ‘messy’; there is no clear
Multilevel weighted least squares polynomial approximation
Haji-Ali, Abdul-Lateef; Nobile, Fabio; Tempone, Raul; Wolfers, Sö ren
2017-01-01
, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose
Low Rank Approximation Algorithms, Implementation, Applications
Markovsky, Ivan
2012-01-01
Matrix low-rank approximation is intimately related to data modelling; a problem that arises frequently in many different fields. Low Rank Approximation: Algorithms, Implementation, Applications is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory. Applications described include: system and control theory: approximate realization, model reduction, output error, and errors-in-variables identification; signal processing: harmonic retrieval, sum-of-damped exponentials, finite impulse response modeling, and array processing; machine learning: multidimensional scaling and recommender system; computer vision: algebraic curve fitting and fundamental matrix estimation; bioinformatics for microarray data analysis; chemometrics for multivariate calibration; ...
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.
Euclidean shortest paths exact or approximate algorithms
Li, Fajie
2014-01-01
This book reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. The coverage includes mathematical proofs for many of the given statements.
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)
Approximation for the adjoint neutron spectrum
International Nuclear Information System (INIS)
Suster, Luis Carlos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da
2002-01-01
The proposal of this work is the determination of an analytical approximation which is capable to reproduce the adjoint neutron flux for the energy range of the narrow resonances (NR). In a previous work we developed a method for the calculation of the adjoint spectrum which was calculated from the adjoint neutron balance equations, that were obtained by the collision probabilities method, this method involved a considerable quantity of numerical calculation. In the analytical method some approximations were done, like the multiplication of the escape probability in the fuel by the adjoint flux in the moderator, and after these approximations, taking into account the case of the narrow resonances, were substituted in the adjoint neutron balance equation for the fuel, resulting in an analytical approximation for the adjoint flux. The results obtained in this work were compared to the results generated with the reference method, which demonstrated a good and precise results for the adjoint neutron flux for the narrow resonances. (author)
Saddlepoint approximation methods in financial engineering
Kwok, Yue Kuen
2018-01-01
This book summarizes recent advances in applying saddlepoint approximation methods to financial engineering. It addresses pricing exotic financial derivatives and calculating risk contributions to Value-at-Risk and Expected Shortfall in credit portfolios under various default correlation models. These standard problems involve the computation of tail probabilities and tail expectations of the corresponding underlying state variables. The text offers in a single source most of the saddlepoint approximation results in financial engineering, with different sets of ready-to-use approximation formulas. Much of this material may otherwise only be found in original research publications. The exposition and style are made rigorous by providing formal proofs of most of the results. Starting with a presentation of the derivation of a variety of saddlepoint approximation formulas in different contexts, this book will help new researchers to learn the fine technicalities of the topic. It will also be valuable to quanti...
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.
Pion-nucleus cross sections approximation
International Nuclear Information System (INIS)
Barashenkov, V.S.; Polanski, A.; Sosnin, A.N.
1990-01-01
Analytical approximation of pion-nucleus elastic and inelastic interaction cross-section is suggested, with could be applied in the energy range exceeding several dozens of MeV for nuclei heavier than beryllium. 3 refs.; 4 tabs
APPROXIMATE DEVELOPMENTS FOR SURFACES OF REVOLUTION
Directory of Open Access Journals (Sweden)
Mădălina Roxana Buneci
2016-12-01
Full Text Available The purpose of this paper is provide a set of Maple procedures to construct approximate developments of a general surface of revolution generalizing the well-known gore method for sphere
Steepest descent approximations for accretive operator equations
International Nuclear Information System (INIS)
Chidume, C.E.
1993-03-01
A necessary and sufficient condition is established for the strong convergence of the steepest descent approximation to a solution of equations involving quasi-accretive operators defined on a uniformly smooth Banach space. (author). 49 refs
Seismic wave extrapolation using lowrank symbol approximation
Fomel, Sergey
2012-04-30
We consider the problem of constructing a wave extrapolation operator in a variable and possibly anisotropic medium. Our construction involves Fourier transforms in space combined with the help of a lowrank approximation of the space-wavenumber wave-propagator matrix. A lowrank approximation implies selecting a small set of representative spatial locations and a small set of representative wavenumbers. We present a mathematical derivation of this method, a description of the lowrank approximation algorithm and numerical examples that confirm the validity of the proposed approach. Wave extrapolation using lowrank approximation can be applied to seismic imaging by reverse-time migration in 3D heterogeneous isotropic or anisotropic media. © 2012 European Association of Geoscientists & Engineers.
An overview on Approximate Bayesian computation*
Directory of Open Access Journals (Sweden)
Baragatti Meïli
2014-01-01
Full Text Available Approximate Bayesian computation techniques, also called likelihood-free methods, are one of the most satisfactory approach to intractable likelihood problems. This overview presents recent results since its introduction about ten years ago in population genetics.
Approximate Computing Techniques for Iterative Graph Algorithms
Energy Technology Data Exchange (ETDEWEB)
Panyala, Ajay R.; Subasi, Omer; Halappanavar, Mahantesh; Kalyanaraman, Anantharaman; Chavarria Miranda, Daniel G.; Krishnamoorthy, Sriram
2017-12-18
Approximate computing enables processing of large-scale graphs by trading off quality for performance. Approximate computing techniques have become critical not only due to the emergence of parallel architectures but also the availability of large scale datasets enabling data-driven discovery. Using two prototypical graph algorithms, PageRank and community detection, we present several approximate computing heuristics to scale the performance with minimal loss of accuracy. We present several heuristics including loop perforation, data caching, incomplete graph coloring and synchronization, and evaluate their efficiency. We demonstrate performance improvements of up to 83% for PageRank and up to 450x for community detection, with low impact of accuracy for both the algorithms. We expect the proposed approximate techniques will enable scalable graph analytics on data of importance to several applications in science and their subsequent adoption to scale similar graph algorithms.
THE LIFETIME AND POWERS OF FR IIs IN GALAXY CLUSTERS
Energy Technology Data Exchange (ETDEWEB)
Antognini, Joe; Bird, Jonathan; Martini, Paul, E-mail: antognini@astronomy.ohio-state.edu, E-mail: bird@astronomy.ohio-state.edu, E-mail: martini@astronomy.ohio-state.edu [Department of Astronomy, Ohio State University, 140 W 18th Avenue, Columbus, OH 43210 (United States)
2012-09-10
We have identified and studied a sample of 151 FR IIs found in brightest cluster galaxies (BCGs) in the MaxBCG cluster catalog with data from FIRST and NVSS. We have compared the radio luminosities and projected lengths of these FR IIs to the projected length distribution of a range of mock catalogs generated by an FR II model and estimate the FR II lifetime to be 1.9 Multiplication-Sign 10{sup 8} yr. The uncertainty in the lifetime calculation is a factor of two, primarily due to uncertainties in the intracluster medium (ICM) density and the FR II axial ratio. We furthermore measure the jet power distribution of FR IIs in BCGs and find that it is well described by a log-normal distribution with a median power of 1.1 Multiplication-Sign 10{sup 37} W and a coefficient of variation of 2.2. These jet powers are nearly linearly related to the observed luminosities, and this relation is steeper than many other estimates, although it is dependent on the jet model. We investigate correlations between FR II and cluster properties and find that galaxy luminosity is correlated with jet power. This implies that jet power is also correlated with black hole mass, as the stellar luminosity of a BCG should be a good proxy for its spheroid mass and therefore the black hole mass. Jet power, however, is not correlated with cluster richness, nor is FR II lifetime strongly correlated with any cluster properties. We calculate the enthalpy of the lobes to examine the impact of the FR IIs on the ICM and find that heating due to adiabatic expansion is too small to offset radiative cooling by a factor of at least six. In contrast, the jet power is approximately an order of magnitude larger than required to counteract cooling. We conclude that if feedback from FR IIs offsets cooling of the ICM, then heating must be primarily due to another mechanism associated with FR II expansion.
Size dependent magnetism of mass selected deposited transition metal clusters
International Nuclear Information System (INIS)
Lau, T.
2002-05-01
The size dependent magnetic properties of small iron clusters deposited on ultrathin Ni/Cu(100) films have been studied with circularly polarised synchrotron radiation. For X-ray magnetic circular dichroism studies, the magnetic moments of size selected clusters were aligned perpendicular to the sample surface. Exchange coupling of the clusters to the ultrathin Ni/Cu(100) film determines the orientation of their magnetic moments. All clusters are coupled ferromagnetically to the underlayer. With the use of sum rules, orbital and spin magnetic moments as well as their ratios have been extracted from X-ray magnetic circular dichroism spectra. The ratio of orbital to spin magnetic moments varies considerably as a function of cluster size, reflecting the dependence of magnetic properties on cluster size and geometry. These variations can be explained in terms of a strongly size dependent orbital moment. Both orbital and spin magnetic moments are significantly enhanced in small clusters as compared to bulk iron, although this effect is more pronounced for the spin moment. Magnetic properties of deposited clusters are governed by the interplay of cluster specific properties on the one hand and cluster-substrate interactions on the other hand. Size dependent variations of magnetic moments are modified upon contact with the substrate. (orig.)
Approximative solutions of stochastic optimization problem
Czech Academy of Sciences Publication Activity Database
Lachout, Petr
2010-01-01
Roč. 46, č. 3 (2010), s. 513-523 ISSN 0023-5954 R&D Projects: GA ČR GA201/08/0539 Institutional research plan: CEZ:AV0Z10750506 Keywords : Stochastic optimization problem * sensitivity * approximative solution Subject RIV: BA - General Mathematics Impact factor: 0.461, year: 2010 http://library.utia.cas.cz/separaty/2010/SI/lachout-approximative solutions of stochastic optimization problem.pdf
Lattice quantum chromodynamics with approximately chiral fermions
Energy Technology Data Exchange (ETDEWEB)
Hierl, Dieter
2008-05-15
In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the {theta}{sup +} pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)
An approximate analytical approach to resampling averages
DEFF Research Database (Denmark)
Malzahn, Dorthe; Opper, M.
2004-01-01
Using a novel reformulation, we develop a framework to compute approximate resampling data averages analytically. The method avoids multiple retraining of statistical models on the samples. Our approach uses a combination of the replica "trick" of statistical physics and the TAP approach for appr...... for approximate Bayesian inference. We demonstrate our approach on regression with Gaussian processes. A comparison with averages obtained by Monte-Carlo sampling shows that our method achieves good accuracy....
Stochastic quantization and mean field approximation
International Nuclear Information System (INIS)
Jengo, R.; Parga, N.
1983-09-01
In the context of the stochastic quantization we propose factorized approximate solutions for the Fokker-Planck equation for the XY and Zsub(N) spin systems in D dimensions. The resulting differential equation for a factor can be solved and it is found to give in the limit of t→infinity the mean field or, in the more general case, the Bethe-Peierls approximation. (author)
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
Magnus approximation in the adiabatic picture
International Nuclear Information System (INIS)
Klarsfeld, S.; Oteo, J.A.
1991-01-01
A simple approximate nonperturbative method is described for treating time-dependent problems that works well in the intermediate regime far from both the sudden and the adiabatic limits. The method consists of applying the Magnus expansion after transforming to the adiabatic basis defined by the eigenstates of the instantaneous Hamiltonian. A few exactly soluble examples are considered in order to assess the domain of validity of the approximation. (author) 32 refs., 4 figs
Lattice quantum chromodynamics with approximately chiral fermions
International Nuclear Information System (INIS)
Hierl, Dieter
2008-05-01
In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the Θ + pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)
Direct application of Padé approximant for solving nonlinear differential equations.
Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Garcia-Gervacio, Jose Luis; Huerta-Chua, Jesus; Morales-Mendoza, Luis Javier; Gonzalez-Lee, Mario
2014-01-01
This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. 34L30.
Approximating centrality in evolving graphs: toward sublinearity
Priest, Benjamin W.; Cybenko, George
2017-05-01
The identification of important nodes is a ubiquitous problem in the analysis of social networks. Centrality indices (such as degree centrality, closeness centrality, betweenness centrality, PageRank, and others) are used across many domains to accomplish this task. However, the computation of such indices is expensive on large graphs. Moreover, evolving graphs are becoming increasingly important in many applications. It is therefore desirable to develop on-line algorithms that can approximate centrality measures using memory sublinear in the size of the graph. We discuss the challenges facing the semi-streaming computation of many centrality indices. In particular, we apply recent advances in the streaming and sketching literature to provide a preliminary streaming approximation algorithm for degree centrality utilizing CountSketch and a multi-pass semi-streaming approximation algorithm for closeness centrality leveraging a spanner obtained through iteratively sketching the vertex-edge adjacency matrix. We also discuss possible ways forward for approximating betweenness centrality, as well as spectral measures of centrality. We provide a preliminary result using sketched low-rank approximations to approximate the output of the HITS algorithm.
International Nuclear Information System (INIS)
Zhang, Jianbao; Ma, Zhongjun; Chen, Guanrong
2014-01-01
All edges in the classical Watts and Strogatz's small-world network model are unweighted and cooperative (positive). By introducing competitive (negative) inter-cluster edges and assigning edge weights to mimic more realistic networks, this paper develops a modified model which possesses co-competitive weighted couplings and cluster structures while maintaining the common small-world network properties of small average shortest path lengths and large clustering coefficients. Based on theoretical analysis, it is proved that the new model with inter-cluster co-competition balance has an important dynamical property of robust cluster synchronous pattern formation. More precisely, clusters will neither merge nor split regardless of adding or deleting nodes and edges, under the condition of inter-cluster co-competition balance. Numerical simulations demonstrate the robustness of the model against the increase of the coupling strength and several topological variations
Zhang, Jianbao; Ma, Zhongjun; Chen, Guanrong
2014-06-01
All edges in the classical Watts and Strogatz's small-world network model are unweighted and cooperative (positive). By introducing competitive (negative) inter-cluster edges and assigning edge weights to mimic more realistic networks, this paper develops a modified model which possesses co-competitive weighted couplings and cluster structures while maintaining the common small-world network properties of small average shortest path lengths and large clustering coefficients. Based on theoretical analysis, it is proved that the new model with inter-cluster co-competition balance has an important dynamical property of robust cluster synchronous pattern formation. More precisely, clusters will neither merge nor split regardless of adding or deleting nodes and edges, under the condition of inter-cluster co-competition balance. Numerical simulations demonstrate the robustness of the model against the increase of the coupling strength and several topological variations.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Jianbao [School of Science, Hangzhou Dianzi University, Hangzhou 310018 (China); Ma, Zhongjun, E-mail: mzj1234402@163.com [School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004 (China); Chen, Guanrong [Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong (China)
2014-06-15
All edges in the classical Watts and Strogatz's small-world network model are unweighted and cooperative (positive). By introducing competitive (negative) inter-cluster edges and assigning edge weights to mimic more realistic networks, this paper develops a modified model which possesses co-competitive weighted couplings and cluster structures while maintaining the common small-world network properties of small average shortest path lengths and large clustering coefficients. Based on theoretical analysis, it is proved that the new model with inter-cluster co-competition balance has an important dynamical property of robust cluster synchronous pattern formation. More precisely, clusters will neither merge nor split regardless of adding or deleting nodes and edges, under the condition of inter-cluster co-competition balance. Numerical simulations demonstrate the robustness of the model against the increase of the coupling strength and several topological variations.
Variational principles for the projected breakup amplitude
International Nuclear Information System (INIS)
Hahn, Y.
1976-01-01
Two alternate forms of variational principles for the breakup amplitude describing the two- to three-cluster transition are derived such that all the integrals involved in the intermediate stages are well defined. The first form contains a trial Green's function with which both the initial and final state trial wave functions are constructed. The earlier form of the Kohn-type variational principle derived by Lieber, Rosenberg, and Spruch is recovered, however, when this connection between the trial functions is removed. The second form of the variational principle is derived by projecting out from the trial functions all the open channel components which correspond to the two-cluster structures including the rearrangement channels. The remaining part of the wave functions describes the channels with three-cluster structures, and the integrals involving this part are then mathematically well defined
Boundary Value Problems and Approximate Solutions
African Journals Online (AJOL)
Tadesse
Department of Mathematics, College of Natural and Computational Scineces, Mekelle ..... In this section, the Variational Iteration Method is applied to different forms of .... Some problems in non-Newtonian fluid mechanics, Ph.D. thesis, Wales.
P3-approximation for gaseous media and vacuum
International Nuclear Information System (INIS)
Raevskaya, V.E.
1986-01-01
The problems connected with calculation of neutron field in a fuel assembly (FA) of a gas cooled reactor are discussed. The problem of P 3 -approximation applicability for the description of neutron fields in closed vacuum and gas volumes is considered. Under the assumption of the field azimuthal symmetry derived are the formulas for determination of the field in cylindrical vacuum layer of multizone FA as well as the solution for the cluster central zone, where the rods with vacuum between them are placed. Because of the finiteness of voids surrounded by medium it is possible to use the condition of neutron flux density continuity as the boundary conditions for the interface with vacuum. For representation of boundary conditions for rod surfaces and the cluster central zone with vacuum the addition theorems for the field in vacuum between the roads are derived. The formulas for mean neutron fluxes in vacuum cylindrical layer and in vacuum between rods are derived. The numerical calculations performed according to various programs confirmed the validity of the derived formulas
Agricultural Clusters in the Netherlands
Schouten, M.A.; Heijman, W.J.M.
2012-01-01
Michael Porter was the first to use the term cluster in an economic context. He introduced the term in The Competitive Advantage of Nations (1990). The term cluster is also known as business cluster, industry cluster, competitive cluster or Porterian cluster. This article aims at determining and
Momentum-space cluster dual-fermion method
Iskakov, Sergei; Terletska, Hanna; Gull, Emanuel
2018-03-01
Recent years have seen the development of two types of nonlocal extensions to the single-site dynamical mean field theory. On one hand, cluster approximations, such as the dynamical cluster approximation, recover short-range momentum-dependent correlations nonperturbatively. On the other hand, diagrammatic extensions, such as the dual-fermion theory, recover long-ranged corrections perturbatively. The correct treatment of both strong short-ranged and weak long-ranged correlations within the same framework is therefore expected to lead to a quick convergence of results, and offers the potential of obtaining smooth self-energies in nonperturbative regimes of phase space. In this paper, we present an exact cluster dual-fermion method based on an expansion around the dynamical cluster approximation. Unlike previous formulations, our method does not employ a coarse-graining approximation to the interaction, which we show to be the leading source of error at high temperature, and converges to the exact result independently of the size of the underlying cluster. We illustrate the power of the method with results for the second-order cluster dual-fermion approximation to the single-particle self-energies and double occupancies.
Open source clustering software.
de Hoon, M J L; Imoto, S; Nolan, J; Miyano, S
2004-06-12
We have implemented k-means clustering, hierarchical clustering and self-organizing maps in a single multipurpose open-source library of C routines, callable from other C and C++ programs. Using this library, we have created an improved version of Michael Eisen's well-known Cluster program for Windows, Mac OS X and Linux/Unix. In addition, we generated a Python and a Perl interface to the C Clustering Library, thereby combining the flexibility of a scripting language with the speed of C. The C Clustering Library and the corresponding Python C extension module Pycluster were released under the Python License, while the Perl module Algorithm::Cluster was released under the Artistic License. The GUI code Cluster 3.0 for Windows, Macintosh and Linux/Unix, as well as the corresponding command-line program, were released under the same license as the original Cluster code. The complete source code is available at http://bonsai.ims.u-tokyo.ac.jp/mdehoon/software/cluster. Alternatively, Algorithm::Cluster can be downloaded from CPAN, while Pycluster is also available as part of the Biopython distribution.
What semi-inclusive data say about clusters
International Nuclear Information System (INIS)
Arneodo, A.; Plaut, G.
1976-01-01
A global analysis of inclusive high-energy multi-particle production data in the cluster model framework is extended to semi-inclusive data. The cluster model embodies leading particle effects and kinematical constraints, which are shown to be of great importance. It appears that models with light clusters decaying on average into approximately equal to 2 charged particles, with a rapidity width delta approximately equal to 0.6 - 0.7 and a distribution much narrower than a Poisson-type, allow one to fit in a nice way both inclusive and semi-inclusive data. It is pointed out that the most constraining semi-inclusive data are those regarding longitudinal correlations, which definitely exclude heavy cluster models, whereas the data on zone characteristics only bear out that a non-negligible percentage of clusters have to carry an electric charge. (Auth.)
Dynamical evolution in clusters of galaxies with low-frequency radio emission
International Nuclear Information System (INIS)
Guthrie, B.N.G.
1977-01-01
Clusters of galaxies in which radio emission at low frequencies ( approximately 10 9 yr). Confinement would probably occur for radio sources associated with bright galaxies in the cores of clusters and cD galaxies in clusters. However, cD galaxies may have recurrent radio outbursts so that steep spectra are not always observed. (Auth.)
Energy Technology Data Exchange (ETDEWEB)
Song, Zhaoyu [Tianjin Key Laboratory of Applied Catalysis Science and Technology, School of Chemical Engineering, Tianjin University, Tianjin 300354 (China); Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin 300354 (China); Shi, Xiangpeng [Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin 300354 (China); Key Laboratory of Green Chemical Technology of Ministry of Education, School of Chemical Engineering, Tianjin University, Tianjin 300354 (China); Ning, Hongyan; Liu, Guilong; Zhong, Huixian [Tianjin Key Laboratory of Applied Catalysis Science and Technology, School of Chemical Engineering, Tianjin University, Tianjin 300354 (China); Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin 300354 (China); Liu, Yuan, E-mail: yuanliu@tju.edu.cn [Tianjin Key Laboratory of Applied Catalysis Science and Technology, School of Chemical Engineering, Tianjin University, Tianjin 300354 (China); Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin 300354 (China)
2017-05-31
Highlights: • La{sub 0.95}Ce{sub 0.05}Co{sub 0.7}Cu{sub 0.3}O{sub 3}/ZrO{sub 2} catalyst has showed good activity and high selectivity to ethanol. • After reaction for 1000 h, the catalyst was covered by a membrane-like coating. • Carbon deposition is the main reason for the deactivation of the catalyst. - Abstract: A new scheme was proposed to intensify interactions between copper with cobalt and between Cu−Co with the promoters, namely, the ions of copper, cobalt, lanthanum and cerium were confined into La{sub 0.95}Ce{sub 0.05}Co{sub 0.7}Cu{sub 0.3}O{sub 3} with perovskite structure and were supported on zirconia. The catalyst was prepared by impregnation method and used for ethanol synthesis (ES) from syngas and was characterized by using XRD, TG, BET, XPS, ICP-MS and TEM techniques. La{sub 0.95}Ce{sub 0.05}Co{sub 0.7}Cu{sub 0.3}O{sub 3}/ZrO{sub 2} showed very good catalytic performance with selectivity to total alcohols higher than 60% and selectivity to ethanol about 50% in the total alcohols. After reduction, clusters composed of Cu−Co alloy nanoparticles, ceria and lanthanum oxide was formed and loaded on zirconia. Investigation on the variation of the catalyst structure with reaction time showed that with the reaction going on, the clusters spread over the surface of ZrO{sub 2} and at last, all the clusters fused together to form a membrane loaded on the ZrO{sub 2} and the whole catalyst was covered by a membrane-like coating formed by Co{sub 2}C. The characterization results showed that the carbon deposition was the main reason for the deactivation of La{sub 0.95}Ce{sub 0.05}Co{sub 0.7}Cu{sub 0.3}O{sub 3}/ZrO{sub 2} catalyst. This catalyst design scheme could be extended for preparing a lot of catalyst for many reactions.
Global Clusters as Laboratories for Stellar Evolution
Catelan, Marcio; Valcarce, Aldo A. R.; Sweigart, Allen V.
2010-01-01
Globular clusters have long been considered the closest approximation to a physicist's laboratory in astrophysics, and as such a near-ideal laboratory for (low-mass) stellar evolution, However, recent observations have cast a shadow on this long-standing paradigm, suggesting the presence of multiple populations with widely different abundance patterns, and - crucially - with widely different helium abundances as welL In this review we discuss which features of the Hertzsprung-Russell diagram may be used as helium abundance indicators, and present an overview of available constraints on the helium abundance in globular clusters,
The Age of the Inner Halo Globular Cluster NGC 6652
Chaboyer, Brian; Sarajedini, Ata; Armandroff, Taft E.
2000-01-01
HST (V,I) photometry has been obtained for the inner halo globular cluster NGC 6652. The photometry reaches approximately 4 mag below the turn-off and includes a well populated horizontal branch. This cluster is located close to the Galactic center at a galactocentric distance of approximately 2.0 kpc with a reddening of E(V-I) = 0.15 +/- 0.02 and has a metallicity of [Fe/H] approximately -0.85. Based upon Delta(V) between the point on the sub-giant branch which is 0.05 mag redder than the tu...