Anisotropic evolution of 5D Friedmann-Robertson-Walker spacetime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Middleton, Chad A.; Stanley, Ethan

2011-10-15

We examine the time evolution of the five-dimensional Einstein field equations subjected to a flat, anisotropic Robertson-Walker metric, where the 3D and higher-dimensional scale factors are allowed to dynamically evolve at different rates. By adopting equations of state relating the 3D and higher-dimensional pressures to the density, we obtain an exact expression relating the higher-dimensional scale factor to a function of the 3D scale factor. This relation allows us to write the Friedmann-Robertson-Walker field equations exclusively in terms of the 3D scale factor, thus yielding a set of 4D effective Friedmann-Robertson-Walker field equations. We examine the effective field equations inmore » the general case and obtain an exact expression relating a function of the 3D scale factor to the time. This expression involves a hypergeometric function and cannot, in general, be inverted to yield an analytical expression for the 3D scale factor as a function of time. When the hypergeometric function is expanded for small and large arguments, we obtain a generalized treatment of the dynamical compactification scenario of Mohammedi [Phys. Rev. D 65, 104018 (2002)] and the 5D vacuum solution of Chodos and Detweiler [Phys. Rev. D 21, 2167 (1980)], respectively. By expanding the hypergeometric function near a branch point, we obtain the perturbative solution for the 3D scale factor in the small time regime. This solution exhibits accelerated expansion, which, remarkably, is independent of the value of the 4D equation of state parameter w. This early-time epoch of accelerated expansion arises naturally out of the anisotropic evolution of 5D spacetime when the pressure in the extra dimension is negative and offers a possible alternative to scalar field inflationary theory.« less

Modeling Uncertainty in Steady State Diffusion Problems via Generalized Polynomial Chaos

DTIC Science & Technology

2002-07-25

Some basic hypergeometric polynomials that generalize Jacobi polynomials . Memoirs Amer. Math. Soc., AMS... orthogonal polynomial functionals from the Askey scheme, as a generalization of the original polynomial chaos idea of Wiener (1938). A Galerkin projection...1) by generalized polynomial chaos expansion, where the uncertainties can be introduced through κ, f , or g, or some combinations. It is worth

Generalized spheroidal wave equation and limiting cases

NASA Astrophysics Data System (ADS)

Figueiredo, B. D. Bonorino

2007-01-01

We find sets of solutions to the generalized spheroidal wave equation (GSWE) or, equivalently, to the confluent Heun equation. Each set is constituted by three solutions, one given by a series of ascending powers of the independent variable, and the others by series of regular and irregular confluent hypergeometric functions. For a fixed set, the solutions converge over different regions of the complex plane but present series coefficients proportional to each other. These solutions for the GSWE afford solutions to a double-confluent Heun equation by a taking-limit process due to Leaver. [E. W. Leaver, J. Math. Phys. 27, 1238 (1986)]. Another procedure, called Whittaker-Ince limit [B. D. Figueiredo, J. Math. Phys. 46, 113503 (2005)], provides solutions in series of powers and Bessel functions for two other equations with a different type of singularity at infinity. In addition, new solutions are obtained for the Whittaker-Hill and Mathieu equations [F. M. Arscott, Proc. R. Soc. Edinburg A67, 265 (1967)] by considering these as special cases of both the confluent and double-confluent Heun equations. In particular, we find that each of the Lindemann-Stieltjes solutions for the Mathieu equation [E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, Cambridge University Press (1945)] is associated with two expansions in series of Bessel functions. We also discuss a set of solutions in series of hypergeometric and confluent hypergeometric functions for the GSWE and use their Leaver limits to obtain infinite-series solutions for the Schrödinger equation with an asymmetric double-Morse potential. Finally, the possibility of extending the solutions of the GSWE to the general Heun equation is briefly discussed.

Stochastic Modeling of Flow-Structure Interactions using Generalized Polynomial Chaos

DTIC Science & Technology

2001-09-11

Some basic hypergeometric polynomials that generalize Jacobi polynomials . Memoirs Amer. Math. Soc...scheme, which is represented as a tree structure in figure 1 (following [24]), classifies the hypergeometric orthogonal polynomials and indicates the...2F0(1) 2F0(0) Figure 1: The Askey scheme of orthogonal polynomials The orthogonal polynomials associated with the generalized polynomial chaos,

On mini-superspace limit of boundary three-point function in Liouville field theory

NASA Astrophysics Data System (ADS)

Apresyan, Elena; Sarkissian, Gor

2017-12-01

We study the mini-superspace semiclassical limit of the boundary three-point function in the Liouville field theory. We compute also matrix elements for the Morse potential quantum mechanics. An exact agreement between the former and the latter is found. We show that both of them are given by the generalized hypergeometric functions.

Dirac-Kähler particle in Riemann spherical space: boson interpretation

NASA Astrophysics Data System (ADS)

Ishkhanyan, A. M.; Florea, O.; Ovsiyuk, E. M.; Red'kov, V. M.

2015-11-01

In the context of the composite boson interpretation, we construct the exact general solution of the Dirac--K\\"ahler equation for the case of the spherical Riemann space of constant positive curvature, for which due to the geometry itself one may expect to have a discrete energy spectrum. In the case of the minimal value of the total angular momentum, $j=0$, the radial equations are reduced to second-order ordinary differential equations, which are straightforwardly solved in terms of the hypergeometric functions. For non-zero values of the total angular momentum, however, the radial equations are reduced to a pair of complicated fourth-order differential equations. Employing the factorization approach, we derive the general solution of these equations involving four independent fundamental solutions written in terms of combinations of the hypergeometric functions. The corresponding discrete energy spectrum is then determined via termination of the involved hypergeometric series, resulting in quasi-polynomial wave-functions. The constructed solutions lead to notable observations when compared with those for the ordinary Dirac particle. The energy spectrum for the Dirac-K\\"ahler particle in spherical space is much more complicated. Its structure substantially differs from that for the Dirac particle since it consists of two paralleled energy level series each of which is twofold degenerate. Besides, none of the two separate series coincides with the series for the Dirac particle. Thus, the Dirac--K\\"ahler field cannot be interpreted as a system of four Dirac fermions. Additional arguments supporting this conclusion are discussed.

Dissociative Electron Attachment to Rovibrationally Excited Molecules

DTIC Science & Technology

1987-08-31

obtained in some recent papers.4’ - In Sec. IV of the present L,(0, (00 paper we will obtain some general recursion relations among where these matrix... general five-term From the generating function of Hermite polynomials , recursion relation (32) is obtained which is valid for the matrix elements of...for the generation of the functions for increasing 1. One convenient way to evaluate a Q, function is to write it in terms of Gaussian hypergeometric

On the solving of one type of problems of mathematical physics

NASA Astrophysics Data System (ADS)

Chebakova, V. J.; Gerasimov, A. V.; Kirpichnikov, A. P.

2016-11-01

A relationship between generalized hypergeometric functions of a special type and modified Bessel functions has been established. Using this relationship the solution of inhomogeneous differential equations of Bessel type containing even degrees of an independent variable in the right-hand part can be expressed in a form convenient for engineering and technical applications.

New formulae between Jacobi polynomials and some fractional Jacobi functions generalizing some connection formulae

NASA Astrophysics Data System (ADS)

Abd-Elhameed, W. M.

2017-07-01

In this paper, a new formula relating Jacobi polynomials of arbitrary parameters with the squares of certain fractional Jacobi functions is derived. The derived formula is expressed in terms of a certain terminating hypergeometric function of the type _4F3(1) . With the aid of some standard reduction formulae such as Pfaff-Saalschütz's and Watson's identities, the derived formula can be reduced in simple forms which are free of any hypergeometric functions for certain choices of the involved parameters of the Jacobi polynomials and the Jacobi functions. Some other simplified formulae are obtained via employing some computer algebra algorithms such as the algorithms of Zeilberger, Petkovsek and van Hoeij. Some connection formulae between some Jacobi polynomials are deduced. From these connection formulae, some other linearization formulae of Chebyshev polynomials are obtained. As an application to some of the introduced formulae, a numerical algorithm for solving nonlinear Riccati differential equation is presented and implemented by applying a suitable spectral method.

A Conditionally Integrable Bi-confluent Heun Potential Involving Inverse Square Root and Centrifugal Barrier Terms

NASA Astrophysics Data System (ADS)

Ishkhanyan, Tigran A.; Krainov, Vladimir P.; Ishkhanyan, Artur M.

2018-05-01

We present a conditionally integrable potential, belonging to the bi-confluent Heun class, for which the Schrödinger equation is solved in terms of the confluent hypergeometric functions. The potential involves an attractive inverse square root term x-1/2 with arbitrary strength and a repulsive centrifugal barrier core x-2 with the strength fixed to a constant. This is a potential well defined on the half-axis. Each of the fundamental solutions composing the general solution of the Schrödinger equation is written as an irreducible linear combination, with non-constant coefficients, of two confluent hypergeometric functions. We present the explicit solution in terms of the non-integer order Hermite functions of scaled and shifted argument and discuss the bound states supported by the potential. We derive the exact equation for the energy spectrum and approximate that by a highly accurate transcendental equation involving trigonometric functions. Finally, we construct an accurate approximation for the bound-state energy levels.

Plasma Dispersion Function for the Kappa Distribution

NASA Technical Reports Server (NTRS)

Podesta, John J.

2004-01-01

The plasma dispersion function is computed for a homogeneous isotropic plasma in which the particle velocities are distributed according to a Kappa distribution. An ordinary differential equation is derived for the plasma dispersion function and it is shown that the solution can be written in terms of Gauss' hypergeometric function. Using the extensive theory of the hypergeometric function, various mathematical properties of the plasma dispersion function are derived including symmetry relations, series expansions, integral representations, and closed form expressions for integer and half-integer values of K.

On square-integrability of solutions of the stationary Schrödinger equation for the quantum harmonic oscillator in two dimensional constant curvature spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Noguera, Norman, E-mail: norman.noguera@ucr.ac.cr; Rózga, Krzysztof, E-mail: krzysztof.rozga@upr.edu

In this work, one provides a justification of the condition that is usually imposed on the parameters of the hypergeometric equation, related to the solutions of the stationary Schrödinger equation for the harmonic oscillator in two-dimensional constant curvature spaces, in order to determine the solutions which are square-integrable. One proves that in case of negative curvature, it is a necessary condition of square integrability and in case of positive curvature, a necessary condition of regularity. The proof is based on the analytic continuation formulas for the hypergeometric function. It is observed also that the same is true in case ofmore » a slightly more general potential than the one for harmonic oscillator.« less

Riemann-Liouville Fractional Calculus of Certain Finite Class of Classical Orthogonal Polynomials

NASA Astrophysics Data System (ADS)

Malik, Pradeep; Swaminathan, A.

2010-11-01

In this work we consider certain class of classical orthogonal polynomials defined on the positive real line. These polynomials have their weight function related to the probability density function of F distribution and are finite in number up to orthogonality. We generalize these polynomials for fractional order by considering the Riemann-Liouville type operator on these polynomials. Various properties like explicit representation in terms of hypergeometric functions, differential equations, recurrence relations are derived.

Hypergeometric Gaussian beam and its propagation in turbulence

NASA Astrophysics Data System (ADS)

Eyyuboğlu, Halil Tanyer; Cai, Yangjian

2012-10-01

We study propagation characteristics of hypergeometric Gaussian beam in turbulence. In this context, we formulate the receiver plane intensity using extended Huygens-Fresnel integral. From the graphical results, it is seen that, after propagation, hypergeometric Gaussian will in general assume the shape of a dark hollow beam at topological charges other than zero. Increasing values of topological charge will make the beam broader with steeper walls. On the other hand, higher values of hollowness parameter will contract into a narrower shape. Raising the topological charge or the hollowness parameter individually will cause outer rings to appear. Both increased levels of turbulence and longer propagation distances will accelerate the beam evolution and help reach the final Gaussian shape sooner. At lower wavelengths, there will be less beam spreading.

Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Pöschl Teller Ginocchio potential wave functions

NASA Astrophysics Data System (ADS)

Michel, N.; Stoitsov, M. V.

2008-04-01

The fast computation of the Gauss hypergeometric function F12 with all its parameters complex is a difficult task. Although the F12 function verifies numerous analytical properties involving power series expansions whose implementation is apparently immediate, their use is thwarted by instabilities induced by cancellations between very large terms. Furthermore, small areas of the complex plane, in the vicinity of z=e, are inaccessible using F12 power series linear transformations. In order to solve these problems, a generalization of R.C. Forrey's transformation theory has been developed. The latter has been successful in treating the F12 function with real parameters. As in real case transformation theory, the large canceling terms occurring in F12 analytical formulas are rigorously dealt with, but by way of a new method, directly applicable to the complex plane. Taylor series expansions are employed to enter complex areas outside the domain of validity of power series analytical formulas. The proposed algorithm, however, becomes unstable in general when |a|, |b|, |c| are moderate or large. As a physical application, the calculation of the wave functions of the analytical Pöschl-Teller-Ginocchio potential involving F12 evaluations is considered. Program summaryProgram title: hyp_2F1, PTG_wf Catalogue identifier: AEAE_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAE_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 6839 No. of bytes in distributed program, including test data, etc.: 63 334 Distribution format: tar.gz Programming language: C++, Fortran 90 Computer: Intel i686 Operating system: Linux, Windows Word size: 64 bits Classification: 4.7 Nature of problem: The Gauss hypergeometric function F12, with all its parameters complex, is uniquely calculated in the frame of transformation theory with power series summations, thus providing a very fast algorithm. The evaluation of the wave functions of the analytical Pöschl-Teller-Ginocchio potential is treated as a physical application. Solution method: The Gauss hypergeometric function F12 verifies linear transformation formulas allowing consideration of arguments of a small modulus which then can be handled by a power series. They, however, give rise to indeterminate or numerically unstable cases, when b-a and c-a-b are equal or close to integers. They are properly dealt with through analytical manipulations of the Lanczos expression providing the Gamma function. The remaining zones of the complex plane uncovered by transformation formulas are dealt with Taylor expansions of the F12 function around complex points where linear transformations can be employed. The Pöschl-Teller-Ginocchio potential wave functions are calculated directly with F12 evaluations. Restrictions: The algorithm provides full numerical precision in almost all cases for |a|, |b|, and |c| of the order of one or smaller, but starts to be less precise or unstable when they increase, especially through a, b, and c imaginary parts. While it is possible to run the code for moderate or large |a|, |b|, and |c| and obtain satisfactory results for some specified values, the code is very likely to be unstable in this regime. Unusual features: Two different codes, one for the hypergeometric function and one for the Pöschl-Teller-Ginocchio potential wave functions, are provided in C++ and Fortran 90 versions. Running time: 20,000 F12 function evaluations take an average of one second.

Complex Analysis and Related Topics. Proceedings of the Conference held in Amsterdam on 27 - 29 January 1993

DTIC Science & Technology

1993-01-29

Bessel functions and Jacobi functions (cf. [2]). References [1] R. Askey & J. Wilson, Some basic hypergeometric orthogonal polynomials that gen- eralize...1; 1] can be treated as a part of general theory of T-systems (see [81 for that theory and [7] for some aspects of the Chebyshev polynomials theory...waves in elastic media. It has been known for some time that these multiplicities sometimes occur for topological reasons and are present generically , see

Laplace approximation for Bessel functions of matrix argument

NASA Astrophysics Data System (ADS)

Butler, Ronald W.; Wood, Andrew T. A.

2003-06-01

We derive Laplace approximations to three functions of matrix argument which arise in statistics and elsewhere: matrix Bessel A[nu]; matrix Bessel B[nu]; and the type II confluent hypergeometric function of matrix argument, [Psi]. We examine the theoretical and numerical properties of the approximations. On the theoretical side, it is shown that the Laplace approximations to A[nu], B[nu] and [Psi] given here, together with the Laplace approximations to the matrix argument functions 1F1 and 2F1 presented in Butler and Wood (Laplace approximations to hyper-geometric functions with matrix argument, Ann. Statist. (2002)), satisfy all the important confluence relations and symmetry relations enjoyed by the original functions.

A scan statistic for binary outcome based on hypergeometric probability model, with an application to detecting spatial clusters of Japanese encephalitis.

PubMed

Zhao, Xing; Zhou, Xiao-Hua; Feng, Zijian; Guo, Pengfei; He, Hongyan; Zhang, Tao; Duan, Lei; Li, Xiaosong

2013-01-01

As a useful tool for geographical cluster detection of events, the spatial scan statistic is widely applied in many fields and plays an increasingly important role. The classic version of the spatial scan statistic for the binary outcome is developed by Kulldorff, based on the Bernoulli or the Poisson probability model. In this paper, we apply the Hypergeometric probability model to construct the likelihood function under the null hypothesis. Compared with existing methods, the likelihood function under the null hypothesis is an alternative and indirect method to identify the potential cluster, and the test statistic is the extreme value of the likelihood function. Similar with Kulldorff's methods, we adopt Monte Carlo test for the test of significance. Both methods are applied for detecting spatial clusters of Japanese encephalitis in Sichuan province, China, in 2009, and the detected clusters are identical. Through a simulation to independent benchmark data, it is indicated that the test statistic based on the Hypergeometric model outweighs Kulldorff's statistics for clusters of high population density or large size; otherwise Kulldorff's statistics are superior.

Analysis of Eigenvalue and Eigenfunction of Klein Gordon Equation Using Asymptotic Iteration Method for Separable Non-central Cylindrical Potential

NASA Astrophysics Data System (ADS)

Suparmi, A.; Cari, C.; Lilis Elviyanti, Isnaini

2018-04-01

Analysis of relativistic energy and wave function for zero spin particles using Klein Gordon equation was influenced by separable noncentral cylindrical potential was solved by asymptotic iteration method (AIM). By using cylindrical coordinates, the Klein Gordon equation for the case of symmetry spin was reduced to three one-dimensional Schrodinger like equations that were solvable using variable separation method. The relativistic energy was calculated numerically with Matlab software, and the general unnormalized wave function was expressed in hypergeometric terms.

Linear dispersion properties of ring velocity distribution functions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vandas, Marek, E-mail: marek.vandas@asu.cas.cz; Hellinger, Petr; Institute of Atmospheric Physics, AS CR, Bocni II/1401, CZ-14100 Prague

2015-06-15

Linear properties of ring velocity distribution functions are investigated. The dispersion tensor in a form similar to the case of a Maxwellian distribution function, but for a general distribution function separable in velocities, is presented. Analytical forms of the dispersion tensor are derived for two cases of ring velocity distribution functions: one obtained from physical arguments and one for the usual, ad hoc ring distribution. The analytical expressions involve generalized hypergeometric, Kampé de Fériet functions of two arguments. For a set of plasma parameters, the two ring distribution functions are compared. At the parallel propagation with respect to the ambientmore » magnetic field, the two ring distributions give the same results identical to the corresponding bi-Maxwellian distribution. At oblique propagation, the two ring distributions give similar results only for strong instabilities, whereas for weak growth rates their predictions are significantly different; the two ring distributions have different marginal stability conditions.« less

Fast summation of divergent series and resurgent transseries from Meijer-G approximants

NASA Astrophysics Data System (ADS)

Mera, Héctor; Pedersen, Thomas G.; Nikolić, Branislav K.

2018-05-01

We develop a resummation approach based on Meijer-G functions and apply it to approximate the Borel sum of divergent series and the Borel-Écalle sum of resurgent transseries in quantum mechanics and quantum field theory (QFT). The proposed method is shown to vastly outperform the conventional Borel-Padé and Borel-Padé-Écalle summation methods. The resulting Meijer-G approximants are easily parametrized by means of a hypergeometric ansatz and can be thought of as a generalization to arbitrary order of the Borel-hypergeometric method [Mera et al., Phys. Rev. Lett. 115, 143001 (2015), 10.1103/PhysRevLett.115.143001]. Here we demonstrate the accuracy of this technique in various examples from quantum mechanics and QFT, traditionally employed as benchmark models for resummation, such as zero-dimensional ϕ4 theory; the quartic anharmonic oscillator; the calculation of critical exponents for the N -vector model; ϕ4 with degenerate minima; self-interacting QFT in zero dimensions; and the summation of one- and two-instanton contributions in the quantum-mechanical double-well problem.

Higher-order automatic differentiation of mathematical functions

NASA Astrophysics Data System (ADS)

Charpentier, Isabelle; Dal Cappello, Claude

2015-04-01

Functions of mathematical physics such as the Bessel functions, the Chebyshev polynomials, the Gauss hypergeometric function and so forth, have practical applications in many scientific domains. On the one hand, differentiation formulas provided in reference books apply to real or complex variables. These do not account for the chain rule. On the other hand, based on the chain rule, the automatic differentiation has become a natural tool in numerical modeling. Nevertheless automatic differentiation tools do not deal with the numerous mathematical functions. This paper describes formulas and provides codes for the higher-order automatic differentiation of mathematical functions. The first method is based on Faà di Bruno's formula that generalizes the chain rule. The second one makes use of the second order differential equation they satisfy. Both methods are exemplified with the aforementioned functions.

Exact Mass-Coupling Relation for the Homogeneous Sine-Gordon Model.

PubMed

Bajnok, Zoltán; Balog, János; Ito, Katsushi; Satoh, Yuji; Tóth, Gábor Zsolt

2016-05-06

We derive the exact mass-coupling relation of the simplest multiscale quantum integrable model, i.e., the homogeneous sine-Gordon model with two mass scales. The relation is obtained by comparing the perturbed conformal field theory description of the model valid at short distances to the large distance bootstrap description based on the model's integrability. In particular, we find a differential equation for the relation by constructing conserved tensor currents, which satisfy a generalization of the Θ sum rule Ward identity. The mass-coupling relation is written in terms of hypergeometric functions.

Coupling coefficients for tensor product representations of quantum SU(2)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Groenevelt, Wolter, E-mail: w.g.m.groenevelt@tudelft.nl

2014-10-15

We study tensor products of infinite dimensional irreducible {sup *}-representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometricmore » orthogonal polynomials and q-Bessel-type functions.« less

Special solutions to Chazy equation

NASA Astrophysics Data System (ADS)

Varin, V. P.

2017-02-01

We consider the classical Chazy equation, which is known to be integrable in hypergeometric functions. But this solution has remained purely existential and was never used numerically. We give explicit formulas for hypergeometric solutions in terms of initial data. A special solution was found in the upper half plane H with the same tessellation of H as that of the modular group. This allowed us to derive some new identities for the Eisenstein series. We constructed a special solution in the unit disk and gave an explicit description of singularities on its natural boundary. A global solution to Chazy equation in elliptic and theta functions was found that allows parametrization of an arbitrary solution to Chazy equation. The results have applications to analytic number theory.

HYPERSAMP - HYPERGEOMETRIC ATTRIBUTE SAMPLING SYSTEM BASED ON RISK AND FRACTION DEFECTIVE

NASA Technical Reports Server (NTRS)

De, Salvo L. J.

1994-01-01

HYPERSAMP is a demonstration of an attribute sampling system developed to determine the minimum sample size required for any preselected value for consumer's risk and fraction of nonconforming. This statistical method can be used in place of MIL-STD-105E sampling plans when a minimum sample size is desirable, such as when tests are destructive or expensive. HYPERSAMP utilizes the Hypergeometric Distribution and can be used for any fraction nonconforming. The program employs an iterative technique that circumvents the obstacle presented by the factorial of a non-whole number. HYPERSAMP provides the required Hypergeometric sample size for any equivalent real number of nonconformances in the lot or batch under evaluation. Many currently used sampling systems, such as the MIL-STD-105E, utilize the Binomial or the Poisson equations as an estimate of the Hypergeometric when performing inspection by attributes. However, this is primarily because of the difficulty in calculation of the factorials required by the Hypergeometric. Sampling plans based on the Binomial or Poisson equations will result in the maximum sample size possible with the Hypergeometric. The difference in the sample sizes between the Poisson or Binomial and the Hypergeometric can be significant. For example, a lot size of 400 devices with an error rate of 1.0% and a confidence of 99% would require a sample size of 400 (all units would need to be inspected) for the Binomial sampling plan and only 273 for a Hypergeometric sampling plan. The Hypergeometric results in a savings of 127 units, a significant reduction in the required sample size. HYPERSAMP is a demonstration program and is limited to sampling plans with zero defectives in the sample (acceptance number of zero). Since it is only a demonstration program, the sample size determination is limited to sample sizes of 1500 or less. The Hypergeometric Attribute Sampling System demonstration code is a spreadsheet program written for IBM PC compatible computers running DOS and Lotus 1-2-3 or Quattro Pro. This program is distributed on a 5.25 inch 360K MS-DOS format diskette, and the program price includes documentation. This statistical method was developed in 1992.

New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan's tau function.

PubMed

Milne, S C

1996-12-24

In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi's (1829) 4 and 8 squares identities to 4n(2) or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan's tau function tau(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the eta-function identities in appendix I of Macdonald's work [Macdonald, I. G. (1972) Invent. Math. 15, 91-143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415-456] identities involving representing a positive integer by sums of 4n(2) or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson's C(l) nonterminating (6)phi(5) summation theorem, and Andrews' basic hypergeometric series proof of Jacobi's 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n(2) or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others.

Classes of exact Einstein Maxwell solutions

NASA Astrophysics Data System (ADS)

Komathiraj, K.; Maharaj, S. D.

2007-12-01

We find new classes of exact solutions to the Einstein Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.

Hypergeometric continuation of divergent perturbation series: I. Critical exponents of the Bose-Hubbard model

NASA Astrophysics Data System (ADS)

Sanders, Sören; Holthaus, Martin

2017-10-01

We study the connection between the exponent of the order parameter of the Mott insulator-to-superfluid transition occurring in the two-dimensional Bose-Hubbard model, and the divergence exponents of its one- and two-particle correlation functions. We find that at the multicritical points all divergence exponents are related to each other, allowing us to express the critical exponent in terms of one single divergence exponent. This approach correctly reproduces the critical exponent of the three-dimensional XY universality class. Because divergence exponents can be computed in an efficient manner by hypergeometric analytic continuation, our strategy is applicable to a wide class of systems.

Product of Ginibre matrices: Fuss-Catalan and Raney distributions

NASA Astrophysics Data System (ADS)

Penson, Karol A.; Życzkowski, Karol

2011-06-01

Squared singular values of a product of s square random Ginibre matrices are asymptotically characterized by probability distributions Ps(x), such that their moments are equal to the Fuss-Catalan numbers of order s. We find a representation of the Fuss-Catalan distributions Ps(x) in terms of a combination of s hypergeometric functions of the type sFs-1. The explicit formula derived here is exact for an arbitrary positive integer s, and for s=1 it reduces to the Marchenko-Pastur distribution. Using similar techniques, involving the Mellin transform and the Meijer G function, we find exact expressions for the Raney probability distributions, the moments of which are given by a two-parameter generalization of the Fuss-Catalan numbers. These distributions can also be considered as a two-parameter generalization of the Wigner semicircle law.

Product of Ginibre matrices: Fuss-Catalan and Raney distributions.

PubMed

Penson, Karol A; Zyczkowski, Karol

2011-06-01

Squared singular values of a product of s square random Ginibre matrices are asymptotically characterized by probability distributions P(s)(x), such that their moments are equal to the Fuss-Catalan numbers of order s. We find a representation of the Fuss-Catalan distributions P(s)(x) in terms of a combination of s hypergeometric functions of the type (s)F(s-1). The explicit formula derived here is exact for an arbitrary positive integer s, and for s=1 it reduces to the Marchenko-Pastur distribution. Using similar techniques, involving the Mellin transform and the Meijer G function, we find exact expressions for the Raney probability distributions, the moments of which are given by a two-parameter generalization of the Fuss-Catalan numbers. These distributions can also be considered as a two-parameter generalization of the Wigner semicircle law.

Completeness of the Coulomb Wave Functions in Quantum Mechanics

ERIC Educational Resources Information Center

Mukunda, N.

1978-01-01

Gives an explicit and elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory. (Author/GA)

New class of generalized photon-added coherent states and some of their non-classical properties

NASA Astrophysics Data System (ADS)

Mojaveri, B.; Dehghani, A.; Mahmoodi, S.

2014-08-01

In this paper, we construct a new class of generalized photon added coherent states (GPACSs), |z,m{{\\rangle }_{r}} by excitations on a newly introduced family of generalized coherent states (GCSs) |z{{\\rangle }_{r}} (A Dehghani and B Mojaveri 2012 J. Phys. A: Math. Theor. 45 095304), obtained via generalized hypergeometric type displacement operators acting on the vacuum state of the simple harmonic oscillator. We show that these states realize resolution of the identity property through positive definite measures on the complex plane. Meanwhile, we demonstrate that the introduced states can also be interpreted as nonlinear coherent states (NLCSs), with a spacial nonlinearity function. Finally, some of their non-classical features as well as their quantum statistical properties are compared with Agarwal's photon-added coherent states (PACSs), \\left| z,m \\right\\rangle .

Evaluating Feynman integrals by the hypergeometry

NASA Astrophysics Data System (ADS)

Feng, Tai-Fu; Chang, Chao-Hsi; Chen, Jian-Bin; Gu, Zhi-Hua; Zhang, Hai-Bin

2018-02-01

The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear partial differential equations satisfied by the corresponding scalar integrals. Taking examples of the one-loop B0 and massless C0 functions, as well as the scalar integrals of two-loop vacuum and sunset diagrams, we verify our expressions coinciding with the well-known results of literatures. Based on the multiple hypergeometric functions of independent kinematic variables, the systems of homogeneous linear partial differential equations satisfied by the mentioned scalar integrals are established. Using the calculus of variations, one recognizes the system of linear partial differential equations as stationary conditions of a functional under some given restrictions, which is the cornerstone to perform the continuation of the scalar integrals to whole kinematic domains numerically with the finite element methods. In principle this method can be used to evaluate the scalar integrals of any Feynman diagrams.

QCD triple Pomeron coupling from string amplitudes

NASA Astrophysics Data System (ADS)

Bialas, A.; Navelet, H.; Peschanski, R.

1998-06-01

Using the recent solution of the triple Pomeron coupling in the QCD dipole picture as a closed string amplitude with six legs, its analytical form in terms of hypergeometric functions and numerical value are derived.

Magnetic expansion of Nekrasov theory: The SU(2) pure gauge theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

He Wei; Miao Yangang

It is recently claimed by Nekrasov and Shatashvili that the N=2 gauge theories in the {Omega} background with {epsilon}{sub 1}=({h_bar}/2{pi}), {epsilon}{sub 2}=0 are related to the quantization of certain algebraic integrable systems. We study the special case of SU(2) pure gauge theory; the corresponding integrable model is the A{sub 1} Toda model, which reduces to the sine-Gordon quantum mechanics problem. The quantum effects can be expressed as the WKB series written analytically in terms of hypergeometric functions. We obtain the magnetic and dyonic expansions of the Nekrasov theory by studying the property of hypergeometric functions in the magnetic and dyonicmore » regions on the moduli space. We also discuss the relation between the electric-magnetic duality of gauge theory and the action-action duality of the integrable system.« less

Evaluation of Fuel Cell Operation and Degradation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Williams, Mark; Gemmen, Randall; Richards, George

The concepts of area specific resistance (ASR) and degradation are developed for different fuel cell operating modes. The concepts of exergetic efficiency and entropy production were applied to ASR and degradation. It is shown that exergetic efficiency is a time-dependent function useful describing the thermal efficiency of a fuel cell and the change in thermal efficiency of a degrading fuel cell. Entropy production was evaluated for the cases of constant voltage operation and constant current operation of the fuel cell for a fuel cell undergoing ohmic degradation. It was discovered that the Gaussian hypergeometric function describes the cumulative entropy andmore » electrical work produced by fuel cells operating at constant voltage. The Gaussian hypergeometric function is found in many applications in modern physics. This paper builds from and is an extension of several papers recently published by the authors in the Journal of The Electrochemical Society (ECS), ECS Transactions, Journal of Power Sources, and the Journal of Fuel Cell Science and Technology.« less

Analytical Solutions of the Gravitational Field Equations in de Sitter and Anti-de Sitter Spacetimes

NASA Astrophysics Data System (ADS)

Da Rocha, R.; Capelas Oliveira, E.

2009-01-01

The generalized Laplace partial differential equation, describing gravitational fields, is investigated in de Sitter spacetime from several metric approaches—such as the Riemann, Beltrami, Börner-Dürr, and Prasad metrics—and analytical solutions of the derived Riccati radial differential equations are explicitly obtained. All angular differential equations trivially have solutions given by the spherical harmonics and all radial differential equations can be written as Riccati ordinary differential equations, which analytical solutions involve hypergeometric and Bessel functions. In particular, the radial differential equations predict the behavior of the gravitational field in de Sitter and anti-de Sitter spacetimes, and can shed new light on the investigations of quasinormal modes of perturbations of electromagnetic and gravitational fields in black hole neighborhood. The discussion concerning the geometry of de Sitter and anti-de Sitter spacetimes is not complete without mentioning how the wave equation behaves on such a background. It will prove convenient to begin with a discussion of the Laplace equation on hyperbolic space, partly since this is of interest in itself and also because the wave equation can be investigated by means of an analytic continuation from the hyperbolic space. We also solve the Laplace equation associated to the Prasad metric. After introducing the so called internal and external spaces—corresponding to the symmetry groups SO(3,2) and SO(4,1) respectively—we show that both radial differential equations can be led to Riccati ordinary differential equations, which solutions are given in terms of associated Legendre functions. For the Prasad metric with the radius of the universe independent of the parametrization, the internal and external metrics are shown to be of AdS-Schwarzschild-like type, and also the radial field equations arising are shown to be equivalent to Riccati equations whose solutions can be written in terms of generalized Laguerre polynomials and hypergeometric confluent functions.

Operator identities involving the bivariate Rogers-Szegö polynomials and their applications to the multiple q-series identities

NASA Astrophysics Data System (ADS)

Zhang, Zhizheng; Wang, Tianze

2008-07-01

In this paper, we first give several operator identities involving the bivariate Rogers-Szegö polynomials. By applying the technique of parameter augmentation to the multiple q-binomial theorems given by Milne [S.C. Milne, Balanced summation theorems for U(n) basic hypergeometric series, AdvE Math. 131 (1997) 93-187], we obtain several new multiple q-series identities involving the bivariate Rogers-Szegö polynomials. These include multiple extensions of Mehler's formula and Rogers's formula. Our U(n+1) generalizations are quite natural as they are also a direct and immediate consequence of their (often classical) known one-variable cases and Milne's fundamental theorem for An or U(n+1) basic hypergeometric series in Theorem 1E49 of [S.C. Milne, An elementary proof of the Macdonald identities for , Adv. Math. 57 (1985) 34-70], as rewritten in Lemma 7.3 on p. 163 of [S.C. Milne, Balanced summation theorems for U(n) basic hypergeometric series, Adv. Math. 131 (1997) 93-187] or Corollary 4.4 on pp. 768-769 of [S.C. Milne, M. Schlosser, A new An extension of Ramanujan's summation with applications to multilateral An series, Rocky Mountain J. Math. 32 (2002) 759-792].

Technique for evaluation of the strong potential Born approximation for electron capture

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sil, N.C.; McGuire, J.H.

1985-04-01

A technique is presented for evaluating differential cross sections in the strong potential Born (SPB) approximation. Our final expression is expressed as a finite sum of one-dimensional integrals, expressible as a finite sum of derivatives of hypergeometric functions.

Motions about a fixed point by hypergeometric functions: new non-complex analytical solutions and integration of the herpolhode

NASA Astrophysics Data System (ADS)

Mingari Scarpello, Giovanni; Ritelli, Daniele

2018-06-01

The present study highlights the dynamics of a body moving about a fixed point and provides analytical closed form solutions. Firstly, for the symmetrical heavy body, that is the Lagrange-Poisson case, we compute the second (precession, ψ ) and third (spin, φ) Euler angles in explicit and real form by means of multiple hypergeometric (Lauricella) functions. Secondly, releasing the weight assumption but adding the complication of the asymmetry, by means of elliptic integrals of third kind, we provide the precession angle ψ completing the treatment of the Euler-Poinsot case. Thirdly, by integrating the relevant differential equation, we reach the finite polar equation of a special motion trajectory named the herpolhode. Finally, we keep the symmetry of the first problem, but without weight, and take into account a viscous dissipation. The use of motion first integrals—adopted for the first two problems—is no longer practicable in this situation; therefore, the Euler equations, faced directly, are driving to particular occurrences of Bessel functions of order - 1/2.

Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism

NASA Astrophysics Data System (ADS)

Broedel, Johannes; Duhr, Claude; Dulat, Falko; Tancredi, Lorenzo

2018-05-01

We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring that they have at most simple poles, implying that the iterated integrals have at most logarithmic singularities. We study the properties of our iterated integrals and their relationship to the multiple elliptic polylogarithms from the mathematics literature. On the one hand, we find that our iterated integrals span essentially the same space of functions as the multiple elliptic polylogarithms. On the other, our formulation allows for a more direct use to solve a large variety of problems in high-energy physics. We demonstrate the use of our functions in the evaluation of the Laurent expansion of some hypergeometric functions for values of the indices close to half integers.

Analytical solutions of the Klein-Gordon equation for Manning-Rosen potential with centrifugal term through Nikiforov-Uvarov method

NASA Astrophysics Data System (ADS)

Hatami, N.; Setare, M. R.

2017-10-01

We present approximate analytical solutions of the Klein-Gordon equation with arbitrary l state for the Manning-Rosen potential using the Nikiforov-Uvarov method and adopting the approximation scheme for the centrifugal term. We provide the bound state energy spectrum and the wave function in terms of the hypergeometric functions.

A massive Feynman integral and some reduction relations for Appell functions

NASA Astrophysics Data System (ADS)

Shpot, M. A.

2007-12-01

New explicit expressions are derived for the one-loop two-point Feynman integral with arbitrary external momentum and masses m12 and m22 in D dimensions. The results are given in terms of Appell functions, manifestly symmetric with respect to the masses mi2. Equating our expressions with previously known results in terms of Gauss hypergeometric functions yields reduction relations for the involved Appell functions that are apparently new mathematical results.

Luigi Gatteschi's work on asymptotics of special functions and their zeros

NASA Astrophysics Data System (ADS)

Gautschi, Walter; Giordano, Carla

2008-12-01

A good portion of Gatteschi's research publications-about 65%-is devoted to asymptotics of special functions and their zeros. Most prominently among the special functions studied figure classical orthogonal polynomials, notably Jacobi polynomials and their special cases, Laguerre polynomials, and Hermite polynomials by implication. Other important classes of special functions dealt with are Bessel functions of the first and second kind, Airy functions, and confluent hypergeometric functions, both in Tricomi's and Whittaker's form. This work is reviewed here, and organized along methodological lines.

Distinguishing between Binomial, Hypergeometric and Negative Binomial Distributions

ERIC Educational Resources Information Center

Wroughton, Jacqueline; Cole, Tarah

2013-01-01

Recognizing the differences between three discrete distributions (Binomial, Hypergeometric and Negative Binomial) can be challenging for students. We present an activity designed to help students differentiate among these distributions. In addition, we present assessment results in the form of pre- and post-tests that were designed to assess the…

Analytical approximation schemes for solving exact renormalization group equations in the local potential approximation

NASA Astrophysics Data System (ADS)

Bervillier, C.; Boisseau, B.; Giacomini, H.

2008-02-01

The relation between the Wilson-Polchinski and the Litim optimized ERGEs in the local potential approximation is studied with high accuracy using two different analytical approaches based on a field expansion: a recently proposed genuine analytical approximation scheme to two-point boundary value problems of ordinary differential equations, and a new one based on approximating the solution by generalized hypergeometric functions. A comparison with the numerical results obtained with the shooting method is made. A similar accuracy is reached in each case. Both two methods appear to be more efficient than the usual field expansions frequently used in the current studies of ERGEs (in particular for the Wilson-Polchinski case in the study of which they fail).

Wave equations in conformal gravity

NASA Astrophysics Data System (ADS)

Du, Juan-Juan; Wang, Xue-Jing; He, You-Biao; Yang, Si-Jiang; Li, Zhong-Heng

2018-05-01

We study the wave equation governing massless fields of all spins (s = 0, 1 2, 1, 3 2 and 2) in the most general spherical symmetric metric of conformal gravity. The equation is separable, the solution of the angular part is a spin-weighted spherical harmonic, and the radial wave function may be expressed in terms of solutions of the Heun equation which has four regular singular points. We also consider various special cases of the metric and find that the angular wave functions are the same for all cases, the actual shape of the metric functions affects only the radial wave function. It is interesting to note that each radial equation can be transformed into a known ordinary differential equation (i.e. Heun equation, or confluent Heun equation, or hypergeometric equation). The results show that there are analytic solutions for all the wave equations of massless spin fields in the spacetimes of conformal gravity. This is amazing because exact solutions are few and far between for other spacetimes.

Fermionic Approach to Weighted Hurwitz Numbers and Topological Recursion

NASA Astrophysics Data System (ADS)

Alexandrov, A.; Chapuy, G.; Eynard, B.; Harnad, J.

2017-12-01

A fermionic representation is given for all the quantities entering in the generating function approach to weighted Hurwitz numbers and topological recursion. This includes: KP and 2D Toda {τ} -functions of hypergeometric type, which serve as generating functions for weighted single and double Hurwitz numbers; the Baker function, which is expanded in an adapted basis obtained by applying the same dressing transformation to all vacuum basis elements; the multipair correlators and the multicurrent correlators. Multiplicative recursion relations and a linear differential system are deduced for the adapted bases and their duals, and a Christoffel-Darboux type formula is derived for the pair correlator. The quantum and classical spectral curves linking this theory with the topological recursion program are derived, as well as the generalized cut-and-join equations. The results are detailed for four special cases: the simple single and double Hurwitz numbers, the weakly monotone case, corresponding to signed enumeration of coverings, the strongly monotone case, corresponding to Belyi curves and the simplest version of quantum weighted Hurwitz numbers.

Fermionic Approach to Weighted Hurwitz Numbers and Topological Recursion

NASA Astrophysics Data System (ADS)

Alexandrov, A.; Chapuy, G.; Eynard, B.; Harnad, J.

2018-06-01

A fermionic representation is given for all the quantities entering in the generating function approach to weighted Hurwitz numbers and topological recursion. This includes: KP and 2 D Toda {τ} -functions of hypergeometric type, which serve as generating functions for weighted single and double Hurwitz numbers; the Baker function, which is expanded in an adapted basis obtained by applying the same dressing transformation to all vacuum basis elements; the multipair correlators and the multicurrent correlators. Multiplicative recursion relations and a linear differential system are deduced for the adapted bases and their duals, and a Christoffel-Darboux type formula is derived for the pair correlator. The quantum and classical spectral curves linking this theory with the topological recursion program are derived, as well as the generalized cut-and-join equations. The results are detailed for four special cases: the simple single and double Hurwitz numbers, the weakly monotone case, corresponding to signed enumeration of coverings, the strongly monotone case, corresponding to Belyi curves and the simplest version of quantum weighted Hurwitz numbers.

Electron-pair-production cross section in the tip region of the positron spectrum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sud, K.K.; Sharma, D.K.

1984-11-01

The radial integrals for electron-pair production in a point Coulomb potential have been expressed by Sud, Sharma, and Sud in terms of the matrix generalization of the GAMMA function. Two new partial differential equations in photon energy satisfied by the matrix GAMMA function are obtained. We have obtained, on integrating the partial differential equations, accurate radial integrals as a function of photon energy for the pair production by intermediate-energy photons. The cross section in the tip region of the spectrum are calculated for photons of energy 5.0 to 10.0 MeV for /sup 92/U. The new technique results in extensive savingmore » in computer time as the basic radial integrals in terms of the hypergeometric function F/sub 2/ are computed at one photon energy for each pair of partial waves. The results of our calculations are compared with plane-wave Born-approximation results and with the calculations of Dugne and of Deck, Moroi, and Alling.« less

Random matrix theory of singular values of rectangular complex matrices I: Exact formula of one-body distribution function in fixed-trace ensemble

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adachi, Satoshi; Toda, Mikito; Kubotani, Hiroto

The fixed-trace ensemble of random complex matrices is the fundamental model that excellently describes the entanglement in the quantum states realized in a coupled system by its strongly chaotic dynamical evolution [see H. Kubotani, S. Adachi, M. Toda, Phys. Rev. Lett. 100 (2008) 240501]. The fixed-trace ensemble fully takes into account the conservation of probability for quantum states. The present paper derives for the first time the exact analytical formula of the one-body distribution function of singular values of random complex matrices in the fixed-trace ensemble. The distribution function of singular values (i.e. Schmidt eigenvalues) of a quantum state ismore » so important since it describes characteristics of the entanglement in the state. The derivation of the exact analytical formula utilizes two recent achievements in mathematics, which appeared in 1990s. The first is the Kaneko theory that extends the famous Selberg integral by inserting a hypergeometric type weight factor into the integrand to obtain an analytical formula for the extended integral. The second is the Petkovsek-Wilf-Zeilberger theory that calculates definite hypergeometric sums in a closed form.« less

Guidelines for Use of the Approximate Beta-Poisson Dose-Response Model.

PubMed

Xie, Gang; Roiko, Anne; Stratton, Helen; Lemckert, Charles; Dunn, Peter K; Mengersen, Kerrie

2017-07-01

For dose-response analysis in quantitative microbial risk assessment (QMRA), the exact beta-Poisson model is a two-parameter mechanistic dose-response model with parameters α>0 and β>0, which involves the Kummer confluent hypergeometric function. Evaluation of a hypergeometric function is a computational challenge. Denoting PI(d) as the probability of infection at a given mean dose d, the widely used dose-response model PI(d)=1-(1+dβ)-α is an approximate formula for the exact beta-Poisson model. Notwithstanding the required conditions α<β and β>1, issues related to the validity and approximation accuracy of this approximate formula have remained largely ignored in practice, partly because these conditions are too general to provide clear guidance. Consequently, this study proposes a probability measure Pr(0 < r < 1 | α̂, β̂) as a validity measure (r is a random variable that follows a gamma distribution; α̂ and β̂ are the maximum likelihood estimates of α and β in the approximate model); and the constraint conditions β̂>(22α̂)0.50 for 0.02<α̂<2 as a rule of thumb to ensure an accurate approximation (e.g., Pr(0 < r < 1 | α̂, β̂) >0.99) . This validity measure and rule of thumb were validated by application to all the completed beta-Poisson models (related to 85 data sets) from the QMRA community portal (QMRA Wiki). The results showed that the higher the probability Pr(0 < r < 1 | α̂, β̂), the better the approximation. The results further showed that, among the total 85 models examined, 68 models were identified as valid approximate model applications, which all had a near perfect match to the corresponding exact beta-Poisson model dose-response curve. © 2016 Society for Risk Analysis.

Solution to urn models of pairwise interaction with application to social, physical, and biological sciences

NASA Astrophysics Data System (ADS)

Pickering, William; Lim, Chjan

2017-07-01

We investigate a family of urn models that correspond to one-dimensional random walks with quadratic transition probabilities that have highly diverse applications. Well-known instances of these two-urn models are the Ehrenfest model of molecular diffusion, the voter model of social influence, and the Moran model of population genetics. We also provide a generating function method for diagonalizing the corresponding transition matrix that is valid if and only if the underlying mean density satisfies a linear differential equation and express the eigenvector components as terms of ordinary hypergeometric functions. The nature of the models lead to a natural extension to interaction between agents in a general network topology. We analyze the dynamics on uncorrelated heterogeneous degree sequence networks and relate the convergence times to the moments of the degree sequences for various pairwise interaction mechanisms.

Cosmological perturbation theory using the FFTLog: formalism and connection to QFT loop integrals

NASA Astrophysics Data System (ADS)

Simonović, Marko; Baldauf, Tobias; Zaldarriaga, Matias; Carrasco, John Joseph; Kollmeier, Juna A.

2018-04-01

We present a new method for calculating loops in cosmological perturbation theory. This method is based on approximating a ΛCDM-like cosmology as a finite sum of complex power-law universes. The decomposition is naturally achieved using an FFTLog algorithm. For power-law cosmologies, all loop integrals are formally equivalent to loop integrals of massless quantum field theory. These integrals have analytic solutions in terms of generalized hypergeometric functions. We provide explicit formulae for the one-loop and the two-loop power spectrum and the one-loop bispectrum. A chief advantage of our approach is that the difficult part of the calculation is cosmology independent, need be done only once, and can be recycled for any relevant predictions. Evaluation of standard loop diagrams then boils down to a simple matrix multiplication. We demonstrate the promise of this method for applications to higher multiplicity/loop correlation functions.

Representation of the Coulomb Matrix Elements by Means of Appell Hypergeometric Function F 2

NASA Astrophysics Data System (ADS)

Bentalha, Zine el abidine

2018-06-01

Exact analytical representation for the Coulomb matrix elements by means of Appell's double series F 2 is derived. The finite sum obtained for the Appell function F 2 allows us to evaluate explicitly the matrix elements of the two-body Coulomb interaction in the lowest Landau level. An application requiring the matrix elements of Coulomb potential in quantum Hall effect regime is presented.

The Havriliak-Negami relaxation and its relatives: the response, relaxation and probability density functions

NASA Astrophysics Data System (ADS)

Górska, K.; Horzela, A.; Bratek, Ł.; Dattoli, G.; Penson, K. A.

2018-04-01

We study functions related to the experimentally observed Havriliak-Negami dielectric relaxation pattern proportional in the frequency domain to [1+(iωτ0){\\hspace{0pt}}α]-β with τ0 > 0 being some characteristic time. For α = l/k< 1 (l and k being positive and relatively prime integers) and β > 0 we furnish exact and explicit expressions for response and relaxation functions in the time domain and suitable probability densities in their domain dual in the sense of the inverse Laplace transform. All these functions are expressed as finite sums of generalized hypergeometric functions, convenient to handle analytically and numerically. Introducing a reparameterization β = (2-q)/(q-1) and τ0 = (q-1){\\hspace{0pt}}1/α (1 < q < 2) we show that for 0 < α < 1 the response functions fα, β(t/τ0) go to the one-sided Lévy stable distributions when q tends to one. Moreover, applying the self-similarity property of the probability densities gα, β(u) , we introduce two-variable densities and show that they satisfy the integral form of the evolution equation.

Ince's limits for confluent and double-confluent Heun equations

NASA Astrophysics Data System (ADS)

Bonorino Figueiredo, B. D.

2005-11-01

We find pairs of solutions to a differential equation which is obtained as a special limit of a generalized spheroidal wave equation (this is also known as confluent Heun equation). One solution in each pair is given by a series of hypergeometric functions and converges for any finite value of the independent variable z, while the other is given by a series of modified Bessel functions and converges for ∣z∣>∣z0∣, where z0 denotes a regular singularity. For short, the preceding limit is called Ince's limit after Ince who have used the same procedure to get the Mathieu equations from the Whittaker-Hill ones. We find as well that, when z0 tends to zero, the Ince limit of the generalized spheroidal wave equation turns out to be the Ince limit of a double-confluent Heun equation, for which solutions are provided. Finally, we show that the Schrödinger equation for inverse fourth- and sixth-power potentials reduces to peculiar cases of the double-confluent Heun equation and its Ince's limit, respectively.

On Exact Solutions of Rarefaction-Rarefaction Interactions in Compressible Isentropic Flow

NASA Astrophysics Data System (ADS)

Jenssen, Helge Kristian

2017-12-01

Consider the interaction of two centered rarefaction waves in one-dimensional, compressible gas flow with pressure function p(ρ )=a^2ρ ^γ with γ >1. The classic hodograph approach of Riemann provides linear 2nd order equations for the time and space variables t, x as functions of the Riemann invariants r, s within the interaction region. It is well known that t( r, s) can be given explicitly in terms of the hypergeometric function. We present a direct calculation (based on works by Darboux and Martin) of this formula, and show how the same approach provides an explicit formula for x( r, s) in terms of Appell functions (two-variable hypergeometric functions). Motivated by the issue of vacuum and total variation estimates for 1-d Euler flows, we then use the explicit t-solution to monitor the density field and its spatial variation in interactions of two centered rarefaction waves. It is found that the variation is always non-monotone, and that there is an overall increase in density variation if and only if γ >3. We show that infinite duration of the interaction is characterized by approach toward vacuum in the interaction region, and that this occurs if and only if the Riemann problem defined by the extreme initial states generates a vacuum. Finally, it is verified that the minimal density in such interactions decays at rate O(1)/ t.

Production of confluent hypergeometric beam by computer-generated hologram

NASA Astrophysics Data System (ADS)

Chen, Jiannong; Wang, Gang; Xu, Qinfeng

2011-02-01

Because of their spiral wave front, phase singularity, zero-intensity center and orbital angular momentum, dark hollow vortex beams have been found many applications in the field of atom optics such as atom cooling, atom transport and atom guiding. In this paper, a method for generating confluent hypergeometric beam by computer-generated hologram displayed on the spatial light modulator is presented. The hologram is formed by interference between a single ring Laguerre-Gaussian beam and a plane wave. The far-field Fraunhofer diffraction of this optical field transmitted from the hologram is the confluent hypergeometric beam. This beam is a circular symmetric beam which has a phase singularity, spiral wave front, zero-intensity center, and intrinsic orbital angular momentum. It is a new dark hollow vortex beam.

Modified parton branching model for multi-particle production in hadronic collisions: Application to SUSY particle branching

NASA Astrophysics Data System (ADS)

Yuanyuan, Zhang

The stochastic branching model of multi-particle productions in high energy collision has theoretical basis in perturbative QCD, and also successfully describes the experimental data for a wide energy range. However, over the years, little attention has been put on the branching model for supersymmetric (SUSY) particles. In this thesis, a stochastic branching model has been built to describe the pure supersymmetric particle jets evolution. This model is a modified two-phase stochastic branching process, or more precisely a two phase Simple Birth Process plus Poisson Process. The general case that the jets contain both ordinary particle jets and supersymmetric particle jets has also been investigated. We get the multiplicity distribution of the general case, which contains a Hypergeometric function in its expression. We apply this new multiplicity distribution to the current experimental data of pp collision at center of mass energy √s = 0.9, 2.36, 7 TeV. The fitting shows the supersymmetric particles haven't participate branching at current collision energy.

Cosmological constraints and comparison of viable f (R ) models

NASA Astrophysics Data System (ADS)

Pérez-Romero, Judit; Nesseris, Savvas

2018-01-01

In this paper we present cosmological constraints on several well-known f (R ) models, but also on a new class of models that are variants of the Hu-Sawicki one of the form f (R )=R -2/Λ 1 +b y (R ,Λ ) , that interpolate between the cosmological constant model and a matter dominated universe for different values of the parameter b , which is usually expected to be small for viable models and which in practice measures the deviation from general relativity. We use the latest growth rate, cosmic microwave background, baryon acoustic oscillations, supernovae type Ia and Hubble parameter data to place stringent constraints on the models and to compare them to the cosmological constant model but also other viable f (R ) models such as the Starobinsky or the degenerate hypergeometric models. We find that these kinds of Hu-Sawicki variant parametrizations are in general compatible with the currently available data and can provide useful toy models to explore the available functional space of f (R ) models, something very useful with the current and upcoming surveys that will test deviations from general relativity.

Orthogonal Polynomials Associated with Complementary Chain Sequences

NASA Astrophysics Data System (ADS)

Behera, Kiran Kumar; Sri Ranga, A.; Swaminathan, A.

2016-07-01

Using the minimal parameter sequence of a given chain sequence, we introduce the concept of complementary chain sequences, which we view as perturbations of chain sequences. Using the relation between these complementary chain sequences and the corresponding Verblunsky coefficients, the para-orthogonal polynomials and the associated Szegő polynomials are analyzed. Two illustrations, one involving Gaussian hypergeometric functions and the other involving Carathéodory functions are also provided. A connection between these two illustrations by means of complementary chain sequences is also observed.

f1: a code to compute Appell's F1 hypergeometric function

NASA Astrophysics Data System (ADS)

Colavecchia, F. D.; Gasaneo, G.

2004-02-01

In this work we present the FORTRAN code to compute the hypergeometric function F1( α, β1, β2, γ, x, y) of Appell. The program can compute the F1 function for real values of the variables { x, y}, and complex values of the parameters { α, β1, β2, γ}. The code uses different strategies to calculate the function according to the ideas outlined in [F.D. Colavecchia et al., Comput. Phys. Comm. 138 (1) (2001) 29]. Program summaryTitle of the program: f1 Catalogue identifier: ADSJ Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSJ Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: none Computers: PC compatibles, SGI Origin2∗ Operating system under which the program has been tested: Linux, IRIX Programming language used: Fortran 90 Memory required to execute with typical data: 4 kbytes No. of bits in a word: 32 No. of bytes in distributed program, including test data, etc.: 52 325 Distribution format: tar gzip file External subprograms used: Numerical Recipes hypgeo [W.H. Press et al., Numerical Recipes in Fortran 77, Cambridge Univ. Press, 1996] or chyp routine of R.C. Forrey [J. Comput. Phys. 137 (1997) 79], rkf45 [L.F. Shampine and H.H. Watts, Rep. SAND76-0585, 1976]. Keywords: Numerical methods, special functions, hypergeometric functions, Appell functions, Gauss function Nature of the physical problem: Computing the Appell F1 function is relevant in atomic collisions and elementary particle physics. It is usually the result of multidimensional integrals involving Coulomb continuum states. Method of solution: The F1 function has a convergent-series definition for | x|<1 and | y|<1, and several analytic continuations for other regions of the variable space. The code tests the values of the variables and selects one of the precedent cases. In the convergence region the program uses the series definition near the origin of coordinates, and a numerical integration of the third-order differential parametric equation for the F1 function. Also detects several special cases according to the values of the parameters. Restrictions on the complexity of the problem: The code is restricted to real values of the variables { x, y}. Also, there are some parameter domains that are not covered. These usually imply differences between integer parameters that lead to negative integer arguments of Gamma functions. Typical running time: Depends basically on the variables. The computation of Table 4 of [F.D. Colavecchia et al., Comput. Phys. Comm. 138 (1) (2001) 29] (64 functions) requires approximately 0.33 s in a Athlon 900 MHz processor.

Generating functions for weighted Hurwitz numbers

NASA Astrophysics Data System (ADS)

Guay-Paquet, Mathieu; Harnad, J.

2017-08-01

Double Hurwitz numbers enumerating weighted n-sheeted branched coverings of the Riemann sphere or, equivalently, weighted paths in the Cayley graph of Sn generated by transpositions are determined by an associated weight generating function. A uniquely determined 1-parameter family of 2D Toda τ -functions of hypergeometric type is shown to consist of generating functions for such weighted Hurwitz numbers. Four classical cases are detailed, in which the weighting is uniform: Okounkov's double Hurwitz numbers for which the ramification is simple at all but two specified branch points; the case of Belyi curves, with three branch points, two with specified profiles; the general case, with a specified number of branch points, two with fixed profiles, the rest constrained only by the genus; and the signed enumeration case, with sign determined by the parity of the number of branch points. Using the exponentiated quantum dilogarithm function as a weight generator, three new types of weighted enumerations are introduced. These determine quantum Hurwitz numbers depending on a deformation parameter q. By suitable interpretation of q, the statistical mechanics of quantum weighted branched covers may be related to that of Bosonic gases. The standard double Hurwitz numbers are recovered in the classical limit.

Functionals of Gegenbauer polynomials and D-dimensional hydrogenic momentum expectation values

NASA Astrophysics Data System (ADS)

Van Assche, W.; Yáñez, R. J.; González-Férez, R.; Dehesa, Jesús S.

2000-09-01

The system of Gegenbauer or ultraspherical polynomials {Cnλ(x);n=0,1,…} is a classical family of polynomials orthogonal with respect to the weight function ωλ(x)=(1-x2)λ-1/2 on the support interval [-1,+1]. Integral functionals of Gegenbauer polynomials with integrand f(x)[Cnλ(x)]2ωλ(x), where f(x) is an arbitrary function which does not depend on n or λ, are considered in this paper. First, a general recursion formula for these functionals is obtained. Then, the explicit expression for some specific functionals of this type is found in a closed and compact form; namely, for the functionals with f(x) equal to (1-x)α(1+x)β, log(1-x2), and (1+x)log(1+x), which appear in numerous physico-mathematical problems. Finally, these functionals are used in the explicit evaluation of the momentum expectation values and of the D-dimensional hydrogenic atom with nuclear charge Z⩾1. The power expectation values are given by means of a terminating 5F4 hypergeometric function with unit argument, which is a considerable improvement with respect to Hey's expression (the only one existing up to now) which requires a double sum.

Elementary functions in thermodynamic Bethe ansatz

NASA Astrophysics Data System (ADS)

Suzuki, J.

2015-05-01

Some years ago, Fendley found an explicit solution to the thermodynamic Bethe ansatz (TBA) equation for an N=2 supersymmetric theory in 2D with a specific F-term. Motivated by this, we seek explicit solutions for other super-potential cases utilizing the idea from the ODE/IM correspondence. We find that the TBA equations, corresponding to a wider class of super-potentials, admit solutions in terms of elementary functions such as modified Bessel functions and confluent hyper-geometric series. Based on talks given at ‘Infinite Analysis 2014’ (Tokyo, 2014) and at ‘Integrable lattice models and quantum field theories’ (Bad Honnef, 2014).

Umbral Calculus and Holonomic Modules in Positive Characteristic

NASA Astrophysics Data System (ADS)

Kochubei, Anatoly N.

2006-03-01

In the framework of analysis over local fields of positive characteristic, we develop algebraic tools for introducing and investigating various polynomial systems. In this survey paper we describe a function field version of umbral calculus developed on the basis of a relation of binomial type satisfied by the Carlitz polynomials. We consider modules over the Weyl-Carlitz ring, a function field counterpart of the Weyl algebra. It is shown that some basic objects of function field arithmetic, like the Carlitz module, Thakur's hypergeometric polynomials, and analogs of binomial coefficients arising in the positive characteristic version of umbral calculus, generate holonomic modules.

Efficient algorithms for construction of recurrence relations for the expansion and connection coefficients in series of Al-Salam Carlitz I polynomials

NASA Astrophysics Data System (ADS)

Doha, E. H.; Ahmed, H. M.

2005-12-01

Two formulae expressing explicitly the derivatives and moments of Al-Salam-Carlitz I polynomials of any degree and for any order in terms of Al-Salam-Carlitz I themselves are proved. Two other formulae for the expansion coefficients of general-order derivatives Dpqf(x), and for the moments xellDpqf(x), of an arbitrary function f(x) in terms of its original expansion coefficients are also obtained. Application of these formulae for solving q-difference equations with varying coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained. An algebraic symbolic approach (using Mathematica) in order to build and solve recursively for the connection coefficients between Al-Salam-Carlitz I polynomials and any system of basic hypergeometric orthogonal polynomials, belonging to the q-Hahn class, is described.

Faà di Bruno's formula and the distributions of random partitions in population genetics and physics.

PubMed

Hoppe, Fred M

2008-06-01

We show that the formula of Faà di Bruno for the derivative of a composite function gives, in special cases, the sampling distributions in population genetics that are due to Ewens and to Pitman. The composite function is the same in each case. Other sampling distributions also arise in this way, such as those arising from Dirichlet, multivariate hypergeometric, and multinomial models, special cases of which correspond to Bose-Einstein, Fermi-Dirac, and Maxwell-Boltzmann distributions in physics. Connections are made to compound sampling models.

Diffraction Theory for Polygonal Apertures

DTIC Science & Technology

1988-07-01

and utilized oblate spheroidal vector wave functions, and Nomura and Katsura (1955), who employed an expansion of the hypergeometric polynomial ...21 2 - 1 4, 2 - 1 3 4k3 - 3k 8 3 - 4 factor relates directly to the orthogonality relations for the Chebyshev polynomials given below. I T(Q TieQdk...convergence. 3.1.2.2 Gaussian Illuminated Corner In the sample calculation just discussed we discovered some of the basic characteristics of the GBE

- XSUMMER- Transcendental functions and symbolic summation in FORM

NASA Astrophysics Data System (ADS)

Moch, S.; Uwer, P.

2006-05-01

Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums, where the harmonic sums and their generalizations appear as building blocks, originating for example, from the expansion of generalized hypergeometric functions around integer values of the parameters. In this paper we discuss the implementation of several algorithms to solve these sums by algebraic means, using the computer algebra system FORM. Program summaryTitle of program:XSUMMER Catalogue identifier:ADXQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXQ_v1_0 Program obtainable from:CPC Program Library, Queen's University of Belfast, N. Ireland License:GNU Public License and FORM License Computers:all Operating system:all Program language:FORM Memory required to execute:Depending on the complexity of the problem, recommended at least 64 MB RAM No. of lines in distributed program, including test data, etc.:9854 No. of bytes in distributed program, including test data, etc.:126 551 Distribution format:tar.gz Other programs called:none External files needed:none Nature of the physical problem:Systematic expansion of higher transcendental functions in a small parameter. The expansions arise in the calculation of loop integrals in perturbative quantum field theory. Method of solution:Algebraic manipulations of nested sums. Restrictions on complexity of the problem:Usually limited only by the available disk space. Typical running time:Dependent on the complexity of the problem.

Extended nonlinear feedback model for describing episodes of high inflation

NASA Astrophysics Data System (ADS)

Szybisz, Martín A.; Szybisz, Leszek

2017-01-01

An extension of the nonlinear feedback (NLF) formalism to describe regimes of hyper- and high-inflation in economy is proposed in the present work. In the NLF model the consumer price index (CPI) exhibits a finite time singularity of the type 1 /(tc - t) (1 - β) / β, with β > 0, predicting a blow up of the economy at a critical time tc. However, this model fails in determining tc in the case of weak hyperinflation regimes like, e.g., that occurred in Israel. To overcome this trouble, the NLF model is extended by introducing a parameter γ, which multiplies all terms with past growth rate index (GRI). In this novel approach the solution for CPI is also analytic being proportional to the Gaussian hypergeometric function 2F1(1 / β , 1 / β , 1 + 1 / β ; z) , where z is a function of β, γ, and tc. For z → 1 this hypergeometric function diverges leading to a finite time singularity, from which a value of tc can be determined. This singularity is also present in GRI. It is shown that the interplay between parameters β and γ may produce phenomena of multiple equilibria. An analysis of the severe hyperinflation occurred in Hungary proves that the novel model is robust. When this model is used for examining data of Israel a reasonable tc is got. High-inflation regimes in Mexico and Iceland, which exhibit weaker inflations than that of Israel, are also successfully described.

Analytical study of fractional equations describing anomalous diffusion of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, A. M.; Fichtner, H.; Schlickeiser, R.; Elhanbaly, A.

2017-06-01

To present the main influence of anomalous diffusion on the energetic particle propagation, the fractional derivative model of transport is developed by deriving the fractional modified Telegraph and Rayleigh equations. Analytical solutions of the fractional modified Telegraph and the fractional Rayleigh equations, which are defined in terms of Caputo fractional derivatives, are obtained by using the Laplace transform and the Mittag-Leffler function method. The solutions of these fractional equations are given in terms of special functions like Fox’s H, Mittag-Leffler, Hermite and Hyper-geometric functions. The predicted travelling pulse solutions are discussed in each case for different values of fractional order.

High-temperature asymptotics of supersymmetric partition functions

DOE PAGES

Ardehali, Arash Arabi

2016-07-05

We study the supersymmetric partition function of 4d supersymmetric gauge theories with a U(1) R-symmetry on Euclidean S 3 × S β 1, with S 3 the unit-radius squashed three-sphere, and β the circumference of the circle. For superconformal theories, this partition function coincides (up to a Casimir energy factor) with the 4d superconformal index. The partition function can be computed exactly using the supersymmetric localization of the gauge theory path-integral. It takes the form of an elliptic hypergeometric integral, which may be viewed as a matrix-integral over the moduli space of the holonomies of the gauge fields around Smore » β 1. At high temperatures (β → 0, corresponding to the hyperbolic limit of the elliptic hypergeometric integral) we obtain from the matrix-integral a quantum effective potential for the holonomies. The effective potential is proportional to the temperature. Therefore the high-temperature limit further localizes the matrix-integral to the locus of the minima of the potential. If the effective potential is positive semi-definite, the leading high-temperature asymptotics of the partition function is given by the formula of Di Pietro and Komargodski, and the subleading asymptotics is connected to the Coulomb branch dynamics on R 3 × S 1. In theories where the effective potential is not positive semi-definite, the Di Pietro-Komargodski formula needs to be modified. In particular, this modification occurs in the SU(2) theory of Intriligator-Seiberg-Shenker, and the SO(N) theory of Brodie-Cho-Intriligator, both believed to exhibit “misleading” anomaly matchings, and both believed to yield interacting superconformal field theories with c < a. Lastly, two new simple tests for dualities between 4d supersymmetric gauge theories emerge as byproducts of our analysis.« less

Kicking the rugby ball: perturbations of 6D gauged chiral supergravity

NASA Astrophysics Data System (ADS)

Burgess, C. P.; de Rham, C.; Hoover, D.; Mason, D.; Tolley, A. J.

2007-02-01

We analyse the axially symmetric scalar perturbations of 6D chiral gauged supergravity compactified on the general warped geometries in the presence of two source branes. We find that all of the conical geometries are marginally stable for normalizable perturbations (in disagreement with some recent calculations) and the non-conical ones for regular perturbations, even though none of them are supersymmetric (apart from the trivial Salam Sezgin solution, for which there are no source branes). The marginal direction is the one whose presence is required by the classical scaling property of the field equations, and all other modes have positive squared mass. In the special case of the conical solutions, including (but not restricted to) the unwarped 'rugby-ball' solutions, we find closed-form expressions for the mode functions in terms of Legendre and hypergeometric functions. In so doing we show how to match the asymptotic near-brane form for the solution to the physics of the source branes, and thereby how to physically interpret perturbations which can be singular at the brane positions.

Acceptance sampling for attributes via hypothesis testing and the hypergeometric distribution

NASA Astrophysics Data System (ADS)

Samohyl, Robert Wayne

2017-10-01

This paper questions some aspects of attribute acceptance sampling in light of the original concepts of hypothesis testing from Neyman and Pearson (NP). Attribute acceptance sampling in industry, as developed by Dodge and Romig (DR), generally follows the international standards of ISO 2859, and similarly the Brazilian standards NBR 5425 to NBR 5427 and the United States Standards ANSI/ASQC Z1.4. The paper evaluates and extends the area of acceptance sampling in two directions. First, by suggesting the use of the hypergeometric distribution to calculate the parameters of sampling plans avoiding the unnecessary use of approximations such as the binomial or Poisson distributions. We show that, under usual conditions, discrepancies can be large. The conclusion is that the hypergeometric distribution, ubiquitously available in commonly used software, is more appropriate than other distributions for acceptance sampling. Second, and more importantly, we elaborate the theory of acceptance sampling in terms of hypothesis testing rigorously following the original concepts of NP. By offering a common theoretical structure, hypothesis testing from NP can produce a better understanding of applications even beyond the usual areas of industry and commerce such as public health and political polling. With the new procedures, both sample size and sample error can be reduced. What is unclear in traditional acceptance sampling is the necessity of linking the acceptable quality limit (AQL) exclusively to the producer and the lot quality percent defective (LTPD) exclusively to the consumer. In reality, the consumer should also be preoccupied with a value of AQL, as should the producer with LTPD. Furthermore, we can also question why type I error is always uniquely associated with the producer as producer risk, and likewise, the same question arises with consumer risk which is necessarily associated with type II error. The resolution of these questions is new to the literature. The article presents R code throughout.

Hantush Well Function revisited

NASA Astrophysics Data System (ADS)

Veling, E. J. M.; Maas, C.

2010-11-01

SummaryIn this paper, we comment on some recent numerical and analytical work to evaluate the Hantush Well Function. We correct an expression found in a Comment by Nadarajah [Nadarajah, S., 2007. A comment on numerical evaluation of Theis and Hantush-Jacob well functions. Journal of Hydrology 338, 152-153] to a paper by Prodanoff et al. [Prodanoff, J.A., Mansur, W.J., Mascarenhas, F.C.B., 2006. Numerical evaluation of Theis and Hantush-Jacob well functions. Journal of Hydrology 318, 173-183]. We subsequently derived another analytic representation based on a generalized hypergeometric function in two variables and from the hydrological literature we cite an analytic representation by Hunt [Hunt, B., 1977. Calculation of the leaky aquifer function. Journal of Hydrology 33, 179-183]. We have implemented both representations and compared the results. Using a convergence accelerator Hunt's representation of Hantush Well Function is efficient and accurate. While checking our implementations we found that Bear's table of the Hantush Well Function [Bear, J., 1979. Hydraulics of Groundwater. McGraw-Hill, New York, Tables 8-6] contains a number of typographical errors that are not present in the original table published by Hantush [Hantush, M.S., 1956. Analysis of data from pumping tests in leaky aquifers. Transactions, American Geophysical Union 37, 702-714]. Finally, we offer a very fast approximation with a maximum relative error of 0.0033 for the parameter range in the table given by Bear.

A family of analytic equilibrium solutions for the Grad-Shafranov equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guazzotto, L.; Freidberg, J. P.

2007-11-15

A family of exact solutions to the Grad-Shafranov equation, similar to those described by Atanasiu et al. [C. V. Atanasiu, S. Guenter, K. Lackner, and I. G. Miron, Phys. Plasmas 11, 3510 (2004)], is presented. The solution allows for finite plasma aspect ratio, elongation and triangularity, while only requiring the evaluation of a small number of well-known hypergeometric functions. Plasma current, pressure, and pressure gradients are set to zero at the plasma edge. Realistic equilibria for standard and spherical tokamaks are presented.

A bispectral q-hypergeometric basis for a class of quantum integrable models

NASA Astrophysics Data System (ADS)

Baseilhac, Pascal; Martin, Xavier

2018-01-01

For the class of quantum integrable models generated from the q-Onsager algebra, a basis of bispectral multivariable q-orthogonal polynomials is exhibited. In the first part, it is shown that the multivariable Askey-Wilson polynomials with N variables and N + 3 parameters introduced by Gasper and Rahman [Dev. Math. 13, 209 (2005)] generate a family of infinite dimensional modules for the q-Onsager algebra, whose fundamental generators are realized in terms of the multivariable q-difference and difference operators proposed by Iliev [Trans. Am. Math. Soc. 363, 1577 (2011)]. Raising and lowering operators extending those of Sahi [SIGMA 3, 002 (2007)] are also constructed. In the second part, finite dimensional modules are constructed and studied for a certain class of parameters and if the N variables belong to a discrete support. In this case, the bispectral property finds a natural interpretation within the framework of tridiagonal pairs. In the third part, eigenfunctions of the q-Dolan-Grady hierarchy are considered in the polynomial basis. In particular, invariant subspaces are identified for certain conditions generalizing Nepomechie's relations. In the fourth part, the analysis is extended to the special case q = 1. This framework provides a q-hypergeometric formulation of quantum integrable models such as the open XXZ spin chain with generic integrable boundary conditions (q ≠ 1).

Supersymmetric Casimir energy and SL(3,Z) transformations

NASA Astrophysics Data System (ADS)

Brünner, Frederic; Regalado, Diego; Spiridonov, Vyacheslav P.

2017-07-01

We provide a recipe to extract the supersymmetric Casimir energy of theories defined on primary Hopf surfaces directly from the superconformal index. It involves an SL(3,Z) transformation acting on the complex structure moduli of the background geometry. In particular, the known relation between Casimir energy, index and partition function emerges naturally from this framework, allowing rewriting of the latter as a modified elliptic hypergeometric integral. We show this explicitly for N=1 SQCD and N=4 supersymmetric Yang-Mills theory for all classical gauge groups, and conjecture that it holds more generally. We also use our method to derive an expression for the Casimir energy of the nonlagrangian N=2 SCFT with E6 flavour symmetry. Furthermore, we predict an expression for Casimir energy of the N=1 SP(2N) theory with SU(8) × U(1) flavour symmetry that is part of a multiple duality network, and for the doubled N=1 theory with enhanced E7 flavour symmetry.

A closed form of a kurtosis parameter of a hypergeometric-Gaussian type-II beam

NASA Astrophysics Data System (ADS)

F, Khannous; A, A. A. Ebrahim; A, Belafhal

2016-04-01

Based on the irradiance moment definition and the analytical expression of waveform propagation for hypergeometric-Gaussian type-II beams passing through an ABCD system, the kurtosis parameter is derived analytically and illustrated numerically. The kurtosis parameters of the Gaussian beam, modified Bessel modulated Gaussian beam with quadrature radial and elegant Laguerre-Gaussian beams are obtained by treating them as special cases of the present treatment. The obtained results show that the kurtosis parameter depends on the change of the beam order m and the hollowness parameter p, such as its decrease with increasing m and increase with increasing p.

Explicit densities of multidimensional ballistic Lévy walks.

PubMed

Magdziarz, Marcin; Zorawik, Tomasz

2016-08-01

Lévy walks have proved to be useful models of stochastic dynamics with a number of applications in the modeling of real-life phenomena. In this paper we derive explicit formulas for densities of the two- (2D) and three-dimensional (3D) ballistic Lévy walks, which are most important in applications. It turns out that in the 3D case the densities are given by elementary functions. The densities of the 2D Lévy walks are expressed in terms of hypergeometric functions and the right-side Riemann-Liouville fractional derivative, which allows us to efficiently evaluate them numerically. The theoretical results agree perfectly with Monte Carlo simulations.

The elastic field induced by a hemispherical inclusion in the half-space

NASA Astrophysics Data System (ADS)

Wu, Linzhi

2003-06-01

The elastic field induced by a hekispherical inclusion with uniform eigenstrains in a semi-infinite elastic medium is solved by using the Green's function method and series expansion technique. The exact solutions are presented for the displacement and stress fields which can be expressed by complete elliptic integrals of the first, second, and third kinds and hypergeometric functions. The present method can be used to determine the corresponding elastic fields when the shape of the inclusion is a spherical crown or a spherical segment. Finally, numerical results are given for the displacement and stress fields along the axis of symmetry ( x 3-axis).

Birth and evolution of an optical vortex.

PubMed

Vallone, Giuseppe; Sponselli, Anna; D'Ambrosio, Vincenzo; Marrucci, Lorenzo; Sciarrino, Fabio; Villoresi, Paolo

2016-07-25

When a phase singularity is suddenly imprinted on the axis of an ordinary Gaussian beam, an optical vortex appears and starts to grow radially, by effect of diffraction. This radial growth and the subsequent evolution of the optical vortex under focusing or imaging can be well described in general within the recently introduced theory of circular beams, which generalize the hypergeometric-Gaussian beams and which obey novel kinds of ABCD rules. Here, we investigate experimentally these vortex propagation phenomena and test the validity of circular-beam theory. Moreover, we analyze the difference in radial structure between the newly generated optical vortex and the vortex obtained in the image plane, where perfect imaging would lead to complete closure of the vortex core.

Methods in Symbolic Computation and p-Adic Valuations of Polynomials

NASA Astrophysics Data System (ADS)

Guan, Xiao

Symbolic computation has widely appear in many mathematical fields such as combinatorics, number theory and stochastic processes. The techniques created in the area of experimental mathematics provide us efficient ways of symbolic computing and verification of complicated relations. Part I consists of three problems. The first one focuses on a unimodal sequence derived from a quartic integral. Many of its properties are explored with the help of hypergeometric representations and automatic proofs. The second problem tackles the generating function of the reciprocal of Catalan number. It springs from the closed form given by Mathematica. Furthermore, three methods in special functions are used to justify this result. The third issue addresses the closed form solutions for the moments of products of generalized elliptic integrals , which combines the experimental mathematics and classical analysis. Part II concentrates on the p-adic valuations of polynomials from the perspective of trees. For a given polynomial f( n) indexed in positive integers, the package developed in Mathematica will create certain tree structure following a couple of rules. The evolution of such trees are studied both rigorously and experimentally from the view of field extension, nonparametric statistics and random matrix.

Quasinormal modes of the BTZ black hole under scalar perturbations with a non-minimal coupling: exact spectrum

NASA Astrophysics Data System (ADS)

Panotopoulos, Grigoris

2018-06-01

We perturb the non-rotating BTZ black hole with a non-minimally coupled massless scalar field, and we compute the quasinormal spectrum exactly. We solve the radial equation in terms of hypergeometric functions, and we obtain an analytical expression for the quasinormal frequencies. In addition, we compare our analytical results with the 6th order semi-analytical WKB method, and we find an excellent agreement. The impact of the nonminimal coupling as well as of the cosmological constant on the quasinormal spectrum is briefly discussed.

On the arbitrary l-wave solutions of the deformed hyperbolic manning-rosen potential including an improved approximation to the orbital centrifugal term

NASA Astrophysics Data System (ADS)

Xu, Chun-Long; Zhang, Min-Cang

2017-01-01

The arbitrary l-wave solutions to the Schrödinger equation for the deformed hyperbolic Manning-Rosen potential is investigated analytically by using the Nikiforov-Uvarov method, the centrifugal term is treated with an improved Greene and Aldrich's approximation scheme. The wavefunctions depend on the deformation parameter q, which is expressed in terms of the Jocobi polynomial or the hypergeometric function. The bound state energy is obtained, and the discrete spectrum is shown to be independent of the deformation parameter q.

Spiral Galaxy Lensing: A Model with Twist

NASA Astrophysics Data System (ADS)

Bell, Steven R.; Ernst, Brett; Fancher, Sean; Keeton, Charles R.; Komanduru, Abi; Lundberg, Erik

2014-12-01

We propose a single galaxy gravitational lensing model with a mass density that has a spiral structure. Namely, we extend the arcsine gravitational lens (a truncated singular isothermal elliptical model), adding an additional parameter that controls the amount of spiraling in the structure of the mass density. An important feature of our model is that, even though the mass density is sophisticated, we succeed in integrating the deflection term in closed form using a Gauss hypergeometric function. When the spiraling parameter is set to zero, this reduces to the arcsine lens.

Some Remarks on Solutions of Fermats Last Equation in Terms of Wright’s Hypergeometric Function

DTIC Science & Technology

1990-02-16

DISTRIBUTION/AVAILABILITY OF ABSTRACT 121 ABSTRACT SECURITY CLASSIFICATION MUNCLASSIFIED/UNLIMITED C SAME AS RPT 0 DTIC USERS UNCLASSIFIED 22a NAME...A) = (u/vl)", 4’ C \\) = (U/V)%, then from Lemma 2 we have (UsV2)n + (U2VI )n = V2) and the theorem is proved. ANOTHER DERIVATION OF EQ. (10) From Eq. (3... Ramanujan (7, pp. 71, 307] studied and derived solutions of trinonials in Chapter 3 of his notebooks (1903-1914) and in his first quarterly report

MAGNETO-ACOUSTIC WAVES IN A GRAVITATIONALLY STRATIFIED MAGNETIZED PLASMA: EIGEN-SOLUTIONS AND THEIR APPLICATIONS TO THE SOLAR ATMOSPHERE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mather, J. F.; Erdélyi, R., E-mail: robertus@sheffield.ac.uk

2016-05-10

Magneto-acoustic gravity (MAG) waves have been studied intensively in the context of astrophysical plasmas. There are three popular choices of analytic modeling using a Cartesian coordinate system: a magnetic field parallel, perpendicular, or at an angle to the gravitational field. Here, we study a gravitationally stratified plasma embedded in a parallel, so called vertical, magnetic field. We find a governing equation for the auxiliary quantity Θ = p {sub 1}/ ρ {sub 0}, and find solutions in terms of hypergeometric functions. With the convenient relationship between Θ and the vertical velocity component, v {sub z}, we derive the solution formore » v{sub z}. We show that the four linearly independent functions for v{sub z} can also be cast as single hypergeometric functions, rather than the Frobenius series derived by Leroy and Schwartz. We are then able to analyze a case of approximation for a one-layer solution, taking the small wavelength limit. Motivated by solar atmospheric applications, we finally commence study of the eigenmodes of perturbations for a two-layer model using our solutions, solving the dispersion relation numerically. We show that, for a transition between a photospheric and chromospheric plasma embedded in a vertical magnetic field, modes exist that are between the observationally widely investigated three and five minute oscillation periods, interpreted as solar global oscillations in the lower solar atmosphere . It is also shown that, when the density contrast between the layers is large (e.g., applied to photosphere/chromosphere-corona), the global eigenmodes are practically a superposition of the same as in each of the separate one-layer systems.« less

Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials

NASA Astrophysics Data System (ADS)

Hoque, Md. Fazlul; Marquette, Ian; Post, Sarah; Zhang, Yao-Zhong

2018-04-01

We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schrödinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms of Laguerre, Legendre and exceptional Jacobi polynomials (of hypergeometric type). We construct ladder and shift operators based on the corresponding wave functions and obtain their recurrence formulas. These recurrence relations are used to construct higher-order, algebraically independent integrals of motion to prove superintegrability of the Hamiltonian. The integrals form a higher rank polynomial algebra. By constructing the structure functions of the associated deformed oscillator algebras we derive the degeneracy of energy spectrum of the superintegrable system.

Hypergeometric Equation in Modeling Relativistic Isotropic Sphere

NASA Astrophysics Data System (ADS)

Thirukkanesh, S.; Ragel, F. C.

2014-04-01

We study the Einstein system of equations in static spherically symmetric spacetimes. We obtained classes of exact solutions to the Einstein system by transforming the condition for pressure isotropy to a hypergeometric equation choosing a rational form for one of the gravitational potentials. The solutions are given in simple form that is a desirable requisite to study the behavior of relativistic compact objects in detail. A physical analysis indicate that our models satisfy all the fundamental requirements of realistic star and match smoothly with the exterior Schwarzschild metric. The derived masses and densities are consistent with the previously reported experimental and theoretical studies describing strange stars. The models satisfy the standard energy conditions required by normal matter.

Hypergeometric Forms for Ising-Class Integrals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bailey, David H.; Borwein, David; Borwein, Jonathan M.

2006-07-01

We apply experimental-mathematical principles to analyzecertain integrals relevant to the Ising theory of solid-state physics. Wefind representations of the these integrals in terms of MeijerG-functions and nested-Barnes integrals. Our investigations began bycomputing 500-digit numerical values of Cn,k,namely a 2-D array of Isingintegrals for all integers n, k where n is in [2,12]and k is in [0,25].We found that some Cn,k enjoy exact evaluations involving DirichletL-functions or the Riemann zeta function. In theprocess of analyzinghypergeometric representations, we found -- experimentally and strikingly-- that the Cn,k almost certainly satisfy certain inter-indicialrelations including discrete k-recursions. Using generating functions,differential theory, complex analysis, and Wilf-Zeilbergermore » algorithms weare able to prove some central cases of these relations.« less

Calculating three loop ladder and V-topologies for massive operator matrix elements by computer algebra

NASA Astrophysics Data System (ADS)

Ablinger, J.; Behring, A.; Blümlein, J.; De Freitas, A.; von Manteuffel, A.; Schneider, C.

2016-05-01

Three loop ladder and V-topology diagrams contributing to the massive operator matrix element AQg are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable N and the dimensional parameter ε. Given these representations, the desired Laurent series expansions in ε can be obtained with the help of our computer algebra toolbox. Here we rely on generalized hypergeometric functions and Mellin-Barnes representations, on difference ring algorithms for symbolic summation, on an optimized version of the multivariate Almkvist-Zeilberger algorithm for symbolic integration, and on new methods to calculate Laurent series solutions of coupled systems of differential equations. The solutions can be computed for general coefficient matrices directly for any basis also performing the expansion in the dimensional parameter in case it is expressible in terms of indefinite nested product-sum expressions. This structural result is based on new results of our difference ring theory. In the cases discussed we deal with iterative sum- and integral-solutions over general alphabets. The final results are expressed in terms of special sums, forming quasi-shuffle algebras, such as nested harmonic sums, generalized harmonic sums, and nested binomially weighted (cyclotomic) sums. Analytic continuations to complex values of N are possible through the recursion relations obeyed by these quantities and their analytic asymptotic expansions. The latter lead to a host of new constants beyond the multiple zeta values, the infinite generalized harmonic and cyclotomic sums in the case of V-topologies.

Quantum Hurwitz numbers and Macdonald polynomials

NASA Astrophysics Data System (ADS)

Harnad, J.

2016-11-01

Parametric families in the center Z(C[Sn]) of the group algebra of the symmetric group are obtained by identifying the indeterminates in the generating function for Macdonald polynomials as commuting Jucys-Murphy elements. Their eigenvalues provide coefficients in the double Schur function expansion of 2D Toda τ-functions of hypergeometric type. Expressing these in the basis of products of power sum symmetric functions, the coefficients may be interpreted geometrically as parametric families of quantum Hurwitz numbers, enumerating weighted branched coverings of the Riemann sphere. Combinatorially, they give quantum weighted sums over paths in the Cayley graph of Sn generated by transpositions. Dual pairs of bases for the algebra of symmetric functions with respect to the scalar product in which the Macdonald polynomials are orthogonal provide both the geometrical and combinatorial significance of these quantum weighted enumerative invariants.

Construction of normal-regular decisions of Bessel typed special system

NASA Astrophysics Data System (ADS)

Tasmambetov, Zhaksylyk N.; Talipova, Meiramgul Zh.

2017-09-01

Studying a special system of differential equations in the separate production of the second order is solved by the degenerate hypergeometric function reducing to the Bessel functions of two variables. To construct a solution of this system near regular and irregular singularities, we use the method of Frobenius-Latysheva applying the concepts of rank and antirank. There is proved the basic theorem that establishes the existence of four linearly independent solutions of studying system type of Bessel. To prove the existence of normal-regular solutions we establish necessary conditions for the existence of such solutions. The existence and convergence of a normally regular solution are shown using the notion of rank and antirank.

Notes on integral identities for 3d supersymmetric dualities

NASA Astrophysics Data System (ADS)

Aghaei, Nezhla; Amariti, Antonio; Sekiguchi, Yuta

2018-04-01

Four dimensional N=2 Argyres-Douglas theories have been recently conjectured to be described by N=1 Lagrangian theories. Such models, once reduced to 3d, should be mirror dual to Lagrangian N=4 theories. This has been numerically checked through the matching of the partition functions on the three sphere. In this article, we provide an analytic derivation for this result in the A 2 n-1 case via hyperbolic hypergeometric integrals. We study the D 4 case as well, commenting on some open questions and possible resolutions. In the second part of the paper we discuss other integral identities leading to the matching of the partition functions in 3d dual pairs involving higher monopole superpotentials.

Goodness-of-fit tests for open capture-recapture models

USGS Publications Warehouse

Pollock, K.H.; Hines, J.E.; Nichols, J.D.

1985-01-01

General goodness-of-fit tests for the Jolly-Seber model are proposed. These tests are based on conditional arguments using minimal sufficient statistics. The tests are shown to be of simple hypergeometric form so that a series of independent contingency table chi-square tests can be performed. The relationship of these tests to other proposed tests is discussed. This is followed by a simulation study of the power of the tests to detect departures from the assumptions of the Jolly-Seber model. Some meadow vole capture-recapture data are used to illustrate the testing procedure which has been implemented in a computer program available from the authors.

Stability under scalar perturbations and quasinormal modes of 4D Einstein-Born-Infeld dilaton spacetime: exact spectrum

NASA Astrophysics Data System (ADS)

Destounis, Kyriakos; Panotopoulos, Grigoris; Rincón, Ángel

2018-02-01

We study the stability under scalar perturbations, and we compute the quasinormal modes of the Einstein-Born-Infeld dilaton spacetime in 1+3 dimensions. Solving the full radial equation in terms of hypergeometric functions, we provide an exact analytical expression for the spectrum. We find that the frequencies are purely imaginary, and we confirm our results by computing them numerically. Although the scalar field that perturbs the black hole is electrically neutral, an instability similar to that seen in charged scalar perturbations of the Reissner-Nordström black hole is observed.

Fractional dynamics using an ensemble of classical trajectories

NASA Astrophysics Data System (ADS)

Sun, Zhaopeng; Dong, Hao; Zheng, Yujun

2018-01-01

A trajectory-based formulation for fractional dynamics is presented and the trajectories are generated deterministically. In this theoretical framework, we derive a new class of estimators in terms of confluent hypergeometric function (F11) to represent the Riesz fractional derivative. Using this method, the simulation of free and confined Lévy flight are in excellent agreement with the exact numerical and analytical results. In addition, the barrier crossing in a bistable potential driven by Lévy noise of index α is investigated. In phase space, the behavior of trajectories reveal the feature of Lévy flight in a better perspective.

Reliability estimation of a N- M-cold-standby redundancy system in a multicomponent stress-strength model with generalized half-logistic distribution

NASA Astrophysics Data System (ADS)

Liu, Yiming; Shi, Yimin; Bai, Xuchao; Zhan, Pei

2018-01-01

In this paper, we study the estimation for the reliability of a multicomponent system, named N- M-cold-standby redundancy system, based on progressive Type-II censoring sample. In the system, there are N subsystems consisting of M statistically independent distributed strength components, and only one of these subsystems works under the impact of stresses at a time and the others remain as standbys. Whenever the working subsystem fails, one from the standbys takes its place. The system fails when the entire subsystems fail. It is supposed that the underlying distributions of random strength and stress both belong to the generalized half-logistic distribution with different shape parameter. The reliability of the system is estimated by using both classical and Bayesian statistical inference. Uniformly minimum variance unbiased estimator and maximum likelihood estimator for the reliability of the system are derived. Under squared error loss function, the exact expression of the Bayes estimator for the reliability of the system is developed by using the Gauss hypergeometric function. The asymptotic confidence interval and corresponding coverage probabilities are derived based on both the Fisher and the observed information matrices. The approximate highest probability density credible interval is constructed by using Monte Carlo method. Monte Carlo simulations are performed to compare the performances of the proposed reliability estimators. A real data set is also analyzed for an illustration of the findings.

Hipergeometric solutions to some nonhomogeneous equations of fractional order

NASA Astrophysics Data System (ADS)

Olivares, Jorge; Martin, Pablo; Maass, Fernando

2017-12-01

In this paper a study is performed to the solution of the linear non homogeneous fractional order alpha differential equation equal to I 0(x), where I 0(x) is the modified Bessel function of order zero, the initial condition is f(0)=0 and 0 < alpha < 1. Caputo definition for the fractional derivatives is considered. Fractional derivatives have become important in physical and chemical phenomena as visco-elasticity and visco-plasticity, anomalous diffusion and electric circuits. In particular in this work the values of alpha=1/2, 1/4 and 3/4. are explicitly considered . In these cases Laplace transform is applied, and later the inverse Laplace transform leads to the solutions of the differential equation, which become hypergeometric functions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Choun, Yoon Seok, E-mail: ychoun@gmail.com

The Heun function generalizes all well-known special functions such as Spheroidal Wave, Lame, Mathieu, and hypergeometric {sub 2}F{sub 1}, {sub 1}F{sub 1} and {sub 0}F{sub 1} functions. Heun functions are applicable to diverse areas such as theory of black holes, lattice systems in statistical mechanics, solution of the Schrödinger equation of quantum mechanics, and addition of three quantum spins. In this paper I will apply three term recurrence formula (Y.S. Choun, (arXiv:1303.0806), 2013) to the power series expansion in closed forms of Heun function (infinite series and polynomial) including all higher terms of A{sub n}’s. Section 3 contains my analysismore » on applying the power series expansions of Heun function to a recent paper (R.S. Maier, Math. Comp. 33 (2007) 811–843). Due to space restriction final equations for the 192 Heun functions are not included in the paper, but feel free to contact me for the final solutions. Section 4 contains two additional examples using the power series expansions of Heun function. This paper is 3rd out of 10 in series “Special functions and three term recurrence formula (3TRF)”. See Section 5 for all the papers in the series. The previous paper in series deals with three term recurrence formula (3TRF). The next paper in the series describes the integral forms of Heun function and its asymptotic behaviors analytically. -- Highlights: •Power series expansion for infinite series of Heun function using 3 term rec. form. •Power series for polynomial which makes B{sub n} term terminated of Heun function. •Applicable to areas such as the Teukolsky equation in Kerr–Newman–de Sitter geometries.« less

Propagation of hypergeometric Gaussian beams in strongly nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

Tang, Bin; Bian, Lirong; Zhou, Xin; Chen, Kai

2018-01-01

Optical vortex beams have attracted lots of interest due to its potential application in image processing, optical trapping and optical communications, etc. In this work, we theoretically and numerically investigated the propagation properties of hypergeometric Gaussian (HyGG) beams in strongly nonlocal nonlinear media. Based on the Snyder-Mitchell model, analytical expressions for propagation of the HyGG beams in strongly nonlocal nonlinear media were obtained. The influence of input power and optical parameters on the evolutions of the beam width and radius of curvature is illustrated, respectively. The results show that the beam width and radius of curvature of the HyGG beams remain invariant, like a soliton when the input power is equal to the critical power. Otherwise, it varies periodically like a breather, which is the result of competition between the beam diffraction and nonlinearity of the medium.

Evolution of spherical cavitation bubbles: Parametric and closed-form solutions

NASA Astrophysics Data System (ADS)

Mancas, Stefan C.; Rosu, Haret C.

2016-02-01

We present an analysis of the Rayleigh-Plesset equation for a three dimensional vacuous bubble in water. In the simplest case when the effects of surface tension are neglected, the known parametric solutions for the radius and time evolution of the bubble in terms of a hypergeometric function are briefly reviewed. By including the surface tension, we show the connection between the Rayleigh-Plesset equation and Abel's equation, and obtain the parametric rational Weierstrass periodic solutions following the Abel route. In the same Abel approach, we also provide a discussion of the nonintegrable case of nonzero viscosity for which we perform a numerical integration.

Elliptic Integrals in the Minkowski Plane

DTIC Science & Technology

1991-05-09

factorial Pochhammer notation F(a + k) (a)k - (a) Let F(a, b , c denote the hypergeometric function. Assume c - a - b = d , where d is a positive...integer. Then in a neighborhood of C = 1 , ((d) F(a+ b+d) d-1 (a)n (b)n )n(22) F(a , b , a + b + d , () = E~ )rb+ 0-’)n( ) r(a +d) r(b +d) n =O0( ’d’ n...axes a , b and eccentriaty e = c where c = Ta2 - b2 . Let P denote one of the foci of the ellipse. Then (26) 1 1 1 2 and(26) ar+(K, P) 2 -er F(- 1

Robust extraction of functional signals from gene set analysis using a generalized threshold free scoring function

PubMed Central

2009-01-01

Background A central task in contemporary biosciences is the identification of biological processes showing response in genome-wide differential gene expression experiments. Two types of analysis are common. Either, one generates an ordered list based on the differential expression values of the probed genes and examines the tail areas of the list for over-representation of various functional classes. Alternatively, one monitors the average differential expression level of genes belonging to a given functional class. So far these two types of method have not been combined. Results We introduce a scoring function, Gene Set Z-score (GSZ), for the analysis of functional class over-representation that combines two previous analysis methods. GSZ encompasses popular functions such as correlation, hypergeometric test, Max-Mean and Random Sets as limiting cases. GSZ is stable against changes in class size as well as across different positions of the analysed gene list in tests with randomized data. GSZ shows the best overall performance in a detailed comparison to popular functions using artificial data. Likewise, GSZ stands out in a cross-validation of methods using split real data. A comparison of empirical p-values further shows a strong difference in favour of GSZ, which clearly reports better p-values for top classes than the other methods. Furthermore, GSZ detects relevant biological themes that are missed by the other methods. These observations also hold when comparing GSZ with popular program packages. Conclusion GSZ and improved versions of earlier methods are a useful contribution to the analysis of differential gene expression. The methods and supplementary material are available from the website http://ekhidna.biocenter.helsinki.fi/users/petri/public/GSZ/GSZscore.html. PMID:19775443

Diagonal ordering operation technique applied to Morse oscillator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Popov, Dušan, E-mail: dusan_popov@yahoo.co.uk; Dong, Shi-Hai; Popov, Miodrag

2015-11-15

We generalize the technique called as the integration within a normally ordered product (IWOP) of operators referring to the creation and annihilation operators of the harmonic oscillator coherent states to a new operatorial approach, i.e. the diagonal ordering operation technique (DOOT) about the calculations connected with the normally ordered product of generalized creation and annihilation operators that generate the generalized hypergeometric coherent states. We apply this technique to the coherent states of the Morse oscillator including the mixed (thermal) state case and get the well-known results achieved by other methods in the corresponding coherent state representation. Also, in the lastmore » section we construct the coherent states for the continuous dynamics of the Morse oscillator by using two new methods: the discrete–continuous limit, respectively by solving a finite difference equation. Finally, we construct the coherent states corresponding to the whole Morse spectrum (discrete plus continuous) and demonstrate their properties according the Klauder’s prescriptions.« less

Atomic Gaussian type orbitals and their Fourier transforms via the Rayleigh expansion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yükçü, Niyazi

Gaussian type orbitals (GTOs), which are one of the types of exponential type orbitals (ETOs), are used usually as basis functions in the multi-center atomic and molecular integrals to better understand physical and chemical properties of matter. In the Fourier transform method (FTM), basis functions have not simplicity to make mathematical operations, but their Fourier transforms are easier to use. In this work, with the help of FTM, Rayleigh expansion and some properties of unnormalized GTOs, we present new mathematical results for the Fourier transform of GTOs in terms of Laguerre polynomials, hypergeometric and Whittaker functions. Physical and analytical propertiesmore » of GTOs are discussed and some numerical results have been given in a table. Finally, we compare our mathematical results with the other known literature results by using a computer program and details of evaluation are presented.« less

Static electric and magnetic multipole susceptibilities for Dirac one-electron atoms in the ground state

NASA Astrophysics Data System (ADS)

Szmytkowski, Radosław; Łukasik, Grzegorz

2016-09-01

We present tabulated data for several families of static electric and magnetic multipole susceptibilities for hydrogenic atoms with nuclear charge numbers from the range 1 ⩽ Z ⩽ 137. Atomic nuclei are assumed to be point-like and spinless. The susceptibilities considered include the multipole electric polarizabilities α E L → E L and magnetizabilities (magnetic susceptibilities) χ M L → M L with 1 ⩽ L ⩽ 4 (i.e., the dipole, quadrupole, octupole and hexadecapole ones), the electric-to-magnetic cross-susceptibilities α E L → M(L - 1) with 2 ⩽ L ⩽ 5 and α E L → M(L + 1) with 1 ⩽ L ⩽ 4, the magnetic-to-electric cross-susceptibilities χ M L → E(L - 1) with 2 ⩽ L ⩽ 5 and χ M L → E(L + 1) with 1 ⩽ L ⩽ 4 (it holds that χ M L → E(L ∓ 1) =α E(L ∓ 1) → M L), and the electric-to-toroidal-magnetic cross-susceptibilities α E L → T L with 1 ⩽ L ⩽ 4. Numerical values are computed from general exact analytical formulas, derived by us elsewhere within the framework of the Dirac relativistic quantum mechanics, and involving generalized hypergeometric functions 3F2 of the unit argument.

Wilson polynomials/functions and intertwining operators for the generic quantum superintegrable system on the 2-sphere

NASA Astrophysics Data System (ADS)

Miller, W., Jr.; Li, Q.

2015-04-01

The Wilson and Racah polynomials can be characterized as basis functions for irreducible representations of the quadratic symmetry algebra of the quantum superintegrable system on the 2-sphere, HΨ = EΨ, with generic 3-parameter potential. Clearly, the polynomials are expansion coefficients for one eigenbasis of a symmetry operator L2 of H in terms of an eigenbasis of another symmetry operator L1, but the exact relationship appears not to have been made explicit. We work out the details of the expansion to show, explicitly, how the polynomials arise and how the principal properties of these functions: the measure, 3-term recurrence relation, 2nd order difference equation, duality of these relations, permutation symmetry, intertwining operators and an alternate derivation of Wilson functions - follow from the symmetry of this quantum system. This paper is an exercise to show that quantum mechancal concepts and recurrence relations for Gausian hypergeometrc functions alone suffice to explain these properties; we make no assumptions about the structure of Wilson polynomial/functions, but derive them from quantum principles. There is active interest in the relation between multivariable Wilson polynomials and the quantum superintegrable system on the n-sphere with generic potential, and these results should aid in the generalization. Contracting function space realizations of irreducible representations of this quadratic algebra to the other superintegrable systems one can obtain the full Askey scheme of orthogonal hypergeometric polynomials. All of these contractions of superintegrable systems with potential are uniquely induced by Wigner Lie algebra contractions of so(3, C) and e(2,C). All of the polynomials produced are interpretable as quantum expansion coefficients. It is important to extend this process to higher dimensions.

Three friendly walkers

NASA Astrophysics Data System (ADS)

Jensen, Iwan

2017-01-01

More than 15 years ago Guttmann and Vöge (2002 J. Stat. Plan. Inference 101 107), introduced a model of friendly walkers. Since then it has remained unsolved. In this paper we provide the exact solution to a closely allied model which essentially only differs in the boundary conditions. The exact solution is expressed in terms of the reciprocal of the generating function for vicious walkers which is a D-finite function. However, ratios of D-finite functions are inherently not D-finite and in this case we prove that the friendly walkers generating function is the solution to a non-linear differential equation with polynomial coefficients, it is in other words D-algebraic. We find using numerically exact calculations a conjectured expression for the generating function of the original model as a ratio of a D-finite function and the generating function for vicious walkers. We obtain an expression for this D-finite function in terms of a {{}2}{{F}1} hypergeometric function with a rational pullback and its first and second derivatives. Dedicated to Tony Guttmann on the occasion of his 70th birthday.

On the performance of dual-hop mixed RF/FSO wireless communication system in urban area over aggregated exponentiated Weibull fading channels with pointing errors

NASA Astrophysics Data System (ADS)

Wang, Yue; Wang, Ping; Liu, Xiaoxia; Cao, Tian

2018-03-01

The performance of decode-and-forward dual-hop mixed radio frequency / free-space optical system in urban area is studied. The RF link is modeled by the Nakagami-m distribution and the FSO link is described by the composite exponentiated Weibull (EW) fading channels with nonzero boresight pointing errors (NBPE). For comparison, the ABER results without pointing errors (PE) and those with zero boresight pointing errors (ZBPE) are also provided. The closed-form expression for the average bit error rate (ABER) in RF link is derived with the help of hypergeometric function, and that in FSO link is obtained by Meijer's G and generalized Gauss-Laguerre quadrature functions. Then, the end-to-end ABERs with binary phase shift keying modulation are achieved on the basis of the computed ABER results of RF and FSO links. The end-to-end ABER performance is further analyzed with different Nakagami-m parameters, turbulence strengths, receiver aperture sizes and boresight displacements. The result shows that with ZBPE and NBPE considered, FSO link suffers a severe ABER degradation and becomes the dominant limitation of the mixed RF/FSO system in urban area. However, aperture averaging can bring significant ABER improvement of this system. Monte Carlo simulation is provided to confirm the validity of the analytical ABER expressions.

Designing a two-rank acceptance sampling plan for quality inspection of geospatial data products

NASA Astrophysics Data System (ADS)

Tong, Xiaohua; Wang, Zhenhua; Xie, Huan; Liang, Dan; Jiang, Zuoqin; Li, Jinchao; Li, Jun

2011-10-01

To address the disadvantages of classical sampling plans designed for traditional industrial products, we originally propose a two-rank acceptance sampling plan (TRASP) for the inspection of geospatial data outputs based on the acceptance quality level (AQL). The first rank sampling plan is to inspect the lot consisting of map sheets, and the second is to inspect the lot consisting of features in an individual map sheet. The TRASP design is formulated as an optimization problem with respect to sample size and acceptance number, which covers two lot size cases. The first case is for a small lot size with nonconformities being modeled by a hypergeometric distribution function, and the second is for a larger lot size with nonconformities being modeled by a Poisson distribution function. The proposed TRASP is illustrated through two empirical case studies. Our analysis demonstrates that: (1) the proposed TRASP provides a general approach for quality inspection of geospatial data outputs consisting of non-uniform items and (2) the proposed acceptance sampling plan based on TRASP performs better than other classical sampling plans. It overcomes the drawbacks of percent sampling, i.e., "strictness for large lot size, toleration for small lot size," and those of a national standard used specifically for industrial outputs, i.e., "lots with different sizes corresponding to the same sampling plan."

Vacuum polarization in Coulomb field revisited

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zamastil, J., E-mail: zamastil@karlov.mff.cuni.cz; Šimsa, D.

2017-04-15

Simplified derivation of Wichmann–Kroll term is presented. The derivation uses two formulas for hypergeometric functions, but otherwise is elementary. It is found that Laplace transform of the vacuum charge density diverges at zero momentum transfer. This divergence has nothing to do with known ultraviolet divergence. The latter is related to the large momentum behavior of the pertinent integral, while the former to the small momentum behavior. When these divergences are removed, the energy shift caused by vacuum polarization for an ordinary hydrogen obtained here is in an exact agreement with the result obtained by Wichmann and Kroll. Also, for muonicmore » hydrogen the result obtained here reasonably agrees with that given in literature.« less

Nonperturbative Quantum Physics from Low-Order Perturbation Theory.

PubMed

Mera, Héctor; Pedersen, Thomas G; Nikolić, Branislav K

2015-10-02

The Stark effect in hydrogen and the cubic anharmonic oscillator furnish examples of quantum systems where the perturbation results in a certain ionization probability by tunneling processes. Accordingly, the perturbed ground-state energy is shifted and broadened, thus acquiring an imaginary part which is considered to be a paradigm of nonperturbative behavior. Here we demonstrate how the low order coefficients of a divergent perturbation series can be used to obtain excellent approximations to both real and imaginary parts of the perturbed ground state eigenenergy. The key is to use analytic continuation functions with a built-in singularity structure within the complex plane of the coupling constant, which is tailored by means of Bender-Wu dispersion relations. In the examples discussed the analytic continuation functions are Gauss hypergeometric functions, which take as input fourth order perturbation theory and return excellent approximations to the complex perturbed eigenvalue. These functions are Borel consistent and dramatically outperform widely used Padé and Borel-Padé approaches, even for rather large values of the coupling constant.

Integrated metagenomic analysis of the rumen microbiome of cattle reveals key biological mechanisms associated with methane traits.

PubMed

Wang, Haiying; Zheng, Huiru; Browne, Fiona; Roehe, Rainer; Dewhurst, Richard J; Engel, Felix; Hemmje, Matthias; Lu, Xiangwu; Walsh, Paul

2017-07-15

Methane is one of the major contributors to global warming. The rumen microbiota is directly involved in methane production in cattle. The link between variation in rumen microbial communities and host genetics has important applications and implications in bioscience. Having the potential to reveal the full extent of microbial gene diversity and complex microbial interactions, integrated metagenomics and network analysis holds great promise in this endeavour. This study investigates the rumen microbial community in cattle through the integration of metagenomic and network-based approaches. Based on the relative abundance of 1570 microbial genes identified in a metagenomics analysis, the co-abundance network was constructed and functional modules of microbial genes were identified. One of the main contributions is to develop a random matrix theory-based approach to automatically determining the correlation threshold used to construct the co-abundance network. The resulting network, consisting of 549 microbial genes and 3349 connections, exhibits a clear modular structure with certain trait-specific genes highly over-represented in modules. More specifically, all the 20 genes previously identified to be associated with methane emissions are found in a module (hypergeometric test, p<10 -11 ). One third of genes are involved in methane metabolism pathways. The further examination of abundance profiles across 8 samples of genes highlights that the revealed pattern of metagenomics abundance has a strong association with methane emissions. Furthermore, the module is significantly enriched with microbial genes encoding enzymes that are directly involved in methanogenesis (hypergeometric test, p<10 -9 ). Copyright © 2017 Elsevier Inc. All rights reserved.

Mode coupling in vortex beams

NASA Astrophysics Data System (ADS)

Eyyuboğlu, Halil T.

2018-05-01

We examine the mode coupling in vortex beams. Mode coupling also known as the crosstalk takes place due to turbulent characteristics of the atmospheric communication medium. This way, the transmitted intrinsic mode of the vortex beam leaks power to other extrinsic modes, thus preventing the correct detection of the transmitted symbol which is usually encoded into the mode index or the orbital angular momentum state of the vortex beam. Here we investigate the normalized power mode coupling ratios of several types of vortex beams, namely, Gaussian vortex beam, Bessel Gaussian beam, hypergeometric Gaussian beam and Laguerre Gaussian beam. It is found that smaller mode numbers lead to less mode coupling. The same is partially observed for increasing source sizes. Comparing the vortex beams amongst themselves, it is seen that hypergeometric Gaussian beam is the one retaining the most power in intrinsic mode during propagation, but only at lowest mode index of unity. At higher mode indices this advantage passes over to the Gaussian vortex beam.

Variational Dirac-Hartree-Fock calculation of the Breit interaction

NASA Astrophysics Data System (ADS)

Goldman, S. P.

1988-04-01

The calculation of the retarded version of the Breit interaction in the context of the VDHF method is discussed. With the use of Slater-type basis functions, all the terms involved can be calculated in closed form. The results are expressed as an expansion in powers of one-electron energy differences and linear combinations of hypergeometric functions. Convergence is fast and high accuracy is obtained with a small number of terms in the expansion even for high values of the nuclear charge. An added advantage is that the lowest order cancellations occurring in the retardation terms are accounted for exactly a priori. A comparison of the number of terms in the total expansion needed for an accuracy of 12 significant digits in the total energy, as well as a comparison of the results with an without retardation and in the local potential approximation, are presented for the carbon isoelectronic sequence.

Phase function of a spherical particle when scattering an inhomogeneous electromagnetic plane wave.

PubMed

Frisvad, Jeppe Revall

2018-04-01

In absorbing media, electromagnetic plane waves are most often inhomogeneous. Existing solutions for the scattering of an inhomogeneous plane wave by a spherical particle provide no explicit expressions for the scattering components. In addition, current analytical solutions require evaluation of the complex hypergeometric function F 1 2 for every term of a series expansion. In this work, I develop a simpler solution based on associated Legendre functions with argument zero. It is similar to the solution for homogeneous plane waves but with new explicit expressions for the angular dependency of the far-field scattering components, that is, the phase function. I include recurrence formulas for practical evaluation and provide numerical examples to evaluate how well the new expressions match previous work in some limiting cases. The predicted difference in the scattering phase function due to inhomogeneity is not negligible for light entering an absorbing medium at an oblique angle. The presented theory could thus be useful for predicting scattering behavior in dye-based random lasing and in solar cell absorption enhancement.

Coagulation-fragmentation for a finite number of particles and application to telomere clustering in the yeast nucleus

NASA Astrophysics Data System (ADS)

Hozé, Nathanaël; Holcman, David

2012-01-01

We develop a coagulation-fragmentation model to study a system composed of a small number of stochastic objects moving in a confined domain, that can aggregate upon binding to form local clusters of arbitrary sizes. A cluster can also dissociate into two subclusters with a uniform probability. To study the statistics of clusters, we combine a Markov chain analysis with a partition number approach. Interestingly, we obtain explicit formulas for the size and the number of clusters in terms of hypergeometric functions. Finally, we apply our analysis to study the statistical physics of telomeres (ends of chromosomes) clustering in the yeast nucleus and show that the diffusion-coagulation-fragmentation process can predict the organization of telomeres.

Fuchsian triangle groups and Grothendieck dessins. Variations on a theme of Belyi

NASA Astrophysics Data System (ADS)

Cohen, Paula Beazley; Itzykson, Claude; Wolfart, Jürgen

1994-07-01

According to a theorem of Belyi, a smooth projective algebraic curve is defined over a number field if and only if there exists a non-constant element of its function field ramified only over 0, 1 and . The existence of such a Belyi function is equivalent to that of a representation of the curve as a possibly compactified quotient space of the Poincaré upper half plane by a subgroup of finite index in a Fuchsian triangle group. On the other hand, Fuchsian triangle groups arise in many contexts, such as in the theory of hypergeometric functions and certain triangular billiard problems, which would appear at first sight to have no relation to the Galois problems that motivated the above discovery of Belyi. In this note we review several results related to Belyi's theorem and we develop certain aspects giving examples. For preliminary accounts, see the preprint [Wo1], the conference proceedings article [BauItz] and the Comptes Rendus note [CoWo2].

Optimal Keno Strategies and the Central Limit Theorem

ERIC Educational Resources Information Center

Johnson, Roger W.

2006-01-01

For the casino game Keno we determine optimal playing strategies. To decide such optimal strategies, both exact (hypergeometric) and approximate probability calculations are used. The approximate calculations are obtained via the Central Limit Theorem and simulation, and an important lesson about the application of the Central Limit Theorem is…

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ahmed, Jawad; Shahzad, Azeem; Khan, Masood

This article focuses on the exact solution regarding convective heat transfer of a magnetohydrodynamic (MHD) Jeffrey fluid over a stretching sheet. The effects of joule and viscous dissipation, internal heat source/sink and thermal radiation on the heat transfer characteristics are taken in account in the presence of a transverse magnetic field for two types of boundary heating process namely prescribed power law surface temperature (PST) and prescribed heat flux (PHF). Similarity transformations are used to reduce the governing non-linear momentum and thermal boundary layer equations into a set of ordinary differential equations. The exact solutions of the reduced ordinary differentialmore » equations are developed in the form of confluent hypergeometric function. The influence of the pertinent parameters on the temperature profile is examined. In addition the results for the wall temperature gradient are also discussed in detail.« less

Analytic properties for the honeycomb lattice Green function at the origin

NASA Astrophysics Data System (ADS)

Joyce, G. S.

2018-05-01

The analytic properties of the honeycomb lattice Green function are investigated, where is a complex variable which lies in a plane. This double integral defines a single-valued analytic function provided that a cut is made along the real axis from w  =  ‑3 to . In order to analyse the behaviour of along the edges of the cut it is convenient to define the limit function where . It is shown that and can be evaluated exactly for all in terms of various hypergeometric functions, where the argument function is always real-valued and rational. The second-order linear Fuchsian differential equation satisfied by is also used to derive series expansions for and which are valid in the neighbourhood of the regular singular points and . Integral representations are established for and , where with . In particular, it is proved that where J 0(z) and Y 0(z) denote Bessel functions of the first and second kind, respectively. The results derived in the paper are utilized to evaluate the associated logarithmic integral where w lies in the cut plane. A new set of orthogonal polynomials which are connected with the honeycomb lattice Green function are also briefly discussed. Finally, a link between and the theory of Pearson random walks in a plane is established.

Systems Biology Approaches for Discovering Biomarkers for Traumatic Brain Injury

DTIC Science & Technology

2013-07-01

injury (FPI), in which injury is produced by the impact of a pendulum onto a fluid reservoir, or controlled cortical impact (CCI), in which a rigid...algorithm, and the MSigDB Web site in Table 3 allows users to run GSEA on up- loaded data. One drawback to GSEA and the hypergeometric test is that

Exact axially symmetric galactic dynamos

NASA Astrophysics Data System (ADS)

Henriksen, R. N.; Woodfinden, A.; Irwin, J. A.

2018-05-01

We give a selection of exact dynamos in axial symmetry on a galactic scale. These include some steady examples, at least one of which is wholly analytic in terms of simple functions and has been discussed elsewhere. Most solutions are found in terms of special functions, such as associated Lagrange or hypergeometric functions. They may be considered exact in the sense that they are known to any desired accuracy in principle. The new aspect developed here is to present scale-invariant solutions with zero resistivity that are self-similar in time. The time dependence is either a power law or an exponential factor, but since the geometry of the solution is self-similar in time we do not need to fix a time to study it. Several examples are discussed. Our results demonstrate (without the need to invoke any other mechanisms) X-shaped magnetic fields and (axially symmetric) magnetic spiral arms (both of which are well observed and documented) and predict reversing rotation measures in galaxy haloes (now observed in the CHANG-ES sample) as well as the fact that planar magnetic spirals are lifted into the galactic halo.

Reconstruction of the static magnetic field of a magnetron

NASA Astrophysics Data System (ADS)

Krüger, Dennis; Köhn, Kevin; Gallian, Sara; Brinkmann, Ralf Peter

2018-06-01

The simulation of magnetron discharges requires a quantitatively correct mathematical model of the magnetic field structure. This study presents a method to construct such a model on the basis of a spatially restricted set of experimental data and a plausible a priori assumption on the magnetic field configuration. The example in focus is that of a planar circular magnetron. The experimental data are Hall probe measurements of the magnetic flux density in an accessible region above the magnetron plane [P. D. Machura et al., Plasma Sources Sci. Technol. 23, 065043 (2014)]. The a priori assumption reflects the actual design of the device, and it takes the magnetic field emerging from a center magnet of strength m C and vertical position d C and a ring magnet of strength m R , vertical position d R , and radius R. An analytical representation of the assumed field configuration can be formulated in terms of generalized hypergeometric functions. Fitting the ansatz to the experimental data with a least square method results in a fully specified analytical field model that agrees well with the data inside the accessible region and, moreover, is physically plausible in the regions outside of it. The outcome proves superior to the result of an alternative approach which starts from a multimode solution of the vacuum field problem formulated in terms of polar Bessel functions and vertical exponentials. As a first application of the obtained field model, typical electron and ion Larmor radii and the gradient and curvature drift velocities of the electron guiding center are calculated.

On the origins of generalized fractional calculus

NASA Astrophysics Data System (ADS)

Kiryakova, Virginia

2015-11-01

In Fractional Calculus (FC), as in the (classical) Calculus, the notions of derivatives and integrals (of first, second, etc. or arbitrary, incl. non-integer order) are basic and co-related. One of the most frequent approach in FC is to define first the Riemann-Liouville (R-L) integral of fractional order, and then by means of suitable integer-order differentiation operation applied over it (or under its sign) a fractional derivative is defined - in the R-L sense (or in Caputo sense). The first mentioned (R-L type) is closer to the theoretical studies in analysis, but has some shortages - from the point of view of interpretation of the initial conditions for Cauchy problems for fractional differential equations (stated also by means of fractional order derivatives/ integrals), and also for the analysts' confusion that such a derivative of a constant is not zero in general. The Caputo (C-) derivative, arising first in geophysical studies, helps to overcome these problems and to describe models of applied problems with physically consistent initial conditions. The operators of the Generalized Fractional Calculus - GFC (integrals and derivatives) are based on commuting m-tuple (m = 1, 2, 3, …) compositions of operators of the classical FC with power weights (the so-called Erdélyi-Kober operators), but represented in compact and explicit form by means of integral, integro-differential (R-L type) or differential-integral (C-type) operators, where the kernels are special functions of most general hypergeometric kind. The foundations of this theory are given in Kiryakova 18. In this survey we present the genesis of the definitions of the GFC - the generalized fractional integrals and derivatives (of fractional multi-order) of R-L type and Caputo type, analyze their properties and applications. Their special cases are all the known operators of classical FC, their generalizations introduced by other authors, the hyper-Bessel differential operators of higher integer order m as a multi-order (1, 1,…, 1), the Gelfond-Leontiev generalized differentiation operators, many other integral and differential operators in Calculus that have been used in various topics, some of them not related to FC at all, others involved in differential and integral equations for treating fractional order models.

Unsteady flow of fractional Oldroyd-B fluids through rotating annulus

NASA Astrophysics Data System (ADS)

Tahir, Madeeha; Naeem, Muhammad Nawaz; Javaid, Maria; Younas, Muhammad; Imran, Muhammad; Sadiq, Naeem; Safdar, Rabia

2018-04-01

In this paper exact solutions corresponding to the rotational flow of a fractional Oldroyd-B fluid, in an annulus, are determined by applying integral transforms. The fluid starts moving after t = 0+ when pipes start rotating about their axis. The final solutions are presented in the form of usual Bessel and hypergeometric functions, true for initial and boundary conditions. The limiting cases for the solutions for ordinary Oldroyd-B, fractional Maxwell and Maxwell and Newtonian fluids are obtained. Moreover, the solution is obtained for the fluid when one pipe is rotating and the other one is at rest. At the end of this paper some characteristics of fluid motion, the effect of the physical parameters on the flow and a correlation between different fluid models are discussed. Finally, graphical representations confirm the above affirmation.

Dynamics of Proton Spin: Role of qqq Force

NASA Astrophysics Data System (ADS)

Mitra, A. N.

The analytic structure of the qqq wave function, obtained recently in the high momentum regime of QCD, is employed for the formulation of baryonic transition amplitudes via quark loops. A new aspect of this study is the role of a direct (Y -shaped, Mercedes-Benz type) qqq force in generating the qqq wave function The dynamics is that of a Salpeter-like equation (3D support for the kernel) formulated covariantly on the light front, a la Markov-Yukawa Transversality Principle (MYTP) which warrants a 2-way interconnection between the 3D and 4D Bethe-Salpeter (BSE) forms for 2 as well as 3 fermion quarks. The dynamics of this 3-body force shows up through a characteristic singularity in the hypergeometric differential equation for the 3D wave function ϕ, corresponding to a negative eigenvalue of the spin operator iσ1·σ2 × σ3 which is an integral part of the qqq force. As a first application of this wave function to the problem of the proton spin anomaly, the two-gluon contribution to the anomaly yields an estimate of the right sign, although somewhat smaller in magnitude.

Analytical time-domain Green’s functions for power-law media

PubMed Central

Kelly, James F.; McGough, Robert J.; Meerschaert, Mark M.

2008-01-01

Frequency-dependent loss and dispersion are typically modeled with a power-law attenuation coefficient, where the power-law exponent ranges from 0 to 2. To facilitate analytical solution, a fractional partial differential equation is derived that exactly describes power-law attenuation and the Szabo wave equation [“Time domain wave-equations for lossy media obeying a frequency power-law,” J. Acoust. Soc. Am. 96, 491–500 (1994)] is an approximation to this equation. This paper derives analytical time-domain Green’s functions in power-law media for exponents in this range. To construct solutions, stable law probability distributions are utilized. For exponents equal to 0, 1∕3, 1∕2, 2∕3, 3∕2, and 2, the Green’s function is expressed in terms of Dirac delta, exponential, Airy, hypergeometric, and Gaussian functions. For exponents strictly less than 1, the Green’s functions are expressed as Fox functions and are causal. For exponents greater than or equal than 1, the Green’s functions are expressed as Fox and Wright functions and are noncausal. However, numerical computations demonstrate that for observation points only one wavelength from the radiating source, the Green’s function is effectively causal for power-law exponents greater than or equal to 1. The analytical time-domain Green’s function is numerically verified against the material impulse response function, and the results demonstrate excellent agreement. PMID:19045774

Using Patterns of Summed Scores in Paper-and-Pencil Tests and Computer-Adaptive Tests to Detect Misfitting Item Score Patterns

ERIC Educational Resources Information Center

Meijer, Rob R.

2004-01-01

Two new methods have been proposed to determine unexpected sum scores on sub-tests (testlets) both for paper-and-pencil tests and computer adaptive tests. A method based on a conservative bound using the hypergeometric distribution, denoted p, was compared with a method where the probability for each score combination was calculated using a…

Higher order derivatives of R-Jacobi polynomials

NASA Astrophysics Data System (ADS)

Das, Sourav; Swaminathan, A.

2016-06-01

In this work, the R-Jacobi polynomials defined on the nonnegative real axis related to F-distribution are considered. Using their Sturm-Liouville system higher order derivatives are constructed. Orthogonality property of these higher ordered R-Jacobi polynomials are obtained besides their normal form, self-adjoint form and hypergeometric representation. Interesting results on the Interpolation formula and Gaussian quadrature formulae are obtained with numerical examples.

New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems

PubMed Central

Abd-Elhameed, W. M.

2014-01-01

This paper is concerned with deriving some new formulae expressing explicitly the high-order derivatives of Jacobi polynomials whose parameters difference is one or two of any degree and of any order in terms of their corresponding Jacobi polynomials. The derivatives formulae for Chebyshev polynomials of third and fourth kinds of any degree and of any order in terms of their corresponding Chebyshev polynomials are deduced as special cases. Some new reduction formulae for summing some terminating hypergeometric functions of unit argument are also deduced. As an application, and with the aid of the new introduced derivatives formulae, an algorithm for solving special sixth-order boundary value problems are implemented with the aid of applying Galerkin method. A numerical example is presented hoping to ascertain the validity and the applicability of the proposed algorithms. PMID:25386599

On the Runge-Lenz-Pauli vector operator as an aid to the calculation of atomic processes in laboratory and astrophysical plasmas

NASA Astrophysics Data System (ADS)

Hey, J. D.

2015-09-01

On the basis of the original definition and analysis of the vector operator by Pauli (1926 Z. Phys. 36 336-63), and further developments by Flamand (1966 J. Math. Phys. 7 1924-31), and by Becker and Bleuler (1976 Z. Naturforsch. 31a 517-23), we consider the action of the operator on both spherical polar and parabolic basis state wave functions, both with and without direct use of Pauli’s identity (Valent 2003 Am. J. Phys. 71 171-75). Comparison of the results, with the aid of two earlier papers (Hey 2006 J. Phys. B: At. Mol. Opt. Phys. 39 2641-64, Hey 2007 J. Phys. B: At. Mol. Opt. Phys. 40 4077-96), yields a convenient ladder technique in the form of a recurrence relation for calculating the transformation coefficients between the two sets of basis states, without explicit use of generalized hypergeometric functions. This result is therefore very useful for application to Stark effect and impact broadening calculations applied to high-n radio recombination lines from tenuous space plasmas. We also demonstrate the versatility of the Runge-Lenz-Pauli vector operator as a means of obtaining recurrence relations between expectation values of successive powers of quantum mechanical operators, by using it to provide, as an example, a derivation of the Kramers-Pasternack relation. It is suggested that this operator, whose potential use in Stark- and Zeeman-effect calculations for magnetically confined fusion edge plasmas (Rosato, Marandet and Stamm 2014 J. Phys. B: At. Mol. Opt. Phys. 47 105702) and tenuous space plasmas ( H II regions) has not been fully explored and exploited, may yet be found to yield a number of valuable results for applications to plasma diagnostic techniques based upon rate calculations of atomic processes.

Multichannel conformal blocks for scattering amplitudes

NASA Astrophysics Data System (ADS)

Belitsky, A. V.

2018-05-01

By performing resummation of small fermion-antifermion pairs within the pentagon form factor program to scattering amplitudes in planar N = 4 superYang-Mills theory, we construct multichannel conformal blocks within the flux-tube picture for N-sided NMHV polygons. This procedure is equivalent to summation of descendants of conformal primaries in the OPE framework. The resulting conformal partial waves are determined by multivariable hypergeometric series of Lauricella-Saran type.

Firing-rate response of linear and nonlinear integrate-and-fire neurons to modulated current-based and conductance-based synaptic drive.

PubMed

Richardson, Magnus J E

2007-08-01

Integrate-and-fire models are mainstays of the study of single-neuron response properties and emergent states of recurrent networks of spiking neurons. They also provide an analytical base for perturbative approaches that treat important biological details, such as synaptic filtering, synaptic conductance increase, and voltage-activated currents. Steady-state firing rates of both linear and nonlinear integrate-and-fire models, receiving fluctuating synaptic drive, can be calculated from the time-independent Fokker-Planck equation. The dynamic firing-rate response is less easy to extract, even at the first-order level of a weak modulation of the model parameters, but is an important determinant of neuronal response and network stability. For the linear integrate-and-fire model the response to modulations of current-based synaptic drive can be written in terms of hypergeometric functions. For the nonlinear exponential and quadratic models no such analytical forms for the response are available. Here it is demonstrated that a rather simple numerical method can be used to obtain the steady-state and dynamic response for both linear and nonlinear models to parameter modulation in the presence of current-based or conductance-based synaptic fluctuations. To complement the full numerical solution, generalized analytical forms for the high-frequency response are provided. A special case is also identified--time-constant modulation--for which the response to an arbitrarily strong modulation can be calculated exactly.

Analytical theory of mesoscopic Bose-Einstein condensation in an ideal gas

NASA Astrophysics Data System (ADS)

Kocharovsky, Vitaly V.; Kocharovsky, Vladimir V.

2010-03-01

We find the universal structure and scaling of the Bose-Einstein condensation (BEC) statistics and thermodynamics (Gibbs free energy, average energy, heat capacity) for a mesoscopic canonical-ensemble ideal gas in a trap with an arbitrary number of atoms, any volume, and any temperature, including the whole critical region. We identify a universal constraint-cutoff mechanism that makes BEC fluctuations strongly non-Gaussian and is responsible for all unusual critical phenomena of the BEC phase transition in the ideal gas. The main result is an analytical solution to the problem of critical phenomena. It is derived by, first, calculating analytically the universal probability distribution of the noncondensate occupation, or a Landau function, and then using it for the analytical calculation of the universal functions for the particular physical quantities via the exact formulas which express the constraint-cutoff mechanism. We find asymptotics of that analytical solution as well as its simple analytical approximations which describe the universal structure of the critical region in terms of the parabolic cylinder or confluent hypergeometric functions. The obtained results for the order parameter, all higher-order moments of BEC fluctuations, and thermodynamic quantities perfectly match the known asymptotics outside the critical region for both low and high temperature limits. We suggest two- and three-level trap models of BEC and find their exact solutions in terms of the cutoff negative binomial distribution (which tends to the cutoff gamma distribution in the continuous limit) and the confluent hypergeometric distribution, respectively. Also, we present an exactly solvable cutoff Gaussian model of BEC in a degenerate interacting gas. All these exact solutions confirm the universality and constraint-cutoff origin of the strongly non-Gaussian BEC statistics. We introduce a regular refinement scheme for the condensate statistics approximations on the basis of the infrared universality of higher-order cumulants and the method of superposition and show how to model BEC statistics in the actual traps. In particular, we find that the three-level trap model with matching the first four or five cumulants is enough to yield remarkably accurate results for all interesting quantities in the whole critical region. We derive an exact multinomial expansion for the noncondensate occupation probability distribution and find its high-temperature asymptotics (Poisson distribution) and corrections to it. Finally, we demonstrate that the critical exponents and a few known terms of the Taylor expansion of the universal functions, which were calculated previously from fitting the finite-size simulations within the phenomenological renormalization-group theory, can be easily obtained from the presented full analytical solutions for the mesoscopic BEC as certain approximations in the close vicinity of the critical point.

On the Maximum-Weight Clique Problem.

DTIC Science & Technology

1985-06-01

hypergeometric distribution", Discrete Math . 25, 285-287 .* CHVATAL, V. (1983), Linear Programming, W.H. Freeman, New York/San Francisco. COOK, S.A. (1971...Annals Discrete Math . 21, 325-356 GROTSCHEL, M., L. LOVASZ, and A. SCHRIJVER ((1984b), "Relaxations of Vertex Packing", Preprint No. 35...de Grenoble. See also N. Sbihi, "Algorithme de recherche d’un stable de cardinalite maximum dans un graphe sans etoile", Discrete Math . 19 (1980), 53

A Bayesian mixture model for chromatin interaction data.

PubMed

Niu, Liang; Lin, Shili

2015-02-01

Chromatin interactions mediated by a particular protein are of interest for studying gene regulation, especially the regulation of genes that are associated with, or known to be causative of, a disease. A recent molecular technique, Chromatin interaction analysis by paired-end tag sequencing (ChIA-PET), that uses chromatin immunoprecipitation (ChIP) and high throughput paired-end sequencing, is able to detect such chromatin interactions genomewide. However, ChIA-PET may generate noise (i.e., pairings of DNA fragments by random chance) in addition to true signal (i.e., pairings of DNA fragments by interactions). In this paper, we propose MC_DIST based on a mixture modeling framework to identify true chromatin interactions from ChIA-PET count data (counts of DNA fragment pairs). The model is cast into a Bayesian framework to take into account the dependency among the data and the available information on protein binding sites and gene promoters to reduce false positives. A simulation study showed that MC_DIST outperforms the previously proposed hypergeometric model in terms of both power and type I error rate. A real data study showed that MC_DIST may identify potential chromatin interactions between protein binding sites and gene promoters that may be missed by the hypergeometric model. An R package implementing the MC_DIST model is available at http://www.stat.osu.edu/~statgen/SOFTWARE/MDM.

Divergence and evolution of assortative mating in a polygenic trait model of speciation with gene flow.

PubMed

Sachdeva, Himani; Barton, Nicholas H

2017-06-01

Assortative mating is an important driver of speciation in populations with gene flow and is predicted to evolve under certain conditions in few-locus models. However, the evolution of assortment is less understood for mating based on quantitative traits, which are often characterized by high genetic variability and extensive linkage disequilibrium between trait loci. We explore this scenario for a two-deme model with migration, by considering a single polygenic trait subject to divergent viability selection across demes, as well as assortative mating and sexual selection within demes, and investigate how trait divergence is shaped by various evolutionary forces. Our analysis reveals the existence of sharp thresholds of assortment strength, at which divergence increases dramatically. We also study the evolution of assortment via invasion of modifiers of mate discrimination and show that the ES assortment strength has an intermediate value under a range of migration-selection parameters, even in diverged populations, due to subtle effects which depend sensitively on the extent of phenotypic variation within these populations. The evolutionary dynamics of the polygenic trait is studied using the hypergeometric and infinitesimal models. We further investigate the sensitivity of our results to the assumptions of the hypergeometric model, using individual-based simulations. © 2017 The Author(s). Evolution © 2017 The Society for the Study of Evolution.

Exact e-e (exchange) correlations of 2-D quantum dots in magnetic field: Size extensive N = 3 , 4 , … , ‧ n ‧ -electron systems via multi-pole expansion

NASA Astrophysics Data System (ADS)

Aggarwal, Priyanka; Sharma, Shivalika; Singh, Sunny; Kaur, Harsimran; Hazra, Ram Kuntal

2017-04-01

Inclusion of coulomb interaction emerges with the complexity of either convergence of integrals or separation of variables of Schrödinger equations. For an N-electron system, interaction terms grow by N(N-1)/2 factors. Therefore, 2-e system stands as fundamental basic unit for generalized N-e systems. For the first time, we have evaluated e-e correlations in very simple and absolutely terminating finite summed hypergeometric series for 2-D double carrier parabolic quantum dot in both zero and arbitrary non-zero magnetic field (symmetric gauge) and have appraised these integrals in variational methods. The competitive role among confinement strength, magnetic field, mass of the carrier and dielectric constant of the medium on energy level diagram, level-spacing statistics, heat capacities (Cv at 1 K) and magnetization (T ∼ (0-1)K) is studied on systems spanning over wide range of materials (GaAs,Ge,CdS,SiO2 and He, etc). We have also constructed an exact theory for generalized correlated N-e 2-D quantum dots via multi-pole expansion but for the sake of compactness of the article we refrain from data.

DOSE: an R/Bioconductor package for disease ontology semantic and enrichment analysis.

PubMed

Yu, Guangchuang; Wang, Li-Gen; Yan, Guang-Rong; He, Qing-Yu

2015-02-15

Disease ontology (DO) annotates human genes in the context of disease. DO is important annotation in translating molecular findings from high-throughput data to clinical relevance. DOSE is an R package providing semantic similarity computations among DO terms and genes which allows biologists to explore the similarities of diseases and of gene functions in disease perspective. Enrichment analyses including hypergeometric model and gene set enrichment analysis are also implemented to support discovering disease associations of high-throughput biological data. This allows biologists to verify disease relevance in a biological experiment and identify unexpected disease associations. Comparison among gene clusters is also supported. DOSE is released under Artistic-2.0 License. The source code and documents are freely available through Bioconductor (http://www.bioconductor.org/packages/release/bioc/html/DOSE.html). Supplementary data are available at Bioinformatics online. gcyu@connect.hku.hk or tqyhe@jnu.edu.cn. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

NEAT: an efficient network enrichment analysis test.

PubMed

Signorelli, Mirko; Vinciotti, Veronica; Wit, Ernst C

2016-09-05

Network enrichment analysis is a powerful method, which allows to integrate gene enrichment analysis with the information on relationships between genes that is provided by gene networks. Existing tests for network enrichment analysis deal only with undirected networks, they can be computationally slow and are based on normality assumptions. We propose NEAT, a test for network enrichment analysis. The test is based on the hypergeometric distribution, which naturally arises as the null distribution in this context. NEAT can be applied not only to undirected, but to directed and partially directed networks as well. Our simulations indicate that NEAT is considerably faster than alternative resampling-based methods, and that its capacity to detect enrichments is at least as good as the one of alternative tests. We discuss applications of NEAT to network analyses in yeast by testing for enrichment of the Environmental Stress Response target gene set with GO Slim and KEGG functional gene sets, and also by inspecting associations between functional sets themselves. NEAT is a flexible and efficient test for network enrichment analysis that aims to overcome some limitations of existing resampling-based tests. The method is implemented in the R package neat, which can be freely downloaded from CRAN ( https://cran.r-project.org/package=neat ).

Symmetries and Special Solutions of Reductions of the Lattice Potential KdV Equation

NASA Astrophysics Data System (ADS)

Ormerod, Christopher M.

2014-01-01

We identify a periodic reduction of the non-autonomous lattice potential Korteweg-de Vries equation with the additive discrete Painlevé equation with E_6^{(1)} symmetry. We present a description of a set of symmetries of the reduced equations and their relations to the symmetries of the discrete Painlevé equation. Finally, we exploit the simple symmetric form of the reduced equations to find rational and hypergeometric solutions of this discrete Painlevé equation.

Charge-to-mass dispersion methods for abrasion-ablation fragmentation models

NASA Technical Reports Server (NTRS)

Townsend, L. W.; Norbury, J. W.

1985-01-01

Methods to describe the charge-to-mass dispersion distributions of projectile prefragments are presented and used to determine individual isotope cross-sections or various elements produced in the fragmentation of relativistic argon nuclei by carbon targets. Although slight improvements in predicted cross-sections are obtained for the quantum mechanical giant dipole resonance (GDR) distribution when compared qith the predictions of the geometric GDR model, the closest agreement between theory and experiment continues to be obtained with the simple hypergeometric distribution, which treats the nucleons in the nucleus as completely uncorrelated.

Random wandering of laser beams with orbital angular momentum during propagation through atmospheric turbulence.

PubMed

Aksenov, Valerii P; Kolosov, Valeriy V; Pogutsa, Cheslav E

2014-06-10

The propagation of laser beams having orbital angular momenta (OAM) in the turbulent atmosphere is studied numerically. The variance of random wandering of these beams is investigated with the use of the Monte Carlo technique. It is found that, among various types of vortex laser beams, such as the Laguerre-Gaussian (LG) beam, modified Bessel-Gaussian beam, and hypergeometric Gaussian beam, having identical initial effective radii and OAM, the LG beam occupying the largest effective volume in space is the most stable one.

Tensor products of U{sub q}{sup Prime }sl-caret(2)-modules and the big q{sup 2}-Jacobi function transform

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gade, R. M.

2013-01-15

Four tensor products of evaluation modules of the quantum affine algebra U{sub q}{sup Prime }sl-caret(2) obtained from the negative and positive series, the complementary and the strange series representations are investigated. Linear operators R(z) satisfying the intertwining property on finite linear combinations of the canonical basis elements of the tensor products are described in terms of two sets of infinite sums {l_brace}{tau}{sup (r,t)}{r_brace}{sub r,t Element-Of Z{sub {>=}{sub 0}}} and {l_brace}{tau}{sup (r,t)}{r_brace}{sub r,t Element-Of Z{sub {>=}{sub 0}}} involving big q{sup 2}-Jacobi functions or related nonterminating basic hypergeometric series. Inhomogeneous recurrence relations can be derived for both sets. Evaluations of the simplestmore » sums provide the corresponding initial conditions. For the first set of sums the relations entail a big q{sup 2}-Jacobi function transform pair. An integral decomposition is obtained for the sum {tau}{sup (r,t)}. A partial description of the relation between the decompositions of the tensor products with respect to U{sub q}sl(2) or with respect to its complement in U{sub q}{sup Prime }sl-caret(2) can be formulated in terms of Askey-Wilson function transforms. For a particular combination of two tensor products, the occurrence of proper U{sub q}{sup Prime }sl-caret(2)-submodules is discussed.« less

PubMed Phrases, an open set of coherent phrases for searching biomedical literature

PubMed Central

Kim, Sun; Yeganova, Lana; Comeau, Donald C.; Wilbur, W. John; Lu, Zhiyong

2018-01-01

In biomedicine, key concepts are often expressed by multiple words (e.g., ‘zinc finger protein’). Previous work has shown treating a sequence of words as a meaningful unit, where applicable, is not only important for human understanding but also beneficial for automatic information seeking. Here we present a collection of PubMed® Phrases that are beneficial for information retrieval and human comprehension. We define these phrases as coherent chunks that are logically connected. To collect the phrase set, we apply the hypergeometric test to detect segments of consecutive terms that are likely to appear together in PubMed. These text segments are then filtered using the BM25 ranking function to ensure that they are beneficial from an information retrieval perspective. Thus, we obtain a set of 705,915 PubMed Phrases. We evaluate the quality of the set by investigating PubMed user click data and manually annotating a sample of 500 randomly selected noun phrases. We also analyze and discuss the usage of these PubMed Phrases in literature search. PMID:29893755

Applicability of Kinematic and Diffusive models for mud-flows: a steady state analysis

NASA Astrophysics Data System (ADS)

Di Cristo, Cristiana; Iervolino, Michele; Vacca, Andrea

2018-04-01

The paper investigates the applicability of Kinematic and Diffusive Wave models for mud-flows with a power-law shear-thinning rheology. In analogy with a well-known approach for turbulent clear-water flows, the study compares the steady flow depth profiles predicted by approximated models with those of the Full Dynamic Wave one. For all the models and assuming an infinitely wide channel, the analytical solution of the flow depth profiles, in terms of hypergeometric functions, is derived. The accuracy of the approximated models is assessed by computing the average, along the channel length, of the errors, for several values of the Froude and kinematic wave numbers. Assuming the threshold value of the error equal to 5%, the applicability conditions of the two approximations have been individuated for several values of the power-law exponent, showing a crucial role of the rheology. The comparison with the clear-water results indicates that applicability criteria for clear-water flows do not apply to shear-thinning fluids, potentially leading to an incorrect use of approximated models if the rheology is not properly accounted for.

Mood stabilizing drugs regulate transcription of immune, neuronal and metabolic pathway genes in Drosophila.

PubMed

Herteleer, L; Zwarts, L; Hens, K; Forero, D; Del-Favero, J; Callaerts, P

2016-05-01

Lithium and valproate (VPA) are drugs used in the management of bipolar disorder. Even though they reportedly act on various pathways, the transcriptional targets relevant for disease mechanism and therapeutic effect remain unclear. Furthermore, multiple studies used lymphoblasts of bipolar patients as a cellular proxy, but it remains unclear whether peripheral cells provide a good readout for the effects of these drugs in the brain. We used Drosophila culture cells and adult flies to analyze the transcriptional effects of lithium and VPA and define mechanistic pathways. Transcriptional profiles were determined for Drosophila S2-cells and adult fly heads following lithium or VPA treatment. Gene ontology categories were identified using the DAVID functional annotation tool with a cut-off of p < 0.05. Significantly enriched GO terms were clustered using REVIGO and DAVID functional annotation clustering. Significance of overlap between transcript lists was determined with a Fisher's exact hypergeometric test. Treatment of cultured cells and adult flies with lithium and VPA induces transcriptional responses in genes with similar ontology, with as most prominent immune response, neuronal development, neuronal function, and metabolism. (i) Transcriptional effects of lithium and VPA in Drosophila S2 cells and heads show significant overlap. (ii) The overlap between transcriptional alterations in peripheral versus neuronal cells at the single gene level is negligible, but at the gene ontology and pathway level considerable overlap can be found. (iii) Lithium and VPA act on evolutionarily conserved pathways in Drosophila and mammalian models.

Candidate genes for obesity-susceptibility show enriched association within a large genome-wide association study for BMI.

PubMed

Vimaleswaran, Karani S; Tachmazidou, Ioanna; Zhao, Jing Hua; Hirschhorn, Joel N; Dudbridge, Frank; Loos, Ruth J F

2012-10-15

Before the advent of genome-wide association studies (GWASs), hundreds of candidate genes for obesity-susceptibility had been identified through a variety of approaches. We examined whether those obesity candidate genes are enriched for associations with body mass index (BMI) compared with non-candidate genes by using data from a large-scale GWAS. A thorough literature search identified 547 candidate genes for obesity-susceptibility based on evidence from animal studies, Mendelian syndromes, linkage studies, genetic association studies and expression studies. Genomic regions were defined to include the genes ±10 kb of flanking sequence around candidate and non-candidate genes. We used summary statistics publicly available from the discovery stage of the genome-wide meta-analysis for BMI performed by the genetic investigation of anthropometric traits consortium in 123 564 individuals. Hypergeometric, rank tail-strength and gene-set enrichment analysis tests were used to test for the enrichment of association in candidate compared with non-candidate genes. The hypergeometric test of enrichment was not significant at the 5% P-value quantile (P = 0.35), but was nominally significant at the 25% quantile (P = 0.015). The rank tail-strength and gene-set enrichment tests were nominally significant for the full set of genes and borderline significant for the subset without SNPs at P < 10(-7). Taken together, the observed evidence for enrichment suggests that the candidate gene approach retains some value. However, the degree of enrichment is small despite the extensive number of candidate genes and the large sample size. Studies that focus on candidate genes have only slightly increased chances of detecting associations, and are likely to miss many true effects in non-candidate genes, at least for obesity-related traits.

A New Family of Solvable Pearson-Dirichlet Random Walks

NASA Astrophysics Data System (ADS)

Le Caër, Gérard

2011-07-01

An n-step Pearson-Gamma random walk in ℝ d starts at the origin and consists of n independent steps with gamma distributed lengths and uniform orientations. The gamma distribution of each step length has a shape parameter q>0. Constrained random walks of n steps in ℝ d are obtained from the latter walks by imposing that the sum of the step lengths is equal to a fixed value. Simple closed-form expressions were obtained in particular for the distribution of the endpoint of such constrained walks for any d≥ d 0 and any n≥2 when q is either q = d/2 - 1 ( d 0=3) or q= d-1 ( d 0=2) (Le Caër in J. Stat. Phys. 140:728-751, 2010). When the total walk length is chosen, without loss of generality, to be equal to 1, then the constrained step lengths have a Dirichlet distribution whose parameters are all equal to q and the associated walk is thus named a Pearson-Dirichlet random walk. The density of the endpoint position of a n-step planar walk of this type ( n≥2), with q= d=2, was shown recently to be a weighted mixture of 1+ floor( n/2) endpoint densities of planar Pearson-Dirichlet walks with q=1 (Beghin and Orsingher in Stochastics 82:201-229, 2010). The previous result is generalized to any walk space dimension and any number of steps n≥2 when the parameter of the Pearson-Dirichlet random walk is q= d>1. We rely on the connection between an unconstrained random walk and a constrained one, which have both the same n and the same q= d, to obtain a closed-form expression of the endpoint density. The latter is a weighted mixture of 1+ floor( n/2) densities with simple forms, equivalently expressed as a product of a power and a Gauss hypergeometric function. The weights are products of factors which depends both on d and n and Bessel numbers independent of d.

4d N = 1 quiver gauge theories and the An Bailey lemma

NASA Astrophysics Data System (ADS)

Brünner, Frederic; Spiridonov, Vyacheslav P.

2018-03-01

We study the integral Bailey lemma associated with the An-root system and identities for elliptic hypergeometric integrals generated thereby. Interpreting integrals as superconformal indices of four-dimensional N = 1 quiver gauge theories with the gauge groups being products of SU(n + 1), we provide evidence for various new dualities. Further confirmation is achieved by explicitly checking that the `t Hooft anomaly matching conditions holds. We discuss a flavour symmetry breaking phenomenon for supersymmetric quantum chromodynamics (SQCD), and by making use of the Bailey lemma we indicate its manifestation in a web of linear quivers dual to SQCD that exhibits full s-confinement.

Exactly and quasi-exactly solvable 'discrete' quantum mechanics.

PubMed

Sasaki, Ryu

2011-03-28

A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional 'discrete' quantum mechanics is presented. It reproduces all the known Hamiltonians whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. Several new exactly and QES Hamiltonians are constructed. The sinusoidal coordinate plays an essential role.

Gravitational Collapse of Magnetized Clouds. II. The Role of Ohmic Dissipation

NASA Astrophysics Data System (ADS)

Shu, Frank H.; Galli, Daniele; Lizano, Susana; Cai, Mike

2006-08-01

We formulate the problem of magnetic field dissipation during the accretion phase of low-mass star formation, and we carry out the first step of an iterative solution procedure by assuming that the gas is in free fall along radial field lines. This so-called ``kinematic approximation'' ignores the back reaction of the Lorentz force on the accretion flow. In quasi-steady state and assuming the resistivity coefficient to be spatially uniform, the problem is analytically soluble in terms of Legendre's polynomials and hypergeometric confluent functions. The dissipation of the magnetic field occurs inside a region of radius inversely proportional to the mass of the central star (the ``Ohm radius''), where the magnetic field becomes asymptotically straight and uniform. In our solution the magnetic flux problem of star formation is avoided because the magnetic flux dragged in the accreting protostar is always zero. Our results imply that the effective resistivity of the infalling gas must be higher by at least 1 order of magnitude than the microscopic electric resistivity, to avoid conflict with measurements of paleomagnetism in meteorites and with the observed luminosity of regions of low-mass star formation.

GO-Bayes: Gene Ontology-based overrepresentation analysis using a Bayesian approach.

PubMed

Zhang, Song; Cao, Jing; Kong, Y Megan; Scheuermann, Richard H

2010-04-01

A typical approach for the interpretation of high-throughput experiments, such as gene expression microarrays, is to produce groups of genes based on certain criteria (e.g. genes that are differentially expressed). To gain more mechanistic insights into the underlying biology, overrepresentation analysis (ORA) is often conducted to investigate whether gene sets associated with particular biological functions, for example, as represented by Gene Ontology (GO) annotations, are statistically overrepresented in the identified gene groups. However, the standard ORA, which is based on the hypergeometric test, analyzes each GO term in isolation and does not take into account the dependence structure of the GO-term hierarchy. We have developed a Bayesian approach (GO-Bayes) to measure overrepresentation of GO terms that incorporates the GO dependence structure by taking into account evidence not only from individual GO terms, but also from their related terms (i.e. parents, children, siblings, etc.). The Bayesian framework borrows information across related GO terms to strengthen the detection of overrepresentation signals. As a result, this method tends to identify sets of closely related GO terms rather than individual isolated GO terms. The advantage of the GO-Bayes approach is demonstrated with a simulation study and an application example.

Hollow sinh-Gaussian beams and their paraxial properties.

PubMed

Sun, Qiongge; Zhou, Keya; Fang, Guangyu; Zhang, Guoqiang; Liu, Zhengjun; Liu, Shutian

2012-04-23

A new mathematical model of dark-hollow beams, described as hollow sinh-Gaussian (HsG) beams, has been introduced. The intensity distributions of HsG beams are characterized by a single bright ring along the propagation whose size is determined by the order of beams; the shape of the ring can be controlled by beam width and this leads to the elliptical HsG beams. Propagation characteristics of HsG beams through an ABCD optical system have been researched, they can be regarded as superposition of a series of Hypergeometric-Gaussian (HyGG) beams. As a numerical example, the propagation characteristics of HsG beams in free space have been demonstrated graphically. © 2012 Optical Society of America

Superbounce and loop quantum ekpyrotic cosmologies from modified gravity: F(R) , F(G) and F(T) theories

NASA Astrophysics Data System (ADS)

Odintsov, S. D.; Oikonomou, V. K.; Saridakis, Emmanuel N.

2015-12-01

We investigate the realization of two bouncing paradigms, namely of the superbounce and the loop quantum cosmological ekpyrosis, in the framework of various modified gravities. In particular, we focus on the F(R) , F(G) and F(T) gravities, and we reconstruct their specific subclasses which lead to such universe evolutions. These subclasses constitute from power laws, polynomials, or hypergeometric ansatzes, which can be approximated by power laws. The qualitative similarity of the different effective gravities which realize the above two bouncing cosmologies, indicates that a universality might be lying behind the bounce. Finally, performing a linear perturbation analysis, we show that the obtained solutions are conditionally or fully stable.

Advances in the theory of box integrals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bailey, David H.; Borwein, J.M.; Crandall, R.E.

2009-06-25

Box integrals - expectations <|{rvec r}|{sup s}> or <|{rvec r}-{rvec q}|{sup s}> over the unit n-cube (or n-box) - have over three decades been occasionally given closed forms for isolated n,s. By employing experimental mathematics together with a new, global analytic strategy, we prove that for n {le} 4 dimensions the box integrals are for any integer s hypergeometrically closed in a sense we clarify herein. For n = 5 dimensions, we show that a single unresolved integral we call K{sub 5} stands in the way of such hyperclosure proofs. We supply a compendium of exemplary closed forms that naturallymore » arise algorithmically from this theory.« less

Propagation of sound waves through a spatially homogeneous but smoothly time-dependent medium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hayrapetyan, A.G., E-mail: armen@physi.uni-heidelberg.de; Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg; Grigoryan, K.K.

2013-06-15

The propagation of sound through a spatially homogeneous but non-stationary medium is investigated within the framework of fluid dynamics. For a non-vortical fluid, especially, a generalized wave equation is derived for the (scalar) potential of the fluid velocity distribution in dependence of the equilibrium mass density of the fluid and the sound wave velocity. A solution of this equation for a finite transition period τ is determined in terms of the hypergeometric function for a phenomenologically realistic, sigmoidal change of the mass density and sound wave velocity. Using this solution, it is shown that the energy flux of the soundmore » wave is not conserved but increases always for the propagation through a non-stationary medium, independent of whether the equilibrium mass density is increased or decreased. It is found, moreover, that this amplification of the transmitted wave arises from an energy exchange with the medium and that its flux is equal to the (total) flux of the incident and the reflected wave. An interpretation of the reflected wave as a propagation of sound backward in time is given in close analogy to Feynman and Stueckelberg for the propagation of anti-particles. The reflection and transmission coefficients of sound propagating through a non-stationary medium is analyzed in more detail for hypersonic waves with transition periods τ between 15 and 200 ps as well as the transformation of infrasound waves in non-stationary oceans. -- Highlights: •Analytically exact study of sound propagation through a non-stationary medium. •Energy exchange between the non-stationary medium and the sound wave. •Transformation of hypersonic and ultrasound frequencies in non-stationary media. •Propagation of sound backward in time in close analogy to anti-particles. •Prediction of tsunamis both in spatially and temporally inhomogeneous oceans.« less

Systematic analysis of microarray datasets to identify Parkinson's disease‑associated pathways and genes.

PubMed

Feng, Yinling; Wang, Xuefeng

2017-03-01

In order to investigate commonly disturbed genes and pathways in various brain regions of patients with Parkinson's disease (PD), microarray datasets from previous studies were collected and systematically analyzed. Different normalization methods were applied to microarray datasets from different platforms. A strategy combining gene co‑expression networks and clinical information was adopted, using weighted gene co‑expression network analysis (WGCNA) to screen for commonly disturbed genes in different brain regions of patients with PD. Functional enrichment analysis of commonly disturbed genes was performed using the Database for Annotation, Visualization, and Integrated Discovery (DAVID). Co‑pathway relationships were identified with Pearson's correlation coefficient tests and a hypergeometric distribution‑based test. Common genes in pathway pairs were selected out and regarded as risk genes. A total of 17 microarray datasets from 7 platforms were retained for further analysis. Five gene coexpression modules were identified, containing 9,745, 736, 233, 101 and 93 genes, respectively. One module was significantly correlated with PD samples and thus the 736 genes it contained were considered to be candidate PD‑associated genes. Functional enrichment analysis demonstrated that these genes were implicated in oxidative phosphorylation and PD. A total of 44 pathway pairs and 52 risk genes were revealed, and a risk gene pathway relationship network was constructed. Eight modules were identified and were revealed to be associated with PD, cancers and metabolism. A number of disturbed pathways and risk genes were unveiled in PD, and these findings may help advance understanding of PD pathogenesis.

A new molecular evolution model for limited insertion independent of substitution.

PubMed

Lèbre, Sophie; Michel, Christian J

2013-10-01

We recently introduced a new molecular evolution model called the IDIS model for Insertion Deletion Independent of Substitution [13,14]. In the IDIS model, the three independent processes of substitution, insertion and deletion of residues have constant rates. In order to control the genome expansion during evolution, we generalize here the IDIS model by introducing an insertion rate which decreases when the sequence grows and tends to 0 for a maximum sequence length nmax. This new model, called LIIS for Limited Insertion Independent of Substitution, defines a matrix differential equation satisfied by a vector P(t) describing the sequence content in each residue at evolution time t. An analytical solution is obtained for any diagonalizable substitution matrix M. Thus, the LIIS model gives an expression of the sequence content vector P(t) in each residue under evolution time t as a function of the eigenvalues and the eigenvectors of matrix M, the residue insertion rate vector R, the total insertion rate r, the initial and maximum sequence lengths n0 and nmax, respectively, and the sequence content vector P(t0) at initial time t0. The derivation of the analytical solution is much more technical, compared to the IDIS model, as it involves Gauss hypergeometric functions. Several propositions of the LIIS model are derived: proof that the IDIS model is a particular case of the LIIS model when the maximum sequence length nmax tends to infinity, fixed point, time scale, time step and time inversion. Using a relation between the sequence length l and the evolution time t, an expression of the LIIS model as a function of the sequence length l=n(t) is obtained. Formulas for 'insertion only', i.e. when the substitution rates are all equal to 0, are derived at evolution time t and sequence length l. Analytical solutions of the LIIS model are explicitly derived, as a function of either evolution time t or sequence length l, for two classical substitution matrices: the 3-parameter symmetric substitution matrix [12] (LIIS-SYM3) and the HKY asymmetric substitution matrix[9] (LIIS-HKY). An evaluation of the LIIS model (precisely, LIIS-HKY) based on four statistical analyses of the GC content in complete genomes of four prokaryotic taxonomic groups, namely Chlamydiae, Crenarchaeota, Spirochaetes and Thermotogae, shows the expected improvement from the theory of the LIIS model compared to the IDIS model. Copyright © 2013 Elsevier Inc. All rights reserved.

Charged reflecting stars supporting charged massive scalar field configurations

NASA Astrophysics Data System (ADS)

Hod, Shahar

2018-03-01

The recently published no-hair theorems of Hod, Bhattacharjee, and Sarkar have revealed the intriguing fact that horizonless compact reflecting stars cannot support spatially regular configurations made of scalar, vector and tensor fields. In the present paper we explicitly prove that the interesting no-hair behavior observed in these studies is not a generic feature of compact reflecting stars. In particular, we shall prove that charged reflecting stars can support charged massive scalar field configurations in their exterior spacetime regions. To this end, we solve analytically the characteristic Klein-Gordon wave equation for a linearized charged scalar field of mass μ , charge coupling constant q, and spherical harmonic index l in the background of a spherically symmetric compact reflecting star of mass M, electric charge Q, and radius R_{ {s}}≫ M,Q. Interestingly, it is proved that the discrete set {R_{ {s}}(M,Q,μ ,q,l;n)}^{n=∞}_{n=1} of star radii that can support the charged massive scalar field configurations is determined by the characteristic zeroes of the confluent hypergeometric function. Following this simple observation, we derive a remarkably compact analytical formula for the discrete spectrum of star radii in the intermediate regime M≪ R_{ {s}}≪ 1/μ . The analytically derived resonance spectrum is confirmed by direct numerical computations.

Mind as Space

NASA Astrophysics Data System (ADS)

McKinstry, Chris

The present article describes a possible method for the automatic discovery of a universal human semantic-affective hyperspatial approximation of the human subcognitive substrate - the associative network which French (1990) asserts is the ultimate foundation of the human ability to pass the Turing Test - that does not require a machine to have direct human experience or a physical human body. This method involves automatic programming - such as Koza's genetic programming (1992) - guided in the discovery of the proposed universal hypergeometry by feedback from a Minimum Intelligent Signal Test or MIST (McKinstry, 1997) constructed from a very large number of human validated probabilistic propositions collected from a large population of Internet users. It will be argued that though a lifetime of human experience is required to pass a rigorous Turing Test, a probabilistic propositional approximation of this experience can be constructed via public participation on the Internet, and then used as a fitness function to direct the artificial evolution of a universal hypergeometry capable of classifying arbitrary propositions. A model of this hypergeometry will be presented; it predicts Miller's "Magical Number Seven" (1956) as the size of human short-term memory from fundamental hypergeometric properties. A system that can lead to the generation of novel propositions or "artificial thoughts" will also be described.

Detection of Supernova Neutrinos on the Earth for Large θ13

NASA Astrophysics Data System (ADS)

Xu, Jing; Huang, Ming-Yang; Hu, Li-Jun; Guo, Xin-Heng; Young, Bing-Lin

2014-02-01

Supernova (SN) neutrinos detected on the Earth are subject to the shock wave effects, the Mikheyev—Smirnov—Wolfenstein (MSW) effects, the neutrino collective effects and the Earth matter effects. Considering the recent experimental result about the large mixing angle θ13 (≃ 8.8°) provided by the Daya Bay Collaboration and applying the available knowledge for the neutrino conversion probability in the high resonance region of SN, PH, which is in the form of hypergeometric function in the case of large θ13, we deduce the expression of PH taking into account the shock wave effects. It is found that PH is not zero in a certain range of time due to the shock wave effects. After considering all the four physical effects and scanning relevant parameters, we calculate the event numbers of SN neutrinos for the “Garching” distribution of neutrino energy spectrum. From the numerical results, it is found that the behaviors of neutrino event numbers detected on the Earth depend on the neutrino mass hierarchy and neutrino spectrum parameters including the dimensionless pinching parameter βα (where α refers to neutrino flavor), the average energy , and the SN neutrino luminosities Lα. Finally, we give the ranges of SN neutrino event numbers that will be detected at the Daya Bay experiment.

MSD-MAP: A Network-Based Systems Biology Platform for Predicting Disease-Metabolite Links.

PubMed

Wathieu, Henri; Issa, Naiem T; Mohandoss, Manisha; Byers, Stephen W; Dakshanamurthy, Sivanesan

2017-01-01

Cancer-associated metabolites result from cell-wide mechanisms of dysregulation. The field of metabolomics has sought to identify these aberrant metabolites as disease biomarkers, clues to understanding disease mechanisms, or even as therapeutic agents. This study was undertaken to reliably predict metabolites associated with colorectal, esophageal, and prostate cancers. Metabolite and disease biological action networks were compared in a computational platform called MSD-MAP (Multi Scale Disease-Metabolite Association Platform). Using differential gene expression analysis with patient-based RNAseq data from The Cancer Genome Atlas, genes up- or down-regulated in cancer compared to normal tissue were identified. Relational databases were used to map biological entities including pathways, functions, and interacting proteins, to those differential disease genes. Similar relational maps were built for metabolites, stemming from known and in silico predicted metabolite-protein associations. The hypergeometric test was used to find statistically significant relationships between disease and metabolite biological signatures at each tier, and metabolites were assessed for multi-scale association with each cancer. Metabolite networks were also directly associated with various other diseases using a disease functional perturbation database. Our platform recapitulated metabolite-disease links that have been empirically verified in the scientific literature, with network-based mapping of jointly-associated biological activity also matching known disease mechanisms. This was true for colorectal, esophageal, and prostate cancers, using metabolite action networks stemming from both predicted and known functional protein associations. By employing systems biology concepts, MSD-MAP reliably predicted known cancermetabolite links, and may serve as a predictive tool to streamline conventional metabolomic profiling methodologies. Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.org.

Statistical auditing and randomness test of lotto k/N-type games

NASA Astrophysics Data System (ADS)

Coronel-Brizio, H. F.; Hernández-Montoya, A. R.; Rapallo, F.; Scalas, E.

2008-11-01

One of the most popular lottery games worldwide is the so-called “lotto k/N”. It considers N numbers 1,2,…,N from which k are drawn randomly, without replacement. A player selects k or more numbers and the first prize is shared amongst those players whose selected numbers match all of the k randomly drawn. Exact rules may vary in different countries. In this paper, mean values and covariances for the random variables representing the numbers drawn from this kind of game are presented, with the aim of using them to audit statistically the consistency of a given sample of historical results with theoretical values coming from a hypergeometric statistical model. The method can be adapted to test pseudorandom number generators.

Visualization and statistical comparisons of microbial communities using R packages on Phylochip data.

PubMed

Holmes, Susan; Alekseyenko, Alexander; Timme, Alden; Nelson, Tyrrell; Pasricha, Pankaj Jay; Spormann, Alfred

2011-01-01

This article explains the statistical and computational methodology used to analyze species abundances collected using the LNBL Phylochip in a study of Irritable Bowel Syndrome (IBS) in rats. Some tools already available for the analysis of ordinary microarray data are useful in this type of statistical analysis. For instance in correcting for multiple testing we use Family Wise Error rate control and step-down tests (available in the multtest package). Once the most significant species are chosen we use the hypergeometric tests familiar for testing GO categories to test specific phyla and families. We provide examples of normalization, multivariate projections, batch effect detection and integration of phylogenetic covariation, as well as tree equalization and robustification methods.

The relation between global migration and trade networks

NASA Astrophysics Data System (ADS)

Sgrignoli, Paolo; Metulini, Rodolfo; Schiavo, Stefano; Riccaboni, Massimo

2015-01-01

In this paper we develop a methodology to analyze and compare multiple global networks, focusing our analysis on the relation between human migration and trade. First, we identify the subset of products for which the presence of a community of migrants significantly increases trade intensity, where to assure comparability across networks we apply a hypergeometric filter that lets us identify those links which intensity is significantly higher than expected. Next, proposing a new way to define country neighbors based on the most intense links in the trade network, we use spatial econometrics techniques to measure the effect of migration on international trade, while controlling for network interdependences. Overall, we find that migration significantly boosts trade across countries and we are able to identify product categories for which this effect is particularly strong.

A differential equation for the asymptotic fitness distribution in the Bak-Sneppen model with five species.

PubMed

Schlemm, Eckhard

2015-09-01

The Bak-Sneppen model is an abstract representation of a biological system that evolves according to the Darwinian principles of random mutation and selection. The species in the system are characterized by a numerical fitness value between zero and one. We show that in the case of five species the steady-state fitness distribution can be obtained as a solution to a linear differential equation of order five with hypergeometric coefficients. Similar representations for the asymptotic fitness distribution in larger systems may help pave the way towards a resolution of the question of whether or not, in the limit of infinitely many species, the fitness is asymptotically uniformly distributed on the interval [fc, 1] with fc ≳ 2/3. Copyright © 2015 Elsevier Inc. All rights reserved.

Torus Knot Polynomials and Susy Wilson Loops

NASA Astrophysics Data System (ADS)

Giasemidis, Georgios; Tierz, Miguel

2014-12-01

We give, using an explicit expression obtained in (Jones V, Ann Math 126:335, 1987), a basic hypergeometric representation of the HOMFLY polynomial of ( n, m) torus knots, and present a number of equivalent expressions, all related by Heine's transformations. Using this result, the symmetry and the leading polynomial at large N are explicit. We show the latter to be the Wilson loop of 2d Yang-Mills theory on the plane. In addition, after taking one winding to infinity, it becomes the Wilson loop in the zero instanton sector of the 2d Yang-Mills theory, which is known to give averages of Wilson loops in = 4 SYM theory. We also give, using matrix models, an interpretation of the HOMFLY polynomial and the corresponding Jones-Rosso representation in terms of q-harmonic oscillators.

Weak solution concept and Galerkin's matrix for the exterior of an oblate ellipsoid of revolution in the representation of the Earth's gravity potential by buried masses

NASA Astrophysics Data System (ADS)

Holota, Petr; Nesvadba, Otakar

2017-04-01

The paper is motivated by the role of boundary value problems in Earth's gravity field studies. The discussion focuses on Neumann's problem formulated for the exterior of an oblate ellipsoid of revolution as this is considered a basis for an iteration solution of the linear gravimetric boundary value problem in the determination of the disturbing potential. The approach follows the concept of the weak solution and Galerkin's approximations are applied. This means that the solution of the problem is approximated by linear combinations of basis functions with scalar coefficients. The construction of Galerkin's matrix for basis functions generated by elementary potentials (point masses) is discussed. Ellipsoidal harmonics are used as a natural tool and the elementary potentials are expressed by means of series of ellipsoidal harmonics. The problem, however, is the summation of the series that represent the entries of Galerkin's matrix. It is difficult to reduce the number of summation indices since in the ellipsoidal case there is no analogue to the addition theorem known for spherical harmonics. Therefore, the straightforward application of series of ellipsoidal harmonics is complemented by deeper relations contained in the theory of ordinary differential equations of second order and in the theory of Legendre's functions. Subsequently, also hypergeometric functions and series are used. Moreover, within some approximations the entries are split into parts. Some of the resulting series may be summed relatively easily, apart from technical tricks. For the remaining series the summation was converted to elliptic integrals. The approach made it possible to deduce a closed (though approximate) form representation of the entries in Galerkin's matrix. The result rests on concepts and methods of mathematical analysis. In the paper it is confronted with a direct numerical approach applied for the implementation of Legendre's functions. The computation of the entries is more demanding in this case, but conceptually it avoids approximations. Finally, some specific features associated with function bases generated by elementary potentials in case the ellipsoidal solution domain are illustrated and discussed.

Methodological approach for substantiating disease freedom in a heterogeneous small population. Application to ovine scrapie, a disease with a strong genetic susceptibility.

PubMed

Martinez, Marie-José; Durand, Benoit; Calavas, Didier; Ducrot, Christian

2010-06-01

Demonstrating disease freedom is becoming important in different fields including animal disease control. Most methods consider sampling only from a homogeneous population in which each animal has the same probability of becoming infected. In this paper, we propose a new methodology to calculate the probability of detecting the disease if it is present in a heterogeneous population of small size with potentially different risk groups, differences in risk being defined using relative risks. To calculate this probability, for each possible arrangement of the infected animals in the different groups, the probability that all the animals tested are test-negative given this arrangement is multiplied by the probability that this arrangement occurs. The probability formula is developed using the assumption of a perfect test and hypergeometric sampling for finite small size populations. The methodology is applied to scrapie, a disease affecting small ruminants and characterized in sheep by a strong genetic susceptibility defining different risk groups. It illustrates that the genotypes of the tested animals influence heavily the confidence level of detecting scrapie. The results present the statistical power for substantiating disease freedom in a small heterogeneous population as a function of the design prevalence, the structure of the sample tested, the structure of the herd and the associated relative risks. (c) 2010 Elsevier B.V. All rights reserved.

Moran model as a dynamical process on networks and its implications for neutral speciation.

PubMed

de Aguiar, Marcus A M; Bar-Yam, Yaneer

2011-09-01

In population genetics, the Moran model describes the neutral evolution of a biallelic gene in a population of haploid individuals subjected to mutations. We show in this paper that this model can be mapped into an influence dynamical process on networks subjected to external influences. The panmictic case considered by Moran corresponds to fully connected networks and can be completely solved in terms of hypergeometric functions. Other types of networks correspond to structured populations, for which approximate solutions are also available. This approach to the classic Moran model leads to a relation between regular networks based on spatial grids and the mechanism of isolation by distance. We discuss the consequences of this connection for topopatric speciation and the theory of neutral speciation and biodiversity. We show that the effect of mutations in structured populations, where individuals can mate only with neighbors, is greatly enhanced with respect to the panmictic case. If mating is further constrained by genetic proximity between individuals, a balance of opposing tendencies takes place: increasing diversity promoted by enhanced effective mutations versus decreasing diversity promoted by similarity between mates. Resolution of large enough opposing tendencies occurs through speciation via pattern formation. We derive an explicit expression that indicates when speciation is possible involving the parameters characterizing the population. We also show that the time to speciation is greatly reduced in comparison with the panmictic case.

Moran model as a dynamical process on networks and its implications for neutral speciation

NASA Astrophysics Data System (ADS)

de Aguiar, Marcus A. M.; Bar-Yam, Yaneer

2011-03-01

In population genetics, the Moran model describes the neutral evolution of a biallelic gene in a population of haploid individuals subjected to mutations. We show in this paper that this model can be mapped into an influence dynamical process on networks subjected to external influences. The panmictic case considered by Moran corresponds to fully connected networks and can be completely solved in terms of hypergeometric functions. Other types of networks correspond to structured populations, for which approximate solutions are also available. This approach to the classic Moran model leads to a relation between regular networks based on spatial grids and the mechanism of isolation by distance. We discuss the consequences of this connection for topopatric speciation and the theory of neutral speciation and biodiversity. We show that the effect of mutations in structured populations, where individuals can mate only with neighbors, is greatly enhanced with respect to the panmictic case. If mating is further constrained by genetic proximity between individuals, a balance of opposing tendencies takes place: increasing diversity promoted by enhanced effective mutations versus decreasing diversity promoted by similarity between mates. Resolution of large enough opposing tendencies occurs through speciation via pattern formation. We derive an explicit expression that indicates when speciation is possible involving the parameters characterizing the population. We also show that the time to speciation is greatly reduced in comparison with the panmictic case.

Improved accuracy of supervised CRM discovery with interpolated Markov models and cross-species comparison

PubMed Central

Kazemian, Majid; Zhu, Qiyun; Halfon, Marc S.; Sinha, Saurabh

2011-01-01

Despite recent advances in experimental approaches for identifying transcriptional cis-regulatory modules (CRMs, ‘enhancers’), direct empirical discovery of CRMs for all genes in all cell types and environmental conditions is likely to remain an elusive goal. Effective methods for computational CRM discovery are thus a critically needed complement to empirical approaches. However, existing computational methods that search for clusters of putative binding sites are ineffective if the relevant TFs and/or their binding specificities are unknown. Here, we provide a significantly improved method for ‘motif-blind’ CRM discovery that does not depend on knowledge or accurate prediction of TF-binding motifs and is effective when limited knowledge of functional CRMs is available to ‘supervise’ the search. We propose a new statistical method, based on ‘Interpolated Markov Models’, for motif-blind, genome-wide CRM discovery. It captures the statistical profile of variable length words in known CRMs of a regulatory network and finds candidate CRMs that match this profile. The method also uses orthologs of the known CRMs from closely related genomes. We perform in silico evaluation of predicted CRMs by assessing whether their neighboring genes are enriched for the expected expression patterns. This assessment uses a novel statistical test that extends the widely used Hypergeometric test of gene set enrichment to account for variability in intergenic lengths. We find that the new CRM prediction method is superior to existing methods. Finally, we experimentally validate 12 new CRM predictions by examining their regulatory activity in vivo in Drosophila; 10 of the tested CRMs were found to be functional, while 6 of the top 7 predictions showed the expected activity patterns. We make our program available as downloadable source code, and as a plugin for a genome browser installed on our servers. PMID:21821659

Optical model calculations of heavy-ion target fragmentation

NASA Technical Reports Server (NTRS)

Townsend, L. W.; Wilson, J. W.; Cucinotta, F. A.; Norbury, J. W.

1986-01-01

The fragmentation of target nuclei by relativistic protons and heavy ions is described within the context of a simple abrasion-ablation-final-state interaction model. Abrasion is described by a quantum mechanical formalism utilizing an optical model potential approximation. Nuclear charge distributions of the excited prefragments are calculated by both a hypergeometric distribution and a method based upon the zero-point oscillations of the giant dipole resonance. Excitation energies are estimated from the excess surface energy resulting from the abrasion process and the additional energy deposited by frictional spectator interactions of the abraded nucleons. The ablation probabilities are obtained from the EVA-3 computer program. Isotope production cross sections for the spallation of copper targets by relativistic protons and for the fragmenting of carbon targets by relativistic carbon, neon, and iron projectiles are calculated and compared with available experimental data.

On the Theory of the Laval Nozzle

NASA Technical Reports Server (NTRS)

Falkovich, S. V.

1949-01-01

In the present paper, the motion of a gas in a plane-parallel Laval nozzle in the neighborhood of the transition from subsonic to supersonic velocities is studied. In a recently published paper, F. I. Frankl, applying the holograph method of Chaplygin, undertook a detailed investigation of the character of the flow near the line of transition from subsonic to supersonic velocities. From the results of Tricomi's investigation on the theory of differential equations of the mixed elliptic-hyperbolic type, Frankl introduced as one of the independent variables in place of the modulus of the velocity, a certain specially chosen function of this modulus. He thereby succeeded in explaining the character of the flow at the point of intersection of the transition line and the axis of symmetry (center of the nozzle) and in studying the behavior of the stream function in the neighborhood of this point by separating out the principal term having, together with its derivatives, the maximum value as compared with the corresponding corrections. This principal term is represented in Frankl's paper in the form of a linear combination of two hypergeometric functions. In order to find this linear combination, it is necessary to solve a number of boundary problems, which results in a complex analysis. In the investigation of the flow with which this paper is concerned, a second method is applied. This method is based on the transformation of the equations of motion to a form that may be called canonical for the system of differential equations of the mixed elliptic-hyperbolic type to which the system of equations of the motion of an ideal compressible fluid refers. By studying the behavior of the integrals of this system in the neighborhood of the parabolic line, the principal term of the solution is easily separated out in the form of a polynomial of the third degree. As a result, the computation of the transitional part of the nozzle is considerably simplified.

Photon-number-resolving detectors and their role in quantifying quantum correlations

NASA Astrophysics Data System (ADS)

Tan, Si-Hui; Krivitsky, Leonid A.; Englert, Berthold-Georg

2016-09-01

Harnessing entanglement as a resource is the main workhorse of many quantum protocols, and establishing the degree of quantum correlations of quantum states is an important certification process that has to take place prior to any implementations of these quantum protocols. The emergence of photodetectors known as photon-number-resolving detectors (PNRDs) that allow for accounting of photon numbers simultaneously arriving at the detectors has led to the need for modeling accurately and applying them for use in the certification process. Here we study the variance of difference of photocounts (VDP) of two PNRDs, which is one measure of quantum correlations, under the effects of loss and saturation. We found that it would be possible to distinguish between the classical correlation of a two-mode coherent state and the quantum correlation of a twin-beam state within some photo count regime of the detector. We compare the behavior of two such PNRDs. The first for which the photocount statistics follow a binomial distribution accounting for losses, and the second is that of Agarwal, Vogel, and Sperling for which the incident beam is first split and then separately measured by ON/OFF detectors. In our calculations, analytical expressions are derived for the variance of difference where possible. In these cases, Gauss' hypergeometric function appears regularly, giving an insight to the type of quantum statistics the photon counting gives in these PNRDs. The different mechanisms of the two types of PNRDs leads to quantitative differences in their VDP.

Fast Diffusion to Self-Similarity: Complete Spectrum, Long-Time Asymptotics, and Numerology

NASA Astrophysics Data System (ADS)

Denzler, Jochen; McCann, Robert J.

2005-03-01

The complete spectrum is determined for the operator on the Sobolev space W1,2ρ(Rn) formed by closing the smooth functions of compact support with respect to the norm Here the Barenblatt profile ρ is the stationary attractor of the rescaled diffusion equation in the fast, supercritical regime m the same diffusion dynamics represent the steepest descent down an entropy E(u) on probability measures with respect to the Wasserstein distance d2. Formally, the operator H=HessρE is the Hessian of this entropy at its minimum ρ, so the spectral gap H≧α:=2-n(1-m) found below suggests the sharp rate of asymptotic convergence: from any centered initial data 0≦u(0,x) ∈ L1(Rn) with second moments. This bound improves various results in the literature, and suggests the conjecture that the self-similar solution u(t,x)=R(t)-nρ(x/R(t)) is always slowest to converge. The higher eigenfunctions which are polynomials with hypergeometric radial parts and the presence of continuous spectrum yield additional insight into the relations between symmetries of Rn and the flow. Thus the rate of convergence can be improved if we are willing to replace the distance to ρ with the distance to its nearest mass-preserving dilation (or still better, affine image). The strange numerology of the spectrum is explained in terms of the number of moments of ρ.

An oblate ellipsoidal approach to update a high-resolution geopotential model over the oceans: Study case of EGM2008 and DTU10

NASA Astrophysics Data System (ADS)

Sebera, Josef; Bezděk, Aleš; Kostelecký, Jan; Pešek, Ivan; Shum, C. K.

2016-01-01

The most important high-resolution geopotential models such as EGM96 and EGM2008 have been released approximately once per decade. In light of the ability of modern satellite, airborne or terrestrial techniques to provide new data sets every year (e.g., in polar and ocean areas), these data can be readily included in existing models without waiting for a new release. In this article, we present a novel ellipsoidal approach for updating high-resolution models over the oceans with new gridded data. The problem is demonstrated using the EGM2008 model updated with DTU10 geoid and gravity grids that provide additional signal over the Arctic oceans. The result of the procedure are the ellipsoidal and the spherical harmonic coefficients up to degree 4320 and 4400, respectively. These coefficients represent the input data set to within 0.08 mGal globally, with the largest differences located at the land-ocean boundaries, which is two orders of magnitude less than real accuracy of gravity data from satellite altimetry. Along with the harmonic coefficients a detailed map of the second vertical derivative of the anomalous potential (or vertical gravitational gradient) on 1 arc-min grid is anticipated to improve or complement the original DTU10 geoid model. Finally, an optimized set of Jekeli's functions is provided as they allow for computing oblate ellipsoidal harmonics up to a very high degree and order (>10,000) in terms of the hypergeometric formulation.

Analytical solutions for a soil vapor extraction model that incorporates gas phase dispersion and molecular diffusion

NASA Astrophysics Data System (ADS)

Huang, Junqi; Goltz, Mark N.

2017-06-01

To greatly simplify their solution, the equations describing radial advective/dispersive transport to an extraction well in a porous medium typically neglect molecular diffusion. While this simplification is appropriate to simulate transport in the saturated zone, it can result in significant errors when modeling gas phase transport in the vadose zone, as might be applied when simulating a soil vapor extraction (SVE) system to remediate vadose zone contamination. A new analytical solution for the equations describing radial gas phase transport of a sorbing contaminant to an extraction well is presented. The equations model advection, dispersion (including both mechanical dispersion and molecular diffusion), and rate-limited mass transfer of dissolved, separate phase, and sorbed contaminants into the gas phase. The model equations are analytically solved by using the Laplace transform with respect to time. The solutions are represented by confluent hypergeometric functions in the Laplace domain. The Laplace domain solutions are then evaluated using a numerical Laplace inversion algorithm. The solutions can be used to simulate the spatial distribution and the temporal evolution of contaminant concentrations during operation of a soil vapor extraction well. Results of model simulations show that the effect of gas phase molecular diffusion upon concentrations at the extraction well is relatively small, although the effect upon the distribution of concentrations in space is significant. This study provides a tool that can be useful in designing SVE remediation strategies, as well as verifying numerical models used to simulate SVE system performance.

Integrative Analysis Reveals Regulatory Programs in Endometriosis

PubMed Central

Yang, Huan; Kang, Kai; Cheng, Chao; Mamillapalli, Ramanaiah; Taylor, Hugh S.

2015-01-01

Endometriosis is a common gynecological disease found in approximately 10% of reproductive-age women. Gene expression analysis has been performed to explore alterations in gene expression associated with endometriosis; however, the underlying transcription factors (TFs) governing such expression changes have not been investigated in a systematic way. In this study, we propose a method to integrate gene expression with TF binding data and protein–protein interactions to construct an integrated regulatory network (IRN) for endometriosis. The IRN has shown that the most regulated gene in endometriosis is RUNX1, which is targeted by 14 of 26 TFs also involved in endometriosis. Using 2 published cohorts, GSE7305 (Hover, n = 20) and GSE7307 (Roth, n = 36) from the Gene Expression Omnibus database, we identified a network of TFs, which bind to target genes that are differentially expressed in endometriosis. Enrichment analysis based on the hypergeometric distribution allowed us to predict the TFs involved in endometriosis (n = 40). This included known TFs such as androgen receptor (AR) and critical factors in the pathology of endometriosis, estrogen receptor α, and estrogen receptor β. We also identified several new ones from which we selected FOXA2 and TFAP2C, and their regulation was confirmed by quantitative real-time polymerase chain reaction and immunohistochemistry (IHC). Further, our analysis revealed that the function of AR and p53 in endometriosis is regulated by posttranscriptional changes and not by differential gene expression. Our integrative analysis provides new insights into the regulatory programs involved in endometriosis. PMID:26134036

Diffusion of finite-sized hard-core interacting particles in a one-dimensional box: Tagged particle dynamics.

PubMed

Lizana, L; Ambjörnsson, T

2009-11-01

We solve a nonequilibrium statistical-mechanics problem exactly, namely, the single-file dynamics of N hard-core interacting particles (the particles cannot pass each other) of size Delta diffusing in a one-dimensional system of finite length L with reflecting boundaries at the ends. We obtain an exact expression for the conditional probability density function rhoT(yT,t|yT,0) that a tagged particle T (T=1,...,N) is at position yT at time t given that it at time t=0 was at position yT,0. Using a Bethe ansatz we obtain the N -particle probability density function and, by integrating out the coordinates (and averaging over initial positions) of all particles but particle T , we arrive at an exact expression for rhoT(yT,t|yT,0) in terms of Jacobi polynomials or hypergeometric functions. Going beyond previous studies, we consider the asymptotic limit of large N , maintaining L finite, using a nonstandard asymptotic technique. We derive an exact expression for rhoT(yT,t|yT,0) for a tagged particle located roughly in the middle of the system, from which we find that there are three time regimes of interest for finite-sized systems: (A) for times much smaller than the collision time ttaucoll but times smaller than the equilibrium time ttaue , rhoT(yT,t|yT,0) approaches a polynomial-type equilibrium probability density function. Notably, only regimes (A) and (B) are found in the previously considered infinite systems.

Spatio-temporal optimization of sampling for bluetongue vectors (Culicoides) near grazing livestock

PubMed Central

2013-01-01

Background Estimating the abundance of Culicoides using light traps is influenced by a large variation in abundance in time and place. This study investigates the optimal trapping strategy to estimate the abundance or presence/absence of Culicoides on a field with grazing animals. We used 45 light traps to sample specimens from the Culicoides obsoletus species complex on a 14 hectare field during 16 nights in 2009. Findings The large number of traps and catch nights enabled us to simulate a series of samples consisting of different numbers of traps (1-15) on each night. We also varied the number of catch nights when simulating the sampling, and sampled with increasing minimum distances between traps. We used resampling to generate a distribution of different mean and median abundance in each sample. Finally, we used the hypergeometric distribution to estimate the probability of falsely detecting absence of vectors on the field. The variation in the estimated abundance decreased steeply when using up to six traps, and was less pronounced when using more traps, although no clear cutoff was found. Conclusions Despite spatial clustering in vector abundance, we found no effect of increasing the distance between traps. We found that 18 traps were generally required to reach 90% probability of a true positive catch when sampling just one night. But when sampling over two nights the same probability level was obtained with just three traps per night. The results are useful for the design of vector monitoring programmes on fields with grazing animals. PMID:23705770

Improved accuracy of supervised CRM discovery with interpolated Markov models and cross-species comparison.

PubMed

Kazemian, Majid; Zhu, Qiyun; Halfon, Marc S; Sinha, Saurabh

2011-12-01

Despite recent advances in experimental approaches for identifying transcriptional cis-regulatory modules (CRMs, 'enhancers'), direct empirical discovery of CRMs for all genes in all cell types and environmental conditions is likely to remain an elusive goal. Effective methods for computational CRM discovery are thus a critically needed complement to empirical approaches. However, existing computational methods that search for clusters of putative binding sites are ineffective if the relevant TFs and/or their binding specificities are unknown. Here, we provide a significantly improved method for 'motif-blind' CRM discovery that does not depend on knowledge or accurate prediction of TF-binding motifs and is effective when limited knowledge of functional CRMs is available to 'supervise' the search. We propose a new statistical method, based on 'Interpolated Markov Models', for motif-blind, genome-wide CRM discovery. It captures the statistical profile of variable length words in known CRMs of a regulatory network and finds candidate CRMs that match this profile. The method also uses orthologs of the known CRMs from closely related genomes. We perform in silico evaluation of predicted CRMs by assessing whether their neighboring genes are enriched for the expected expression patterns. This assessment uses a novel statistical test that extends the widely used Hypergeometric test of gene set enrichment to account for variability in intergenic lengths. We find that the new CRM prediction method is superior to existing methods. Finally, we experimentally validate 12 new CRM predictions by examining their regulatory activity in vivo in Drosophila; 10 of the tested CRMs were found to be functional, while 6 of the top 7 predictions showed the expected activity patterns. We make our program available as downloadable source code, and as a plugin for a genome browser installed on our servers. © The Author(s) 2011. Published by Oxford University Press.

Product ion isotopologue pattern: A tool to improve the reliability of elemental composition elucidations of unknown compounds in complex matrices.

PubMed

Kaufmann, A; Walker, S; Mol, G

2016-04-15

Elucidation of the elemental compositions of unknown compounds (e.g., in metabolomics) generally relies on the availability of accurate masses and isotopic ratios. This study focuses on the information provided by the abundance ratio within a product ion pair (monoisotopic versus the first isotopic peak) when isolating and fragmenting the first isotopic ion (first isotopic mass spectrum) of the precursor. This process relies on the capability of the quadrupole within the Q Orbitrap instrument to isolate a very narrow mass window. Selecting only the first isotopic peak (first isotopic mass spectrum) leads to the observation of a unique product ion pair. The lighter ion within such an isotopologue pair is monoisotopic, while the heavier ion contains a single carbon isotope. The observed abundance ratio is governed by the percentage of carbon atoms lost during the fragmentation and can be described by a hypergeometric distribution. The observed carbon isotopologue abundance ratio (product ion isotopologue pattern) gives reliable information regarding the percentage of carbon atoms lost in the fragmentation process. It therefore facilitates the elucidation of the involved precursor and product ions. Unlike conventional isotopic abundances, the product ion isotopologue pattern is hardly affected by isobaric interferences. Furthermore, the appearance of these pairs greatly aids in cleaning up a 'matrix-contaminated' product ion spectrum. The product ion isotopologue pattern is a valuable tool for structural elucidation. It increases confidence in results and permits structural elucidations for heavier ions. This tool is also very useful in elucidating the elemental composition of product ions. Such information is highly valued in the field of multi-residue analysis, where the accurate mass of product ions is required for the confirmation process. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Statistics of Delta v magnitude for a trajectory correction maneuver containing deterministic and random components

NASA Technical Reports Server (NTRS)

Bollman, W. E.; Chadwick, C.

1982-01-01

A number of interplanetary missions now being planned involve placing deterministic maneuvers along the flight path to alter the trajectory. Lee and Boain (1973) examined the statistics of trajectory correction maneuver (TCM) magnitude with no deterministic ('bias') component. The Delta v vector magnitude statistics were generated for several values of random Delta v standard deviations using expansions in terms of infinite hypergeometric series. The present investigation uses a different technique (Monte Carlo simulation) to generate Delta v magnitude statistics for a wider selection of random Delta v standard deviations and also extends the analysis to the case of nonzero deterministic Delta v's. These Delta v magnitude statistics are plotted parametrically. The plots are useful in assisting the analyst in quickly answering questions about the statistics of Delta v magnitude for single TCM's consisting of both a deterministic and a random component. The plots provide quick insight into the nature of the Delta v magnitude distribution for the TCM.

Note on: 'EMLCLLER-A program for computing the EM response of a large loop source over a layered earth model' by N.P. Singh and T. Mogi, Computers & Geosciences 29 (2003) 1301-1307

NASA Astrophysics Data System (ADS)

Jamie, Majid

2016-11-01

Singh and Mogi (2003) presented a forward modeling (FWD) program, coded in FORTRAN 77 called "EMLCLLER", which is capable of computing the frequency-domain electromagnetic (EM) response of a large circular loop, in terms of vertical magnetic component (Hz), over 1D layer earth models; computations at this program could be performed by assuming variable transmitter-receiver configurations and incorporating both conduction and displacement currents into computations. Integral equations at this program are computed through digital linear filters based on the Hankel transforms together with analytic solutions based on hyper-geometric functions. Despite capabilities of EMLCLLER, there are some mistakes at this program that make its FWD results unreliable. The mistakes in EMLCLLER arise in using wrong algorithm for computing reflection coefficient of the EM wave in TE-mode (rTE), and using flawed algorithms for computing phase and normalized phase values relating to Hz; in this paper corrected form of these mistakes are presented. Moreover, in order to illustrate how these mistakes can affect FWD results, EMLCLLER and corrected version of this program presented in this paper titled "EMLCLLER_Corr" are conducted on different two- and three-layered earth models; afterwards their FWD results in terms of real and imaginary parts of Hz, its normalized amplitude, and the corresponding normalized phase curves are plotted versus frequency and compared to each other. In addition, in Singh and Mogi (2003) extra derivations for computing radial component of the magnetic field (Hr) and angular component of the electric field (Eϕ) are also presented where the numerical solution presented for Hr is incorrect; in this paper the correct numerical solution for this derivation is also presented.

The Harvard Clean Energy Project: High-throughput screening of organic photovoltaic materials using cheminformatics, machine learning, and pattern recognition

NASA Astrophysics Data System (ADS)

Olivares-Amaya, Roberto; Hachmann, Johannes; Amador-Bedolla, Carlos; Daly, Aidan; Jinich, Adrian; Atahan-Evrenk, Sule; Boixo, Sergio; Aspuru-Guzik, Alán

2012-02-01

Organic photovoltaic devices have emerged as competitors to silicon-based solar cells, currently reaching efficiencies of over 9% and offering desirable properties for manufacturing and installation. We study conjugated donor polymers for high-efficiency bulk-heterojunction photovoltaic devices with a molecular library motivated by experimental feasibility. We use quantum mechanics and a distributed computing approach to explore this vast molecular space. We will detail the screening approach starting from the generation of the molecular library, which can be easily extended to other kinds of molecular systems. We will describe the screening method for these materials which ranges from descriptor models, ubiquitous in the drug discovery community, to eventually reaching first principles quantum chemistry methods. We will present results on the statistical analysis, based principally on machine learning, specifically partial least squares and Gaussian processes. Alongside, clustering methods and the use of the hypergeometric distribution reveal moieties important for the donor materials and allow us to quantify structure-property relationships. These efforts enable us to accelerate materials discovery in organic photovoltaics through our collaboration with experimental groups.

Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. III. Cylindrical approximations for heat waves traveling inwards

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berkel, M. van; Fellow of the Japan Society for the Promotion of Science; FOM Institute DIFFER-Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM, Trilateral Euregio Cluster, P.O. Box 1207, 3430 BE Nieuwegein

In this paper, a number of new explicit approximations are introduced to estimate the perturbative diffusivity (χ), convectivity (V), and damping (τ) in cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based on the heat equation in cylindrical geometry using the symmetry (Neumann) boundary condition at the plasma center. This means that the approximations derived here should be used only to estimate transport coefficients between the plasma center and the off-axis perturbative source. If the effect of cylindrical geometry is small, it is also possiblemore » to use semi-infinite domain approximations presented in Part I and Part II of this series. A number of new approximations are derived in this part, Part III, based upon continued fractions of the modified Bessel function of the first kind and the confluent hypergeometric function of the first kind. These approximations together with the approximations based on semi-infinite domains are compared for heat waves traveling towards the center. The relative error for the different derived approximations is presented for different values of the frequency, transport coefficients, and dimensionless radius. Moreover, it is shown how combinations of different explicit formulas can be used to estimate the transport coefficients over a large parameter range for cases without convection and damping, cases with damping only, and cases with convection and damping. The relative error between the approximation and its underlying model is below 2% for the case, where only diffusivity and damping are considered. If also convectivity is considered, the diffusivity can be estimated well in a large region, but there is also a large region in which no suitable approximation is found. This paper is the third part (Part III) of a series of three papers. In Part I, the semi-infinite slab approximations have been treated. In Part II, cylindrical approximations are treated for heat waves traveling towards the plasma edge assuming a semi-infinite domain.« less

Subtle differences in selective pressures applied on the envelope gene of HIV-1 in pregnant versus non-pregnant women.

PubMed

Ransy, Doris G; Lord, Etienne; Caty, Martine; Lapointe, Normand; Boucher, Marc; Diallo, Abdoulaye Baniré; Soudeyns, Hugo

2018-04-17

Pregnancy is associated with modulations of maternal immunity that contribute to foeto-maternal tolerance. To understand whether and how these alterations impact antiviral immunity, a detailed cross-sectional analysis of selective pressures exerted on HIV-1 envelope amino-acid sequences was performed in a group of pregnant (n = 32) and non-pregnant (n = 44) HIV-infected women in absence of treatment with antiretroviral therapy (ART). Independent of HIV-1 subtype, p-distance, dN and dS were all strongly correlated with one another but were not significantly different in pregnant as compared to non-pregnant patients. Differential levels of selective pressure applied on different Env subdomains displayed similar yet non-identical patterns between the two groups, with pressure applied on C1 being significantly lower in constant regions C1 and C2 than in V1, V2, V3 and C3. To draw a general picture of the selection applied on the envelope and compensate for inter-individual variations, we performed a binomial test on selection frequency data pooled from pregnant and non-pregnant women. This analysis uncovered 42 positions, present in both groups, exhibiting statistically-significant frequency of selection that invariably mapped to the surface of the Env protein, with the great majority located within epitopes recognized by Env-specific antibodies or sites associated with the development of cross-reactive neutralizing activity. The median frequency of occurrence of positive selection per site was significantly lower in pregnant versus non-pregnant women. Furthermore, examination of the distribution of positively selected sites using a hypergeometric test revealed that only 2 positions (D137 and S142) significantly differed between the 2 groups. Taken together, these result indicate that pregnancy is associated with subtle yet distinctive changes in selective pressures exerted on the HIV-1 Env protein that are compatible with transient modulations of maternal immunity. Copyright © 2018 Elsevier B.V. All rights reserved.

Response of Human Skin to Aesthetic Scarification

PubMed Central

Gabriel, Vincent A.; McClellan, Elizabeth A.; Scheuermann, Richard H.

2014-01-01

This study was undertaken to investigate changes in RNA expression in previously healthy adult human skin following thermal injury induced by contact with hot metal that was undertaken as part of aesthetic scarification, a body modification practice. Subjects were recruited to have pre-injury skin and serial wound biopsies performed. 4 mm punch biopsies were taken prior to branding and 1 hour, 1 week, and 1, 2 and 3 months post injury. RNA was extracted and quality assured prior to the use of a whole-genome based bead array platform to describe expression changes in the samples using the pre-injury skin as a comparator. Analysis of the array data was performed using k-means clustering and a hypergeometric probability distribution without replacement and corrections for multiple comparisons were done. Confirmatory q-PCR was performed. Using a k of 10, several clusters of genes were shown to co-cluster together based on Gene Ontology classification with probabilities unlikely to occur by chance alone. OF particular interest were clusters relating to cell cycle, proteinaceous extracellular matrix and keratinization. Given the consistent expression changes at one week following injury in the cell cycle cluster, there is an opportunity to intervene early following burn injury to influence scar development. PMID:24582755

Detection of type 2 diabetes related modules and genes based on epigenetic networks

PubMed Central

2014-01-01

Background Type 2 diabetes (T2D) is one of the most common chronic metabolic diseases characterized by insulin resistance and the decrease of insulin secretion. Genetic variation can only explain part of the heritability of T2D, so there need new methods to detect the susceptibility genes of the disease. Epigenetics could establish the interface between the environmental factor and the T2D Pathological mechanism. Results Based on the network theory and by combining epigenetic characteristics with human interactome, the weighted human DNA methylation network (WMPN) was constructed, and a T2D-related subnetwork (TMSN) was obtained through T2D-related differentially methylated genes. It is found that TMSN had a T2D specific network structure that non-fatal metabolic disease causing genes were often located in the topological and functional periphery of network. Combined with chromatin modifications, the weighted chromatin modification network (WCPN) was built, and a T2D-related chromatin modification pattern subnetwork was obtained by the TMSN gene set. TCSN had a densely connected network community, indicating that TMSN and TCSN could represent a collection of T2D-related epigenetic dysregulated sub-pathways. Using the cumulative hypergeometric test, 24 interplay modules of DNA methylation and chromatin modifications were identified. By the analysis of gene expression in human T2D islet tissue, it is found that there existed genes with the variant expression level caused by the aberrant DNA methylation and (or) chromatin modifications, which might affect and promote the development of T2D. Conclusions Here we have detected the potential interplay modules of DNA methylation and chromatin modifications for T2D. The study of T2D epigenetic networks provides a new way for understanding the pathogenic mechanism of T2D caused by epigenetic disorders. PMID:24565181

Harnessing the theoretical foundations of the exponential and beta-Poisson dose-response models to quantify parameter uncertainty using Markov Chain Monte Carlo.

PubMed

Schmidt, Philip J; Pintar, Katarina D M; Fazil, Aamir M; Topp, Edward

2013-09-01

Dose-response models are the essential link between exposure assessment and computed risk values in quantitative microbial risk assessment, yet the uncertainty that is inherent to computed risks because the dose-response model parameters are estimated using limited epidemiological data is rarely quantified. Second-order risk characterization approaches incorporating uncertainty in dose-response model parameters can provide more complete information to decisionmakers by separating variability and uncertainty to quantify the uncertainty in computed risks. Therefore, the objective of this work is to develop procedures to sample from posterior distributions describing uncertainty in the parameters of exponential and beta-Poisson dose-response models using Bayes's theorem and Markov Chain Monte Carlo (in OpenBUGS). The theoretical origins of the beta-Poisson dose-response model are used to identify a decomposed version of the model that enables Bayesian analysis without the need to evaluate Kummer confluent hypergeometric functions. Herein, it is also established that the beta distribution in the beta-Poisson dose-response model cannot address variation among individual pathogens, criteria to validate use of the conventional approximation to the beta-Poisson model are proposed, and simple algorithms to evaluate actual beta-Poisson probabilities of infection are investigated. The developed MCMC procedures are applied to analysis of a case study data set, and it is demonstrated that an important region of the posterior distribution of the beta-Poisson dose-response model parameters is attributable to the absence of low-dose data. This region includes beta-Poisson models for which the conventional approximation is especially invalid and in which many beta distributions have an extreme shape with questionable plausibility. © Her Majesty the Queen in Right of Canada 2013. Reproduced with the permission of the Minister of the Public Health Agency of Canada.

Analysis of gas absorption to a thin liquid film in the presence of a zero-order chemical reaction

NASA Technical Reports Server (NTRS)

Rajagopalan, S.; Rahman, M. M.

1995-01-01

The paper presents a detailed theoretical analysis of the process of gas absorption to a thin liquid film adjacent to a horizontal rotating disk. The film is formed by the impingement of a controlled liquid jet at the center of the disk and subsequent radial spreading of liquid along the disk. The chemical reaction between the gas and the liquid film can be expressed as a zero-order homogeneous reaction. The process was modeled by establishing equations for the conservation of mass, momentum, and species concentration and solving them analytically. A scaling analysis was used to determine dominant transport processes. Appropriate boundary conditions were used to solve these equations to develop expressions for the local concentration of gas across the thickness of the film and distributions of film height, bulk concentration, and Sherwood number along the radius of the disk. The partial differential equation for species concentration was solved using the separation of variables technique along with the Duhamel's theorem and the final analytical solution was expressed using confluent hypergeometric functions. Tables for eigenvalues and eigenfunctions are presented for a number of reaction rate constants. A parametric study was performed using Reynolds number, Ekman number, and dimensionless reaction rate as parameters. At all radial locations, Sherwood number increased with Reynolds number (flow rate) as well as Ekman number (rate of rotation). The enhancement of mass transfer due to chemical reaction was found to be small when compared to the case of no reaction (pure absorption), but the enhancement factor was very significant when compared to pure absorption in a stagnant liquid film. The zero-order reaction processes considered in the present investigation included the absorption of oxygen in aqueous alkaline solutions of sodiumdithionite and rhodium complex catalyzed carbonylation of methanol. Present analytical results were compared to previous theoretical results for limiting conditions, and were found to have very good agreement.

Random noise effects in pulse-mode digital multilayer neural networks.

PubMed

Kim, Y C; Shanblatt, M A

1995-01-01

A pulse-mode digital multilayer neural network (DMNN) based on stochastic computing techniques is implemented with simple logic gates as basic computing elements. The pulse-mode signal representation and the use of simple logic gates for neural operations lead to a massively parallel yet compact and flexible network architecture, well suited for VLSI implementation. Algebraic neural operations are replaced by stochastic processes using pseudorandom pulse sequences. The distributions of the results from the stochastic processes are approximated using the hypergeometric distribution. Synaptic weights and neuron states are represented as probabilities and estimated as average pulse occurrence rates in corresponding pulse sequences. A statistical model of the noise (error) is developed to estimate the relative accuracy associated with stochastic computing in terms of mean and variance. Computational differences are then explained by comparison to deterministic neural computations. DMNN feedforward architectures are modeled in VHDL using character recognition problems as testbeds. Computational accuracy is analyzed, and the results of the statistical model are compared with the actual simulation results. Experiments show that the calculations performed in the DMNN are more accurate than those anticipated when Bernoulli sequences are assumed, as is common in the literature. Furthermore, the statistical model successfully predicts the accuracy of the operations performed in the DMNN.

Mark-resight superpopulation estimation of a wintering elk Cervus elaphus canadensis herd

USGS Publications Warehouse

Gould, W.R.; Smallidge, S.T.; Thompson, B.C.

2005-01-01

We executed four mark-resight helicopter surveys during the winter months January-February for each of the three years 1999-2001 at 7-10 day intervals to estimate population size of a wintering elk Cervus elaphus canadensis herd in northern New Mexico. We counted numbers of radio-collared and uncollared elk on a simple random sample of quadrats from the study area. Because we were unable to survey the entire study area, we adopted a superpopulation approach to estimating population size, in which the total number of collared animals within and proximate to the entire study area was determined from an independent fixed-wing aircraft. The total number of collared animals available on the quadrats surveyed was also determined and facilitated detectability estimation. We executed superpopulation estimation via the joint hypergeometric estimator using the ratio of marked elk counted to the known number extant as an estimate of effective detectability. Superpopulation size estimates were approximately four times larger than previously suspected in the vicinity of the study area. Despite consistent survey methodology, actual detection rates varied within winter periods, indicating that multiple resight flights are important for improved estimator performance. Variable detectability also suggests that reliance on mere counts of observed individuals in our area may not accurately reflect abundance. ?? Wildlife Biology (2005).

Identification of Chemical Features Linked to Thyroperoxidase ...

EPA Pesticide Factsheets

Disruption of maternal serum thyroid hormone (TH) adversely affects fetal neurodevelopment. Therefore, assay development within the US EPA ToxCast program is ongoing to enable screening for chemicals that may disrupt TH, in support of the Endocrine Disruption Screening Program (EDSP21). The AUR-TPO assay was recently developed to screen >1,000 ToxCast chemicals for potential thyroperoxidase (TPO) inhibition activity. TPO is critical for TH synthesis and is a known target of thyroid-disrupting chemicals. The bioactivity results from the AUR-TPO assay were used to identify chemical substructures associated with in vitro TPO inhibition. Substructure profiles were generated for each chemical in the ToxCast test set using the publicly-available ToxPrint 2.0 chemotypes. Chemotypes enriched among the putative TPO inhibitors were identified using a cumulative hypergeometric probability (p < 0.01). Of the total 729 chemotypes evaluated, 31 were overrepresented among TPO inhibitors. Examination of those 31 chemotypes revealed four basic pharmacophores that accounted for 70% of the ToxCast chemicals active in the AUR-TPO assay: aromatic alcohols, aromatic amines, thiocarbonyls and phosphothioates. Chemico-structural analysis of AUR-TPO screening results enabled the identification of chemical features that likely drive TPO inhibition in the AUR-TPO assay. This highlights the potential to identify thyroid-disrupting chemicals in silico using structural alerts identified by

A High-Throughput Screening Assay to Detect ...

EPA Pesticide Factsheets

In support of the Endocrine Disruption Screening Program (EDSP21), the US EPA ToxCast program is developing assays to enable screening for chemicals that may disrupt thyroid hormone synthesis. Thyroperoxidase (TPO) is critical for TH synthesis and is a known target of thyroid-disrupting chemicals that adversely impact neurodevelopment. The AUR-TPO assay was recently developed to screen >1,900 ToxCast chemicals for potential TPO inhibition activity. Parallel assays were used to determine which AUR-TPO actives were more selective for TPO inhibition. Additionally, the TPO inhibition activities of 150 chemicals were compared between the AUR-TPO assay and an orthogonal peroxidase oxidation assay using guaiacol as substrate to confirm putative TPO inhibition profiles. Bioactivity results from the AUR-TPO assay were used to identify chemical substructures associated with in vitro TPO inhibition. Substructure profiles were generated for each chemical in the ToxCast test set using the publicly-available ToxPrint 2.0 chemotypes. Chemotypes enriched among the putative TPO inhibitors were identified using a cumulative hypergeometric probability (p < 0.01). Of the total 729 chemotypes evaluated, 44 were overrepresented among TPO inhibitors. Another 24 chemotypes were found to be significantly underrepresented among AUR-TPO actives. Examination of these chemotypes revealed four basic pharmacophores that accounted for 70% of the ToxCast chemicals active in the AUR-TPO assay:

Finite-key analysis for quantum key distribution with weak coherent pulses based on Bernoulli sampling

NASA Astrophysics Data System (ADS)

Kawakami, Shun; Sasaki, Toshihiko; Koashi, Masato

2017-07-01

An essential step in quantum key distribution is the estimation of parameters related to the leaked amount of information, which is usually done by sampling of the communication data. When the data size is finite, the final key rate depends on how the estimation process handles statistical fluctuations. Many of the present security analyses are based on the method with simple random sampling, where hypergeometric distribution or its known bounds are used for the estimation. Here we propose a concise method based on Bernoulli sampling, which is related to binomial distribution. Our method is suitable for the Bennett-Brassard 1984 (BB84) protocol with weak coherent pulses [C. H. Bennett and G. Brassard, Proceedings of the IEEE Conference on Computers, Systems and Signal Processing (IEEE, New York, 1984), Vol. 175], reducing the number of estimated parameters to achieve a higher key generation rate compared to the method with simple random sampling. We also apply the method to prove the security of the differential-quadrature-phase-shift (DQPS) protocol in the finite-key regime. The result indicates that the advantage of the DQPS protocol over the phase-encoding BB84 protocol in terms of the key rate, which was previously confirmed in the asymptotic regime, persists in the finite-key regime.

Measuring lexical diversity in narrative discourse of people with aphasia.

PubMed

Fergadiotis, Gerasimos; Wright, Heather H; West, Thomas M

2013-05-01

A microlinguistic content analysis for assessing lexical semantics in people with aphasia (PWA) is lexical diversity (LD). Sophisticated techniques have been developed to measure LD. However, validity evidence for these methodologies when applied to the discourse of PWA is lacking. The purpose of this study was to evaluate four measures of LD to determine how effective they were at measuring LD in PWA. Four measures of LD were applied to short discourse samples produced by 101 PWA: (a) the Measure of Textual Lexical Diversity (MTLD; McCarthy, 2005), (b) the Moving-Average Type-Token Ratio (MATTR; Covington, 2007), (c) D (McKee, Malvern, & Richards, 2000), and (d) the Hypergeometric Distribution (HD-D; McCarthy & Jarvis, 2007). LD was estimated using each method, and the scores were subjected to a series of analyses (e.g., curve-fitting, analysis of variance, confirmatory factor analysis). Results from the confirmatory factor analysis suggested that MTLD and MATTR reflect LD and little of anything else. Further, two indices (HD-D and D) were found to be equivalent, suggesting that either one can be used when samples are >50 tokens. MTLD and MATTR yielded the strongest evidence for producing unbiased LD scores, suggesting that they may be the best measures for capturing LD in PWA.

Doppler Temperature Coefficient Calculations Using Adjoint-Weighted Tallies and Continuous Energy Cross Sections in MCNP6

NASA Astrophysics Data System (ADS)

Gonzales, Matthew Alejandro

The calculation of the thermal neutron Doppler temperature reactivity feedback co-efficient, a key parameter in the design and safe operation of advanced reactors, using first order perturbation theory in continuous energy Monte Carlo codes is challenging as the continuous energy adjoint flux is not readily available. Traditional approaches of obtaining the adjoint flux attempt to invert the random walk process as well as require data corresponding to all temperatures and their respective temperature derivatives within the system in order to accurately calculate the Doppler temperature feedback. A new method has been developed using adjoint-weighted tallies and On-The-Fly (OTF) generated continuous energy cross sections within the Monte Carlo N-Particle (MCNP6) transport code. The adjoint-weighted tallies are generated during the continuous energy k-eigenvalue Monte Carlo calculation. The weighting is based upon the iterated fission probability interpretation of the adjoint flux, which is the steady state population in a critical nuclear reactor caused by a neutron introduced at that point in phase space. The adjoint-weighted tallies are produced in a forward calculation and do not require an inversion of the random walk. The OTF cross section database uses a high order functional expansion between points on a user-defined energy-temperature mesh in which the coefficients with respect to a polynomial fitting in temperature are stored. The coefficients of the fits are generated before run- time and called upon during the simulation to produce cross sections at any given energy and temperature. The polynomial form of the OTF cross sections allows the possibility of obtaining temperature derivatives of the cross sections on-the-fly. The use of Monte Carlo sampling of adjoint-weighted tallies and the capability of computing derivatives of continuous energy cross sections with respect to temperature are used to calculate the Doppler temperature coefficient in a research version of MCNP6. Temperature feedback results from the cross sections themselves, changes in the probability density functions, as well as changes in the density of the materials. The focus of this work is specific to the Doppler temperature feedback which result from Doppler broadening of cross sections as well as changes in the probability density function within the scattering kernel. This method is compared against published results using Mosteller's numerical benchmark to show accurate evaluations of the Doppler temperature coefficient, fuel assembly calculations, and a benchmark solution based on the heavy gas model for free-gas elastic scattering. An infinite medium benchmark for neutron free gas elastic scattering for large scattering ratios and constant absorption cross section has been developed using the heavy gas model. An exact closed form solution for the neutron energy spectrum is obtained in terms of the confluent hypergeometric function and compared against spectra for the free gas scattering model in MCNP6. Results show a quick increase in convergence of the analytic energy spectrum to the MCNP6 code with increasing target size, showing absolute relative differences of less than 5% for neutrons scattering with carbon. The analytic solution has been generalized to accommodate piecewise constant in energy absorption cross section to produce temperature feedback. Results reinforce the constraints in which heavy gas theory may be applied resulting in a significant target size to accommodate increasing cross section structure. The energy dependent piecewise constant cross section heavy gas model was used to produce a benchmark calculation of the Doppler temperature coefficient to show accurate calculations when using the adjoint-weighted method. Results show the Doppler temperature coefficient using adjoint weighting and cross section derivatives accurately obtains the correct solution within statistics as well as reduce computer runtimes by a factor of 50.

Introduction to Generalized Functions with Applications in Aerodynamics and Aeroacoustics

NASA Technical Reports Server (NTRS)

Farassat, F.

1994-01-01

Generalized functions have many applications in science and engineering. One useful aspect is that discontinuous functions can be handled as easily as continuous or differentiable functions and provide a powerful tool in formulating and solving many problems of aerodynamics and acoustics. Furthermore, generalized function theory elucidates and unifies many ad hoc mathematical approaches used by engineers and scientists. We define generalized functions as continuous linear functionals on the space of infinitely differentiable functions with compact support, then introduce the concept of generalized differentiation. Generalized differentiation is the most important concept in generalized function theory and the applications we present utilize mainly this concept. First, some results of classical analysis, are derived with the generalized function theory. Other applications of the generalized function theory in aerodynamics discussed here are the derivations of general transport theorems for deriving governing equations of fluid mechanics, the interpretation of the finite part of divergent integrals, the derivation of the Oswatitsch integral equation of transonic flow, and the analysis of velocity field discontinuities as sources of vorticity. Applications in aeroacoustics include the derivation of the Kirchhoff formula for moving surfaces, the noise from moving surfaces, and shock noise source strength based on the Ffowcs Williams-Hawkings equation.

CALL FOR PAPERS: Special issue: One hundred years of PVI, the Fuchs Painlevé equation

NASA Astrophysics Data System (ADS)

Clarkson, P. A.; Joshi, N.; Mazzocco, M.; Nijhoff, F. W.; Noumi, M.

2005-10-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and General entitled `One hundred years of Painlevé VI, the Fuchs Painlevé equation'. The motivation behind this special issue is to celebrate the centenary of the discovery of this famous differential equation. The Editorial Board has invited P A Clarkson, N Joshi, M Mazzocco, F W Nijhoff and M Noumi to serve as Guest Editors for the issue. The nonlinear ordinary differential equation, which is nowadays known as the Painlevé VI (PVI) equation, is one of the most important differential equations in mathematical physics. It was discovered 100 years ago by Richard Fuchs (son of the famous mathematician Lazarus Fuchs) and reported for the first time in Comptes Rendus de l'Academie des Sciences Paris 141 555 8 (1905). Gambier, in his seminal paper of 1906, included this equation as the top equation in the list of what are now known as the six Painlevé transcendental equations. The Painlevé list emerged from the work on the classification of all ordinary second-order differential equations whose general solution are `uniform', in the sense that there are no movable (i.e. as a function of the initial data) singularities (meaning branch points) worse than poles. The latter is known as the Painlevé property. As the top equation in the Painlevé list of transcendental equations, the importance of PVI can be appreciated by recognizing that this is a universal differential equation, which is the most general (in terms of number of free parameters) of the known second order ODEs defining nonlinear special functions. As such, parallels can be drawn between the role played by PVI transcendents in the nonlinear case and the hypergeometric functions at the linear level. In fact, the monograph From Gauss to Painlevé by K Iwasaki, H Kimura, S Shimomura and M Yoshida (Vieweg, 1991), draws very clearly the line stretching over more than 150 years of special function theory in which PVI is placed as the key equation. In recent years these lines have been extended into the discrete domain, i.e. the field of nonlinear ordinary difference equations, and discrete analogues of PVI have opened entirely new fields of investigation. The aim of the special issue, dedicated specifically to the PVI equations and its avatars rather than to general Painlevé theory, is to consolidate the state-of-the-art knowledge of the properties of this equation and to highlight modern developments (including generalizations of PVI, such as the Garnier system, as well as discrete versions of the equation). The issue should be a repository of high-quality original research papers as well as some invited topical reviews. Scope of the special issue The special issue is dedicated to the study of the Painlevé VI equation, its solutions and properties, and to its generalizations—either in the direction of higher-order differential equations associated with PVI (and related Garnier and Schlesinger systems), or in the direction of difference analogues of the equation. The special issue will welcome contributions that go into the analysis (including asymptotic theory) of Painlevé VI transcendents, the corresponding monodromy theory, the representation theory aspects, the underlying algebraic geometry of the solution manifolds, associated combinatorics and random matrix theory, as well as q-difference and discrete versions of the equation, and last but not least applications in physics. Papers dealing primarily with Painlevé equations other than PVI, or with general Painlevé theory, are not encouraged as these would deflect the contents of the special issue from its specific celebrational motivation. Editorial policy All contributions to the special issue will be refereed in accordance with the refereeing policy of the journal. The Guest Editors will reserve the right to judge whether a contribution fits the scope of the topic of the special issue. Guidelines for preparation of contributions • We aim to publish the special issue in the first half of 2006, in order not to lose the connection with the celebrational year 2005, marking the 100-year anniversary of the discovery of PVI. To realize this, the deadline for contributed papers will be 31 January 2006. • There is a page limit of 16 printed pages (approximately 9600 words) per contribution. For submitted papers exceeding this length the Guest Editors reserve the right to request a reduction in length. Further advice on document preparation can be found at www.iop.org/Journals/jphysa • Contributions to the special issue should if possible be submitted electronically by web upload at www.iop.org/Journals/jphysa, or by email to jphysa@iop.org, quoting `J. Phys. A Special Issue: Painlevé VI'. Submissions should ideally be in standard LaTeX form; we are, however, able to accept most formats including Microsoft Word. Please see the website for further information on electronic submissions. • Authors unable to submit electronically may send hard-copy contributions to: Publishing Administrators, Journal of Physics A, Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK, enclosing electronic code on floppy disk if available and quoting `J. Phys. A Special Issue: Painlevé VI'. • All contributions should be accompanied by a read-me file or covering letter giving the postal and email address for correspondence. The Publishing Office should be notified of any subsequent change of address. The special issue will be published in the paper and online version of the journal. The corresponding author of each contribution will receive a complimentary copy of the issue.

Study of 300,486 individuals identifies 148 independent genetic loci influencing general cognitive function.

PubMed

Davies, Gail; Lam, Max; Harris, Sarah E; Trampush, Joey W; Luciano, Michelle; Hill, W David; Hagenaars, Saskia P; Ritchie, Stuart J; Marioni, Riccardo E; Fawns-Ritchie, Chloe; Liewald, David C M; Okely, Judith A; Ahola-Olli, Ari V; Barnes, Catriona L K; Bertram, Lars; Bis, Joshua C; Burdick, Katherine E; Christoforou, Andrea; DeRosse, Pamela; Djurovic, Srdjan; Espeseth, Thomas; Giakoumaki, Stella; Giddaluru, Sudheer; Gustavson, Daniel E; Hayward, Caroline; Hofer, Edith; Ikram, M Arfan; Karlsson, Robert; Knowles, Emma; Lahti, Jari; Leber, Markus; Li, Shuo; Mather, Karen A; Melle, Ingrid; Morris, Derek; Oldmeadow, Christopher; Palviainen, Teemu; Payton, Antony; Pazoki, Raha; Petrovic, Katja; Reynolds, Chandra A; Sargurupremraj, Muralidharan; Scholz, Markus; Smith, Jennifer A; Smith, Albert V; Terzikhan, Natalie; Thalamuthu, Anbupalam; Trompet, Stella; van der Lee, Sven J; Ware, Erin B; Windham, B Gwen; Wright, Margaret J; Yang, Jingyun; Yu, Jin; Ames, David; Amin, Najaf; Amouyel, Philippe; Andreassen, Ole A; Armstrong, Nicola J; Assareh, Amelia A; Attia, John R; Attix, Deborah; Avramopoulos, Dimitrios; Bennett, David A; Böhmer, Anne C; Boyle, Patricia A; Brodaty, Henry; Campbell, Harry; Cannon, Tyrone D; Cirulli, Elizabeth T; Congdon, Eliza; Conley, Emily Drabant; Corley, Janie; Cox, Simon R; Dale, Anders M; Dehghan, Abbas; Dick, Danielle; Dickinson, Dwight; Eriksson, Johan G; Evangelou, Evangelos; Faul, Jessica D; Ford, Ian; Freimer, Nelson A; Gao, He; Giegling, Ina; Gillespie, Nathan A; Gordon, Scott D; Gottesman, Rebecca F; Griswold, Michael E; Gudnason, Vilmundur; Harris, Tamara B; Hartmann, Annette M; Hatzimanolis, Alex; Heiss, Gerardo; Holliday, Elizabeth G; Joshi, Peter K; Kähönen, Mika; Kardia, Sharon L R; Karlsson, Ida; Kleineidam, Luca; Knopman, David S; Kochan, Nicole A; Konte, Bettina; Kwok, John B; Le Hellard, Stephanie; Lee, Teresa; Lehtimäki, Terho; Li, Shu-Chen; Liu, Tian; Koini, Marisa; London, Edythe; Longstreth, Will T; Lopez, Oscar L; Loukola, Anu; Luck, Tobias; Lundervold, Astri J; Lundquist, Anders; Lyytikäinen, Leo-Pekka; Martin, Nicholas G; Montgomery, Grant W; Murray, Alison D; Need, Anna C; Noordam, Raymond; Nyberg, Lars; Ollier, William; Papenberg, Goran; Pattie, Alison; Polasek, Ozren; Poldrack, Russell A; Psaty, Bruce M; Reppermund, Simone; Riedel-Heller, Steffi G; Rose, Richard J; Rotter, Jerome I; Roussos, Panos; Rovio, Suvi P; Saba, Yasaman; Sabb, Fred W; Sachdev, Perminder S; Satizabal, Claudia L; Schmid, Matthias; Scott, Rodney J; Scult, Matthew A; Simino, Jeannette; Slagboom, P Eline; Smyrnis, Nikolaos; Soumaré, Aïcha; Stefanis, Nikos C; Stott, David J; Straub, Richard E; Sundet, Kjetil; Taylor, Adele M; Taylor, Kent D; Tzoulaki, Ioanna; Tzourio, Christophe; Uitterlinden, André; Vitart, Veronique; Voineskos, Aristotle N; Kaprio, Jaakko; Wagner, Michael; Wagner, Holger; Weinhold, Leonie; Wen, K Hoyan; Widen, Elisabeth; Yang, Qiong; Zhao, Wei; Adams, Hieab H H; Arking, Dan E; Bilder, Robert M; Bitsios, Panos; Boerwinkle, Eric; Chiba-Falek, Ornit; Corvin, Aiden; De Jager, Philip L; Debette, Stéphanie; Donohoe, Gary; Elliott, Paul; Fitzpatrick, Annette L; Gill, Michael; Glahn, David C; Hägg, Sara; Hansell, Narelle K; Hariri, Ahmad R; Ikram, M Kamran; Jukema, J Wouter; Vuoksimaa, Eero; Keller, Matthew C; Kremen, William S; Launer, Lenore; Lindenberger, Ulman; Palotie, Aarno; Pedersen, Nancy L; Pendleton, Neil; Porteous, David J; Räikkönen, Katri; Raitakari, Olli T; Ramirez, Alfredo; Reinvang, Ivar; Rudan, Igor; Dan Rujescu; Schmidt, Reinhold; Schmidt, Helena; Schofield, Peter W; Schofield, Peter R; Starr, John M; Steen, Vidar M; Trollor, Julian N; Turner, Steven T; Van Duijn, Cornelia M; Villringer, Arno; Weinberger, Daniel R; Weir, David R; Wilson, James F; Malhotra, Anil; McIntosh, Andrew M; Gale, Catharine R; Seshadri, Sudha; Mosley, Thomas H; Bressler, Jan; Lencz, Todd; Deary, Ian J

2018-05-29

General cognitive function is a prominent and relatively stable human trait that is associated with many important life outcomes. We combine cognitive and genetic data from the CHARGE and COGENT consortia, and UK Biobank (total N = 300,486; age 16-102) and find 148 genome-wide significant independent loci (P < 5 × 10 -8 ) associated with general cognitive function. Within the novel genetic loci are variants associated with neurodegenerative and neurodevelopmental disorders, physical and psychiatric illnesses, and brain structure. Gene-based analyses find 709 genes associated with general cognitive function. Expression levels across the cortex are associated with general cognitive function. Using polygenic scores, up to 4.3% of variance in general cognitive function is predicted in independent samples. We detect significant genetic overlap between general cognitive function, reaction time, and many health variables including eyesight, hypertension, and longevity. In conclusion we identify novel genetic loci and pathways contributing to the heritability of general cognitive function.

28 CFR 0.120 - General functions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 28 Judicial Administration 1 2010-07-01 2010-07-01 false General functions. 0.120 Section 0.120... Community Oriented Policing Services § 0.120 General functions. The Director, Office of Community Oriented Policing Services shall: (a) Exercise the powers and perform the functions vested in the Attorney General...

Generalized Wall Function for Complex Turbulent Flows

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Povinelli, Louis A.; Liu, Nan-Suey; Chen, Kuo-Huey

2000-01-01

A generalized wall function was proposed by Shih et al., (1999). It accounts the effect of pressure gradients on the flow near the wall. Theory shows that the effect of pressure gradients on the flow in the inertial sublayer is very significant and the standard wall function should be replaced by a generalized wall function. Since the theory is also valid for boundary layer flows toward separation, the generalized wall function may be applied to complex turbulent flows with acceleration, deceleration, separation and recirculation. This paper is to verify the generalized wall function with numerical simulations for boundary layer flows with various adverse and favorable pressure gradients, including flows about to separate. Furthermore, a general procedure of implementation of the generalized wall function for National Combustion Code (NCC) is described, it can be applied to both structured and unstructured CFD codes.

28 CFR 0.25 - General functions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 28 Judicial Administration 1 2010-07-01 2010-07-01 false General functions. 0.25 Section 0.25... Counsel § 0.25 General functions. The following-described matters are assigned to, and shall be conducted... agencies of the Government; and assisting the Attorney General in the performance of his functions as legal...

28 CFR 0.130 - General functions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 28 Judicial Administration 1 2010-07-01 2010-07-01 false General functions. 0.130 Section 0.130..., Tobacco, Firearms, and Explosives § 0.130 General functions. Subject to the direction of the Attorney... functions and powers of the Attorney General under the following provisions of law: (1) 18 U.S.C. chapters...

28 CFR 0.30 - General functions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 28 Judicial Administration 1 2010-07-01 2010-07-01 false General functions. 0.30 Section 0.30... Service § 0.30 General functions. The following-described matters are assigned to, and shall be conducted... performance of the functions vested in the Attorney General by sections 204(d), 205, 1002, and 1003(a) of the...

Identification of active miRNA and transcription factor regulatory pathways in human obesity-related inflammation.

PubMed

Zhang, Xi-Mei; Guo, Lin; Chi, Mei-Hua; Sun, Hong-Mei; Chen, Xiao-Wen

2015-03-07

Obesity-induced chronic inflammation plays a fundamental role in the pathogenesis of metabolic syndrome (MS). Recently, a growing body of evidence supports that miRNAs are largely dysregulated in obesity and that specific miRNAs regulate obesity-associated inflammation. We applied an approach aiming to identify active miRNA-TF-gene regulatory pathways in obesity. Firstly, we detected differentially expressed genes (DEGs) and differentially expressed miRNAs (DEmiRs) from mRNA and miRNA expression profiles, respectively. Secondly, by mapping the DEGs and DEmiRs to the curated miRNA-TF-gene regulatory network as active seed nodes and connect them with their immediate neighbors, we obtained the potential active miRNA-TF-gene regulatory subnetwork in obesity. Thirdly, using a Breadth-First-Search (BFS) algorithm, we identified potential active miRNA-TF-gene regulatory pathways in obesity. Finally, through the hypergeometric test, we identified the active miRNA-TF-gene regulatory pathways that were significantly related to obesity. The potential active pathways with FDR < 0.0005 were considered to be the active miRNA-TF regulatory pathways in obesity. The union of the active pathways is visualized and identical nodes of the active pathways were merged. We identified 23 active miRNA-TF-gene regulatory pathways that were significantly related to obesity-related inflammation.

A robust design mark-resight abundance estimator allowing heterogeneity in resighting probabilities

USGS Publications Warehouse

McClintock, B.T.; White, Gary C.; Burnham, K.P.

2006-01-01

This article introduces the beta-binomial estimator (BBE), a closed-population abundance mark-resight model combining the favorable qualities of maximum likelihood theory and the allowance of individual heterogeneity in sighting probability (p). The model may be parameterized for a robust sampling design consisting of multiple primary sampling occasions where closure need not be met between primary occasions. We applied the model to brown bear data from three study areas in Alaska and compared its performance to the joint hypergeometric estimator (JHE) and Bowden's estimator (BOWE). BBE estimates suggest heterogeneity levels were non-negligible and discourage the use of JHE for these data. Compared to JHE and BOWE, confidence intervals were considerably shorter for the AICc model-averaged BBE. To evaluate the properties of BBE relative to JHE and BOWE when sample sizes are small, simulations were performed with data from three primary occasions generated under both individual heterogeneity and temporal variation in p. All models remained consistent regardless of levels of variation in p. In terms of precision, the AICc model-averaged BBE showed advantages over JHE and BOWE when heterogeneity was present and mean sighting probabilities were similar between primary occasions. Based on the conditions examined, BBE is a reliable alternative to JHE or BOWE and provides a framework for further advances in mark-resight abundance estimation. ?? 2006 American Statistical Association and the International Biometric Society.

Generalized -deformed correlation functions as spectral functions of hyperbolic geometry

NASA Astrophysics Data System (ADS)

Bonora, L.; Bytsenko, A. A.; Guimarães, M. E. X.

2014-08-01

We analyze the role of vertex operator algebra and 2d amplitudes from the point of view of the representation theory of infinite-dimensional Lie algebras, MacMahon and Ruelle functions. By definition p-dimensional MacMahon function, with , is the generating function of p-dimensional partitions of integers. These functions can be represented as amplitudes of a two-dimensional c = 1 CFT, and, as such, they can be generalized to . With some abuse of language we call the latter amplitudes generalized MacMahon functions. In this paper we show that generalized p-dimensional MacMahon functions can be rewritten in terms of Ruelle spectral functions, whose spectrum is encoded in the Patterson-Selberg function of three-dimensional hyperbolic geometry.

28 CFR 0.20 - General functions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 28 Judicial Administration 1 2010-07-01 2010-07-01 false General functions. 0.20 Section 0.20 Judicial Administration DEPARTMENT OF JUSTICE ORGANIZATION OF THE DEPARTMENT OF JUSTICE Office of the Solicitor General § 0.20 General functions. The following-described matters are assigned to, and shall be...

28 CFR 0.100 - General functions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 28 Judicial Administration 1 2010-07-01 2010-07-01 false General functions. 0.100 Section 0.100... Administration § 0.100 General functions. The following-described matters are assigned to, and shall be conducted, handled, or supervised by, the Administrator of the Drug Enforcement Administration: (a) Functions vested...

28 CFR 0.70 - General functions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 28 Judicial Administration 1 2010-07-01 2010-07-01 false General functions. 0.70 Section 0.70 Judicial Administration DEPARTMENT OF JUSTICE ORGANIZATION OF THE DEPARTMENT OF JUSTICE Tax Division § 0.70 General functions. The following functions are assigned to and shall be conducted, handled, or supervised...

28 CFR 0.34 - General functions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 28 Judicial Administration 1 2010-07-01 2010-07-01 false General functions. 0.34 Section 0.34 Judicial Administration DEPARTMENT OF JUSTICE ORGANIZATION OF THE DEPARTMENT OF JUSTICE 2 INTERPOL-United States National Central Bureau § 0.34 General functions. The following functions are assigned to, and...

Explanation and inference: mechanistic and functional explanations guide property generalization.

PubMed

Lombrozo, Tania; Gwynne, Nicholas Z

2014-01-01

The ability to generalize from the known to the unknown is central to learning and inference. Two experiments explore the relationship between how a property is explained and how that property is generalized to novel species and artifacts. The experiments contrast the consequences of explaining a property mechanistically, by appeal to parts and processes, with the consequences of explaining the property functionally, by appeal to functions and goals. The findings suggest that properties that are explained functionally are more likely to be generalized on the basis of shared functions, with a weaker relationship between mechanistic explanations and generalization on the basis of shared parts and processes. The influence of explanation type on generalization holds even though all participants are provided with the same mechanistic and functional information, and whether an explanation type is freely generated (Experiment 1), experimentally provided (Experiment 2), or experimentally induced (Experiment 2). The experiments also demonstrate that explanations and generalizations of a particular type (mechanistic or functional) can be experimentally induced by providing sample explanations of that type, with a comparable effect when the sample explanations come from the same domain or from a different domains. These results suggest that explanations serve as a guide to generalization, and contribute to a growing body of work supporting the value of distinguishing mechanistic and functional explanations.

Relationships between the generalized functional method and other methods of nonimaging optical design.

PubMed

Bortz, John; Shatz, Narkis

2011-04-01

The recently developed generalized functional method provides a means of designing nonimaging concentrators and luminaires for use with extended sources and receivers. We explore the mathematical relationships between optical designs produced using the generalized functional method and edge-ray, aplanatic, and simultaneous multiple surface (SMS) designs. Edge-ray and dual-surface aplanatic designs are shown to be special cases of generalized functional designs. In addition, it is shown that dual-surface SMS designs are closely related to generalized functional designs and that certain computational advantages accrue when the two design methods are combined. A number of examples are provided. © 2011 Optical Society of America

12 CFR 265.2 - Delegation of functions generally.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 12 Banks and Banking 3 2010-01-01 2010-01-01 false Delegation of functions generally. 265.2... RESERVE SYSTEM RULES REGARDING DELEGATION OF AUTHORITY § 265.2 Delegation of functions generally. (a) The Board has determined to delegate authority to exercise the functions described in this part. (b) The...

28 CFR 0.23 - General functions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 28 Judicial Administration 1 2010-07-01 2010-07-01 false General functions. 0.23 Section 0.23... Policy § 0.23 General functions. The Office of Legal Policy shall be headed by an Assistant Attorney... Departmental goals. (i) Perform such other duties and functions as may be specially assigned by the Attorney...

28 CFR 0.29a - General functions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 28 Judicial Administration 1 2010-07-01 2010-07-01 false General functions. 0.29a Section 0.29a Judicial Administration DEPARTMENT OF JUSTICE ORGANIZATION OF THE DEPARTMENT OF JUSTICE 4-Office of the Inspector General § 0.29a General functions. (a) The OIG is a statutorily created independent entity within...

An introduction to generalized functions with some applications in aerodynamics and aeroacoustics

NASA Technical Reports Server (NTRS)

Farassat, F.

1994-01-01

In this paper, we start with the definition of generalized functions as continuous linear functionals on the space of infinitely differentiable functions with compact support. The concept of generalization differentiation is introduced next. This is the most important concept in generalized function theory and the applications we present utilize mainly this concept. First, some of the results of classical analysis, such as Leibniz rule of differentiation under the integral sign and the divergence theorem, are derived using the generalized function theory. It is shown that the divergence theorem remains valid for discontinuous vector fields provided that the derivatives are all viewed as generalized derivatives. This implies that all conservation laws of fluid mechanics are valid as they stand for discontinuous fields with all derivatives treated as generalized deriatives. Once these derivatives are written as ordinary derivatives and jumps in the field parameters across discontinuities, the jump conditions can be easily found. For example, the unsteady shock jump conditions can be derived from mass and momentum conservation laws. By using a generalized function theory, this derivative becomes trivial. Other applications of the generalized function theory in aerodynamics discussed in this paper are derivation of general transport theorems for deriving governing equations of fluid mechanics, the interpretation of finite part of divergent integrals, derivation of Oswatiitsch integral equation of transonic flow, and analysis of velocity field discontinuities as sources of vorticity. Applications in aeroacoustics presented here include the derivation of the Kirchoff formula for moving surfaces,the noise from moving surfaces, and shock noise source strength based on the Ffowcs Williams-Hawkings equation.

Generalized wall function and its application to compressible turbulent boundary layer over a flat plate

NASA Astrophysics Data System (ADS)

Liu, J.; Wu, S. P.

2017-04-01

Wall function boundary conditions including the effects of compressibility and heat transfer are improved for compressible turbulent boundary flows. Generalized wall function formulation at zero-pressure gradient is proposed based on coupled velocity and temperature profiles in the entire near-wall region. The parameters in the generalized wall function are well revised. The proposed boundary conditions are integrated into Navier-Stokes computational fluid dynamics code that includes the shear stress transport turbulence model. Numerical results are presented for a compressible boundary layer over a flat plate at zero-pressure gradient. Compared with experimental data, the computational results show that the generalized wall function reduces the first grid spacing in the directed normal to the wall and proves the feasibility and effectivity of the generalized wall function method.

The norms and variances of the Gabor, Morlet and general harmonic wavelet functions

NASA Astrophysics Data System (ADS)

Simonovski, I.; Boltežar, M.

2003-07-01

This paper deals with certain properties of the continuous wavelet transform and wavelet functions. The norms and the spreads in time and frequency of the common Gabor and Morlet wavelet functions are presented. It is shown that the norm of the Morlet wavelet function does not satisfy the normalization condition and that the normalized Morlet wavelet function is identical to the Gabor wavelet function with the parameter σ=1. The general harmonic wavelet function is developed using frequency modulation of the Hanning and Hamming window functions. Several properties of the general harmonic wavelet function are also presented and compared to the Gabor wavelet function. The time and frequency spreads of the general harmonic wavelet function are only slightly higher than the time and frequency spreads of the Gabor wavelet function. However, the general harmonic wavelet function is simpler to use than the Gabor wavelet function. In addition, the general harmonic wavelet function can be constructed in such a way that the zero average condition is truly satisfied. The average value of the Gabor wavelet function can approach a value of zero but it cannot reach it. When calculating the continuous wavelet transform, errors occur at the start- and the end-time indexes. This is called the edge effect and is caused by the fact that the wavelet transform is calculated from a signal of finite length. In this paper, we propose a method that uses signal mirroring to reduce the errors caused by the edge effect. The success of the proposed method is demonstrated by using a simulated signal.

Neural networks: further insights into error function, generalized weights and others

PubMed Central

2016-01-01

The article is a continuum of a previous one providing further insights into the structure of neural network (NN). Key concepts of NN including activation function, error function, learning rate and generalized weights are introduced. NN topology can be visualized with generic plot() function by passing a “nn” class object. Generalized weights assist interpretation of NN model with respect to the independent effect of individual input variables. A large variance of generalized weights for a covariate indicates non-linearity of its independent effect. If generalized weights of a covariate are approximately zero, the covariate is considered to have no effect on outcome. Finally, prediction of new observations can be performed using compute() function. Make sure that the feature variables passed to the compute() function are in the same order to that in the training NN. PMID:27668220

28 CFR 0.27 - General functions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 28 Judicial Administration 1 2010-07-01 2010-07-01 false General functions. 0.27 Section 0.27 Judicial Administration DEPARTMENT OF JUSTICE ORGANIZATION OF THE DEPARTMENT OF JUSTICE 2-Office of Legislative and Intergovernmental Affairs § 0.27 General functions. The following-described matters are...

28 CFR 0.115 - General functions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 28 Judicial Administration 1 2010-07-01 2010-07-01 false General functions. 0.115 Section 0.115 Judicial Administration DEPARTMENT OF JUSTICE ORGANIZATION OF THE DEPARTMENT OF JUSTICE Executive Office for Immigration Review § 0.115 General functions. (a) The Executive Office for Immigration Review...

Sexual, marital, and general life functioning in couples coping with colorectal cancer: a dyadic study across time.

PubMed

Traa, Marjan J; Braeken, Johan; De Vries, Jolanda; Roukema, Jan A; Slooter, Gerrit D; Crolla, Rogier M P H; Borremans, Monique P M; Den Oudsten, Brenda L

2015-09-01

This study evaluated the following: (a) levels of sexual, marital, and general life functioning for both patients and partners; (b) interdependence between both members of the couple; and (c) longitudinal change in sexual, marital, and general life functioning and longitudinal stress-spillover effects in these three domains from a dyadic perspective. Couples (n = 102) completed the Maudsley Marital Questionnaire preoperatively and 3 and 6 months postoperatively. Mean scores were compared with norm scores. A multivariate general linear model and a multivariate latent difference score - structural equation modeling (LDS-SEM), which took into account actor and partner effects, were evaluated. Patients and partners reported lower sexual, mostly similar marital, and higher general life functioning compared with norm scores. Moderate to high within-dyad associations were found. The LDS-SEM model mostly showed actor effects. Yet the longitudinal change in the partners' sexual functioning was determined not only by their own preoperative sexual functioning but also by that of the patient. Preoperative sexual functioning did not spill over to the other two domains for patients and partners, whereas the patients' preoperative general life functioning influenced postoperative change in marital and sexual functioning. Health care professionals should examine potential sexual problems but have to be aware that these problems may not spill over to the marital and general life domains. In contrast, low functioning in the general life domain may spill over to the marital and sexual domains. The interdependence between patients and partners implies that a couple-based perspective (e.g., couple-based interventions/therapies) to coping with cancer is needed. Copyright © 2015 John Wiley & Sons, Ltd.

28 CFR 0.111 - General functions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 28 Judicial Administration 1 2010-07-01 2010-07-01 false General functions. 0.111 Section 0.111 Judicial Administration DEPARTMENT OF JUSTICE ORGANIZATION OF THE DEPARTMENT OF JUSTICE United States Marshals Service § 0.111 General functions. The Director of the United States Marshals Service shall direct...

An evaluation of generalization of mands during functional communication training.

PubMed

Falcomata, Terry S; Wacker, David P; Ringdahl, Joel E; Vinquist, Kelly; Dutt, Anuradha

2013-01-01

The primary purpose of this study was to evaluate the generalization of mands during functional communication training (FCT) and sign language training across functional contexts (i.e., positive reinforcement, negative reinforcement). A secondary purpose was to evaluate a training procedure based on stimulus control to teach manual signs. During the treatment evaluation, we implemented sign language training in 1 functional context (e.g., positive reinforcement by attention) while continuing the functional analysis conditions in 2 other contexts (e.g., positive reinforcement by tangible item; negative reinforcement by escape). During the generalization evaluation, we tested for the generalization of trained mands across functional contexts (i.e., positive reinforcement; negative reinforcement) by implementing extinction in the 2 nontarget contexts. The results suggested that the stimulus control training procedure effectively taught manual signs and treated destructive behavior. Specific patterns of generalization of trained mands and destructive behavior also were observed. © Society for the Experimental Analysis of Behavior.

Intrauterine growth restriction and placental gene expression in severe preeclampsia, comparing early-onset and late-onset forms.

PubMed

Nevalainen, Jaana; Skarp, Sini; Savolainen, Eeva-Riitta; Ryynänen, Markku; Järvenpää, Jouko

2017-10-26

To evaluate placental gene expression in severe early- or late-onset preeclampsia with intrauterine growth restriction compared to controls. Chorionic villus sampling was conducted after cesarean section from the placentas of five women with early- or late-onset severe preeclampsia and five controls for each preeclampsia group. Microarray analysis was performed to identify gene expression differences between the groups. Pathway analysis showed over-representation of gene ontology (GO) biological process terms related to inflammatory and immune response pathways, platelet development, vascular development, female pregnancy and reproduction in early-onset preeclampsia. Pathways related to immunity, complement and coagulation cascade were overrepresented in the hypergeometric test for the Kyoto Encyclopedia of Genes and Genomes (KEGG) database. Ten genes (ABI3BP, C7, HLA-G, IL2RB, KRBOX1, LRRC15, METTL7B, MPP5, RFLNB and SLC20A) had a ≥±1 fold expression difference in severe early-onset preeclampsia group compared to early controls. There were 362 genes that had a ≥±1 fold expression difference in severe early-onset preeclampsia group compared to late-onset preeclampsia group including ABI3BP, C7, HLA-G and IL2RB. There are significant differences in placental gene expression between severe early- and late-onset preeclampsia when both are associated with intrauterine growth restriction. ABI3BP, C7, HLA-G and IL2RB might contribute to the development of early form of severe preeclampsia.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oberhardt, Matthew A.; Zarecki, Raphy; Reshef, Leah

Recent insights suggest that non-specific and/or promiscuous enzymes are common and active across life. Understanding the role of such enzymes is an important open question in biology. Here we develop a genome-wide method, PROPER, that uses a permissive PSI-BLAST approach to predict promiscuous activities of metabolic genes. Enzyme promiscuity is typically studied experimentally using multicopy suppression, in which over-expression of a promiscuous ‘replacer’ gene rescues lethality caused by inactivation of a ‘target’ gene. We use PROPER to predict multicopy suppression in Escherichia coli, achieving highly significant overlap with published cases (hypergeometric p = 4.4e-13). We then validate three novel predictedmore » target-replacer gene pairs in new multicopy suppression experiments. We next go beyond PROPER and develop a network-based approach, GEM-PROPER, that integrates PROPER with genome-scale metabolic modeling to predict promiscuous replacements via alternative metabolic pathways. GEM-PROPER predicts a new indirect replacer (thiG) for an essential enzyme (pdxB) in production of pyridoxal 5’-phosphate (the active form of Vitamin B 6), which we validate experimentally via multicopy suppression. Here, we perform a structural analysis of thiG to determine its potential promiscuous active site, which we validate experimentally by inactivating the pertaining residues and showing a loss of replacer activity. Thus, this study is a successful example where a computational investigation leads to a network-based identification of an indirect promiscuous replacement of a key metabolic enzyme, which would have been extremely difficult to identify directly.« less

Diagnostic test accuracy and prevalence inferences based on joint and sequential testing with finite population sampling.

PubMed

Su, Chun-Lung; Gardner, Ian A; Johnson, Wesley O

2004-07-30

The two-test two-population model, originally formulated by Hui and Walter, for estimation of test accuracy and prevalence estimation assumes conditionally independent tests, constant accuracy across populations and binomial sampling. The binomial assumption is incorrect if all individuals in a population e.g. child-care centre, village in Africa, or a cattle herd are sampled or if the sample size is large relative to population size. In this paper, we develop statistical methods for evaluating diagnostic test accuracy and prevalence estimation based on finite sample data in the absence of a gold standard. Moreover, two tests are often applied simultaneously for the purpose of obtaining a 'joint' testing strategy that has either higher overall sensitivity or specificity than either of the two tests considered singly. Sequential versions of such strategies are often applied in order to reduce the cost of testing. We thus discuss joint (simultaneous and sequential) testing strategies and inference for them. Using the developed methods, we analyse two real and one simulated data sets, and we compare 'hypergeometric' and 'binomial-based' inferences. Our findings indicate that the posterior standard deviations for prevalence (but not sensitivity and specificity) based on finite population sampling tend to be smaller than their counterparts for infinite population sampling. Finally, we make recommendations about how small the sample size should be relative to the population size to warrant use of the binomial model for prevalence estimation. Copyright 2004 John Wiley & Sons, Ltd.

28 CFR 0.22 - General functions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 28 Judicial Administration 1 2010-07-01 2010-07-01 false General functions. 0.22 Section 0.22 Judicial Administration DEPARTMENT OF JUSTICE ORGANIZATION OF THE DEPARTMENT OF JUSTICE 1-Executive Office for U.S. Attorneys § 0.22 General functions. The Executive Office for United States Attorneys shall be...

12 CFR 265.2 - Delegation of functions generally.

Code of Federal Regulations, 2011 CFR

2011-01-01

... 12 Banks and Banking 3 2011-01-01 2011-01-01 false Delegation of functions generally. 265.2 Section 265.2 Banks and Banking FEDERAL RESERVE SYSTEM (CONTINUED) BOARD OF GOVERNORS OF THE FEDERAL RESERVE SYSTEM RULES REGARDING DELEGATION OF AUTHORITY § 265.2 Delegation of functions generally. (a) The...

47 CFR 0.13 - Functions of the Office.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 47 Telecommunication 1 2010-10-01 2010-10-01 false Functions of the Office. 0.13 Section 0.13 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL COMMISSION ORGANIZATION Organization Office of Inspector General § 0.13 Functions of the Office. The Office of Inspector General is directly responsible to the...

47 CFR 0.41 - Functions of the Office.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 47 Telecommunication 1 2010-10-01 2010-10-01 false Functions of the Office. 0.41 Section 0.41 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL COMMISSION ORGANIZATION Organization Office of General Counsel § 0.41 Functions of the Office. The Office of the General Counsel has the following duties and...

Generalized fluid impulse functions for oscillating marine structures

NASA Astrophysics Data System (ADS)

Janardhanan, K.; Price, W. G.; Wu, Y.

1992-03-01

A selection of generalized impulse response functions is presented for a variety of rigid and flexible marine structures (i.e. mono-hull, SWATH, floating drydock and twin dock, fixed flexible pile). These functions are determined from calculated and experimental frequency-dependent hydrodynamic data, and the characteristics of these data depend on the type of structure considered. This information is reflected in the shape and duration of the generalized impulse response functions which are pre-requisites for a generalized integro-differential mathematical model describing the dynamic behaviour of the structures to seaway excitation.

28 CFR 59.5 - Functions and authorities of the Deputy Assistant Attorneys General.

Code of Federal Regulations, 2010 CFR

2010-07-01

... Assistant Attorneys General. 59.5 Section 59.5 Judicial Administration DEPARTMENT OF JUSTICE (CONTINUED... authorities of the Deputy Assistant Attorneys General. The functions and authorities of the Deputy Assistant Attorneys General set out in this part may at any time be exercised by an Assistant Attorney General, the...

General functioning predicts reward and punishment learning in schizophrenia.

PubMed

Somlai, Zsuzsanna; Moustafa, Ahmed A; Kéri, Szabolcs; Myers, Catherine E; Gluck, Mark A

2011-04-01

Previous studies investigating feedback-driven reinforcement learning in patients with schizophrenia have provided mixed results. In this study, we explored the clinical predictors of reward and punishment learning using a probabilistic classification learning task. Patients with schizophrenia (n=40) performed similarly to healthy controls (n=30) on the classification learning task. However, more severe negative and general symptoms were associated with lower reward-learning performance, whereas poorer general psychosocial functioning was correlated with both lower reward- and punishment-learning performances. Multiple linear regression analyses indicated that general psychosocial functioning was the only significant predictor of reinforcement learning performance when education, antipsychotic dose, and positive, negative and general symptoms were included in the analysis. These results suggest a close relationship between reinforcement learning and general psychosocial functioning in schizophrenia. Published by Elsevier B.V.

Racism-Related Stress, General Life Stress, and Psychological Functioning among Black American Women

ERIC Educational Resources Information Center

Pieterse, Alex L.; Carter, Robert T.; Ray, Kilynda V.

2013-01-01

The relationship between general life stress, perceived racism, and psychological functioning was explored in a sample of 118 Black American women. Findings indicate that racism-related stress was not a significant predictor of psychological functioning when controlling for general life stress. Perceived racism was positively associated with…

75 FR 4982 - Redelegation of Functions; Delegation of Authority to Drug Enforcement Administration Official

Federal Register 2010, 2011, 2012, 2013, 2014

2010-02-01

... which were vested in the Attorney General by the Controlled Substances Act and subsequently delegated to...-certification (21 CFR 1314.40). Redelegation of Authority The Attorney General has delegated his functions under...(b)). The Attorney General has also authorized the Administrator to redelegate any of his functions...

Generalizing Is Necessary or Even Unavoidable

ERIC Educational Resources Information Center

Otte, Michael F.; Mendonça, Tânia M.; de Barros, Luiz

2015-01-01

The problems of geometry and mechanics have driven forward the generalization of the concepts of number and function. This shows how application and generalization together prevent that mathematics becomes a mere formalism. Thoughts are signs and signs have meaning within a certain context. Meaning is a function of a term: This function produces a…

10 CFR 1023.3 - Principles of general applicability.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 10 Energy 4 2010-01-01 2010-01-01 false Principles of general applicability. 1023.3 Section 1023.3 Energy DEPARTMENT OF ENERGY (GENERAL PROVISIONS) CONTRACT APPEALS Overview: Organization, Functions and Authorities § 1023.3 Principles of general applicability. (a) Adjudicatory functions. The following principles...

10 CFR 1023.9 - General guidelines.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 10 Energy 4 2010-01-01 2010-01-01 false General guidelines. 1023.9 Section 1023.9 Energy DEPARTMENT OF ENERGY (GENERAL PROVISIONS) CONTRACT APPEALS Overview: Organization, Functions and Authorities § 1023.9 General guidelines. (a) The principles of this Overview shall apply to all Board functions...

Comparison and Contrast of Two General Functional Regression Modeling Frameworks

PubMed Central

Morris, Jeffrey S.

2017-01-01

In this article, Greven and Scheipl describe an impressively general framework for performing functional regression that builds upon the generalized additive modeling framework. Over the past number of years, my collaborators and I have also been developing a general framework for functional regression, functional mixed models, which shares many similarities with this framework, but has many differences as well. In this discussion, I compare and contrast these two frameworks, to hopefully illuminate characteristics of each, highlighting their respecitve strengths and weaknesses, and providing recommendations regarding the settings in which each approach might be preferable. PMID:28736502

Comparison and Contrast of Two General Functional Regression Modeling Frameworks.

PubMed

Morris, Jeffrey S

2017-02-01

In this article, Greven and Scheipl describe an impressively general framework for performing functional regression that builds upon the generalized additive modeling framework. Over the past number of years, my collaborators and I have also been developing a general framework for functional regression, functional mixed models, which shares many similarities with this framework, but has many differences as well. In this discussion, I compare and contrast these two frameworks, to hopefully illuminate characteristics of each, highlighting their respecitve strengths and weaknesses, and providing recommendations regarding the settings in which each approach might be preferable.

Symptom load and general function among patients with erythema migrans: a prospective study with a 1-year follow-up after antibiotic treatment in Norwegian general practice.

PubMed

Eliassen, Knut Eirik; Hjetland, Reidar; Reiso, Harald; Lindbæk, Morten; Tschudi-Madsen, Hedda

2017-03-01

Promptly treated erythema migrans (EM) has good prognosis. However, some patients report persistent symptoms. Do patients with EM have more symptoms than the general population? We describe individual symptoms and general function in EM-patients at time of diagnosis and one year after treatment. Prospective study with 1-year follow up after treatment. Questionnaires included a modified version of the Subjective Health Complaints Inventory, comprising three additional Lyme borreliosis (LB) related symptoms. General function was assessed using a five-point scale modified from the COOP/WONCA charts. Norwegian general practice. A total of 188 patients were included in a randomized controlled trial comparing three antibiotic regimens for EM, of whom 139 had complete data for this study. Individual symptoms, symptom load and general function. Mild symptoms were common, reported by 84.9% at baseline and by 85.6% at follow-up. At baseline, patients reported a mean of 5.4 symptoms, compared with 6.2 after one year. Severely bothersome symptoms and severely impaired general function were rare. Tiredness was the most reported symptom both at baseline and at follow-up. Palsy (other than facial) was the least reported symptom, but the only one with a significant increase. However, this was not associated to the EM. The symptom load was comparable to that reported in the general population. We found an increase in symptom load at follow-up that did not significantly affect general function. Monitoring patients' symptom loads prior to treatment reduce the probability of attributing follow-up symptoms to LB. Key points Erythema migrans has a good prognosis.Patients treated for erythema migrans have a slight increase in symptom load one year after treatment. This increase does not affect general function. The levels of subjective health complaints in patients treated for erythema migrans are comparable to the background population.

(q,{mu}) and (p,q,{zeta})-exponential functions: Rogers-Szego'' polynomials and Fourier-Gauss transform

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hounkonnou, Mahouton Norbert; Nkouankam, Elvis Benzo Ngompe

2010-10-15

From the realization of q-oscillator algebra in terms of generalized derivative, we compute the matrix elements from deformed exponential functions and deduce generating functions associated with Rogers-Szego polynomials as well as their relevant properties. We also compute the matrix elements associated with the (p,q)-oscillator algebra (a generalization of the q-one) and perform the Fourier-Gauss transform of a generalization of the deformed exponential functions.

Moderation of genetic factors by parental divorce in adolescents' evaluations of family functioning and subjective wellbeing.

PubMed

van der Aa, Niels; Boomsma, Dorret I; Rebollo-Mesa, Irene; Hudziak, James J; Bartels, Meike

2010-04-01

Adolescents' evaluations of family functioning may have a significant impact on their subjective well-being and adjustment. The aim of the study was to investigate the degree to which genetic and environmental influences affect variation in evaluations of general family functioning, family conflict, and quality of life and the overlap between them. We assessed whether genetic and environmental influences are moderated by parental divorce by analyzing self-report data from 6,773 adolescent twins and their non-twin siblings. Genetic, shared, and nonshared environmental influences accounted for variation in general family functioning and family conflict, with genetic influences being relatively more important in girls than boys in general family functioning. Genetic and nonshared environmental influences accounted for variation in quality of life, with genetic influences being relatively more important in girls. Evidence was found for interaction between genetic factors and parental divorce: genetic influence on general family functioning was larger in participants from divorced families. The overlap between general family functioning and quality of life, and family conflict and quality of life was accounted for the largest part by genetic effects, with nonshared environmental effects accounting for the remaining part. By examining the data from monozygotic twins, we found evidence for interaction between genotype and nonshared, non-measured, environmental influences on evaluations of general family functioning, family conflict, and quality of life.

Generalized plasma dispersion function: One-solve-all treatment, visualizations, and application to Landau damping

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xie, Hua-Sheng

2013-09-15

A unified, fast, and effective approach is developed for numerical calculation of the well-known plasma dispersion function with extensions from Maxwellian distribution to almost arbitrary distribution functions, such as the δ, flat top, triangular, κ or Lorentzian, slowing down, and incomplete Maxwellian distributions. The singularity and analytic continuation problems are also solved generally. Given that the usual conclusion γ∝∂f{sub 0}/∂v is only a rough approximation when discussing the distribution function effects on Landau damping, this approach provides a useful tool for rigorous calculations of the linear wave and instability properties of plasma for general distribution functions. The results are alsomore » verified via a linear initial value simulation approach. Intuitive visualizations of the generalized plasma dispersion function are also provided.« less

The generalized quadratic knapsack problem. A neuronal network approach.

PubMed

Talaván, Pedro M; Yáñez, Javier

2006-05-01

The solution of an optimization problem through the continuous Hopfield network (CHN) is based on some energy or Lyapunov function, which decreases as the system evolves until a local minimum value is attained. A new energy function is proposed in this paper so that any 0-1 linear constrains programming with quadratic objective function can be solved. This problem, denoted as the generalized quadratic knapsack problem (GQKP), includes as particular cases well-known problems such as the traveling salesman problem (TSP) and the quadratic assignment problem (QAP). This new energy function generalizes those proposed by other authors. Through this energy function, any GQKP can be solved with an appropriate parameter setting procedure, which is detailed in this paper. As a particular case, and in order to test this generalized energy function, some computational experiments solving the traveling salesman problem are also included.

Perturbed invariant subspaces and approximate generalized functional variable separation solution for nonlinear diffusion-convection equations with weak source

NASA Astrophysics Data System (ADS)

Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng

2018-03-01

In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.

Human growth is associated with distinct patterns of gene expression in evolutionarily conserved networks

PubMed Central

2013-01-01

Background A co-ordinated tissue-independent gene expression profile associated with growth is present in rodent models and this is hypothesised to extend to all mammals. Growth in humans has similarities to other mammals but the return to active long bone growth in the pubertal growth spurt is a distinctly human growth event. The aim of this study was to describe gene expression and biological pathways associated with stages of growth in children and to assess tissue-independent expression patterns in relation to human growth. Results We conducted gene expression analysis on a library of datasets from normal children with age annotation, collated from the NCBI Gene Expression Omnibus (GEO) and EBI Arrayexpress databases. A primary data set was generated using cells of lymphoid origin from normal children; the expression of 688 genes (ANOVA false discovery rate modified p-value, q < 0.1) was associated with age, and subsets of these genes formed clusters that correlated with the phases of growth – infancy, childhood, puberty and final height. Network analysis on these clusters identified evolutionarily conserved growth pathways (NOTCH, VEGF, TGFB, WNT and glucocorticoid receptor – Hyper-geometric test, q < 0.05). The greatest degree of network ‘connectivity’ and hence functional significance was present in infancy (Wilcoxon test, p < 0.05), which then decreased through to adulthood. These observations were confirmed in a separate validation data set from lymphoid tissue. Similar biological pathways were observed to be associated with development-related gene expression in other tissues (conjunctival epithelia, temporal lobe brain tissue and bone marrow) suggesting the existence of a tissue-independent genetic program for human growth and maturation. Conclusions Similar evolutionarily conserved pathways have been associated with gene expression and child growth in multiple tissues. These expression profiles associate with the developmental phases of growth including the return to active long bone growth in puberty, a distinctly human event. These observations also have direct medical relevance to pathological changes that induce disease in children. Taking into account development-dependent gene expression profiles for normal children will be key to the appropriate selection of genes and pathways as potential biomarkers of disease or as drug targets. PMID:23941278

Algorithms and analytical solutions for rapidly approximating long-term dispersion from line and area sources

NASA Astrophysics Data System (ADS)

Barrett, Steven R. H.; Britter, Rex E.

Predicting long-term mean pollutant concentrations in the vicinity of airports, roads and other industrial sources are frequently of concern in regulatory and public health contexts. Many emissions are represented geometrically as ground-level line or area sources. Well developed modelling tools such as AERMOD and ADMS are able to model dispersion from finite (i.e. non-point) sources with considerable accuracy, drawing upon an up-to-date understanding of boundary layer behaviour. Due to mathematical difficulties associated with line and area sources, computationally expensive numerical integration schemes have been developed. For example, some models decompose area sources into a large number of line sources orthogonal to the mean wind direction, for which an analytical (Gaussian) solution exists. Models also employ a time-series approach, which involves computing mean pollutant concentrations for every hour over one or more years of meteorological data. This can give rise to computer runtimes of several days for assessment of a site. While this may be acceptable for assessment of a single industrial complex, airport, etc., this level of computational cost precludes national or international policy assessments at the level of detail available with dispersion modelling. In this paper, we extend previous work [S.R.H. Barrett, R.E. Britter, 2008. Development of algorithms and approximations for rapid operational air quality modelling. Atmospheric Environment 42 (2008) 8105-8111] to line and area sources. We introduce approximations which allow for the development of new analytical solutions for long-term mean dispersion from line and area sources, based on hypergeometric functions. We describe how these solutions can be parameterized from a single point source run from an existing advanced dispersion model, thereby accounting for all processes modelled in the more costly algorithms. The parameterization method combined with the analytical solutions for long-term mean dispersion are shown to produce results several orders of magnitude more efficiently with a loss of accuracy small compared to the absolute accuracy of advanced dispersion models near sources. The method can be readily incorporated into existing dispersion models, and may allow for additional computation time to be expended on modelling dispersion processes more accurately in future, rather than on accounting for source geometry.

Vector critical points and generalized quasi-efficient solutions in nonsmooth multi-objective programming.

PubMed

Wang, Zhen; Li, Ru; Yu, Guolin

2017-01-01

In this work, several extended approximately invex vector-valued functions of higher order involving a generalized Jacobian are introduced, and some examples are presented to illustrate their existences. The notions of higher-order (weak) quasi-efficiency with respect to a function are proposed for a multi-objective programming. Under the introduced generalization of higher-order approximate invexities assumptions, we prove that the solutions of generalized vector variational-like inequalities in terms of the generalized Jacobian are the generalized quasi-efficient solutions of nonsmooth multi-objective programming problems. Moreover, the equivalent conditions are presented, namely, a vector critical point is a weakly quasi-efficient solution of higher order with respect to a function.

On the specificity of face cognition compared with general cognitive functioning across adult age.

PubMed

Hildebrandt, Andrea; Wilhelm, Oliver; Schmiedek, Florian; Herzmann, Grit; Sommer, Werner

2011-09-01

Face cognition is considered a specific human ability, clearly differentiable from general cognitive functioning. Its specificity is primarily supported by cognitive-experimental and neuroimaging research, but recently also from an individual differences perspective. However, no comprehensive behavioral data are available, which would allow estimating lifespan changes of the covariance structure of face-cognition abilities and general cognitive functioning as well as age-differences in face cognition after accounting for interindividual variability in general cognition. The present study aimed to fill this gap. In an age-heterogeneous (18-82 years) sample of 448 adults, we found no factorial dedifferentiation between face cognition and general cognition. Age-related differences in face memory were still salient after taking into account changes in general cognitive functioning. Face cognition thus remains a specific human ability compared with general cognition, even until old age. We discuss implications for models of cognitive aging and suggest that it is necessary to include more explicitly special social abilities in those models.

The vertex operator for a generalization of MacMahon’s formula

NASA Astrophysics Data System (ADS)

Cai, Liqiang; Wang, Lifang; Wu, Ke; Yang, Jie

2015-10-01

We provide a vertex operator realization for a two-parameter generalization of MacMahon’s formula introduced by M. Vuletić [Trans. Amer. Math. Soc. 361, 2789 (2009)]. Since the generalized MacMahon function is the kernel function of some Macdonald symmetric function, we consider the action of two vertex operators on a state corresponding to a Macdonald symmetric function. It becomes evident that the vertex operators appear to be the creation and annihilation operators, respectively on the state.

Generalized Functions for the Fractional Calculus

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

1999-01-01

Previous papers have used two important functions for the solution of fractional order differential equations, the Mittag-Leffler functionE(sub q)[at(exp q)](1903a, 1903b, 1905), and the F-function F(sub q)[a,t] of Hartley & Lorenzo (1998). These functions provided direct solution and important understanding for the fundamental linear fractional order differential equation and for the related initial value problem (Hartley and Lorenzo, 1999). This paper examines related functions and their Laplace transforms. Presented for consideration are two generalized functions, the R-function and the G-function, useful in analysis and as a basis for computation in the fractional calculus. The R-function is unique in that it contains all of the derivatives and integrals of the F-function. The R-function also returns itself on qth order differ-integration. An example application of the R-function is provided. A further generalization of the R-function, called the G-function brings in the effects of repeated and partially repeated fractional poles.

Linking Brief Functional Analysis to Intervention Design in General Education Settings

ERIC Educational Resources Information Center

Ishuin, Tifanie

2009-01-01

This study focused on the utility and applicability of brief functional analysis in general education settings. The purpose of the study was to first identify the environmental variables maintaining noncompliance through a brief functional analysis, and then to design and implement a functionally equivalent intervention. The participant exhibited…

Relationship of amotivation to neurocognition, self-efficacy and functioning in first-episode psychosis: a structural equation modeling approach.

PubMed

Chang, W C; Kwong, V W Y; Hui, C L M; Chan, S K W; Lee, E H M; Chen, E Y H

2017-03-01

Better understanding of the complex interplay among key determinants of functional outcome is crucial to promoting recovery in psychotic disorders. However, this is understudied in the early course of illness. We aimed to examine the relationships among negative symptoms, neurocognition, general self-efficacy and global functioning in first-episode psychosis (FEP) patients using structural equation modeling (SEM). Three hundred and twenty-one Chinese patients aged 26-55 years presenting with FEP to an early intervention program in Hong Kong were recruited. Assessments encompassing symptom profiles, functioning, perceived general self-efficacy and a battery of neurocognitive tests were conducted. Negative symptom measurement was subdivided into amotivation and diminished expression (DE) domain scores based on the ratings in the Scale for the Assessment of Negative Symptoms. An initial SEM model showed no significant association between functioning and DE which was removed from further analysis. A final trimmed model yielded very good model fit (χ2 = 15.48, p = 0.63; comparative fit index = 1.00; root mean square error of approximation <0.001) and demonstrated that amotivation, neurocognition and general self-efficacy had a direct effect on global functioning. Amotivation was also found to mediate a significant indirect effect of neurocognition and general self-efficacy on functioning. Neurocognition was not significantly related to general self-efficacy. Our results indicate a critical intermediary role of amotivation in linking neurocognitive impairment to functioning in FEP. General self-efficacy may represent a promising treatment target for improvement of motivational deficits and functional outcome in the early illness stage.

Derivation and application of the reciprocity relations for radiative transfer with internal illumination

NASA Technical Reports Server (NTRS)

Cogley, A. C.

1975-01-01

A Green's function formulation is used to derive basic reciprocity relations for planar radiative transfer in a general medium with internal illumination. Reciprocity (or functional symmetry) allows an explicit and generalized development of the equivalence between source and probability functions. Assuming similar symmetry in three-dimensional space, a general relationship is derived between planar-source intensity and point-source total directional energy. These quantities are expressed in terms of standard (universal) functions associated with the planar medium, while all results are derived from the differential equation of radiative transfer.

Generalized Convexity and Concavity Properties of the Optimal Value Function in Parametric Nonlinear Programming.

DTIC Science & Technology

1983-04-11

existing ones. * -37- !I T-472 REFERENCES [1] Avriel, M., W. E. Diewert, S. Schaible and W. T. Ziemba (1981). Introduction to concave and generalized concave...functions. In Generalized Concavity in Optimization and Economics (S. Schaible and W. T. Ziemba , eds.), Academic Press, New York, pp. 21-50. (21 Bank...Optimality conditions involving generalized convex mappings. In Generalized Concavity in Optimization and Economics (S. Schaible and W. T. Ziemba

Systems-Wide Prediction of Enzyme Promiscuity Reveals a New Underground Alternative Route for Pyridoxal 5’-Phosphate Production in E. coli

DOE PAGES

Oberhardt, Matthew A.; Zarecki, Raphy; Reshef, Leah; ...

2016-01-28

Recent insights suggest that non-specific and/or promiscuous enzymes are common and active across life. Understanding the role of such enzymes is an important open question in biology. Here we develop a genome-wide method, PROPER, that uses a permissive PSI-BLAST approach to predict promiscuous activities of metabolic genes. Enzyme promiscuity is typically studied experimentally using multicopy suppression, in which over-expression of a promiscuous ‘replacer’ gene rescues lethality caused by inactivation of a ‘target’ gene. We use PROPER to predict multicopy suppression in Escherichia coli, achieving highly significant overlap with published cases (hypergeometric p = 4.4e-13). We then validate three novel predictedmore » target-replacer gene pairs in new multicopy suppression experiments. We next go beyond PROPER and develop a network-based approach, GEM-PROPER, that integrates PROPER with genome-scale metabolic modeling to predict promiscuous replacements via alternative metabolic pathways. GEM-PROPER predicts a new indirect replacer (thiG) for an essential enzyme (pdxB) in production of pyridoxal 5’-phosphate (the active form of Vitamin B 6), which we validate experimentally via multicopy suppression. Here, we perform a structural analysis of thiG to determine its potential promiscuous active site, which we validate experimentally by inactivating the pertaining residues and showing a loss of replacer activity. Thus, this study is a successful example where a computational investigation leads to a network-based identification of an indirect promiscuous replacement of a key metabolic enzyme, which would have been extremely difficult to identify directly.« less

Optimal prediction of the number of unseen species

PubMed Central

Orlitsky, Alon; Suresh, Ananda Theertha; Wu, Yihong

2016-01-01

Estimating the number of unseen species is an important problem in many scientific endeavors. Its most popular formulation, introduced by Fisher et al. [Fisher RA, Corbet AS, Williams CB (1943) J Animal Ecol 12(1):42−58], uses n samples to predict the number U of hitherto unseen species that would be observed if t⋅n new samples were collected. Of considerable interest is the largest ratio t between the number of new and existing samples for which U can be accurately predicted. In seminal works, Good and Toulmin [Good I, Toulmin G (1956) Biometrika 43(102):45−63] constructed an intriguing estimator that predicts U for all t≤1. Subsequently, Efron and Thisted [Efron B, Thisted R (1976) Biometrika 63(3):435−447] proposed a modification that empirically predicts U even for some t>1, but without provable guarantees. We derive a class of estimators that provably predict U all of the way up to t∝log⁡n. We also show that this range is the best possible and that the estimator’s mean-square error is near optimal for any t. Our approach yields a provable guarantee for the Efron−Thisted estimator and, in addition, a variant with stronger theoretical and experimental performance than existing methodologies on a variety of synthetic and real datasets. The estimators are simple, linear, computationally efficient, and scalable to massive datasets. Their performance guarantees hold uniformly for all distributions, and apply to all four standard sampling models commonly used across various scientific disciplines: multinomial, Poisson, hypergeometric, and Bernoulli product. PMID:27830649

Benchmarking protein-protein interface predictions: why you should care about protein size.

PubMed

Martin, Juliette

2014-07-01

A number of predictive methods have been developed to predict protein-protein binding sites. Each new method is traditionally benchmarked using sets of protein structures of various sizes, and global statistics are used to assess the quality of the prediction. Little attention has been paid to the potential bias due to protein size on these statistics. Indeed, small proteins involve proportionally more residues at interfaces than large ones. If a predictive method is biased toward small proteins, this can lead to an over-estimation of its performance. Here, we investigate the bias due to the size effect when benchmarking protein-protein interface prediction on the widely used docking benchmark 4.0. First, we simulate random scores that favor small proteins over large ones. Instead of the 0.5 AUC (Area Under the Curve) value expected by chance, these biased scores result in an AUC equal to 0.6 using hypergeometric distributions, and up to 0.65 using constant scores. We then use real prediction results to illustrate how to detect the size bias by shuffling, and subsequently correct it using a simple conversion of the scores into normalized ranks. In addition, we investigate the scores produced by eight published methods and show that they are all affected by the size effect, which can change their relative ranking. The size effect also has an impact on linear combination scores by modifying the relative contributions of each method. In the future, systematic corrections should be applied when benchmarking predictive methods using data sets with mixed protein sizes. © 2014 Wiley Periodicals, Inc.

Optimal prediction of the number of unseen species.

PubMed

Orlitsky, Alon; Suresh, Ananda Theertha; Wu, Yihong

2016-11-22

Estimating the number of unseen species is an important problem in many scientific endeavors. Its most popular formulation, introduced by Fisher et al. [Fisher RA, Corbet AS, Williams CB (1943) J Animal Ecol 12(1):42-58], uses n samples to predict the number U of hitherto unseen species that would be observed if [Formula: see text] new samples were collected. Of considerable interest is the largest ratio t between the number of new and existing samples for which U can be accurately predicted. In seminal works, Good and Toulmin [Good I, Toulmin G (1956) Biometrika 43(102):45-63] constructed an intriguing estimator that predicts U for all [Formula: see text] Subsequently, Efron and Thisted [Efron B, Thisted R (1976) Biometrika 63(3):435-447] proposed a modification that empirically predicts U even for some [Formula: see text], but without provable guarantees. We derive a class of estimators that provably predict U all of the way up to [Formula: see text] We also show that this range is the best possible and that the estimator's mean-square error is near optimal for any t Our approach yields a provable guarantee for the Efron-Thisted estimator and, in addition, a variant with stronger theoretical and experimental performance than existing methodologies on a variety of synthetic and real datasets. The estimators are simple, linear, computationally efficient, and scalable to massive datasets. Their performance guarantees hold uniformly for all distributions, and apply to all four standard sampling models commonly used across various scientific disciplines: multinomial, Poisson, hypergeometric, and Bernoulli product.

Sympatric speciation by sexual selection alone is unlikely.

PubMed

Arnegard, Matthew E; Kondrashov, Alexey S

2004-02-01

According to Darwin, sympatric speciation is driven by disruptive, frequency-dependent natural selection caused by competition for diverse resources. Recently, several authors have argued that disruptive sexual selection can also cause sympatric speciation. Here, we use hypergeometric phenotypic and individual-based genotypic models to explore sympatric speciation by sexual selection under a broad range of conditions. If variabilities of preference and display traits are each caused by more than one or two polymorphic loci, sympatric speciation requires rather strong sexual selection when females exert preferences for extreme male phenotypes. Under this kind of mate choice, speciation can occur only if initial distributions of preference and display are close to symmetric. Otherwise, the population rapidly loses variability. Thus, unless allele replacements at very few loci are enough for reproductive isolation, female preferences for extreme male displays are unlikely to drive sympatric speciation. By contrast, similarity-based female preferences that do not cause sexual selection are less destabilizing to the maintenance of genetic variability and may result in sympatric speciation across a broader range of initial conditions. Certain groups of African cichlids have served as the exclusive motivation for the hypothesis of sympatric speciation by sexual selection. Mate choice in these fishes appears to be driven by female preferences for extreme male phenotypes rather than similarity-based preferences, and the evolution of premating reproductive isolation commonly involves at least several genes. Therefore, differences in female preferences and male display in cichlids and other species of sympatric origin are more likely to have evolved as isolating mechanisms under disruptive natural selection.

Wavefront Curvature Sensing from Image Projections

DTIC Science & Technology

2006-09-01

entrance pupil. The generalized pupil function, denoted P, provides a basic 1-7 mathematical model for the optical �eld at the system pupil: P(x; y...pupil or aperture radius, RP , may be included in Zernike functions and windowing functions to give the notation more generality . Given some ...promises a much faster read out time from the CCD along with some amount of information useful for estimating pupil phase. A General Image Projection

Extensions of different type parameterized inequalities for generalized [Formula: see text]-preinvex mappings via k-fractional integrals.

PubMed

Zhang, Yao; Du, Ting-Song; Wang, Hao; Shen, Yan-Jun; Kashuri, Artion

2018-01-01

The authors discover a general k -fractional integral identity with multi-parameters for twice differentiable functions. By using this integral equation, the authors derive some new bounds on Hermite-Hadamard's and Simpson's inequalities for generalized [Formula: see text]-preinvex functions through k -fractional integrals. By taking the special parameter values for various suitable choices of function h , some interesting results are also obtained.

A hierarchy of generalized Jaulent-Miodek equations and their explicit solutions

NASA Astrophysics Data System (ADS)

Geng, Xianguo; Guan, Liang; Xue, Bo

A hierarchy of generalized Jaulent-Miodek (JM) equations related to a new spectral problem with energy-dependent potentials is proposed. Depending on the Lax matrix and elliptic variables, the generalized JM hierarchy is decomposed into two systems of solvable ordinary differential equations. Explicit theta function representations of the meromorphic function and the Baker-Akhiezer function are constructed, the solutions of the hierarchy are obtained based on the theory of algebraic curves.

Generic short-time propagation of sharp-boundaries wave packets

NASA Astrophysics Data System (ADS)

Granot, E.; Marchewka, A.

2005-11-01

A general solution to the "shutter" problem is presented. The propagation of an arbitrary initially bounded wave function is investigated, and the general solution for any such function is formulated. It is shown that the exact solution can be written as an expression that depends only on the values of the function (and its derivatives) at the boundaries. In particular, it is shown that at short times (t << 2mx2/hbar, where x is the distance to the boundaries) the wave function propagation depends only on the wave function's values (or its derivatives) at the boundaries of the region. Finally, we generalize these findings to a non-singular wave function (i.e., for wave packets with finite-width boundaries) and suggest an experimental verification.

Current Density Functional Theory Using Meta-Generalized Gradient Exchange-Correlation Functionals.

PubMed

Furness, James W; Verbeke, Joachim; Tellgren, Erik I; Stopkowicz, Stella; Ekström, Ulf; Helgaker, Trygve; Teale, Andrew M

2015-09-08

We present the self-consistent implementation of current-dependent (hybrid) meta-generalized gradient approximation (mGGA) density functionals using London atomic orbitals. A previously proposed generalized kinetic energy density is utilized to implement mGGAs in the framework of Kohn-Sham current density functional theory (KS-CDFT). A unique feature of the nonperturbative implementation of these functionals is the ability to seamlessly explore a wide range of magnetic fields up to 1 au (∼235 kT) in strength. CDFT functionals based on the TPSS and B98 forms are investigated, and their performance is assessed by comparison with accurate coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) data. In the weak field regime, magnetic properties such as magnetizabilities and nuclear magnetic resonance shielding constants show modest but systematic improvements over generalized gradient approximations (GGA). However, in the strong field regime, the mGGA-based forms lead to a significantly improved description of the recently proposed perpendicular paramagnetic bonding mechanism, comparing well with CCSD(T) data. In contrast to functionals based on the vorticity, these forms are found to be numerically stable, and their accuracy at high field suggests that the extension of mGGAs to CDFT via the generalized kinetic energy density should provide a useful starting point for further development of CDFT approximations.

Item Purification in Differential Item Functioning Using Generalized Linear Mixed Models

ERIC Educational Resources Information Center

Liu, Qian

2011-01-01

For this dissertation, four item purification procedures were implemented onto the generalized linear mixed model for differential item functioning (DIF) analysis, and the performance of these item purification procedures was investigated through a series of simulations. Among the four procedures, forward and generalized linear mixed model (GLMM)…

48 CFR 6105.501 - Scope [Rule 501].

Code of Federal Regulations, 2010 CFR

2010-10-01

... formerly issued by the Comptroller General under 31 U.S.C. 3529. Section 204 of the General Accounting... that function to another agency or agencies. The Director has delegated the authority to issue these decisions to the Administrator of General Services, who has redelegated that function to the Civilian Board...

Generalization of the subsonic kernel function in the s-plane, with applications to flutter analysis

NASA Technical Reports Server (NTRS)

Cunningham, H. J.; Desmarais, R. N.

1984-01-01

A generalized subsonic unsteady aerodynamic kernel function, valid for both growing and decaying oscillatory motions, is developed and applied in a modified flutter analysis computer program to solve the boundaries of constant damping ratio as well as the flutter boundary. Rates of change of damping ratios with respect to dynamic pressure near flutter are substantially lower from the generalized-kernel-function calculations than from the conventional velocity-damping (V-g) calculation. A rational function approximation for aerodynamic forces used in control theory for s-plane analysis gave rather good agreement with kernel-function results, except for strongly damped motion at combinations of high (subsonic) Mach number and reduced frequency.

Generalized hydrodynamic correlations and fractional memory functions

NASA Astrophysics Data System (ADS)

Rodríguez, Rosalio F.; Fujioka, Jorge

2015-12-01

A fractional generalized hydrodynamic (GH) model of the longitudinal velocity fluctuations correlation, and its associated memory function, for a complex fluid is analyzed. The adiabatic elimination of fast variables introduces memory effects in the transport equations, and the dynamic of the fluctuations is described by a generalized Langevin equation with long-range noise correlations. These features motivate the introduction of Caputo time fractional derivatives and allows us to calculate analytic expressions for the fractional longitudinal velocity correlation function and its associated memory function. Our analysis eliminates a spurious constant term in the non-fractional memory function found in the non-fractional description. It also produces a significantly slower power-law decay of the memory function in the GH regime that reduces to the well-known exponential decay in the non-fractional Navier-Stokes limit.

Recent developments in LIBXC - A comprehensive library of functionals for density functional theory

NASA Astrophysics Data System (ADS)

Lehtola, Susi; Steigemann, Conrad; Oliveira, Micael J. T.; Marques, Miguel A. L.

2018-01-01

LIBXC is a library of exchange-correlation functionals for density-functional theory. We are concerned with semi-local functionals (or the semi-local part of hybrid functionals), namely local-density approximations, generalized-gradient approximations, and meta-generalized-gradient approximations. Currently we include around 400 functionals for the exchange, correlation, and the kinetic energy, spanning more than 50 years of research. Moreover, LIBXC is by now used by more than 20 codes, not only from the atomic, molecular, and solid-state physics, but also from the quantum chemistry communities.

Dispersion relations for a general anisotropic distribution function represented as a sum over Legendre polynomials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shaisultanov, Rashid; Eichler, David

2011-03-15

The dielectric tensor is obtained for a general anisotropic distribution function that is represented as a sum over Legendre polynomials. The result is valid over all of k-space. We obtain growth rates for the Weibel instability for some basic examples of distribution functions.

An Evaluation of Generalization of Mands during Functional Communication Training

ERIC Educational Resources Information Center

Falcomata, Terry S.; Wacker, David P.; Ringdahl, Joel E.; Vinquist, Kelly; Dutt, Anuradha

2013-01-01

The primary purpose of this study was to evaluate the generalization of mands during functional communication training (FCT) and sign language training across functional contexts (i.e., positive reinforcement, negative reinforcement). A secondary purpose was to evaluate a training procedure based on stimulus control to teach manual signs. During…

Stability of a general mixed additive-cubic functional equation in non-Archimedean fuzzy normed spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu Tianzhou; Rassias, John Michael; Xu Wanxin

2010-09-15

We establish some stability results concerning the general mixed additive-cubic functional equation in non-Archimedean fuzzy normed spaces. In addition, we establish some results of approximately general mixed additive-cubic mappings in non-Archimedean fuzzy normed spaces. The results improve and extend some recent results.

On a General Class of Trigonometric Functions and Fourier Series

ERIC Educational Resources Information Center

Pavao, H. Germano; Capelas de Oliveira, E.

2008-01-01

We discuss a general class of trigonometric functions whose corresponding Fourier series can be used to calculate several interesting numerical series. Particular cases are presented. (Contains 4 notes.)

QUEST+: A general multidimensional Bayesian adaptive psychometric method.

PubMed

Watson, Andrew B

2017-03-01

QUEST+ is a Bayesian adaptive psychometric testing method that allows an arbitrary number of stimulus dimensions, psychometric function parameters, and trial outcomes. It is a generalization and extension of the original QUEST procedure and incorporates many subsequent developments in the area of parametric adaptive testing. With a single procedure, it is possible to implement a wide variety of experimental designs, including conventional threshold measurement; measurement of psychometric function parameters, such as slope and lapse; estimation of the contrast sensitivity function; measurement of increment threshold functions; measurement of noise-masking functions; Thurstone scale estimation using pair comparisons; and categorical ratings on linear and circular stimulus dimensions. QUEST+ provides a general method to accelerate data collection in many areas of cognitive and perceptual science.

Multilocality and fusion rules on the generalized structure functions in two-dimensional and three-dimensional Navier-Stokes turbulence.

PubMed

Gkioulekas, Eleftherios

2016-09-01

Using the fusion-rules hypothesis for three-dimensional and two-dimensional Navier-Stokes turbulence, we generalize a previous nonperturbative locality proof to multiple applications of the nonlinear interactions operator on generalized structure functions of velocity differences. We call this generalization of nonperturbative locality to multiple applications of the nonlinear interactions operator "multilocality." The resulting cross terms pose a new challenge requiring a new argument and the introduction of a new fusion rule that takes advantage of rotational symmetry. Our main result is that the fusion-rules hypothesis implies both locality and multilocality in both the IR and UV limits for the downscale energy cascade of three-dimensional Navier-Stokes turbulence and the downscale enstrophy cascade and inverse energy cascade of two-dimensional Navier-Stokes turbulence. We stress that these claims relate to nonperturbative locality of generalized structure functions on all orders and not the term-by-term perturbative locality of diagrammatic theories or closure models that involve only two-point correlation and response functions.

Integration of the Quadratic Function and Generalization

ERIC Educational Resources Information Center

Mitsuma, Kunio

2011-01-01

We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…

21 CFR 13.15 - Separation of functions; ex parte communications; administrative support.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 21 Food and Drugs 1 2010-04-01 2010-04-01 false Separation of functions; ex parte communications... HUMAN SERVICES GENERAL PUBLIC HEARING BEFORE A PUBLIC BOARD OF INQUIRY General Provisions § 13.15 Separation of functions; ex parte communications; administrative support. (a) The proceeding of a Board are...

The Effects of Teacher-Student Small Talk on Out-of-Seat Behavior

ERIC Educational Resources Information Center

Patterson, Steven T.

2009-01-01

This paper presents the results of a function-based study initiated by a general education teacher to reduce a general education student's out-of-seat behavior. Procedures included direct observation, data collection, functional behavior assessment using a Functional Assessment Protocol (FAP; Schroeder, n.d.), hypothesis development, and creating…

The Green's functions for peridynamic non-local diffusion.

PubMed

Wang, L J; Xu, J F; Wang, J X

2016-09-01

In this work, we develop the Green's function method for the solution of the peridynamic non-local diffusion model in which the spatial gradient of the generalized potential in the classical theory is replaced by an integral of a generalized response function in a horizon. We first show that the general solutions of the peridynamic non-local diffusion model can be expressed as functionals of the corresponding Green's functions for point sources, along with volume constraints for non-local diffusion. Then, we obtain the Green's functions by the Fourier transform method for unsteady and steady diffusions in infinite domains. We also demonstrate that the peridynamic non-local solutions converge to the classical differential solutions when the non-local length approaches zero. Finally, the peridynamic analytical solutions are applied to an infinite plate heated by a Gauss source, and the predicted variations of temperature are compared with the classical local solutions. The peridynamic non-local diffusion model predicts a lower rate of variation of the field quantities than that of the classical theory, which is consistent with experimental observations. The developed method is applicable to general diffusion-type problems.

38 CFR 14.500 - Functions and responsibilities of General Counsel.

Code of Federal Regulations, 2012 CFR

2012-07-01

... VETERANS AFFAIRS LEGAL SERVICES, GENERAL COUNSEL, AND MISCELLANEOUS CLAIMS § 14.500 Functions and... construction or application of laws, including statutes, regulations, and decisional as well as common law. (c...

An integrative architecture for general intelligence and executive function revealed by lesion mapping

PubMed Central

Colom, Roberto; Solomon, Jeffrey; Krueger, Frank; Forbes, Chad; Grafman, Jordan

2012-01-01

Although cognitive neuroscience has made remarkable progress in understanding the involvement of the prefrontal cortex in executive control, the broader functional networks that support high-level cognition and give rise to general intelligence remain to be well characterized. Here, we investigated the neural substrates of the general factor of intelligence (g) and executive function in 182 patients with focal brain damage using voxel-based lesion–symptom mapping. The Wechsler Adult Intelligence Scale and Delis–Kaplan Executive Function System were used to derive measures of g and executive function, respectively. Impaired performance on these measures was associated with damage to a distributed network of left lateralized brain areas, including regions of frontal and parietal cortex and white matter association tracts, which bind these areas into a coordinated system. The observed findings support an integrative framework for understanding the architecture of general intelligence and executive function, supporting their reliance upon a shared fronto-parietal network for the integration and control of cognitive representations and making specific recommendations for the application of the Wechsler Adult Intelligence Scale and Delis–Kaplan Executive Function System to the study of high-level cognition in health and disease. PMID:22396393

Learning curves in highly skilled chess players: a test of the generality of the power law of practice.

PubMed

Howard, Robert W

2014-09-01

The power law of practice holds that a power function best interrelates skill performance and amount of practice. However, the law's validity and generality are moot. Some researchers argue that it is an artifact of averaging individual exponential curves while others question whether the law generalizes to complex skills and to performance measures other than response time. The present study tested the power law's generality to development over many years of a very complex cognitive skill, chess playing, with 387 skilled participants, most of whom were grandmasters. A power or logarithmic function best fit grouped data but individuals showed much variability. An exponential function usually was the worst fit to individual data. Groups differing in chess talent were compared and a power function best fit the group curve for the more talented players while a quadratic function best fit that for the less talented. After extreme amounts of practice, a logarithmic function best fit grouped data but a quadratic function best fit most individual curves. Individual variability is great and the power law or an exponential law are not the best descriptions of individual chess skill development. Copyright © 2014 Elsevier B.V. All rights reserved.

Some operational tools for solving fractional and higher integer order differential equations: A survey on their mutual relations

NASA Astrophysics Data System (ADS)

Kiryakova, Virginia S.

2012-11-01

The Laplace Transform (LT) serves as a basis of the Operational Calculus (OC), widely explored by engineers and applied scientists in solving mathematical models for their practical needs. This transform is closely related to the exponential and trigonometric functions (exp, cos, sin) and to the classical differentiation and integration operators, reducing them to simple algebraic operations. Thus, the classical LT and the OC give useful tool to handle differential equations and systems with constant coefficients. Several generalizations of the LT have been introduced to allow solving, in a similar way, of differential equations with variable coefficients and of higher integer orders, as well as of fractional (arbitrary non-integer) orders. Note that fractional order mathematical models are recently widely used to describe better various systems and phenomena of the real world. This paper surveys briefly some of our results on classes of such integral transforms, that can be obtained from the LT by means of "transmutations" which are operators of the generalized fractional calculus (GFC). On the list of these Laplace-type integral transforms, we consider the Borel-Dzrbashjan, Meijer, Krätzel, Obrechkoff, generalized Obrechkoff (multi-index Borel-Dzrbashjan) transforms, etc. All of them are G- and H-integral transforms of convolutional type, having as kernels Meijer's G- or Fox's H-functions. Besides, some special functions (also being G- and H-functions), among them - the generalized Bessel-type and Mittag-Leffler (M-L) type functions, are generating Gel'fond-Leontiev (G-L) operators of generalized differentiation and integration, which happen to be also operators of GFC. Our integral transforms have operational properties analogous to those of the LT - they do algebrize the G-L generalized integrations and differentiations, and thus can serve for solving wide classes of differential equations with variable coefficients of arbitrary, including non-integer order. Throughout the survey, we illustrate the parallels in the relationships: Laplace type integral transforms - special functions as kernels - operators of generalized integration and differentiation generated by special functions - special functions as solutions of related differential equations. The role of the so-called Special Functions of Fractional Calculus is emphasized.

Human intelligence and brain networks

PubMed Central

Colom, Roberto; Karama, Sherif; Jung, Rex E.; Haier, Richard J.

2010-01-01

Intelligence can be defined as a general mental ability for reasoning, problem solving, and learning. Because of its general nature, intelligence integrates cognitive functions such as perception, attention, memory, language, or planning. On the basis of this definition, intelligence can be reliably measured by standardized tests with obtained scores predicting several broad social outcomes such as educational achievement, job performance, health, and longevity. A detailed understanding of the brain mechanisms underlying this general mental ability could provide significant individual and societal benefits. Structural and functional neuroimaging studies have generally supported a frontoparietal network relevant for intelligence. This same network has also been found to underlie cognitive functions related to perception, short-term memory storage, and language. The distributed nature of this network and its involvement in a wide range of cognitive functions fits well with the integrative nature of intelligence. A new key phase of research is beginning to investigate how functional networks relate to structural networks, with emphasis on how distributed brain areas communicate with each other. PMID:21319494

Functional thermo-dynamics: a generalization of dynamic density functional theory to non-isothermal situations.

PubMed

Anero, Jesús G; Español, Pep; Tarazona, Pedro

2013-07-21

We present a generalization of Density Functional Theory (DFT) to non-equilibrium non-isothermal situations. By using the original approach set forth by Gibbs in his consideration of Macroscopic Thermodynamics (MT), we consider a Functional Thermo-Dynamics (FTD) description based on the density field and the energy density field. A crucial ingredient of the theory is an entropy functional, which is a concave functional. Therefore, there is a one to one connection between the density and energy fields with the conjugate thermodynamic fields. The connection between the three levels of description (MT, DFT, FTD) is clarified through a bridge theorem that relates the entropy of different levels of description and that constitutes a generalization of Mermin's theorem to arbitrary levels of description whose relevant variables are connected linearly. Although the FTD level of description does not provide any new information about averages and correlations at equilibrium, it is a crucial ingredient for the dynamics in non-equilibrium states. We obtain with the technique of projection operators the set of dynamic equations that describe the evolution of the density and energy density fields from an initial non-equilibrium state towards equilibrium. These equations generalize time dependent density functional theory to non-isothermal situations. We also present an explicit model for the entropy functional for hard spheres.

Temporal Dynamics of Activation of Thematic and Functional Knowledge During Conceptual Processing of Manipulable Artifacts

PubMed Central

Kalénine, Solène; Mirman, Daniel; Middleton, Erica L.; Buxbaum, Laurel J.

2012-01-01

The current research aimed at specifying the activation time course of different types of semantic information during object conceptual processing and the effect of context on this time course. We distinguished between thematic and functional knowledge and the specificity of functional similarity. Two experiments were conducted with healthy older adults using eye tracking in a word-to-picture matching task. The time course of gaze fixations was used to assess activation of distractor objects during the identification of manipulable artifact targets (e.g., broom). Distractors were (a) thematically related (e.g., dustpan), (b) related by a specific function (e.g., vacuum cleaner), or (c) related by a general function (e.g., sponge). Growth curve analyses were used to assess competition effects when target words were presented in isolation (Experiment 1) and embedded in contextual sentences of different generality levels (Experiment 2). In the absence of context, there was earlier and shorter lasting activation of thematically related as compared to functionally related objects. The time course difference was more pronounced for general functions than specific functions. When contexts were provided, functional similarities that were congruent with context generality level increased in salience with earlier activation of those objects. Context had little impact on thematic activation time course. These data demonstrate that processing a single manipulable artifact concept implicitly activates thematic and functional knowledge with different time courses and that context speeds activation of context-congruent functional similarity. PMID:22449134

Physical and psychosocial prerequisites of functioning in relation to work ability and general subjective well-being among office workers.

PubMed

Sjögren-Rönkä, Tuulikki; Ojanen, Markku T; Leskinen, Esko K; Tmustalampi, Sirpa; Mälkiä, Esko A

2002-06-01

The purpose of the study was to investigate the physical and psychological prerequisites of functioning, as well as the social environment at work and personal factors, in relation to work ability and general subjective well-being in a group of office workers. The study was a descriptive cross-sectional investigation, using path analysis, of office workers. The subjects comprised 88 volunteers, 24 men and 64 women, from the same workplace [mean age 45.7 (SD 8.6) years]. The independent variables were measured using psychosocial and physical questionnaires and physical measurements. The first dependent variable, work ability, was measured by a work ability index. The second dependent variable, general subjective well-being, was assessed by life satisfaction and meaning of life. The variables were structured according to a modified version of the International Classification of Functioning, Disability and Health. Forward flexion of the spine, intensity of musculoskeletal symptoms, self-confidence, and mental stress at work explained 58% of work ability and had indirect effects on general subjective well-being. Self-confidence, mood, and work ability had a direct effect on general subjective well-being. The model developed explained 68% of general subjective well-being. Age played a significant role in this study population. The prerequisites of physical functioning are important in maintaining work ability, particularly among aging workers, and psychological prerequisites of functioning are of even greater importance in maintaining general subjective well-being.

Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations.

PubMed

Banks, H Thomas; Robbins, Danielle; Sutton, Karyn L

2013-01-01

In this paper we present new results for differentiability of delay systems with respect to initial conditions and delays. After motivating our results with a wide range of delay examples arising in biology applications, we further note the need for sensitivity functions (both traditional and generalized sensitivity functions), especially in control and estimation problems. We summarize general existence and uniqueness results before turning to our main results on differentiation with respect to delays, etc. Finally we discuss use of our results in the context of estimation problems.

General, crystallized and fluid intelligence are not associated with functional global network efficiency: A replication study with the human connectome project 1200 data set.

PubMed

Kruschwitz, J D; Waller, L; Daedelow, L S; Walter, H; Veer, I M

2018-05-01

One hallmark example of a link between global topological network properties of complex functional brain connectivity and cognitive performance is the finding that general intelligence may depend on the efficiency of the brain's intrinsic functional network architecture. However, although this association has been featured prominently over the course of the last decade, the empirical basis for this broad association of general intelligence and global functional network efficiency is quite limited. In the current study, we set out to replicate the previously reported association between general intelligence and global functional network efficiency using the large sample size and high quality data of the Human Connectome Project, and extended the original study by testing for separate association of crystallized and fluid intelligence with global efficiency, characteristic path length, and global clustering coefficient. We were unable to provide evidence for the proposed association between general intelligence and functional brain network efficiency, as was demonstrated by van den Heuvel et al. (2009), or for any other association with the global network measures employed. More specifically, across multiple network definition schemes, ranging from voxel-level networks to networks of only 100 nodes, no robust associations and only very weak non-significant effects with a maximal R 2 of 0.01 could be observed. Notably, the strongest (non-significant) effects were observed in voxel-level networks. We discuss the possibility that the low power of previous studies and publication bias may have led to false positive results fostering the widely accepted notion of general intelligence being associated to functional global network efficiency. Copyright © 2018 Elsevier Inc. All rights reserved.

Generalized nonequilibrium vertex correction method in coherent medium theory for quantum transport simulation of disordered nanoelectronics

NASA Astrophysics Data System (ADS)

Yan, Jiawei; Ke, Youqi

2016-07-01

Electron transport properties of nanoelectronics can be significantly influenced by the inevitable and randomly distributed impurities/defects. For theoretical simulation of disordered nanoscale electronics, one is interested in both the configurationally averaged transport property and its statistical fluctuation that tells device-to-device variability induced by disorder. However, due to the lack of an effective method to do disorder averaging under the nonequilibrium condition, the important effects of disorders on electron transport remain largely unexplored or poorly understood. In this work, we report a general formalism of Green's function based nonequilibrium effective medium theory to calculate the disordered nanoelectronics. In this method, based on a generalized coherent potential approximation for the Keldysh nonequilibrium Green's function, we developed a generalized nonequilibrium vertex correction method to calculate the average of a two-Keldysh-Green's-function correlator. We obtain nine nonequilibrium vertex correction terms, as a complete family, to express the average of any two-Green's-function correlator and find they can be solved by a set of linear equations. As an important result, the averaged nonequilibrium density matrix, averaged current, disorder-induced current fluctuation, and averaged shot noise, which involve different two-Green's-function correlators, can all be derived and computed in an effective and unified way. To test the general applicability of this method, we applied it to compute the transmission coefficient and its fluctuation with a square-lattice tight-binding model and compared with the exact results and other previously proposed approximations. Our results show very good agreement with the exact results for a wide range of disorder concentrations and energies. In addition, to incorporate with density functional theory to realize first-principles quantum transport simulation, we have also derived a general form of conditionally averaged nonequilibrium Green's function for multicomponent disorders.

Covariant extension of the GPD overlap representation at low Fock states

DOE PAGES

Chouika, N.; Mezrag, C.; Moutarde, H.; ...

2017-12-26

Here, we present a novel approach to compute generalized parton distributions within the lightfront wave function overlap framework. We show how to systematically extend generalized parton distributions computed within the DGLAP region to the ERBL one, fulfilling at the same time both the polynomiality and positivity conditions. We exemplify our method using pion lightfront wave functions inspired by recent results of non-perturbative continuum techniques and algebraic nucleon lightfront wave functions. We also test the robustness of our algorithm on reggeized phenomenological parameterizations. This approach paves the way to a better understanding of the nucleon structure from non-perturbative techniques and tomore » a unification of generalized parton distributions and transverse momentum dependent parton distribution functions phenomenology through lightfront wave functions.« less

20 CFR 200.2 - The general course and method by which the Board's functions are channeled and determined.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 20 Employees' Benefits 1 2010-04-01 2010-04-01 false The general course and method by which the Board's functions are channeled and determined. 200.2 Section 200.2 Employees' Benefits RAILROAD... the Board's functions are channeled and determined. (a) Retirement and death benefits. (1) Retirement...

Assessment of parametric uncertainty for groundwater reactive transport modeling,

USGS Publications Warehouse

Shi, Xiaoqing; Ye, Ming; Curtis, Gary P.; Miller, Geoffery L.; Meyer, Philip D.; Kohler, Matthias; Yabusaki, Steve; Wu, Jichun

2014-01-01

The validity of using Gaussian assumptions for model residuals in uncertainty quantification of a groundwater reactive transport model was evaluated in this study. Least squares regression methods explicitly assume Gaussian residuals, and the assumption leads to Gaussian likelihood functions, model parameters, and model predictions. While the Bayesian methods do not explicitly require the Gaussian assumption, Gaussian residuals are widely used. This paper shows that the residuals of the reactive transport model are non-Gaussian, heteroscedastic, and correlated in time; characterizing them requires using a generalized likelihood function such as the formal generalized likelihood function developed by Schoups and Vrugt (2010). For the surface complexation model considered in this study for simulating uranium reactive transport in groundwater, parametric uncertainty is quantified using the least squares regression methods and Bayesian methods with both Gaussian and formal generalized likelihood functions. While the least squares methods and Bayesian methods with Gaussian likelihood function produce similar Gaussian parameter distributions, the parameter distributions of Bayesian uncertainty quantification using the formal generalized likelihood function are non-Gaussian. In addition, predictive performance of formal generalized likelihood function is superior to that of least squares regression and Bayesian methods with Gaussian likelihood function. The Bayesian uncertainty quantification is conducted using the differential evolution adaptive metropolis (DREAM(zs)) algorithm; as a Markov chain Monte Carlo (MCMC) method, it is a robust tool for quantifying uncertainty in groundwater reactive transport models. For the surface complexation model, the regression-based local sensitivity analysis and Morris- and DREAM(ZS)-based global sensitivity analysis yield almost identical ranking of parameter importance. The uncertainty analysis may help select appropriate likelihood functions, improve model calibration, and reduce predictive uncertainty in other groundwater reactive transport and environmental modeling.

Serum osteoprotegerin and renal function in the general population: the Tromsø Study.

PubMed

Vik, Anders; Brodin, Ellen E; Mathiesen, Ellisiv B; Brox, Jan; Jørgensen, Lone; Njølstad, Inger; Brækkan, Sigrid K; Hansen, John-Bjarne

2017-02-01

Serum osteoprotegerin (OPG) is elevated in patients with chronic kidney disease (CKD) and increases with decreasing renal function. However, there are limited data regarding the association between OPG and renal function in the general population. The aim of the present study was to explore the relation between serum OPG and renal function in subjects recruited from the general population. We conducted a cross-sectional study with 6689 participants recruited from the general population in Tromsø, Norway. Estimated glomerular filtration rate (eGFR) was calculated using the Chronic Kidney Disease Epidemiology Collaboration equations. OPG was modelled both as a continuous and categorical variable. General linear models and linear regression with adjustment for possible confounders were used to study the association between OPG and eGFR. Analyses were stratified by the median age, as serum OPG and age displayed a significant interaction on eGFR. In participants ≤62.2 years with normal renal function (eGFR ≥90 mL/min/1.73 m 2 ) eGFR increased by 0.35 mL/min/1.73 m 2 (95% CI 0.13-0.56) per 1 standard deviation (SD) increase in serum OPG after multiple adjustment. In participants older than the median age with impaired renal function (eGFR <90 mL/min/1.73 m 2 ), eGFR decreased by 1.54 (95% CI -2.06 to -1.01) per 1 SD increase in serum OPG. OPG was associated with an increased eGFR in younger subjects with normal renal function and with a decreased eGFR in older subjects with reduced renal function. Our findings imply that the association between OPG and eGFR varies with age and renal function.

mBEEF-vdW: Robust fitting of error estimation density functionals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lundgaard, Keld T.; Wellendorff, Jess; Voss, Johannes

Here, we propose a general-purpose semilocal/nonlocal exchange-correlation functional approximation, named mBEEF-vdW. The exchange is a meta generalized gradient approximation, and the correlation is a semilocal and nonlocal mixture, with the Rutgers-Chalmers approximation for van der Waals (vdW) forces. The functional is fitted within the Bayesian error estimation functional (BEEF) framework. We improve the previously used fitting procedures by introducing a robust MM-estimator based loss function, reducing the sensitivity to outliers in the datasets. To more reliably determine the optimal model complexity, we furthermore introduce a generalization of the bootstrap 0.632 estimator with hierarchical bootstrap sampling and geometric mean estimator overmore » the training datasets. Using this estimator, we show that the robust loss function leads to a 10% improvement in the estimated prediction error over the previously used least-squares loss function. The mBEEF-vdW functional is benchmarked against popular density functional approximations over a wide range of datasets relevant for heterogeneous catalysis, including datasets that were not used for its training. Overall, we find that mBEEF-vdW has a higher general accuracy than competing popular functionals, and it is one of the best performing functionals on chemisorption systems, surface energies, lattice constants, and dispersion. We also show the potential-energy curve of graphene on the nickel(111) surface, where mBEEF-vdW matches the experimental binding length. mBEEF-vdW is currently available in gpaw and other density functional theory codes through Libxc, version 3.0.0.« less

mBEEF-vdW: Robust fitting of error estimation density functionals

DOE PAGES

Lundgaard, Keld T.; Wellendorff, Jess; Voss, Johannes; ...

2016-06-15

Here, we propose a general-purpose semilocal/nonlocal exchange-correlation functional approximation, named mBEEF-vdW. The exchange is a meta generalized gradient approximation, and the correlation is a semilocal and nonlocal mixture, with the Rutgers-Chalmers approximation for van der Waals (vdW) forces. The functional is fitted within the Bayesian error estimation functional (BEEF) framework. We improve the previously used fitting procedures by introducing a robust MM-estimator based loss function, reducing the sensitivity to outliers in the datasets. To more reliably determine the optimal model complexity, we furthermore introduce a generalization of the bootstrap 0.632 estimator with hierarchical bootstrap sampling and geometric mean estimator overmore » the training datasets. Using this estimator, we show that the robust loss function leads to a 10% improvement in the estimated prediction error over the previously used least-squares loss function. The mBEEF-vdW functional is benchmarked against popular density functional approximations over a wide range of datasets relevant for heterogeneous catalysis, including datasets that were not used for its training. Overall, we find that mBEEF-vdW has a higher general accuracy than competing popular functionals, and it is one of the best performing functionals on chemisorption systems, surface energies, lattice constants, and dispersion. We also show the potential-energy curve of graphene on the nickel(111) surface, where mBEEF-vdW matches the experimental binding length. mBEEF-vdW is currently available in gpaw and other density functional theory codes through Libxc, version 3.0.0.« less

Linguistic Diversity in the Pacific: On the Sources of Diversity. Working Papers in Linguistics, Vol. 7, No. 3.

ERIC Educational Resources Information Center

Grace, George W.

The Pacific area is generally acknowledged to manifest great linguistic diversity. Such diversity is generally assumed to be dysfunctional, an obstacle to efficient functioning of society. Such diversity must, however, have its functions at least in the circumstances in which it arose. It is also generally assumed that such diversity is the result…

General solution of the Bagley-Torvik equation with fractional-order derivative

NASA Astrophysics Data System (ADS)

Wang, Z. H.; Wang, X.

2010-05-01

This paper investigates the general solution of the Bagley-Torvik equation with 1/2-order derivative or 3/2-order derivative. This fractional-order differential equation is changed into a sequential fractional-order differential equation (SFDE) with constant coefficients. Then the general solution of the SFDE is expressed as the linear combination of fundamental solutions that are in terms of α-exponential functions, a kind of functions that play the same role of the classical exponential function. Because the number of fundamental solutions of the SFDE is greater than 2, the general solution of the SFDE depends on more than two free (independent) constants. This paper shows that the general solution of the Bagley-Torvik equation involves actually two free constants only, and it can be determined fully by the initial displacement and initial velocity.

Alterations in the coupling functions between cortical and cardio-respiratory oscillations due to anaesthesia with propofol and sevoflurane

NASA Astrophysics Data System (ADS)

Stankovski, Tomislav; Petkoski, Spase; Raeder, Johan; Smith, Andrew F.; McClintock, Peter V. E.; Stefanovska, Aneta

2016-05-01

The precise mechanisms underlying general anaesthesia pose important and still open questions. To address them, we have studied anaesthesia induced by the widely used (intravenous) propofol and (inhalational) sevoflurane anaesthetics, computing cross-frequency coupling functions between neuronal, cardiac and respiratory oscillations in order to determine their mutual interactions. The phase domain coupling function reveals the form of the function defining the mechanism of an interaction, as well as its coupling strength. Using a method based on dynamical Bayesian inference, we have thus identified and analysed the coupling functions for six relationships. By quantitative assessment of the forms and strengths of the couplings, we have revealed how these relationships are altered by anaesthesia, also showing that some of them are differently affected by propofol and sevoflurane. These findings, together with the novel coupling function analysis, offer a new direction in the assessment of general anaesthesia and neurophysiological interactions, in general.

Effective Biot theory and its generalization to poroviscoelastic models

NASA Astrophysics Data System (ADS)

Liu, Xu; Greenhalgh, Stewart; Zhou, Bing; Greenhalgh, Mark

2018-02-01

A method is suggested to express the effective bulk modulus of the solid frame of a poroelastic material as a function of the saturated bulk modulus. This method enables effective Biot theory to be described through the use of seismic dispersion measurements or other models developed for the effective saturated bulk modulus. The effective Biot theory is generalized to a poroviscoelastic model of which the moduli are represented by the relaxation functions of the generalized fractional Zener model. The latter covers the general Zener and the Cole-Cole models as special cases. A global search method is described to determine the parameters of the relaxation functions, and a simple deterministic method is also developed to find the defining parameters of the single Cole-Cole model. These methods enable poroviscoelastic models to be constructed, which are based on measured seismic attenuation functions, and ensure that the model dispersion characteristics match the observations.

Absorption of inertia-gravity waves in vertically sheared rotating stratified flows

NASA Astrophysics Data System (ADS)

Millet, C.; Lott, F.

2012-12-01

It is well established that gravity waves have a substantial role on the large-scale atmospheric circulation, particularly in the middle atmosphere. In the present work, we re-examine the reflection and transmission of gravity waves through a critical layer surrounded by two inertial levels for the case of a constant vertically sheared flow. In this configuration, the vertical structure of the disturbance can be described as quasi-geostrophic from the critical layer up to the inertial levels, at which the Doppler-shifted frequency is equal to the Coriolis parameter. Near and beyond these levels, the balanced approximations do not apply and there is a transition from the quasi-geostrophic solution to propagating gravity waves. The three-dimensional disturbance solution is obtained analytically using both an exact method, in terms of hypergeometric functions, and a WKB approximation valid for large Richardson numbers; the latter includes an exponentially small term which captures the radiation feedback in the region between the inertial levels. We first focused on the homogeneous part of the disturbance equations, under the assumption of an unbounded domain. In contrast with past studies which show that there is a finite reflection and did not analyze the transmission (Yamanaka and Tanaka, 1984), we find that the reflection coefficient is too small to be significant and that the transmission coefficient is exactly like in the much simpler non-rotating case analyzed by Booker and Bretherton (1966). Our theoretical predictions are found to be in very good agreement with those obtained by numerically integrating the complete hydrostatic-Boussinesq equations with a small Rayleigh damping. The discrepancies between our results and those in Yamanaka and Tanaka (1984) are related to the fact that the solutions are given in term of multivalued functions and the values of the reflection and transmission coefficients are exponentially small, e.g. quite difficult to cross check numerically. More specifically, we suspect that the differences come from their treatment of the analytic continuations in the matching regions (e.g. the inertial layers). Our results are useful to study the evolution of initial disturbances. As an illustration, we consider the problem of gravity waves generated by potential-vorticity anomalies, a problem that was recently studied in Lott et al. (2013) for an unbounded atmosphere. The vertical structure of the potential-vorticity anomaly is represented by a Dirac distribution localized at the critical level. The disturbance field can be deduced from the homogeneous solutions above and below the critical level, by using suitable jump conditions. It is shown how the inclusion of a boundary condition within the problem, below the potential-vorticity anomaly, changes the amplitude of the radiated gravity wave, especially when the Richardson number is not too large. This process may be related to the occurrence of radiative instability waves in sheared rotating stratified flows.

Trajectories of positive, negative and general psychopathology symptoms in first episode psychosis and their relationship with functioning over a 2-year follow-up period.

PubMed

Abdin, Edimansyah; Chong, Siow Ann; Vaingankar, Janhavi Ajit; Peh, Chao Xu; Poon, Lye Yin; Rao, Sujatha; Verma, Swapna; Subramaniam, Mythily

2017-01-01

Few studies have examined the trajectories of symptom severity in first episode psychosis (FEP) and their impact on functioning. This study aimed to identify discrete trajectories of positive, negative and general psychopathological symptoms and functioning, determine predictors of the identified symptom trajectories and subsequently investigate the relationship between symptom and functioning trajectories over the 2-year follow-up period. Data were extracted from the Singapore Early Psychosis Intervention Programme clinical database. Trajectories of the Positive and Negative Syndrome Scale and Global Assessment of Functioning (GAF) scale over the two-year follow up were modelled using latent class growth curve modelling. Two distinct trajectories (early response and stable trajectory and delayed response trajectory) for positive symptoms, four distinct trajectories (early response and stable trajectory, early response and relapse trajectory, slower response and no response trajectory and delayed response trajectory) for negative and general psychopathology symptoms and three distinct trajectories for functioning (high functioning trajectory, moderately stable functioning trajectory and deterioration in functioning trajectory) were identified in our sample. Compared to individuals in the early response and stable trajectory, those in the delayed response trajectory for positive and negative symptoms, early response and relapse for negative and general psychopathology symptoms and slower response and no response trajectories for general psychopathology symptoms were significantly associated with higher odds of having deterioration in functioning over time. Poor symptom trajectories were also significantly predicted by younger age, male gender, unemployed and economically inactive status, lower education, longer duration of untreated psychosis and diagnosis of schizophrenia spectrum and delusional disorders. The results confirm that the symptoms trajectories among patients with FEP are heterogeneous and suggest that a small group of patients may be at higher risk of deterioration in symptom severity and functioning over the 2-year follow-up.

A generalized exponential link function to map a conflict indicator into severity index within safety continuum framework.

PubMed

Zheng, Lai; Ismail, Karim

2017-05-01

Traffic conflict indicators measure the temporal and spatial proximity of conflict-involved road users. These indicators can reflect the severity of traffic conflicts to a reliable extent. Instead of using the indicator value directly as a severity index, many link functions have been developed to map the conflict indicator to a severity index. However, little information is available about the choice of a particular link function. To guard against link misspecification or subjectivity, a generalized exponential link function was developed. The severity index generated by this link was introduced to a parametric safety continuum model which objectively models the centre and tail regions. An empirical method, together with full Bayesian estimation method was adopted to estimate model parameters. The safety implication of return level was calculated based on the model parameters. The proposed approach was applied to the conflict and crash data collected from 21 segments from three freeways located in Guangdong province, China. The Pearson's correlation test between return levels and observed crashes showed that a θ value of 1.2 was the best choice of the generalized parameter for current data set. This provides statistical support for using the generalized exponential link function. With the determined generalized exponential link function, the visualization of parametric safety continuum was found to be a gyroscope-shaped hierarchy. Copyright © 2017 Elsevier Ltd. All rights reserved.

R-Function Relationships for Application in the Fractional Calculus

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

2000-01-01

The F-function, and its generalization the R-function, are of fundamental importance in the fractional calculus. It has been shown that the solution of the fundamental linear fractional differential equation may be expressed in terms of these functions. These functions serve as generalizations of the exponential function in the solution of fractional differential equations. Because of this central role in the fractional calculus, this paper explores various intrarelationships of the R-function, which will be useful in further analysis. Relationships of the R-function to the common exponential function, e(t), and its fractional derivatives are shown. From the relationships developed, some important approximations are observed. Further, the inverse relationships of the exponential function, el, in terms of the R-function are developed. Also, some approximations for the R-function are developed.

R-function relationships for application in the fractional calculus.

PubMed

Lorenzo, Carl F; Hartley, Tom T

2008-01-01

The F-function, and its generalization the R-function, are of fundamental importance in the fractional calculus. It has been shown that the solution of the fundamental linear fractional differential equation may be expressed in terms of these functions. These functions serve as generalizations of the exponential function in the solution of fractional differential equations. Because of this central role in the fractional calculus, this paper explores various intrarelationships of the R-function, which will be useful in further analysis. Relationships of the R-function to the common exponential function, et, and its fractional derivatives are shown. From the relationships developed, some important approximations are observed. Further, the inverse relationships of the exponential function, et, in terms of the R-function are developed. Also, some approximations for the R-function are developed.

Sexual functioning in obese adults enrolling in a weight loss study.

PubMed

Ostbye, Truls; Kolotkin, Ronette L; He, Hong; Overcash, Francine; Brouwer, Rebecca; Binks, Martin; Syrjala, Karen L; Gadde, Kishore M

2011-01-01

The authors assessed sexual functioning among treatment-seeking obese men (n = 91) and women (n = 134) using the comprehensive validated Sexual Functioning Questionnaire. Scores were lower for women than for men, indicating reduced sexual functioning. Men's scores fell between those of a group of cancer survivors and a general population group, whereas women generally had lower scores than both of these groups. Increasing body mass index was associated with decreasing sexual functioning only for arousal and behavior. Sexual functioning was also reduced on most subscales for individuals who reported sexual inactivity in the past month.

MRI correlates of general intelligence in neurotypical adults.

PubMed

Malpas, Charles B; Genc, Sila; Saling, Michael M; Velakoulis, Dennis; Desmond, Patricia M; O'Brien, Terence J

2016-02-01

There is growing interest in the neurobiological substrate of general intelligence. Psychometric estimates of general intelligence are reduced in a range of neurological disorders, leading to practical application as sensitive, but non-specific, markers of cerebral disorder. This study examined estimates of general intelligence in neurotypical adults using diffusion tensor imaging and resting-state functional connectivity analysis. General intelligence was related to white matter organisation across multiple brain regions, confirming previous work in older healthy adults. We also found that variation in general intelligence was related to a large functional sub-network involving all cortical lobes of the brain. These findings confirm that individual variance in general intelligence is related to diffusely represented brain networks. Copyright © 2015 Elsevier Ltd. All rights reserved.

An Initial Investigation of the Generalization of a School-Based Social Competence Intervention for Youth with High-Functioning Autism

PubMed Central

Schmidt, Carla; Stichter, Janine P.; Lierheimer, Kristin; McGhee, Stephanie; O'Connor, Karen V.

2011-01-01

This study evaluated the impact of generalization of the Social Competence Intervention-Adolescent (SCI-A) curriculum in a school setting for individuals with high-functioning autism or Asperger's Syndrome (N = 6). This study examined to what degree the generalization of the SCI-A curriculum could be measured when delivered in a school setting. Across the six participants preliminary results suggest improvement on teacher reports of social skills and executive functioning. Some improvements were also evident in direct measures of facial-expression recognition. Data collected in the nonintervention settings indicated that some generalization of social interaction skills may have occurred for all six participants. Future research directions are discussed. PMID:22937252

Executive functions and aphasia treatment outcomes: data from an ortho-phonological cueing therapy for anomia in Chinese.

PubMed

Yeung, Olivia; Law, Sam-Po

2010-12-01

This study examined the existence of a possible relationship between anomic treatment outcomes and executive functions. An ortho-phonological cueing method was used to facilitate object naming in 12 Cantonese-speaking anomic individuals. Treatment effectiveness for each participant was quantified and correlated with the performance of executive functions and language tasks. It was found that 10 participants showed significant improvement in naming treated items. Eight of the participants were able to maintain treatment gains for at least 1 month. Phonological generalization effects were observed in two participants. Performance on the Test of Nonverbal Intelligence (TONI-3) was significantly correlated with effect sizes of treatment, treatment generalization and maintenance and the Attention Network Test (ANT) was significantly correlated with phonological generalization. The result of a simultaneous multiple regression suggested that the performance of the ANT played an important role in phonological generalization. The findings reinforce the current view about the role of executive functions in language rehabilitation. They also shed light on the effect of inhibitory control on treatment generalization.

General Anesthetics Have Additive Actions on Three Ligand-Gated Ion Channels

PubMed Central

Jenkins, Andrew; Lobo, Ingrid A.; Gong, Diane; Trudell, James R.; Solt, Ken; Harris, R. Adron; Eger, Edmond I

2008-01-01

Background The purpose of this study was to determine whether pairs of compounds, including general anesthetics, could simultaneously modulate receptor function in a synergistic manner, thus demonstrating the existence of multiple intra-protein anesthetic binding sites. Methods Using standard electrophysiologic methods, we measured the effects of at least one combination of benzene, isoflurane, halothane, chloroform, flunitrazepam, zinc and pentobarbital on at least one of the following ligand gated ion channels: N-methyl-D-aspartate receptors (NMDARs), glycine receptors (GlyRs) and γ-aminobutyric acid type A receptors (GABAARs). Results All drug-drug-receptor combinations were found to exhibit additive, not synergistic modulation. Isoflurane with benzene additively depressed NMDAR function. Isoflurane with halothane additively enhanced GlyR function, as did isoflurane with zinc. Isoflurane with halothane additively enhanced GABAAR function as did all of the following: halothane with chloroform, pentobarbital with isoflurane, and flunitrazepam with isoflurane. Conclusions The simultaneous allosteric modulation of ligand gated ion channels by general anesthetics is entirely additive. Where pairs of general anesthetic drugs interact synergistically to produce general anesthesia, they must do so on systems more complex than a single receptor. PMID:18633027

Perceived Family Functioning and Family Resources of Hong Kong Families: Implications for Social Work Practice

ERIC Educational Resources Information Center

Ma, Joyce L. C.; Wong, Timothy K. Y.; Lau, Luk King; Pun, Shuk Han

2009-01-01

This article reports the results of a telephone survey (n = 1,015 respondents) that aims to identify the perceived general family functioning and family resources of Hong Kong Chinese families and their linkage to each other in a rapidly transforming society. The perceived general family functioning of the respondents was average, and the five…

La Seccion Informacion y Documentacion en los Servicios de Pedagogia Universitaria (The Information and Documentation Division of the University Educational Services).

ERIC Educational Resources Information Center

Rossi Etchelouz, Nelly Yvis

This booklet describes the information and documentation services available within the regional area of the National University of Litoral. The basis and general functions of the service are considered, as well as the organizational and functional structure and subjects given priority in the system. The general functions are fourfold: library…

General dynamical density functional theory for classical fluids.

PubMed

Goddard, Benjamin D; Nold, Andreas; Savva, Nikos; Pavliotis, Grigorios A; Kalliadasis, Serafim

2012-09-21

We study the dynamics of a colloidal fluid including inertia and hydrodynamic interactions, two effects which strongly influence the nonequilibrium properties of the system. We derive a general dynamical density functional theory which shows very good agreement with full Langevin dynamics. In suitable limits, we recover existing dynamical density functional theories and a Navier-Stokes-like equation with additional nonlocal terms.

Two-exponent Lavalette function: a generalization for the case of adherents to a religious movement.

PubMed

Ausloos, Marcel

2014-06-01

The Lavalette function is generalized to a two-exponent function in order to represent data looking like a sigmoid on semilogarithmic plots. A Mandelbrot trick is suggested for further investigations, if more fit parameters are needed. The analyzed data is that of the number of adherents to the main religions in the 20th century.

A Generalized Logistic Regression Procedure to Detect Differential Item Functioning among Multiple Groups

ERIC Educational Resources Information Center

Magis, David; Raiche, Gilles; Beland, Sebastien; Gerard, Paul

2011-01-01

We present an extension of the logistic regression procedure to identify dichotomous differential item functioning (DIF) in the presence of more than two groups of respondents. Starting from the usual framework of a single focal group, we propose a general approach to estimate the item response functions in each group and to test for the presence…

Enabling quaternion derivatives: the generalized HR calculus

PubMed Central

Xu, Dongpo; Jahanchahi, Cyrus; Took, Clive C.; Mandic, Danilo P.

2015-01-01

Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective function. The recent HR calculus is a step forward and provides a way to calculate derivatives and gradients of both analytic and non-analytic functions of quaternion variables; however, the HR calculus can become cumbersome in complex optimization problems due to the lack of rigorous product and chain rules, a consequence of the non-commutativity of quaternion algebra. To address this issue, we introduce the generalized HR (GHR) derivatives which employ quaternion rotations in a general orthogonal system and provide the left- and right-hand versions of the quaternion derivative of general functions. The GHR calculus also solves the long-standing problems of product and chain rules, mean-value theorem and Taylor's theorem in the quaternion field. At the core of the proposed GHR calculus is quaternion rotation, which makes it possible to extend the principle to other functional calculi in non-commutative settings. Examples in statistical learning theory and adaptive signal processing support the analysis. PMID:26361555

Enabling quaternion derivatives: the generalized HR calculus.

PubMed

Xu, Dongpo; Jahanchahi, Cyrus; Took, Clive C; Mandic, Danilo P

2015-08-01

Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective function. The recent HR calculus is a step forward and provides a way to calculate derivatives and gradients of both analytic and non-analytic functions of quaternion variables; however, the HR calculus can become cumbersome in complex optimization problems due to the lack of rigorous product and chain rules, a consequence of the non-commutativity of quaternion algebra. To address this issue, we introduce the generalized HR (GHR) derivatives which employ quaternion rotations in a general orthogonal system and provide the left- and right-hand versions of the quaternion derivative of general functions. The GHR calculus also solves the long-standing problems of product and chain rules, mean-value theorem and Taylor's theorem in the quaternion field. At the core of the proposed GHR calculus is quaternion rotation, which makes it possible to extend the principle to other functional calculi in non-commutative settings. Examples in statistical learning theory and adaptive signal processing support the analysis.

Cognitive function and competitive employment in schizophrenia: relative contribution of insight and psychopathology.

PubMed

Giugiario, Michela; Crivelli, Barbara; Mingrone, Cinzia; Montemagni, Cristiana; Scalese, Mara; Sigaudo, Monica; Rocca, Giuseppe; Rocca, Paola

2012-04-01

This study investigated the relationships among insight, psychopathology, cognitive function, and competitive employment in order to determine whether insight and/or psychopathology carried the influence of cognitive function to competitive employment. We recruited 253 outpatients with stable schizophrenia and we further divided our sample into two groups of patients (unemployed and competitive employment subjects). Clinical and neuropsychological assessments were performed. All clinical variables significantly different between the two groups of subjects were subsequently analyzed using a binary logistic regression to assess their independent contribution to competitive employment in the two patients' groups. On the basis of the regression results two mediation analyses were performed. Verbal memory, general psychopathology, and awareness of mental illness were significantly associated with competitive employment in our sample. Both awareness of mental illness and general psychopathology had a role in mediating the verbal memory-competitive employment relationship. Taken together, these findings confirmed the importance of cognitive function in obtaining competitive employment. Our results also highlighted the independent role of general psychopathology and awareness of illness on occupational functioning in schizophrenia. Thus, a greater attention must be given to the systematic investigation of insight and general psychopathology in light of an amelioration of vocational functioning in stable schizophrenia.

The Green’s functions for peridynamic non-local diffusion

PubMed Central

Wang, L. J.; Xu, J. F.

2016-01-01

In this work, we develop the Green’s function method for the solution of the peridynamic non-local diffusion model in which the spatial gradient of the generalized potential in the classical theory is replaced by an integral of a generalized response function in a horizon. We first show that the general solutions of the peridynamic non-local diffusion model can be expressed as functionals of the corresponding Green’s functions for point sources, along with volume constraints for non-local diffusion. Then, we obtain the Green’s functions by the Fourier transform method for unsteady and steady diffusions in infinite domains. We also demonstrate that the peridynamic non-local solutions converge to the classical differential solutions when the non-local length approaches zero. Finally, the peridynamic analytical solutions are applied to an infinite plate heated by a Gauss source, and the predicted variations of temperature are compared with the classical local solutions. The peridynamic non-local diffusion model predicts a lower rate of variation of the field quantities than that of the classical theory, which is consistent with experimental observations. The developed method is applicable to general diffusion-type problems. PMID:27713658

Enriched pathways for major depressive disorder identified from a genome-wide association study.

PubMed

Kao, Chung-Feng; Jia, Peilin; Zhao, Zhongming; Kuo, Po-Hsiu

2012-11-01

Major depressive disorder (MDD) has caused a substantial burden of disease worldwide with moderate heritability. Despite efforts through conducting numerous association studies and now, genome-wide association (GWA) studies, the success of identifying susceptibility loci for MDD has been limited, which is partially attributed to the complex nature of depression pathogenesis. A pathway-based analytic strategy to investigate the joint effects of various genes within specific biological pathways has emerged as a powerful tool for complex traits. The present study aimed to identify enriched pathways for depression using a GWA dataset for MDD. For each gene, we estimated its gene-wise p value using combined and minimum p value, separately. Canonical pathways from the Kyoto Encyclopedia of Genes and Genomes (KEGG) and BioCarta were used. We employed four pathway-based analytic approaches (gene set enrichment analysis, hypergeometric test, sum-square statistic, sum-statistic). We adjusted for multiple testing using Benjamini & Hochberg's method to report significant pathways. We found 17 significantly enriched pathways for depression, which presented low-to-intermediate crosstalk. The top four pathways were long-term depression (p⩽1×10-5), calcium signalling (p⩽6×10-5), arrhythmogenic right ventricular cardiomyopathy (p⩽1.6×10-4) and cell adhesion molecules (p⩽2.2×10-4). In conclusion, our comprehensive pathway analyses identified promising pathways for depression that are related to neurotransmitter and neuronal systems, immune system and inflammatory response, which may be involved in the pathophysiological mechanisms underlying depression. We demonstrated that pathway enrichment analysis is promising to facilitate our understanding of complex traits through a deeper interpretation of GWA data. Application of this comprehensive analytic strategy in upcoming GWA data for depression could validate the findings reported in this study.

Estimating numbers of greater prairie-chickens using mark-resight techniques

USGS Publications Warehouse

Clifton, A.M.; Krementz, D.G.

2006-01-01

Current monitoring efforts for greater prairie-chicken (Tympanuchus cupido pinnatus) populations indicate that populations are declining across their range. Monitoring the population status of greater prairie-chickens is based on traditional lek surveys (TLS) that provide an index without considering detectability. Estimators, such as immigration-emigration joint maximum-likelihood estimator from a hypergeometric distribution (IEJHE), can account for detectability and provide reliable population estimates based on resightings. We evaluated the use of mark-resight methods using radiotelemetry to estimate population size and density of greater prairie-chickens on 2 sites at a tallgrass prairie in the Flint Hills of Kansas, USA. We used average distances traveled from lek of capture to estimate density. Population estimates and confidence intervals at the 2 sites were 54 (CI 50-59) on 52.9 km 2 and 87 (CI 82-94) on 73.6 km2. The TLS performed at the same sites resulted in population ranges of 7-34 and 36-63 and always produced a lower population index than the mark-resight population estimate with a larger range. Mark-resight simulations with varying male:female ratios of marks indicated that this ratio was important in designing a population study on prairie-chickens. Confidence intervals for estimates when no marks were placed on females at the 2 sites (CI 46-50, 76-84) did not overlap confidence intervals when 40% of marks were placed on females (CI 54-64, 91-109). Population estimates derived using this mark-resight technique were apparently more accurate than traditional methods and would be more effective in detecting changes in prairie-chicken populations. Our technique could improve prairie-chicken management by providing wildlife biologists and land managers with a tool to estimate the population size and trends of lekking bird species, such as greater prairie-chickens.

GSA-PCA: gene set generation by principal component analysis of the Laplacian matrix of a metabolic network

PubMed Central

2012-01-01

Background Gene Set Analysis (GSA) has proven to be a useful approach to microarray analysis. However, most of the method development for GSA has focused on the statistical tests to be used rather than on the generation of sets that will be tested. Existing methods of set generation are often overly simplistic. The creation of sets from individual pathways (in isolation) is a poor reflection of the complexity of the underlying metabolic network. We have developed a novel approach to set generation via the use of Principal Component Analysis of the Laplacian matrix of a metabolic network. We have analysed a relatively simple data set to show the difference in results between our method and the current state-of-the-art pathway-based sets. Results The sets generated with this method are semi-exhaustive and capture much of the topological complexity of the metabolic network. The semi-exhaustive nature of this method has also allowed us to design a hypergeometric enrichment test to determine which genes are likely responsible for set significance. We show that our method finds significant aspects of biology that would be missed (i.e. false negatives) and addresses the false positive rates found with the use of simple pathway-based sets. Conclusions The set generation step for GSA is often neglected but is a crucial part of the analysis as it defines the full context for the analysis. As such, set generation methods should be robust and yield as complete a representation of the extant biological knowledge as possible. The method reported here achieves this goal and is demonstrably superior to previous set analysis methods. PMID:22876834

Evaluation of genome-wide association study results through development of ontology fingerprints

PubMed Central

Tsoi, Lam C.; Boehnke, Michael; Klein, Richard L.; Zheng, W. Jim

2009-01-01

Motivation: Genome-wide association (GWA) studies may identify multiple variants that are associated with a disease or trait. To narrow down candidates for further validation, quantitatively assessing how identified genes relate to a phenotype of interest is important. Results: We describe an approach to characterize genes or biological concepts (phenotypes, pathways, diseases, etc.) by ontology fingerprint—the set of Gene Ontology (GO) terms that are overrepresented among the PubMed abstracts discussing the gene or biological concept together with the enrichment p-value of these terms generated from a hypergeometric enrichment test. We then quantify the relevance of genes to the trait from a GWA study by calculating similarity scores between their ontology fingerprints using enrichment p-values. We validate this approach by correctly identifying corresponding genes for biological pathways with a 90% average area under the ROC curve (AUC). We applied this approach to rank genes identified through a GWA study that are associated with the lipid concentrations in plasma as well as to prioritize genes within linkage disequilibrium (LD) block. We found that the genes with highest scores were: ABCA1, lipoprotein lipase (LPL) and cholesterol ester transfer protein, plasma for high-density lipoprotein; low-density lipoprotein receptor, APOE and APOB for low-density lipoprotein; and LPL, APOA1 and APOB for triglyceride. In addition, we identified genes relevant to lipid metabolism from the literature even in cases where such knowledge was not reflected in current annotation of these genes. These results demonstrate that ontology fingerprints can be used effectively to prioritize genes from GWA studies for experimental validation. Contact: zhengw@musc.edu Supplementary information: Supplementary data are available at Bioinformatics online. PMID:19349285

Translational Identification of Transcriptional Signatures of Major Depression and Antidepressant Response

PubMed Central

Hervé, Mylène; Bergon, Aurélie; Le Guisquet, Anne-Marie; Leman, Samuel; Consoloni, Julia-Lou; Fernandez-Nunez, Nicolas; Lefebvre, Marie-Noëlle; El-Hage, Wissam; Belzeaux, Raoul; Belzung, Catherine; Ibrahim, El Chérif

2017-01-01

Major depressive disorder (MDD) is a highly prevalent mental illness whose therapy management remains uncertain, with more than 20% of patients who do not achieve response to antidepressants. Therefore, identification of reliable biomarkers to predict response to treatment will greatly improve MDD patient medical care. Due to the inaccessibility and lack of brain tissues from living MDD patients to study depression, researches using animal models have been useful in improving sensitivity and specificity of identifying biomarkers. In the current study, we used the unpredictable chronic mild stress (UCMS) model and correlated stress-induced depressive-like behavior (n = 8 unstressed vs. 8 stressed mice) as well as the fluoxetine-induced recovery (n = 8 stressed and fluoxetine-treated mice vs. 8 unstressed and fluoxetine-treated mice) with transcriptional signatures obtained by genome-wide microarray profiling from whole blood, dentate gyrus (DG), and the anterior cingulate cortex (ACC). Hierarchical clustering and rank-rank hypergeometric overlap (RRHO) procedures allowed us to identify gene transcripts with variations that correlate with behavioral profiles. As a translational validation, some of those transcripts were assayed by RT-qPCR with blood samples from 10 severe major depressive episode (MDE) patients and 10 healthy controls over the course of 30 weeks and four visits. Repeated-measures ANOVAs revealed candidate trait biomarkers (ARHGEF1, CMAS, IGHMBP2, PABPN1 and TBC1D10C), whereas univariate linear regression analyses uncovered candidates state biomarkers (CENPO, FUS and NUBP1), as well as prediction biomarkers predictive of antidepressant response (CENPO, NUBP1). These data suggest that such a translational approach may offer new leads for clinically valid panels of biomarkers for MDD. PMID:28848385

41 CFR 105-53.116 - General regulations.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 41 Public Contracts and Property Management 3 2010-07-01 2010-07-01 false General regulations. 105... Regulations System (Continued) GENERAL SERVICES ADMINISTRATION 53-STATEMENT OF ORGANIZATION AND FUNCTIONS General § 105-53.116 General regulations. Regulations of the General Services Administration and its...

Correlation functions for Hermitian many-body systems: Necessary conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brown, E.B.

1994-02-01

Lee [Phys. Rev. B 47, 8293 (1993)] has shown that the odd-numbered derivatives of the Kubo autocorrelation function vanish at [ital t]=0. We show that this condition is based on a more general property of nondiagonal Kubo correlation functions. This general property provides that certain functional forms (e.g., simple exponential decay) are not admissible for any symmetric or antisymmetric Kubo correlation function in a Hermitian many-body system. Lee's result emerges as a special case of this result. Applications to translationally invariant systems and systems with rotational symmetries are also demonstrated.

Generalized neurofuzzy network modeling algorithms using Bézier-Bernstein polynomial functions and additive decomposition.

PubMed

Hong, X; Harris, C J

2000-01-01

This paper introduces a new neurofuzzy model construction algorithm for nonlinear dynamic systems based upon basis functions that are Bézier-Bernstein polynomial functions. This paper is generalized in that it copes with n-dimensional inputs by utilising an additive decomposition construction to overcome the curse of dimensionality associated with high n. This new construction algorithm also introduces univariate Bézier-Bernstein polynomial functions for the completeness of the generalized procedure. Like the B-spline expansion based neurofuzzy systems, Bézier-Bernstein polynomial function based neurofuzzy networks hold desirable properties such as nonnegativity of the basis functions, unity of support, and interpretability of basis function as fuzzy membership functions, moreover with the additional advantages of structural parsimony and Delaunay input space partition, essentially overcoming the curse of dimensionality associated with conventional fuzzy and RBF networks. This new modeling network is based on additive decomposition approach together with two separate basis function formation approaches for both univariate and bivariate Bézier-Bernstein polynomial functions used in model construction. The overall network weights are then learnt using conventional least squares methods. Numerical examples are included to demonstrate the effectiveness of this new data based modeling approach.

On the analogues of Szegő's theorem for ergodic operators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kirsch, W; Pastur, L A

2015-01-31

Szegő's theorem on the asymptotic behaviour of the determinants of large Toeplitz matrices is generalized to the class of ergodic operators. The generalization is formulated in terms of a triple consisting of an ergodic operator and two functions, the symbol and the test function. It is shown that in the case of the one-dimensional discrete Schrödinger operator with random ergodic or quasiperiodic potential and various choices of the symbol and the test function this generalization leads to asymptotic formulae which have no analogues in the situation of Toeplitz operators. Bibliography: 22 titles.

Dorsolateral Prefrontal Contributions to Human Intelligence

PubMed Central

Barbey, Aron K.; Colom, Roberto; Grafman, Jordan

2012-01-01

Although cognitive neuroscience has made remarkable progress in understanding the involvement of the prefrontal cortex in executive control functions for human intelligence, the necessity of the dorsolateral prefrontal cortex (dlPFC) for key competencies of general intelligence and executive function remains to be well established. Here we studied human brain lesion patients with dlPFC lesions to investigate whether this region is computationally necessary for performance on neuropsychological tests of general intelligence and executive function, administering the Wechsler Adult Intelligence Scale (WAIS) and subtests of the Delis Kaplan Executive Function System (D-KEFS) to three groups: dlPFC lesions (n = 19), non-dlPFC lesions (n = 152), and no brain lesions (n = 55). The key results indicate that: (1) patients with focal dlPFC damage exhibit lower scores, at the latent variable level, than controls in general intelligence (g) and executive function; (2) dlPFC patients demonstrate lower scores than controls in several executive measures; and (3) these latter differences are no longer significant when the pervasive influence of the general factor of intelligence (g) is statistically removed. The observed findings support a central role for the dlPFC in general intelligence and make specific recommendations for the interpretation and application of the WAIS and D-KEFS to the study of high-level cognition in health and disease. PMID:22634247

Pilates versus general exercise effectiveness on pain and functionality in non-specific chronic low back pain subjects.

PubMed

Mostagi, Fernanda Queiroz Ribeiro Cerci; Dias, Josilainne Marcelino; Pereira, Ligia Maxwell; Obara, Karen; Mazuquin, Bruno Fles; Silva, Mariana Felipe; Silva, Monica Angelica Cardoso; de Campos, Renata Rosa; Barreto, Maria Simone Tavares; Nogueira, Jéssyca Fernandes; Lima, Tarcísio Brandão; Carregaro, Rodrigo Luiz; Cardoso, Jefferson Rosa

2015-10-01

Low back pain (LBP) is one of the most common causes of disability, and the Pilates method has been associated with improvements in symptoms. The purpose of this study was to assess the effectiveness of the Pilates method, when compared to general exercises, on pain and functionality after eight weeks (16 sessions, 2×/week) and a follow-up of three months, in subjects with non-specific chronic low back pain (NSCLBP). A randomised controlled trial composed of 22 subjects was proposed. Subjects were allocated into two groups: the Pilates group (PG) (n = 11) and the general exercise group (GEG) (n = 11). The PG protocol was based on the Pilates method and the GEG performed exercises to manage NSCLBP. There were no differences between the groups. When analysed over time, the GEG demonstrated improvements in functionality between baseline and the end of treatment (P = .02; Cohen'sd¯ = 0.34) and baseline and follow-up (P = .04; Cohen'sd¯ = 0.31). There were no differences between the Pilates and general exercises with regard to pain and functionality in NSCLBP subjects but general exercises were better than Pilates for increasing functionality and flexibility. Copyright © 2014 Elsevier Ltd. All rights reserved.

Decision making generalized by a cumulative probability weighting function

NASA Astrophysics Data System (ADS)

dos Santos, Lindomar Soares; Destefano, Natália; Martinez, Alexandre Souto

2018-01-01

Typical examples of intertemporal decision making involve situations in which individuals must choose between a smaller reward, but more immediate, and a larger one, delivered later. Analogously, probabilistic decision making involves choices between options whose consequences differ in relation to their probability of receiving. In Economics, the expected utility theory (EUT) and the discounted utility theory (DUT) are traditionally accepted normative models for describing, respectively, probabilistic and intertemporal decision making. A large number of experiments confirmed that the linearity assumed by the EUT does not explain some observed behaviors, as nonlinear preference, risk-seeking and loss aversion. That observation led to the development of new theoretical models, called non-expected utility theories (NEUT), which include a nonlinear transformation of the probability scale. An essential feature of the so-called preference function of these theories is that the probabilities are transformed by decision weights by means of a (cumulative) probability weighting function, w(p) . We obtain in this article a generalized function for the probabilistic discount process. This function has as particular cases mathematical forms already consecrated in the literature, including discount models that consider effects of psychophysical perception. We also propose a new generalized function for the functional form of w. The limiting cases of this function encompass some parametric forms already proposed in the literature. Far beyond a mere generalization, our function allows the interpretation of probabilistic decision making theories based on the assumption that individuals behave similarly in the face of probabilities and delays and is supported by phenomenological models.

Probability Weighting Functions Derived from Hyperbolic Time Discounting: Psychophysical Models and Their Individual Level Testing.

PubMed

Takemura, Kazuhisa; Murakami, Hajime

2016-01-01

A probability weighting function (w(p)) is considered to be a nonlinear function of probability (p) in behavioral decision theory. This study proposes a psychophysical model of probability weighting functions derived from a hyperbolic time discounting model and a geometric distribution. The aim of the study is to show probability weighting functions from the point of view of waiting time for a decision maker. Since the expected value of a geometrically distributed random variable X is 1/p, we formulized the probability weighting function of the expected value model for hyperbolic time discounting as w(p) = (1 - k log p)(-1). Moreover, the probability weighting function is derived from Loewenstein and Prelec's (1992) generalized hyperbolic time discounting model. The latter model is proved to be equivalent to the hyperbolic-logarithmic weighting function considered by Prelec (1998) and Luce (2001). In this study, we derive a model from the generalized hyperbolic time discounting model assuming Fechner's (1860) psychophysical law of time and a geometric distribution of trials. In addition, we develop median models of hyperbolic time discounting and generalized hyperbolic time discounting. To illustrate the fitness of each model, a psychological experiment was conducted to assess the probability weighting and value functions at the level of the individual participant. The participants were 50 university students. The results of individual analysis indicated that the expected value model of generalized hyperbolic discounting fitted better than previous probability weighting decision-making models. The theoretical implications of this finding are discussed.

Continuous time random walk model with asymptotical probability density of waiting times via inverse Mittag-Leffler function

NASA Astrophysics Data System (ADS)

Liang, Yingjie; Chen, Wen

2018-04-01

The mean squared displacement (MSD) of the traditional ultraslow diffusion is a logarithmic function of time. Recently, the continuous time random walk model is employed to characterize this ultraslow diffusion dynamics by connecting the heavy-tailed logarithmic function and its variation as the asymptotical waiting time density. In this study we investigate the limiting waiting time density of a general ultraslow diffusion model via the inverse Mittag-Leffler function, whose special case includes the traditional logarithmic ultraslow diffusion model. The MSD of the general ultraslow diffusion model is analytically derived as an inverse Mittag-Leffler function, and is observed to increase even more slowly than that of the logarithmic function model. The occurrence of very long waiting time in the case of the inverse Mittag-Leffler function has the largest probability compared with the power law model and the logarithmic function model. The Monte Carlo simulations of one dimensional sample path of a single particle are also performed. The results show that the inverse Mittag-Leffler waiting time density is effective in depicting the general ultraslow random motion.

The perception of sexuality in older adults and its relationship with cognitive functioning.

PubMed

Hartmans, Carien; Comijs, Hannie; Jonker, Cees

2015-03-01

Investigating whether cognitive functioning is associated with the perception of one's sexuality in old age. Cross-sectional analysis, using observation cycle 2005/2006 of the population-based prospective cohort of the Longitudinal Aging Study Amsterdam. Municipal registries in three Dutch regions. 1,908 older adults (mean [standard deviation] age: 71 [8.87] years; 54% women). Sexuality and intimacy were assessed using four questions. Four cognitive domains were assessed: general cognitive functioning (Mini-Mental State Examination), memory performance (Auditory Verbal Learning Test), processing speed (Coding Task), and fluid intelligence (Raven's Coloured Progressive Matrices). Multinomial regression analysis was used, with sexuality as outcome. The interaction effect between gender and sexuality was also tested. Lower fluid intelligence was associated with perceiving sexuality as unimportant; lower general cognitive functioning was associated with perceiving sexuality as unimportant; and lower immediate memory recall was associated with evaluating sexual life as unpleasant. Associations were also found between lower fluid intelligence, processing speed, and general cognitive functioning, and agreeing with sexuality no longer being important. Lower processing speed, general cognitive functioning, and delayed memory recall were associated with disagreeing with a remaining need for intimacy when getting older. Finally, the association between fluid intelligence and perceiving sexuality as important, and the association between immediate memory recall score and evaluating sexual life as pleasant, was only significant in women. The association between lower general cognitive functioning and perceiving sexuality as unimportant seemed stronger in women compared with men. Higher cognitive functioning was associated with the way in which older people perceive their current sexuality. Copyright © 2015 American Association for Geriatric Psychiatry. Published by Elsevier Inc. All rights reserved.

mBEEF-vdW: Robust fitting of error estimation density functionals

NASA Astrophysics Data System (ADS)

Lundgaard, Keld T.; Wellendorff, Jess; Voss, Johannes; Jacobsen, Karsten W.; Bligaard, Thomas

2016-06-01

We propose a general-purpose semilocal/nonlocal exchange-correlation functional approximation, named mBEEF-vdW. The exchange is a meta generalized gradient approximation, and the correlation is a semilocal and nonlocal mixture, with the Rutgers-Chalmers approximation for van der Waals (vdW) forces. The functional is fitted within the Bayesian error estimation functional (BEEF) framework [J. Wellendorff et al., Phys. Rev. B 85, 235149 (2012), 10.1103/PhysRevB.85.235149; J. Wellendorff et al., J. Chem. Phys. 140, 144107 (2014), 10.1063/1.4870397]. We improve the previously used fitting procedures by introducing a robust MM-estimator based loss function, reducing the sensitivity to outliers in the datasets. To more reliably determine the optimal model complexity, we furthermore introduce a generalization of the bootstrap 0.632 estimator with hierarchical bootstrap sampling and geometric mean estimator over the training datasets. Using this estimator, we show that the robust loss function leads to a 10 % improvement in the estimated prediction error over the previously used least-squares loss function. The mBEEF-vdW functional is benchmarked against popular density functional approximations over a wide range of datasets relevant for heterogeneous catalysis, including datasets that were not used for its training. Overall, we find that mBEEF-vdW has a higher general accuracy than competing popular functionals, and it is one of the best performing functionals on chemisorption systems, surface energies, lattice constants, and dispersion. We also show the potential-energy curve of graphene on the nickel(111) surface, where mBEEF-vdW matches the experimental binding length. mBEEF-vdW is currently available in gpaw and other density functional theory codes through Libxc, version 3.0.0.

Derivative expansion of wave function equivalent potentials

NASA Astrophysics Data System (ADS)

Sugiura, Takuya; Ishii, Noriyoshi; Oka, Makoto

2017-04-01

Properties of the wave function equivalent potentials introduced by the HAL QCD collaboration are studied in a nonrelativistic coupled-channel model. The derivative expansion is generalized, and then applied to the energy-independent and nonlocal potentials. The expansion coefficients are determined from analytic solutions to the Nambu-Bethe-Salpeter wave functions. The scattering phase shifts computed from these potentials are compared with the exact values to examine the convergence of the expansion. It is confirmed that the generalized derivative expansion converges in terms of the scattering phase shift rather than the functional structure of the non-local potentials. It is also found that the convergence can be improved by tuning either the choice of interpolating fields or expansion scale in the generalized derivative expansion.

Analytical methods for describing charged particle dynamics in general focusing lattices using generalized Courant-Snyder theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Qin, Hong; Davidson, Ronald C.; Burby, Joshua W.

2014-04-08

The dynamics of charged particles in general linear focusing lattices with quadrupole, skew-quadrupole, dipole, and solenoidal components, as well as torsion of the fiducial orbit and variation of beam energy is parametrized using a generalized Courant-Snyder (CS) theory, which extends the original CS theory for one degree of freedom to higher dimensions. The envelope function is generalized into an envelope matrix, and the phase advance is generalized into a 4D symplectic rotation, or a Uð2Þ element. The 1D envelope equation, also known as the Ermakov-Milne-Pinney equation in quantum mechanics, is generalized to an envelope matrix equation in higher dimensions. Othermore » components of the original CS theory, such as the transfer matrix, Twiss functions, and CS invariant (also known as the Lewis invariant) all have their counterparts, with remarkably similar expressions, in the generalized theory. The gauge group structure of the generalized theory is analyzed. By fixing the gauge freedom with a desired symmetry, the generalized CS parametrization assumes the form of the modified Iwasawa decomposition, whose importance in phase space optics and phase space quantum mechanics has been recently realized. This gauge fixing also symmetrizes the generalized envelope equation and expresses the theory using only the generalized Twiss function β. The generalized phase advance completely determines the spectral and structural stability properties of a general focusing lattice. For structural stability, the generalized CS theory enables application of the Krein-Moser theory to greatly simplify the stability analysis. The generalized CS theory provides an effective tool to study coupled dynamics and to discover more optimized lattice designs in the larger parameter space of general focusing lattices.« less

Working With the Wave Equation in Aeroacoustics: The Pleasures of Generalized Functions

NASA Technical Reports Server (NTRS)

Farassat, F.; Brentner, Kenneth S.; Dunn, mark H.

2007-01-01

The theme of this paper is the applications of generalized function (GF) theory to the wave equation in aeroacoustics. We start with a tutorial on GFs with particular emphasis on viewing functions as continuous linear functionals. We next define operations on GFs. The operation of interest to us in this paper is generalized differentiation. We give many applications of generalized differentiation, particularly for the wave equation. We discuss the use of GFs in finding Green s function and some subtleties that only GF theory can clarify without ambiguities. We show how the knowledge of the Green s function of an operator L in a given domain D can allow us to solve a whole range of problems with operator L for domains situated within D by the imbedding method. We will show how we can use the imbedding method to find the Kirchhoff formulas for stationary and moving surfaces with ease and elegance without the use of the four-dimensional Green s theorem, which is commonly done. Other subjects covered are why the derivatives in conservation laws should be viewed as generalized derivatives and what are the consequences of doing this. In particular we show how we can imbed a problem in a larger domain for the identical differential equation for which the Green s function is known. The primary purpose of this paper is to convince the readers that GF theory is absolutely essential in aeroacoustics because of its powerful operational properties. Furthermore, learning the subject and using it can be fun.

Hyperfine structure parametrisation in Maple

NASA Astrophysics Data System (ADS)

Gaigalas, G.; Scharf, O.; Fritzsche, S.

2006-02-01

In hyperfine structure examinations, routine high resolution spectroscopy methods have to be combined with exact fine structure calculations. The so-called magnetic A and electric B factor of the fine structure levels allow to check for a correct fine structure analysis, to find errors in the level designation, to find new levels and to probe the electron wavefunctions and its mixing coefficients. This is done by parametrisation of these factors into different contributions of the subshell electrons, which are split further into their radial and spin-angular part. Due to the routine with which hyperfine structure measurements are done, a tool for keeping the necessary information together, performing checks online with the experiment and deriving standard quantities is of great help. MAPLE [Maple is a registered trademark of Waterloo Maple Inc.] is a highly-developed symbolic programming language, often referred to as the pocket calculator of the future. Packages for theoretical atomic calculation exist ( RACAH and JUCYS) and the language meets all the requirements to keep and present information accessible for the user in a fast and practical way. We slightly extended the RACAH package [S. Fritzsche, Comput. Phys. Comm. 103 (1997) 51] and set up an environment for experimental hyperfine structure calculations, the HFS package. Supplying the fine structure and nuclear data, one is in the position to obtain information about the hyperfine spectrum, the different contributions to the splitting and to perform a least square fit of the radial parameters based on the semiempirical method. Experimentalist as well as theoretical physicist can do a complete hyperfine structure analysis using MAPLE. Program summaryTitle of program: H FS Catalogue number: ADXD Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXD Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: none Computers for which the program is designed: All computers with a license of the computer algebra package MAPLE Installations: University of Kassel (Germany) Operating systems under which the program has been tested: Linux 9.0 Program language used:MAPLE, Release 7, 8 and 9 Memory required to execute with typical data: 5 MB No. of lines in distributed program, including test data, etc.: 34 300 No. of bytes in distributed program, including test data, etc.: 954 196 Distribution format: tar.gz Nature of the physical problem: Atomic state functions of an many configuration many electron atom with several open shells are defined by a number of quantum numbers, by their coupling and selection rules such as the Pauli exclusion principal or parity conservation. The matrix elements of any one-particle operator acting on these wavefunctions can be analytically integrated up to the radial part [G. Gaigalas, O. Scharf, S. Fritzsche, Central European J. Phys. 2 (2004) 720]. The decoupling of the interacting electrons is general, the obtained submatrix element holds all the peculiarities of the operator in question. These so-called submatrix elements are the key to do hyperfine structure calculations. The interaction between the electrons and the atomic nucleus leads to an additional splitting of the fine structure lines, the hyperfine structure. The leading components are the magnetic dipole interaction defining the so-called A factor and the electric quadrupole interaction, defining the so-called B factor. They express the energetic splitting of the spectral lines. Moreover, they are obtained directly by experiments and can be calculated theoretically in an ab initio approach. A semiempirical approach allows the fitting of the radial parts of the wavefunction to the experimentally obtained A and B factors. Method of solution: Extending the existing csf_LS() and asf_LS() to several open shells and implementing a data structure level_LS() for the fine structure level, the atomic environment is defined in MAPLE. It is used in a general approach to decouple the interacting shells for any one-particle operator. Further submatrix elements for the magnetic dipole and electric quadrupole interaction are implemented, allowing to calculate the A and B factors up to the radial part. Several procedures for standard quantities of the hyperfine structure are defined, too. The calculations are accelerated by using a hyper-geometric approach for three, six and nine symbols. Restrictions onto the complexity of the problem: Only atomic state functions in nonrelativistic LS-coupling with states having l⩽3 are supported. Typical running time: The program replies promptly on most requests. The least square fit depends heavily on the number of levels and can take a few minutes.

Some elements of a theory of multidimensional complex variables. I - General theory. II - Expansions of analytic functions and application to fluid flows

NASA Technical Reports Server (NTRS)

Martin, E. Dale

1989-01-01

The paper introduces a new theory of N-dimensional complex variables and analytic functions which, for N greater than 2, is both a direct generalization and a close analog of the theory of ordinary complex variables. The algebra in the present theory is a commutative ring, not a field. Functions of a three-dimensional variable were defined and the definition of the derivative then led to analytic functions.

Use of a generalized sigmoid growth function to predict site index for unmanaged loblolly and slash pine plantations in East Texas

Treesearch

Dean W. Coble; Young-Jin Lee

2006-01-01

A generalized sigmoid growth function was used in this study to model site index (SI) for unmanaged or lowintensity managed loblolly pine (Pinus taeda, L.) and slash pine (Pinus elliottii, Engelm.) plantations in east Texas. Schnute's growth function was fit to 11,367 and 5,040 height-age observations of loblolly and slash...

Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pribram-Jones, Aurora; Grabowski, Paul E.; Burke, Kieron

We present that the van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. Finally, this produces a natural method for generating new thermal exchange-correlation approximations.

Differences between Mothers' and Fathers' Ratings of Family Functioning with the Family Assessment Device: The Validity of Combined Parent Scores

ERIC Educational Resources Information Center

Cooke, Dawson; Marais, Ida; Cavanagh, Robert; Kendall, Garth; Priddis, Lynn

2015-01-01

The psychometric properties of the General Functioning subscale of the McMaster Family Assessment Device were examined using the Rasch Model (N = 237 couples). Mothers' and fathers' ratings of the General Functioning subscale of the McMaster Family Assessment Device are recommended, provided these are analyzed separately. More than a quarter of…

Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem

DOE PAGES

Pribram-Jones, Aurora; Grabowski, Paul E.; Burke, Kieron

2016-06-08

We present that the van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. Finally, this produces a natural method for generating new thermal exchange-correlation approximations.

Calibrating the ECCO ocean general circulation model using Green's functions

NASA Technical Reports Server (NTRS)

Menemenlis, D.; Fu, L. L.; Lee, T.; Fukumori, I.

2002-01-01

Green's functions provide a simple, yet effective, method to test and calibrate General-Circulation-Model(GCM) parameterizations, to study and quantify model and data errors, to correct model biases and trends, and to blend estimates from different solutions and data products.

28 CFR 0.100 - General functions.

Code of Federal Regulations, 2012 CFR

2012-07-01

... Comprehensive Drug Abuse Prevention and Control Act of 1970, as amended. This will include functions which may be vested in the Attorney General in subsequent amendments to the Comprehensive Drug Abuse Prevention... Judicial Administration DEPARTMENT OF JUSTICE ORGANIZATION OF THE DEPARTMENT OF JUSTICE Drug Enforcement...

28 CFR 0.100 - General functions.

Code of Federal Regulations, 2014 CFR

2014-07-01

... Comprehensive Drug Abuse Prevention and Control Act of 1970, as amended. This will include functions which may be vested in the Attorney General in subsequent amendments to the Comprehensive Drug Abuse Prevention... Judicial Administration DEPARTMENT OF JUSTICE ORGANIZATION OF THE DEPARTMENT OF JUSTICE Drug Enforcement...

28 CFR 0.100 - General functions.

Code of Federal Regulations, 2013 CFR

2013-07-01

... Comprehensive Drug Abuse Prevention and Control Act of 1970, as amended. This will include functions which may be vested in the Attorney General in subsequent amendments to the Comprehensive Drug Abuse Prevention... Judicial Administration DEPARTMENT OF JUSTICE ORGANIZATION OF THE DEPARTMENT OF JUSTICE Drug Enforcement...

Demonstration Advanced Avionics System (DAAS)

NASA Technical Reports Server (NTRS)

1982-01-01

The feasibility of developing an integrated avionics system suitable for general aviation was determined. A design of reliable integrated avionics which provides expanded functional capability that significantly enhances the utility and safety of general aviation at a cost commensurate with the general aviation market was developed. The use of a data bus, microprocessors, electronic displays and data entry devices, and improved function capabilities were emphasized. An avionics system capable of evaluating the most critical and promising elements of an integrated system was designed, built and flight tested in a twin engine general aviation aircraft.

Convergent close coupling versus the generalized Sturmian function approach: Wave-function analysis

NASA Astrophysics Data System (ADS)

Ambrosio, M.; Mitnik, D. M.; Gasaneo, G.; Randazzo, J. M.; Kadyrov, A. S.; Fursa, D. V.; Bray, I.

2015-11-01

We compare the physical information contained in the Temkin-Poet (TP) scattering wave function representing electron-impact ionization of hydrogen, calculated by the convergent close-coupling (CCC) and generalized Sturmian function (GSF) methodologies. The idea is to show that the ionization cross section can be extracted from the wave functions themselves. Using two different procedures based on hyperspherical Sturmian functions we show that the transition amplitudes contained in both GSF and CCC scattering functions lead to similar single-differential cross sections. The single-continuum channels were also a subject of the present studies, and we show that the elastic and excitation amplitudes are essentially the same as well.

Effects of music and art education in early life and oral functions on the QOL of the Takarazuka Revue Company OG compared with general elderly females.

PubMed

Masutani, Takiko; Yamamoto, Yasuji; Konishi, Junya; Maeda, Kiyoshi

2010-03-01

Today, Japan is becoming a super-aged society, with senior citizens already constituting over 21% of the population. In this situation, the question of how elderly people can extend their lives and enjoy independent lifestyles is becoming more important. The present study aims to clarify the relationship between the Quality of Life (QOL) of elderly females and their current oral functions and experiences of music and art education in early life. We carried out a survey study focusing on elderly females (Takarazuka Revue Company OG group and general female group) by carrying out a questionnaire survey and comparing cognitive function, oral examinations, cerebral atrophy in magnetic resonance imaging, and other characteristics. It was shown that the Takarazuka Revue Company OG group had greater hippocampal volumes and significantly higher cognitive functions than the general female group. In addition, in the general female group, there was a significant correlation between a decrease in the number of remaining teeth and a decrease in activities in daily living, but in the Takarazuka Revue Company OG group, no such correlation was observed. The results showed that those who have received art education as part of their careers over an extensive period since early life have higher levels of cognitive function, QOL, physical activity, social activity and life satisfaction compared with the general female group; showing that they sense a purpose in life and live with a positive attitude. In contrast, in the general female group, those who have continued to enjoy hobbies have higher levels of cognitive function, QOL, physical activity, social activity and life satisfaction than those who have not, thus showing that they live with a positive attitude.

Quality of life, social functioning, family structure, and treatment history associated with crack cocaine use in youth from the general population.

PubMed

Narvaez, Joana C M; Pechansky, Flávio; Jansen, Karen; Pinheiro, Ricardo T; Silva, Ricardo A; Kapczinski, Flávio; Magalhães, Pedro V

2015-01-01

To assess the relationship between crack cocaine use and dimensions of quality of life and social functioning in young adults. This was a cross-sectional, population-based study involving 1,560 participants in Pelotas, Brazil. Crack cocaine use and abuse were investigated using the Alcohol, Smoking and Substance Involvement Screening Test (ASSIST) inventory. Outcomes of interest were quality of life, religiosity, and social functioning in terms of education, occupational status, family structure, and medical treatment history. Lifetime crack cocaine use was associated with poor quality of life, worse functioning, impaired academic performance, and lower religious involvement. A greater maternal presence and higher paternal absence were more also more pronounced in crack cocaine users, who were also more likely to seek psychological and psychiatric treatment than the general population. Quality of life was severely impacted by crack cocaine use, especially in terms of general and physical health. Social functioning also differed between the general population and crack users, who had lower educational attainment and religious involvement. Maternal presence, paternal absence, and mental health-seeking behaviors were also more frequent among crack cocaine users, although these individuals reported lower rates of treatment satisfaction. Crack cocaine users also had significant social impairment, so that interventions involving family management and a greater focus on general health, quality of life, and functioning may make crucial contributions to the recovery of this group.

Functional Generalized Structured Component Analysis.

PubMed

Suk, Hye Won; Hwang, Heungsun

2016-12-01

An extension of Generalized Structured Component Analysis (GSCA), called Functional GSCA, is proposed to analyze functional data that are considered to arise from an underlying smooth curve varying over time or other continua. GSCA has been geared for the analysis of multivariate data. Accordingly, it cannot deal with functional data that often involve different measurement occasions across participants and a large number of measurement occasions that exceed the number of participants. Functional GSCA addresses these issues by integrating GSCA with spline basis function expansions that represent infinite-dimensional curves onto a finite-dimensional space. For parameter estimation, functional GSCA minimizes a penalized least squares criterion by using an alternating penalized least squares estimation algorithm. The usefulness of functional GSCA is illustrated with gait data.

Fundamental measure theory for the inhomogeneous hard-sphere system based on Santos' consistent free energy.

PubMed

Hansen-Goos, Hendrik; Mortazavifar, Mostafa; Oettel, Martin; Roth, Roland

2015-05-01

Based on Santos' general solution for the scaled-particle differential equation [Phys. Rev. E 86, 040102(R) (2012)], we construct a free-energy functional for the hard-sphere system. The functional is obtained by a suitable generalization and extension of the set of scaled-particle variables using the weighted densities from Rosenfeld's fundamental measure theory for the hard-sphere mixture [Phys. Rev. Lett. 63, 980 (1989)]. While our general result applies to the hard-sphere mixture, we specify remaining degrees of freedom by requiring the functional to comply with known properties of the pure hard-sphere system. Both for mixtures and pure systems, the functional can be systematically extended following the lines of our derivation. We test the resulting functionals regarding their behavior upon dimensional reduction of the fluid as well as their ability to accurately describe the hard-sphere crystal and the liquid-solid transition.

Attention Contributes to Arithmetic Deficits in New-Onset Childhood Absence Epilepsy.

PubMed

Cheng, Dazhi; Yan, Xiuxian; Gao, Zhijie; Xu, Keming; Chen, Qian

2017-01-01

Neuropsychological studies indicate that new-onset childhood absence epilepsy (CAE) is associated with deficits in attention and executive functioning. However, the contribution of these deficits to impaired academic performance remains unclear. We aimed to examine whether attention and executive functioning deficits account for the academic difficulties prevalent in patients with new-onset CAE. We analyzed cognitive performance in several domains, including language, mathematics, psychomotor speed, spatial ability, memory, general intelligence, attention, and executive functioning, in 35 children with new-onset CAE and 33 control participants. Patients with new-onset CAE exhibited deficits in mathematics, general intelligence, attention, and executive functioning. Furthermore, attention deficits, as measured by a visual tracing task, accounted for impaired arithmetic performance in the new-onset CAE group. Therefore, attention deficits, rather than impaired general intelligence or executive functioning, may be responsible for arithmetic performance deficits in patients with new-onset CAE.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vesely, P.; Michel, N.; Toivanen, J.

For over four decades, the Skyrme functional within various parametrizations has been used to calculate nuclear properties. In the last few years there was a number of attempts to improve its performance and introduce generalized forms. In particular, the most general phenomenological quasi-local energy density functional, which contains all combinations of density, spin-density, and their derivatives up to the sixth order (N{sup 3}LO), was proposed in reference [1]. Since in the phenomenological functional approaches the particle-particle (pp) interaction channel is treated independently from the particle-hole (ph) channel, there remains a question of what pairing interaction is suitable to use withinmore » the N{sup 3}LO energy functional. In our study, we use the separable, finite-range, translationally invariant form given in [2], which we generalize to the arbitrary angular momentum channel. We discuss the application of this pairing interaction within the N{sup 3}LO energy functional.« less

A computational method for solving stochastic Itô–Volterra integral equations based on stochastic operational matrix for generalized hat basis functions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heydari, M.H., E-mail: heydari@stu.yazd.ac.ir; The Laboratory of Quantum Information Processing, Yazd University, Yazd; Hooshmandasl, M.R., E-mail: hooshmandasl@yazd.ac.ir

2014-08-01

In this paper, a new computational method based on the generalized hat basis functions is proposed for solving stochastic Itô–Volterra integral equations. In this way, a new stochastic operational matrix for generalized hat functions on the finite interval [0,T] is obtained. By using these basis functions and their stochastic operational matrix, such problems can be transformed into linear lower triangular systems of algebraic equations which can be directly solved by forward substitution. Also, the rate of convergence of the proposed method is considered and it has been shown that it is O(1/(n{sup 2}) ). Further, in order to show themore » accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient in comparison with the block pule functions method.« less

Two-Loop Gell-Mann Function for General Renormalizable N = 1 Supersymmetric Theory, Regularized by Higher Derivatives

NASA Astrophysics Data System (ADS)

Shevtsova, Ekaterina

2011-10-01

For the general renormalizable N=1 supersymmetric Yang-Mills theory, regularized by higher covariant derivatives, a two-loop β-function is calculated. It is shown that all integrals, needed for its obtaining are integrals of total derivatives.

41 CFR 105-53.112 - General statement of functions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... contracting; real and personal property management; transportation, public transportation, public utilities... 41 Public Contracts and Property Management 3 2010-07-01 2010-07-01 false General statement of functions. 105-53.112 Section 105-53.112 Public Contracts and Property Management Federal Property...

28 CFR 0.95 - General functions.

Code of Federal Regulations, 2014 CFR

2014-07-01

... Judicial Administration DEPARTMENT OF JUSTICE ORGANIZATION OF THE DEPARTMENT OF JUSTICE Bureau of Prisons § 0.95 General functions. The Director of the Bureau of Prisons shall direct all activities of the Bureau of Prisons including: (a) Management and regulation of all Federal penal and correctional...

28 CFR 0.95 - General functions.

Code of Federal Regulations, 2013 CFR

2013-07-01

... Judicial Administration DEPARTMENT OF JUSTICE ORGANIZATION OF THE DEPARTMENT OF JUSTICE Bureau of Prisons § 0.95 General functions. The Director of the Bureau of Prisons shall direct all activities of the Bureau of Prisons including: (a) Management and regulation of all Federal penal and correctional...

28 CFR 0.95 - General functions.

Code of Federal Regulations, 2012 CFR

2012-07-01

... Judicial Administration DEPARTMENT OF JUSTICE ORGANIZATION OF THE DEPARTMENT OF JUSTICE Bureau of Prisons § 0.95 General functions. The Director of the Bureau of Prisons shall direct all activities of the Bureau of Prisons including: (a) Management and regulation of all Federal penal and correctional...

12 CFR 905.2 - General statement and statutory authority.

Code of Federal Regulations, 2012 CFR

2012-01-01

....2 Section 905.2 Banks and Banking FEDERAL HOUSING FINANCE BOARD FEDERAL HOUSING FINANCE BOARD ORGANIZATION AND OPERATIONS DESCRIPTION OF ORGANIZATION AND FUNCTIONS Functions and Responsibilities of Finance Board § 905.2 General statement and statutory authority. (a) The Finance Board is an independent...

General well function for soil vapor extraction

NASA Astrophysics Data System (ADS)

Perina, Tomas

2014-04-01

This paper develops a well function applicable to extraction of groundwater or soil vapor from a well under the most common field test conditions. The general well function (Perina and Lee, 2006) [12] is adapted to soil vapor extraction and constant head boundary at the top. For groundwater flow, the general well function now applies to an extraction well of finite diameter with uniform drawdown along the screen, finite-thickness skin, and partially penetrating an unconfined, confined, and leaky aquifer, or an aquifer underneath a reservoir. With a change of arguments, the model applies to soil vapor extraction from a vadose zone with no cover or with leaky cover at the ground surface. The extraction well can operate in specified drawdown (pressure for soil vapor) or specified flowrate mode. Frictional well loss is computed as flow-only dependent component of the drawdown inside the extraction well. In general case, the calculated flow distribution is not proportional to screen length for a multiscreen well.

Lectins of beneficial microbes: system organisation, functioning and functional superfamily.

PubMed

Lakhtin, M; Lakhtin, V; Alyoshkin, V; Afanasyev, S

2011-06-01

In this review our last results and proposals with respect to general aspects of lectin studies are summarised and compared. System presence, organisation and functioning of lectins are proposed, and accents on beneficial symbiotic microbial lectins studies are presented. The proposed general principles of lectin functioning allows for a comparison of lectins with other carbohydrate-recognition systems. A new structure-functional superfamily of symbiotic microbial lectins is proposed and its main properties are described. The proposed superfamily allows for extended searches of the biological activities of any microbial member. Prospects of lectins of beneficial symbiotic microorganisms are discussed.

Personality, function and satisfaction in patients undergoing total hip or knee replacement.

PubMed

Ramaesh, Rishikesan; Jenkins, Paul; Lane, Judith V; Knight, Sara; Macdonald, Deborah; Howie, Colin

2014-03-01

The aim of this study was to investigate the relationships between personality and joint-specific function, general physical and general mental health in patients undergoing total hip (THA) and knee arthroplasty (TKA). One hundred and eighty-four patients undergoing THA and 205 undergoing TKA were assessed using the Eysneck Personality Questionnaire, brief version (EPQ-BV). General physical and mental health was measured using the Short-Form 12 (SF-12) questionnaire and the EuroQol (EQ-5D). Joint-specific function was measured using the Oxford hip or knee score. The "unstable introvert" personality type was associated with poorer pre-operative function and health in patients with hip arthrosis. In patients with knee arthrosis, there was poorer general health in those with "stable extrovert" and "unstable introvert" types. Personality was not an independent predictor of outcome following TKA or THA. The main predictor was pre-operative function and health. Comorbidity was an important covariate of both pre-operative and postoperative function. Personality may play a role in the interaction of these disease processes with function and health perception. It may also affect the response and interpretation of psychometric and patient-reported outcome measures. It may be important to characterise and identify these traits in potential arthroplasty patients as it may help deliver targeted education and management to improve outcomes in certain groups.

Mechanistic Insight into the Host Transcription Inhibition Function of Rift Valley Fever Virus NSs and Its Importance in Virulence

PubMed Central

Terasaki, Kaori; Ramirez, Sydney I.; Makino, Shinji

2016-01-01

Rift Valley fever virus (RVFV), a member of the genus Phlebovirus within the family Bunyaviridae, causes periodic outbreaks in livestocks and humans in countries of the African continent and Middle East. RVFV NSs protein, a nonstructural protein, is a major virulence factor that exhibits several important biological properties. These include suppression of general transcription, inhibition of IFN-β promoter induction and degradation of double-stranded RNA-dependent protein kinase R. Although each of these biological functions of NSs are considered important for countering the antiviral response in the host, the individual contributions of these functions towards RVFV virulence remains unclear. To examine this, we generated two RVFV MP-12 strain-derived mutant viruses. Each carried mutations in NSs that specifically targeted its general transcription inhibition function without affecting its ability to degrade PKR and inhibit IFN-β promoter induction, through its interaction with Sin3-associated protein 30, a part of the repressor complex at the IFN-β promoter. Using these mutant viruses, we have dissected the transcription inhibition function of NSs and examined its importance in RVFV virulence. Both NSs mutant viruses exhibited a differentially impaired ability to inhibit host transcription when compared with MP-12. It has been reported that NSs suppresses general transcription by interfering with the formation of the transcription factor IIH complex, through the degradation of the p62 subunit and sequestration of the p44 subunit. Our study results lead us to suggest that the ability of NSs to induce p62 degradation is the major contributor to its general transcription inhibition property, whereas its interaction with p44 may not play a significant role in this function. Importantly, RVFV MP-12-NSs mutant viruses with an impaired general transcription inhibition function showed a reduced cytotoxicity in cell culture and attenuated virulence in young mice, compared with its parental virus MP-12, highlighting the contribution of NSs-mediated general transcription inhibition towards RVFV virulence. PMID:27711108

Mechanistic Insight into the Host Transcription Inhibition Function of Rift Valley Fever Virus NSs and Its Importance in Virulence.

PubMed

Terasaki, Kaori; Ramirez, Sydney I; Makino, Shinji

2016-10-01

Rift Valley fever virus (RVFV), a member of the genus Phlebovirus within the family Bunyaviridae, causes periodic outbreaks in livestocks and humans in countries of the African continent and Middle East. RVFV NSs protein, a nonstructural protein, is a major virulence factor that exhibits several important biological properties. These include suppression of general transcription, inhibition of IFN-β promoter induction and degradation of double-stranded RNA-dependent protein kinase R. Although each of these biological functions of NSs are considered important for countering the antiviral response in the host, the individual contributions of these functions towards RVFV virulence remains unclear. To examine this, we generated two RVFV MP-12 strain-derived mutant viruses. Each carried mutations in NSs that specifically targeted its general transcription inhibition function without affecting its ability to degrade PKR and inhibit IFN-β promoter induction, through its interaction with Sin3-associated protein 30, a part of the repressor complex at the IFN-β promoter. Using these mutant viruses, we have dissected the transcription inhibition function of NSs and examined its importance in RVFV virulence. Both NSs mutant viruses exhibited a differentially impaired ability to inhibit host transcription when compared with MP-12. It has been reported that NSs suppresses general transcription by interfering with the formation of the transcription factor IIH complex, through the degradation of the p62 subunit and sequestration of the p44 subunit. Our study results lead us to suggest that the ability of NSs to induce p62 degradation is the major contributor to its general transcription inhibition property, whereas its interaction with p44 may not play a significant role in this function. Importantly, RVFV MP-12-NSs mutant viruses with an impaired general transcription inhibition function showed a reduced cytotoxicity in cell culture and attenuated virulence in young mice, compared with its parental virus MP-12, highlighting the contribution of NSs-mediated general transcription inhibition towards RVFV virulence.

GrDHP: a general utility function representation for dual heuristic dynamic programming.

PubMed

Ni, Zhen; He, Haibo; Zhao, Dongbin; Xu, Xin; Prokhorov, Danil V

2015-03-01

A general utility function representation is proposed to provide the required derivable and adjustable utility function for the dual heuristic dynamic programming (DHP) design. Goal representation DHP (GrDHP) is presented with a goal network being on top of the traditional DHP design. This goal network provides a general mapping between the system states and the derivatives of the utility function. With this proposed architecture, we can obtain the required derivatives of the utility function directly from the goal network. In addition, instead of a fixed predefined utility function in literature, we conduct an online learning process for the goal network so that the derivatives of the utility function can be adaptively tuned over time. We provide the control performance of both the proposed GrDHP and the traditional DHP approaches under the same environment and parameter settings. The statistical simulation results and the snapshot of the system variables are presented to demonstrate the improved learning and controlling performance. We also apply both approaches to a power system example to further demonstrate the control capabilities of the GrDHP approach.

New rules meet established sickness certification practice: a focus-group study on the introduction of functional assessments in Norwegian primary care.

PubMed

Krohne, Kariann; Brage, Søren

2007-09-01

To explore how general practitioners view and handle new standards for functional assessments in sickness certification practice. Qualitative study using focus group interviews. Data were analysed according to Giorgi's phenomenological approach and supported by theories on knowledge. General practitioners from three neighbouring counties in Norway. Four focus groups with a total of 23 participants were recruited through the Norwegian Medical Association and its Continuous Medical Education system. The participants reported difficulties and reluctance to act in accordance with new functional assessment demands on both a practical and a conceptual level. In established sickness certification practice functional assessment was described as an unspoken part of the medical examination. After the introduction of formal, written functional assessments they identified problems of terminology, communication, and trust. Strategies were developed to circumvent these problems. A gap was noticeable between the participants' established practice and the new standards' demand for a more theoretical and communicative functional assessment. The general lack of training, being confronted with new terminology, and increasingly high pressure to reduce sickness absences create an atmosphere of insecurity when assessing function.

Influence of Response Prepotency Strength, General Working Memory Resources, and Specific Working Memory Load on the Ability to Inhibit Predominant Responses: A Comparison of Young and Elderly Participants

ERIC Educational Resources Information Center

Grandjean, Julien; Collette, Fabienne

2011-01-01

One conception of inhibitory functioning suggests that the ability to successfully inhibit a predominant response depends mainly on the strength of that response, the general functioning of working memory processes, and the working memory demand of the task (Roberts, Hager, & Heron, 1994). The proposal that inhibition and functional working memory…

Exact traveling wave solutions of the KP-BBM equation by using the new approach of generalized (G'/G)-expansion method.

PubMed

Alam, Md Nur; Akbar, M Ali

2013-01-01

The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. By means of this scheme, we found some new traveling wave solutions of the above mentioned equation.

Generalized decompositions of dynamic systems and vector Lyapunov functions

NASA Astrophysics Data System (ADS)

Ikeda, M.; Siljak, D. D.

1981-10-01

The notion of decomposition is generalized to provide more freedom in constructing vector Lyapunov functions for stability analysis of nonlinear dynamic systems. A generalized decomposition is defined as a disjoint decomposition of a system which is obtained by expanding the state-space of a given system. An inclusion principle is formulated for the solutions of the expansion to include the solutions of the original system, so that stability of the expansion implies stability of the original system. Stability of the expansion can then be established by standard disjoint decompositions and vector Lyapunov functions. The applicability of the new approach is demonstrated using the Lotka-Volterra equations.

Generalized prolate spheroidal wave functions for optical finite fractional Fourier and linear canonical transforms.

PubMed

Pei, Soo-Chang; Ding, Jian-Jiun

2005-03-01

Prolate spheroidal wave functions (PSWFs) are known to be useful for analyzing the properties of the finite-extension Fourier transform (fi-FT). We extend the theory of PSWFs for the finite-extension fractional Fourier transform, the finite-extension linear canonical transform, and the finite-extension offset linear canonical transform. These finite transforms are more flexible than the fi-FT and can model much more generalized optical systems. We also illustrate how to use the generalized prolate spheroidal functions we derive to analyze the energy-preservation ratio, the self-imaging phenomenon, and the resonance phenomenon of the finite-sized one-stage or multiple-stage optical systems.

Multilayer neural networks with extensively many hidden units.

PubMed

Rosen-Zvi, M; Engel, A; Kanter, I

2001-08-13

The information processing abilities of a multilayer neural network with a number of hidden units scaling as the input dimension are studied using statistical mechanics methods. The mapping from the input layer to the hidden units is performed by general symmetric Boolean functions, whereas the hidden layer is connected to the output by either discrete or continuous couplings. Introducing an overlap in the space of Boolean functions as order parameter, the storage capacity is found to scale with the logarithm of the number of implementable Boolean functions. The generalization behavior is smooth for continuous couplings and shows a discontinuous transition to perfect generalization for discrete ones.

An analogue of Weyl’s law for quantized irreducible generalized flag manifolds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Matassa, Marco, E-mail: marco.matassa@gmail.com, E-mail: mmatassa@math.uio.no

2015-09-15

We prove an analogue of Weyl’s law for quantized irreducible generalized flag manifolds. This is formulated in terms of a zeta function which, similarly to the classical setting, satisfies the following two properties: as a functional on the quantized algebra it is proportional to the Haar state and its first singularity coincides with the classical dimension. The relevant formulas are given for the more general case of compact quantum groups.

On One-Dimensional Stretching Functions for Finite-Difference Calculations

NASA Technical Reports Server (NTRS)

Vinokur, M.

1980-01-01

The class of one dimensional stretching function used in finite difference calculations is studied. For solutions containing a highly localized region of rapid variation, simple criteria for a stretching function are derived using a truncation error analysis. These criteria are used to investigate two types of stretching functions. One is an interior stretching function, for which the location and slope of an interior clustering region are specified. The simplest such function satisfying the criteria is found to be one based on the inverse hyperbolic sine. The other type of function is a two sided stretching function, for which the arbitrary slopes at the two ends of the one dimensional interval are specified. The simplest such general function is found to be one based on the inverse tangent. The general two sided function has many applications in the construction of finite difference grids.

40 CFR 1.3 - Purpose and functions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 40 Protection of Environment 1 2010-07-01 2010-07-01 false Purpose and functions. 1.3 Section 1.3 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY GENERAL STATEMENT OF ORGANIZATION AND GENERAL... coordinated and effective governmental action to assure the protection of the environment by abating and...

40 CFR 1.3 - Purpose and functions.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 40 Protection of Environment 1 2011-07-01 2011-07-01 false Purpose and functions. 1.3 Section 1.3 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY GENERAL STATEMENT OF ORGANIZATION AND GENERAL... coordinated and effective governmental action to assure the protection of the environment by abating and...

Adolescent Depression: Relationships of Self-Report to Intellectual and Adaptive Functioning.

ERIC Educational Resources Information Center

Manikam, Ramasamy; And Others

1995-01-01

Self-report measures of depression, general psychopathology, and social skills were administered to 100 adolescents ranging from moderate mental retardation to above normal intelligence. Adolescents with mental retardation reported more depression and general psychopathology symptoms. Adaptive behavior functioned as a moderator variable, mediating…

Generalized canonical ensembles and ensemble equivalence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Costeniuc, M.; Ellis, R.S.; Turkington, B.

2006-02-15

This paper is a companion piece to our previous work [J. Stat. Phys. 119, 1283 (2005)], which introduced a generalized canonical ensemble obtained by multiplying the usual Boltzmann weight factor e{sup -{beta}}{sup H} of the canonical ensemble with an exponential factor involving a continuous function g of the Hamiltonian H. We provide here a simplified introduction to our previous work, focusing now on a number of physical rather than mathematical aspects of the generalized canonical ensemble. The main result discussed is that, for suitable choices of g, the generalized canonical ensemble reproduces, in the thermodynamic limit, all the microcanonical equilibriummore » properties of the many-body system represented by H even if this system has a nonconcave microcanonical entropy function. This is something that in general the standard (g=0) canonical ensemble cannot achieve. Thus a virtue of the generalized canonical ensemble is that it can often be made equivalent to the microcanonical ensemble in cases in which the canonical ensemble cannot. The case of quadratic g functions is discussed in detail; it leads to the so-called Gaussian ensemble.« less

lsjk—a C++ library for arbitrary-precision numeric evaluation of the generalized log-sine functions

NASA Astrophysics Data System (ADS)

Kalmykov, M. Yu.; Sheplyakov, A.

2005-10-01

Generalized log-sine functions Lsj(k)(θ) appear in higher order ɛ-expansion of different Feynman diagrams. We present an algorithm for the numerical evaluation of these functions for real arguments. This algorithm is implemented as a C++ library with arbitrary-precision arithmetics for integer 0⩽k⩽9 and j⩾2. Some new relations and representations of the generalized log-sine functions are given. Program summaryTitle of program:lsjk Catalogue number:ADVS Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVS Program obtained from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing terms: GNU General Public License Computers:all Operating systems:POSIX Programming language:C++ Memory required to execute:Depending on the complexity of the problem, at least 32 MB RAM recommended No. of lines in distributed program, including testing data, etc.:41 975 No. of bytes in distributed program, including testing data, etc.:309 156 Distribution format:tar.gz Other programs called:The CLN library for arbitrary-precision arithmetics is required at version 1.1.5 or greater External files needed:none Nature of the physical problem:Numerical evaluation of the generalized log-sine functions for real argument in the region 0<θ<π. These functions appear in Feynman integrals Method of solution:Series representation for the real argument in the region 0<θ<π Restriction on the complexity of the problem:Limited up to Lsj(9)(θ), and j is an arbitrary integer number. Thus, all function up to the weight 12 in the region 0<θ<π can be evaluated. The algorithm can be extended up to higher values of k(k>9) without modification Typical running time:Depending on the complexity of problem. See text below.

Properties of real metallic surfaces: Effects of density functional semilocality and van der Waals nonlocality

PubMed Central

Patra, Abhirup; Bates, Jefferson E.; Sun, Jianwei; Perdew, John P.

2017-01-01

We have computed the surface energies, work functions, and interlayer surface relaxations of clean (111), (100), and (110) surfaces of Al, Cu, Ru, Rh, Pd, Ag, Pt, and Au. We interpret the surface energy from liquid metal measurements as the mean of the solid-state surface energies over these three lowest-index crystal faces. We compare experimental (and random phase approximation) reference values to those of a family of nonempirical semilocal density functionals, from the basic local density approximation (LDA) to our most advanced general purpose meta-generalized gradient approximation, strongly constrained and appropriately normed (SCAN). The closest agreement is achieved by the simplest density functional LDA, and by the most sophisticated one, SCAN+rVV10 (Vydrov–Van Voorhis 2010). The long-range van der Waals interaction, incorporated through rVV10, increases the surface energies by about 10%, and increases the work functions by about 3%. LDA works for metal surfaces through two known error cancellations. The Perdew–Burke–Ernzerhof generalized gradient approximation tends to underestimate both surface energies (by about 24%) and work functions (by about 4%), yielding the least-accurate results. The amount by which a functional underestimates these surface properties correlates with the extent to which it neglects van der Waals attraction at intermediate and long range. Qualitative arguments are given for the signs of the van der Waals contributions to the surface energy and work function. A standard expression for the work function in Kohn–Sham (KS) theory is shown to be valid in generalized KS theory. Interlayer relaxations from different functionals are in reasonable agreement with one another, and usually with experiment. PMID:29042509

Large-Scale functional network overlap is a general property of brain functional organization: Reconciling inconsistent fMRI findings from general-linear-model-based analyses

PubMed Central

Xu, Jiansong; Potenza, Marc N.; Calhoun, Vince D.; Zhang, Rubin; Yip, Sarah W.; Wall, John T.; Pearlson, Godfrey D.; Worhunsky, Patrick D.; Garrison, Kathleen A.; Moran, Joseph M.

2016-01-01

Functional magnetic resonance imaging (fMRI) studies regularly use univariate general-linear-model-based analyses (GLM). Their findings are often inconsistent across different studies, perhaps because of several fundamental brain properties including functional heterogeneity, balanced excitation and inhibition (E/I), and sparseness of neuronal activities. These properties stipulate heterogeneous neuronal activities in the same voxels and likely limit the sensitivity and specificity of GLM. This paper selectively reviews findings of histological and electrophysiological studies and fMRI spatial independent component analysis (sICA) and reports new findings by applying sICA to two existing datasets. The extant and new findings consistently demonstrate several novel features of brain functional organization not revealed by GLM. They include overlap of large-scale functional networks (FNs) and their concurrent opposite modulations, and no significant modulations in activity of most FNs across the whole brain during any task conditions. These novel features of brain functional organization are highly consistent with the brain’s properties of functional heterogeneity, balanced E/I, and sparseness of neuronal activity, and may help reconcile inconsistent GLM findings. PMID:27592153

Towards the Improved Discovery and Design of Functional Peptides: Common Features of Diverse Classes Permit Generalized Prediction of Bioactivity

PubMed Central

Mooney, Catherine; Haslam, Niall J.; Pollastri, Gianluca; Shields, Denis C.

2012-01-01

The conventional wisdom is that certain classes of bioactive peptides have specific structural features that endow their particular functions. Accordingly, predictions of bioactivity have focused on particular subgroups, such as antimicrobial peptides. We hypothesized that bioactive peptides may share more general features, and assessed this by contrasting the predictive power of existing antimicrobial predictors as well as a novel general predictor, PeptideRanker, across different classes of peptides. We observed that existing antimicrobial predictors had reasonable predictive power to identify peptides of certain other classes i.e. toxin and venom peptides. We trained two general predictors of peptide bioactivity, one focused on short peptides (4–20 amino acids) and one focused on long peptides ( amino acids). These general predictors had performance that was typically as good as, or better than, that of specific predictors. We noted some striking differences in the features of short peptide and long peptide predictions, in particular, high scoring short peptides favour phenylalanine. This is consistent with the hypothesis that short and long peptides have different functional constraints, perhaps reflecting the difficulty for typical short peptides in supporting independent tertiary structure. We conclude that there are general shared features of bioactive peptides across different functional classes, indicating that computational prediction may accelerate the discovery of novel bioactive peptides and aid in the improved design of existing peptides, across many functional classes. An implementation of the predictive method, PeptideRanker, may be used to identify among a set of peptides those that may be more likely to be bioactive. PMID:23056189

Performance of Density Functional Theory Procedures for the Calculation of Proton-Exchange Barriers: Unusual Behavior of M06-Type Functionals.

PubMed

Chan, Bun; Gilbert, Andrew T B; Gill, Peter M W; Radom, Leo

2014-09-09

We have examined the performance of a variety of density functional theory procedures for the calculation of complexation energies and proton-exchange barriers, with a focus on the Minnesota-class of functionals that are generally highly robust and generally show good accuracy. A curious observation is that M05-type and M06-type methods show an atypical decrease in calculated barriers with increasing proportion of Hartree-Fock exchange. To obtain a clearer picture of the performance of the underlying components of M05-type and M06-type functionals, we have investigated the combination of MPW-type and PBE-type exchange and B95-type and PBE-type correlation procedures. We find that, for the extensive E3 test set, the general performance of the various hybrid-DFT procedures improves in the following order: PBE1-B95 → PBE1-PBE → MPW1-PBE → PW6-B95. As M05-type and M06-type procedures are related to PBE1-B95, it would be of interest to formulate and examine the general performance of an alternative Minnesota DFT method related to PW6-B95.

Exploring the squeezed three-point galaxy correlation function with generalized halo occupation distribution models

NASA Astrophysics Data System (ADS)

Yuan, Sihan; Eisenstein, Daniel J.; Garrison, Lehman H.

2018-04-01

We present the GeneRalized ANd Differentiable Halo Occupation Distribution (GRAND-HOD) routine that generalizes the standard 5 parameter halo occupation distribution model (HOD) with various halo-scale physics and assembly bias. We describe the methodology of 4 different generalizations: satellite distribution generalization, velocity bias, closest approach distance generalization, and assembly bias. We showcase the signatures of these generalizations in the 2-point correlation function (2PCF) and the squeezed 3-point correlation function (squeezed 3PCF). We identify generalized HOD prescriptions that are nearly degenerate in the projected 2PCF and demonstrate that these degeneracies are broken in the redshift-space anisotropic 2PCF and the squeezed 3PCF. We also discuss the possibility of identifying degeneracies in the anisotropic 2PCF and further demonstrate the extra constraining power of the squeezed 3PCF on galaxy-halo connection models. We find that within our current HOD framework, the anisotropic 2PCF can predict the squeezed 3PCF better than its statistical error. This implies that a discordant squeezed 3PCF measurement could falsify the particular HOD model space. Alternatively, it is possible that further generalizations of the HOD model would open opportunities for the squeezed 3PCF to provide novel parameter measurements. The GRAND-HOD Python package is publicly available at https://github.com/SandyYuan/GRAND-HOD.

Stability of a general delayed virus dynamics model with humoral immunity and cellular infection

NASA Astrophysics Data System (ADS)

Elaiw, A. M.; Raezah, A. A.; Alofi, A. S.

2017-06-01

In this paper, we investigate the dynamical behavior of a general nonlinear model for virus dynamics with virus-target and infected-target incidences. The model incorporates humoral immune response and distributed time delays. The model is a four dimensional system of delay differential equations where the production and removal rates of the virus and cells are given by general nonlinear functions. We derive the basic reproduction parameter R˜0 G and the humoral immune response activation number R˜1 G and establish a set of conditions on the general functions which are sufficient to determine the global dynamics of the models. We use suitable Lyapunov functionals and apply LaSalle's invariance principle to prove the global asymptotic stability of the all equilibria of the model. We confirm the theoretical results by numerical simulations.

Unraveling hadron structure with generalized parton distributions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Andrei Belitsky; Anatoly Radyushkin

2004-10-01

The recently introduced generalized parton distributions have emerged as a universal tool to describe hadrons in terms of quark and gluonic degrees of freedom. They combine the features of form factors, parton densities and distribution amplitudes - the functions used for a long time in studies of hadronic structure. Generalized parton distributions are analogous to the phase-space Wigner quasi-probability function of non-relativistic quantum mechanics which encodes full information on a quantum-mechanical system. We give an extensive review of main achievements in the development of this formalism. We discuss physical interpretation and basic properties of generalized parton distributions, their modeling andmore » QCD evolution in the leading and next-to-leading orders. We describe how these functions enter a wide class of exclusive reactions, such as electro- and photo-production of photons, lepton pairs, or mesons.« less

28 CFR 16.29 - Delegation by Assistant Attorneys General.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 28 Judicial Administration 1 2010-07-01 2010-07-01 false Delegation by Assistant Attorneys General... Assistant Attorneys General. With respect to any function that this subpart permits the designee of an Assistant Attorney General to perform, the Assistant Attorneys General are authorized to delegate their...

19 CFR 201.4 - Performance of functions.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 19 Customs Duties 3 2010-04-01 2010-04-01 false Performance of functions. 201.4 Section 201.4 Customs Duties UNITED STATES INTERNATIONAL TRADE COMMISSION GENERAL RULES OF GENERAL APPLICATION... of 1930, or (2) a matter under an investigation pursuant to section 202 of the Trade Act of 1974 (19...

19 CFR 201.4 - Performance of functions.

Code of Federal Regulations, 2013 CFR

2013-04-01

... 19 Customs Duties 3 2013-04-01 2013-04-01 false Performance of functions. 201.4 Section 201.4 Customs Duties UNITED STATES INTERNATIONAL TRADE COMMISSION GENERAL RULES OF GENERAL APPLICATION... of 1930, or (2) a matter under an investigation pursuant to section 202 of the Trade Act of 1974 (19...

19 CFR 201.4 - Performance of functions.

Code of Federal Regulations, 2011 CFR

2011-04-01

... 19 Customs Duties 3 2011-04-01 2011-04-01 false Performance of functions. 201.4 Section 201.4 Customs Duties UNITED STATES INTERNATIONAL TRADE COMMISSION GENERAL RULES OF GENERAL APPLICATION... of 1930, or (2) a matter under an investigation pursuant to section 202 of the Trade Act of 1974 (19...

19 CFR 201.4 - Performance of functions.

Code of Federal Regulations, 2012 CFR

2012-04-01

... 19 Customs Duties 3 2012-04-01 2012-04-01 false Performance of functions. 201.4 Section 201.4 Customs Duties UNITED STATES INTERNATIONAL TRADE COMMISSION GENERAL RULES OF GENERAL APPLICATION... of 1930, or (2) a matter under an investigation pursuant to section 202 of the Trade Act of 1974 (19...

19 CFR 201.4 - Performance of functions.

Code of Federal Regulations, 2014 CFR

2014-04-01

... 19 Customs Duties 3 2014-04-01 2014-04-01 false Performance of functions. 201.4 Section 201.4 Customs Duties UNITED STATES INTERNATIONAL TRADE COMMISSION GENERAL RULES OF GENERAL APPLICATION... of 1930, or (2) a matter under an investigation pursuant to section 202 of the Trade Act of 1974 (19...

A Selected Bibliography of Functional Literacy Materials for Adult Learners.

ERIC Educational Resources Information Center

Berg, Joann La Perla; Wallace, Virginia A.

This document is a selected, annotated bibliography of materials published in the area of coping skills for adults with functional reading skills. Publications are listed alphabetically by title under the following general topics: general coping skills; newspapers; occupational information; consumer economics; pregnancy and parenting; housing;…

Intrinsic Functional Connectivity of Amygdala-Based Networks in Adolescent Generalized Anxiety Disorder

ERIC Educational Resources Information Center

Roy, Amy K.; Fudge, Julie L.; Kelly, Clare; Perry, Justin S. A.; Daniele, Teresa; Carlisi, Christina; Benson, Brenda; Castellanos, F. Xavier; Milham, Michael P.; Pine, Daniel S.; Ernst, Monique

2013-01-01

Objective: Generalized anxiety disorder (GAD) typically begins during adolescence and can persist into adulthood. The pathophysiological mechanisms underlying this disorder remain unclear. Recent evidence from resting state functional magnetic resonance imaging (R-fMRI) studies in adults suggests disruptions in amygdala-based circuitry; the…

Structural optimization of framed structures using generalized optimality criteria

NASA Technical Reports Server (NTRS)

Kolonay, R. M.; Venkayya, Vipperla B.; Tischler, V. A.; Canfield, R. A.

1989-01-01

The application of a generalized optimality criteria to framed structures is presented. The optimality conditions, Lagrangian multipliers, resizing algorithm, and scaling procedures are all represented as a function of the objective and constraint functions along with their respective gradients. The optimization of two plane frames under multiple loading conditions subject to stress, displacement, generalized stiffness, and side constraints is presented. These results are compared to those found by optimizing the frames using a nonlinear mathematical programming technique.

A statistical mechanical approach to restricted integer partition functions

NASA Astrophysics Data System (ADS)

Zhou, Chi-Chun; Dai, Wu-Sheng

2018-05-01

The main aim of this paper is twofold: (1) suggesting a statistical mechanical approach to the calculation of the generating function of restricted integer partition functions which count the number of partitions—a way of writing an integer as a sum of other integers under certain restrictions. In this approach, the generating function of restricted integer partition functions is constructed from the canonical partition functions of various quantum gases. (2) Introducing a new type of restricted integer partition functions corresponding to general statistics which is a generalization of Gentile statistics in statistical mechanics; many kinds of restricted integer partition functions are special cases of this restricted integer partition function. Moreover, with statistical mechanics as a bridge, we reveal a mathematical fact: the generating function of restricted integer partition function is just the symmetric function which is a class of functions being invariant under the action of permutation groups. Using this approach, we provide some expressions of restricted integer partition functions as examples.

Action-angle formulation of generalized, orbit-based, fast-ion diagnostic weight functions

NASA Astrophysics Data System (ADS)

Stagner, L.; Heidbrink, W. W.

2017-09-01

Due to the usually complicated and anisotropic nature of the fast-ion distribution function, diagnostic velocity-space weight functions, which indicate the sensitivity of a diagnostic to different fast-ion velocities, are used to facilitate the analysis of experimental data. Additionally, when velocity-space weight functions are discretized, a linear equation relating the fast-ion density and the expected diagnostic signal is formed. In a technique known as velocity-space tomography, many measurements can be combined to create an ill-conditioned system of linear equations that can be solved using various computational methods. However, when velocity-space weight functions (which by definition ignore spatial dependencies) are used, velocity-space tomography is restricted, both by the accuracy of its forward model and also by the availability of spatially overlapping diagnostic measurements. In this work, we extend velocity-space weight functions to a full 6D generalized coordinate system and then show how to reduce them to a 3D orbit-space without loss of generality using an action-angle formulation. Furthermore, we show how diagnostic orbit-weight functions can be used to infer the full fast-ion distribution function, i.e., orbit tomography. In depth derivations of orbit weight functions for the neutron, neutral particle analyzer, and fast-ion D-α diagnostics are also shown.

Double-hybrid density-functional theory with meta-generalized-gradient approximations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Souvi, Sidi M. O., E-mail: sidi.souvi@irsn.fr; Sharkas, Kamal; Toulouse, Julien, E-mail: julien.toulouse@upmc.fr

2014-02-28

We extend the previously proposed one-parameter double-hybrid density-functional theory [K. Sharkas, J. Toulouse, and A. Savin, J. Chem. Phys. 134, 064113 (2011)] to meta-generalized-gradient-approximation (meta-GGA) exchange-correlation density functionals. We construct several variants of one-parameter double-hybrid approximations using the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA functional and test them on test sets of atomization energies and reaction barrier heights. The most accurate variant uses the uniform coordinate scaling of the density and of the kinetic energy density in the correlation functional, and improves over both standard Kohn-Sham TPSS and second-order Møller-Plesset calculations.

28 CFR 3.2 - Assistant Attorney General, Criminal Division.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 28 Judicial Administration 1 2010-07-01 2010-07-01 false Assistant Attorney General, Criminal... Attorney General, Criminal Division. The Assistant Attorney General, Criminal Division, is authorized to exercise the power and authority of and to perform the functions vested in the Attorney General by the Act...

A Loomis-Sikorski theorem and functional calculus for a generalized Hermitian algebra

NASA Astrophysics Data System (ADS)

Foulis, David J.; Jenčová, Anna; Pulmannová, Sylvia

2017-10-01

A generalized Hermitian (GH-) algebra is a generalization of the partially ordered Jordan algebra of all Hermitian operators on a Hilbert space. We introduce the notion of a gh-tribe, which is a commutative GH-algebra of functions on a nonempty set X with pointwise partial order and operations, and we prove that every commutative GH-algebra is the image of a gh-tribe under a surjective GH-morphism. Using this result, we prove that each element a of a GH-algebra A corresponds to a real observable ξa on the σ-orthomodular lattice of projections in A and that ξa determines the spectral resolution of a. Also, if f is a continuous function defined on the spectrum of a, we formulate a definition of f (a), thus obtaining a continuous functional calculus for A.

Statistical Mechanics of Node-perturbation Learning with Noisy Baseline

NASA Astrophysics Data System (ADS)

Hara, Kazuyuki; Katahira, Kentaro; Okada, Masato

2017-02-01

Node-perturbation learning is a type of statistical gradient descent algorithm that can be applied to problems where the objective function is not explicitly formulated, including reinforcement learning. It estimates the gradient of an objective function by using the change in the object function in response to the perturbation. The value of the objective function for an unperturbed output is called a baseline. Cho et al. proposed node-perturbation learning with a noisy baseline. In this paper, we report on building the statistical mechanics of Cho's model and on deriving coupled differential equations of order parameters that depict learning dynamics. We also show how to derive the generalization error by solving the differential equations of order parameters. On the basis of the results, we show that Cho's results are also apply in general cases and show some general performances of Cho's model.

Generalized Constitutive-Based Theoretical and Empirical Models for Hot Working Behavior of Functionally Graded Steels

NASA Astrophysics Data System (ADS)

Vanini, Seyed Ali Sadough; Abolghasemzadeh, Mohammad; Assadi, Abbas

2013-07-01

Functionally graded steels with graded ferritic and austenitic regions including bainite and martensite intermediate layers produced by electroslag remelting have attracted much attention in recent years. In this article, an empirical model based on the Zener-Hollomon (Z-H) constitutive equation with generalized material constants is presented to investigate the effects of temperature and strain rate on the hot working behavior of functionally graded steels. Next, a theoretical model, generalized by strain compensation, is developed for the flow stress estimation of functionally graded steels under hot compression based on the phase mixture rule and boundary layer characteristics. The model is used for different strains and grading configurations. Specifically, the results for αβγMγ steels from empirical and theoretical models showed excellent agreement with those of experiments of other references within acceptable error.

A concise introduction to Colombeau generalized functions and their applications in classical electrodynamics

NASA Astrophysics Data System (ADS)

Gsponer, Andre

2009-01-01

The objective of this introduction to Colombeau algebras of generalized functions (in which distributions can be freely multiplied) is to explain in elementary terms the essential concepts necessary for their application to basic nonlinear problems in classical physics. Examples are given in hydrodynamics and electrodynamics. The problem of the self-energy of a point electric charge is worked out in detail: the Coulomb potential and field are defined as Colombeau generalized functions, and integrals of nonlinear expressions corresponding to products of distributions (such as the square of the Coulomb field and the square of the delta function) are calculated. Finally, the methods introduced in Gsponer (2007 Eur. J. Phys. 28 267, 2007 Eur. J. Phys. 28 1021 and 2007 Eur. J. Phys. 28 1241), to deal with point-like singularities in classical electrodynamics are confirmed.

Executive functions deficits impair extinction of generalization of fear of movement-related pain.

PubMed

Niederstrasser, N G; Meulders, A; Meulders, M; Struyf, D; Vlaeyen, J W

2017-05-01

Generalization of fear of movement-related pain across novel but similar movements can lead to fear responses to movements that are actually not associated with pain. The peak-shift effect describes a phenomenon whereby particular novel movements elicit even greater fear responses than the original pain-provoking movement (CS+), because they represent a more extreme version of the CS+. There is great variance in the propensity to generalize as well as the speed of extinction learning when these novel movements are not followed by pain. It can be argued that this variance may be associated with executive function capacity, as individuals may be unable to intentionally inhibit fear responses. This study examined whether executive function capacity contributes to generalization and extinction of generalization as well as peak-shift of conditioned fear of movement-related pain and expectancy. Healthy participants performed a proprioceptive fear conditioning task. Executive function tests assessing updating, switching, and inhibition were used to predict changes in (extinction of) fear of movement-related pain and pain expectancy generalization. Low inhibitory capacity was associated with slower extinction of generalized fear of movement-related pain and pain expectancy. Evidence was found in favor of an area-shift, rather than a peak-shift effect, which implies that the peak conditioned fear response extended to, but did not shift to a novel stimulus. Participants with low inhibitory capacity may have difficulties withholding fear responses, leading to a slower decrease of generalized fear over time. The findings may be relevant to inform treatments. Low inhibitory capacity is not associated with slower generalization, but extinction of fear generalization. Fear elicited by a novel safe movement, situated outside the CS+/- continuum on the CS+ side, can be as strong as to the original stimulus predicting the pain-onset. © 2017 European Pain Federation - EFIC®.

Is there a generalized anomeric effect? Analyses from energy components and information-theoretic quantities from density functional reactivity theory

NASA Astrophysics Data System (ADS)

Cao, Xiaofang; Liu, Shaoqian; Rong, Chunying; Lu, Tian; Liu, Shubin

2017-11-01

The nature and origin of the generalized anomeric effect is investigated with energy components and information-theoretic quantities from density functional reactivity theory. Forty-five systems with the general formula of R1-X-CH2-Y-R2 were examined, where R1 and R2 are functional groups and X and Y as electronegative heteroatoms. Our results show that in most cases the effect is valid, and the dominant contribution for the validity of the effect is from the electrostatic interaction. Other contributions such as steric and hyperconjugation play minor but indispensable roles. Its relationship with the conventional anomeric effect is compared and discussed.

Minority stress and relationship functioning among young male same-sex couples: An examination of actor-partner interdependence models.

PubMed

Feinstein, Brian A; McConnell, Elizabeth; Dyar, Christina; Mustanski, Brian; Newcomb, Michael E

2018-05-01

In different-sex couples, individual and partner stress can both have a negative impact on relationship functioning (actor and partner effects). Gay and bisexual men experience unique stress (sexual minority stress), but few studies have examined the effects of this stress on relationship functioning among young male couples. The current study examined (a) actor and partner effects of general and minority stress (internalized stigma, microaggressions, victimization, and outness) on relationship functioning (relationship quality and negative relationship interactions), (b) interactions between individual and partner stress as predictors of relationship functioning, and (c) dyadic coping and relationship length as moderators of actor and partner effects. Actor-partner interdependence models were tested using data from 153 young male couples. There was strong support for actor effects. Higher general stress and internalized stigma were associated with lower relationship quality, but only for those in longer relationships. Additionally, higher general stress, internalized stigma, and microaggressions, and lower outness, were associated with more negative relationship interactions. There was limited support for partner effects. Having a partner with higher internalized stigma was associated with more negative relationship interactions, but none of the other partner effects were significant. There was no support for individual and partner stress interacting to predict relationship functioning or for dyadic coping as a stress buffer. Findings highlight the influence of one's own experiences of general and minority stress on relationship functioning, but raise questions about how partner stress influences relationship functioning among young male couples. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Multireference Density Functional Theory with Generalized Auxiliary Systems for Ground and Excited States.

PubMed

Chen, Zehua; Zhang, Du; Jin, Ye; Yang, Yang; Su, Neil Qiang; Yang, Weitao

2017-09-21

To describe static correlation, we develop a new approach to density functional theory (DFT), which uses a generalized auxiliary system that is of a different symmetry, such as particle number or spin, from that of the physical system. The total energy of the physical system consists of two parts: the energy of the auxiliary system, which is determined with a chosen density functional approximation (DFA), and the excitation energy from an approximate linear response theory that restores the symmetry to that of the physical system, thus rigorously leading to a multideterminant description of the physical system. The electron density of the physical system is different from that of the auxiliary system and is uniquely determined from the functional derivative of the total energy with respect to the external potential. Our energy functional is thus an implicit functional of the physical system density, but an explicit functional of the auxiliary system density. We show that the total energy minimum and stationary states, describing the ground and excited states of the physical system, can be obtained by a self-consistent optimization with respect to the explicit variable, the generalized Kohn-Sham noninteracting density matrix. We have developed the generalized optimized effective potential method for the self-consistent optimization. Among options of the auxiliary system and the associated linear response theory, reformulated versions of the particle-particle random phase approximation (pp-RPA) and the spin-flip time-dependent density functional theory (SF-TDDFT) are selected for illustration of principle. Numerical results show that our multireference DFT successfully describes static correlation in bond dissociation and double bond rotation.

The construction of general basis functions in reweighting ensemble dynamics simulations: Reproduce equilibrium distribution in complex systems from multiple short simulation trajectories

NASA Astrophysics Data System (ADS)

Zhang, Chuan-Biao; Ming, Li; Xin, Zhou

2015-12-01

Ensemble simulations, which use multiple short independent trajectories from dispersive initial conformations, rather than a single long trajectory as used in traditional simulations, are expected to sample complex systems such as biomolecules much more efficiently. The re-weighted ensemble dynamics (RED) is designed to combine these short trajectories to reconstruct the global equilibrium distribution. In the RED, a number of conformational functions, named as basis functions, are applied to relate these trajectories to each other, then a detailed-balance-based linear equation is built, whose solution provides the weights of these trajectories in equilibrium distribution. Thus, the sufficient and efficient selection of basis functions is critical to the practical application of RED. Here, we review and present a few possible ways to generally construct basis functions for applying the RED in complex molecular systems. Especially, for systems with less priori knowledge, we could generally use the root mean squared deviation (RMSD) among conformations to split the whole conformational space into a set of cells, then use the RMSD-based-cell functions as basis functions. We demonstrate the application of the RED in typical systems, including a two-dimensional toy model, the lattice Potts model, and a short peptide system. The results indicate that the RED with the constructions of basis functions not only more efficiently sample the complex systems, but also provide a general way to understand the metastable structure of conformational space. Project supported by the National Natural Science Foundation of China (Grant No. 11175250).

Toward a general theory of conical intersections in systems of identical nuclei

NASA Astrophysics Data System (ADS)

Keating, Sean P.; Mead, C. Alden

1987-02-01

It has been shown previously that the Herzberg-Longuet-Higgins sign change produced in Born-Oppenheimer electronic wave functions when the nuclei traverse a closed path around a conical intersection has implications for the symmetry of wave functions under permutations of identical nuclei. For systems of three or four identical nuclei, there are special features present which have facilitated the detailed analysis. The present paper reports progress toward a general theory for systems of n nuclei. For n=3 or 4, the two key functions which locate conical intersections and define compensating phase factors can conveniently be defined so as to transform under permutations according to a two-dimensional irreducible representation of the permutation group. Since such representations do not exist for n>4, we have chosen to develop a formalism in terms of lab-fixed electronic basis functions, and we show how to define the two key functions in principle. The functions so defined both turn out to be totally symmetric under permutations. We show how they can be used to define compensating phase factors so that all modified electronic wave functions are either totally symmetric or totally antisymmetric under permutations. A detailed analysis is made to cyclic permutations in the neighborhood of Dnh symmetry, which can be extended by continuity arguments to more general configurations, and criteria are obtained for sign changes. There is a qualitative discussion of the treatment of more general permutations.

18 CFR 376.104 - Functions.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 18 Conservation of Power and Water Resources 1 2010-04-01 2010-04-01 false Functions. 376.104... OF ENERGY REVISED GENERAL RULES ORGANIZATION, MISSION, AND FUNCTIONS; OPERATIONS DURING EMERGENCY CONDITIONS Organization, Mission, and Functions § 376.104 Functions. The functions of the Commission include...

[Examination of diagnosis procedure combination survey data that influence function evaluation coefficient II].

PubMed

Nakajima, Hisato; Yano, Kouya; Nagasawa, Kaoko; Kobayashi, Eiji; Yokota, Kuninobu

2015-01-01

On the basis of Diagnosis Procedure Combination (DPC) survey data, the factors that increase the value of function evaluation coefficient II were considered. A total of 1,505 hospitals were divided into groups I, II, and III, and the following items were considered. 1. Significant differences in function evaluation coefficient II and DPC survey data. 2. Examination of using the Mahalanobis-Taguchi (MT) method. 3. Correlation between function evaluation coefficient II and each DPC survey data item. 1. Function evaluation coefficient II was highest in group II. Group I hospitals showed the highest bed capacity, and numbers of hospitalization days, operations, chemotherapies, radiotherapies and general anesthesia procedures. 2. Using the MT method, we found that the number of ambulance conveyances was effective factor in group I hospitals, the number of general anesthesia procedures was effective factor in group II hospitals, and the bed capacity was effective factor in group III hospitals. 3. In group I hospitals, function evaluation coefficient II significantly correlated to the numbers of ambulance conveyances and chemotherapies. In group II hospitals, function evaluation coefficient II significantly correlated to bed capacity, the numbers of ambulance conveyances, hospitalization days, operations, general anesthesia procedures, and mean hospitalization days. In group III hospitals, function evaluation coefficient II significantly correlated to all items. The factors that improve the value of function evaluation coefficient II were the increases in the numbers of ambulance conveyances, chemotherapies and radiotherapies in group I hospitals, increases in the numbers of hospitalization days, operations, ambulance conveyances and general anesthesia procedures in group II hospitals, and increases in the numbers of hospitalization days, operations and ambulance conveyances. These results indicate that the profit of a hospital will increase, which will lead to medical services of good quality.

Reliability and validity of a short version of the general functioning subscale of the McMaster Family Assessment Device.

PubMed

Boterhoven de Haan, Katrina L; Hafekost, Jennifer; Lawrence, David; Sawyer, Michael G; Zubrick, Stephen R

2015-03-01

The General Functioning 12-item subscale (GF12) of The McMaster Family Assessment Device (FAD) has been validated as a single index measure to assess family functioning. This study reports on the reliability and validity of using only the six positive items from the General Functioning subscale (GF6+). Existing data from two Western Australian studies, the Raine Study (RS) and the Western Australian Child Health Survey (WACHS), was used to analyze the psychometric properties of the GF6+ subscale. The results demonstrated that the GF6+ subscale had virtually equivalent psychometric properties and was able to identify almost all of the same families who had healthy or unhealthy levels of functioning as the full GF12 subscale. In consideration of the constraints faced by large-scale population-based surveys, the findings of this study support the use of a GF6+ subscale from the FAD, as a quick and effective tool to assess the overall functioning of families. © 2014 Family Process Institute.

General method of solving the Schroedinger equation of atoms and molecules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakatsuji, Hiroshi

2005-12-15

We propose a general method of solving the Schroedinger equation of atoms and molecules. We first construct the wave function having the exact structure, using the ICI (iterative configuration or complement interaction) method and then optimize the variables involved by the variational principle. Based on the scaled Schroedinger equation and related principles, we can avoid the singularity problem of atoms and molecules and formulate a general method of calculating the exact wave functions in an analytical expansion form. We choose initial function {psi}{sub 0} and scaling g function, and then the ICI method automatically generates the wave function that hasmore » the exact structure by using the Hamiltonian of the system. The Hamiltonian contains all the information of the system. The free ICI method provides a flexible and variationally favorable procedure of constructing the exact wave function. We explain the computational procedure of the analytical ICI method routinely performed in our laboratory. Simple examples are given using hydrogen atom for the nuclear singularity case, the Hooke's atom for the electron singularity case, and the helium atom for both cases.« less

Momentum constraints as integrability conditions for the Hamiltonian constraint in general relativity.

NASA Technical Reports Server (NTRS)

Moncrief, V.; Teitelboim, C.

1972-01-01

It is shown that if the Hamiltonian constraint of general relativity is imposed as a restriction on the Hamilton principal functional in the classical theory, or on the state functional in the quantum theory, then the momentum constraints are automatically satisfied. This result holds both for closed and open spaces and it means that the full content of the theory is summarized by a single functional equation of the Tomonaga-Schwinger type.

Functional Techniques for Data Analysis

NASA Technical Reports Server (NTRS)

Tomlinson, John R.

1997-01-01

This dissertation develops a new general method of solving Prony's problem. Two special cases of this new method have been developed previously. They are the Matrix Pencil and the Osculatory Interpolation. The dissertation shows that they are instances of a more general solution type which allows a wide ranging class of linear functional to be used in the solution of the problem. This class provides a continuum of functionals which provide new methods that can be used to solve Prony's problem.

Personal Perspectives about Sustaining Inclusion in School Environments for Children with High Functioning Autism

ERIC Educational Resources Information Center

Wiatr, Jeanne Malecki

2016-01-01

Students, at a partial hospital setting in Western Tennessee with high functioning autism spectrum disorders (HFASD) were being removed from general education classrooms. Researchers have indicated that restrictive settings preclude interaction with neurotypical peers and access to general education experiences. The purpose of this case study was…

Association between Speech-Language, General Cognitive Functioning and Behaviour Problems in Individuals with Williams Syndrome

ERIC Educational Resources Information Center

Rossi, N. F.; Giacheti, C. M.

2017-01-01

Background: Williams syndrome (WS) phenotype is described as unique and intriguing. The aim of this study was to investigate the associations between speech-language abilities, general cognitive functioning and behavioural problems in individuals with WS, considering age effects and speech-language characteristics of WS sub-groups. Methods: The…

Generalized Variance Function Applications in Forestry

Treesearch

James Alegria; Charles T. Scott; Charles T. Scott

1991-01-01

Adequately predicting the sampling errors of tabular data can reduce printing costs by eliminating the need to publish separate sampling error tables. Two generalized variance functions (GVFs) found in the literature and three GVFs derived for this study were evaluated for their ability to predict the sampling error of tabular forestry estimates. The recommended GVFs...

A systematic study of finite BRST-BFV transformations in generalized Hamiltonian formalism

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.

2014-09-01

We study systematically finite BRST-BFV transformations in the generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate an arbitrary finite change of gauge-fixing functions in the path integral.

28 CFR 0.128a - General functions.

Code of Federal Regulations, 2011 CFR

2011-07-01

... of military operations during World War II and claims of U.S. military personnel and civilian American citizens for having been held in a captured status in specified areas during World War II, the... 28 Judicial Administration 1 2011-07-01 2011-07-01 false General functions. 0.128a Section 0.128a...

28 CFR 0.128a - General functions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... of military operations during World War II and claims of U.S. military personnel and civilian American citizens for having been held in a captured status in specified areas during World War II, the... 28 Judicial Administration 1 2010-07-01 2010-07-01 false General functions. 0.128a Section 0.128a...

28 CFR 0.128a - General functions.

Code of Federal Regulations, 2013 CFR

2013-07-01

... of military operations during World War II and claims of U.S. military personnel and civilian American citizens for having been held in a captured status in specified areas during World War II, the... 28 Judicial Administration 1 2013-07-01 2013-07-01 false General functions. 0.128a Section 0.128a...

28 CFR 0.128a - General functions.

Code of Federal Regulations, 2014 CFR

2014-07-01

... of military operations during World War II and claims of U.S. military personnel and civilian American citizens for having been held in a captured status in specified areas during World War II, the... 28 Judicial Administration 1 2014-07-01 2014-07-01 false General functions. 0.128a Section 0.128a...

28 CFR 0.128a - General functions.

Code of Federal Regulations, 2012 CFR

2012-07-01

... of military operations during World War II and claims of U.S. military personnel and civilian American citizens for having been held in a captured status in specified areas during World War II, the... 28 Judicial Administration 1 2012-07-01 2012-07-01 false General functions. 0.128a Section 0.128a...

Emitter Number Estimation by the General Information Theoretic Criterion from Pulse Trains

DTIC Science & Technology

2002-12-01

negative log likelihood function plus a penalty function. The general information criteria by Yin and Krishnaiah [11] are different from the regular...548-551, Victoria, BC, Canada, March 1999 DRDC Ottawa TR 2002-156 11 11. L. Zhao, P. P. Krishnaiah and Z. Bai, “On some nonparametric methods for

Demographic Accounting and Model-Building. Education and Development Technical Reports.

ERIC Educational Resources Information Center

Stone, Richard

This report describes and develops a model for coordinating a variety of demographic and social statistics within a single framework. The framework proposed, together with its associated methods of analysis, serves both general and specific functions. The general aim of these functions is to give numerical definition to the pattern of society and…

A Concise Introduction to Colombeau Generalized Functions and Their Applications in Classical Electrodynamics

ERIC Educational Resources Information Center

Gsponer, Andre

2009-01-01

The objective of this introduction to Colombeau algebras of generalized functions (in which distributions can be freely multiplied) is to explain in elementary terms the essential concepts necessary for their application to basic nonlinear problems in classical physics. Examples are given in hydrodynamics and electrodynamics. The problem of the…

14 CFR Sec. 2-3 - Distribution of revenues and expenses within entities.

Code of Federal Regulations, 2010 CFR

2010-01-01

... CERTIFICATED AIR CARRIERS General Accounting Provisions Sec. 2-3 Distribution of revenues and expenses within.... (c) Expense items contributing to more than one function shall be charged to the general overhead functions to which applicable except that where only incidental contribution is made to more than a single...

Acceptance of Personality Interpretations as a Function of Assessment Procedures

ERIC Educational Resources Information Center

Snyder, C. R.

1974-01-01

The purpose of the two present studies is to ascertain whether differential acceptance of the same general personality interpretation resulted as a function of telling seperate groups of individuals that their interpretation was based on a projective test, an interview, an objective test, or was "generally true of people." (Author)

Beta-function B-spline smoothing on triangulations

NASA Astrophysics Data System (ADS)

Dechevsky, Lubomir T.; Zanaty, Peter

2013-03-01

In this work we investigate a novel family of Ck-smooth rational basis functions on triangulations for fitting, smoothing, and denoising geometric data. The introduced basis function is closely related to a recently introduced general method introduced in utilizing generalized expo-rational B-splines, which provides Ck-smooth convex resolutions of unity on very general disjoint partitions and overlapping covers of multidimensional domains with complex geometry. One of the major advantages of this new triangular construction is its locality with respect to the star-1 neighborhood of the vertex on which the said base is providing Hermite interpolation. This locality of the basis functions can be in turn utilized in adaptive methods, where, for instance a local refinement of the underlying triangular mesh affects only the refined domain, whereas, in other method one needs to investigate what changes are occurring outside of the refined domain. Both the triangular and the general smooth constructions have the potential to become a new versatile tool of Computer Aided Geometric Design (CAGD), Finite and Boundary Element Analysis (FEA/BEA) and Iso-geometric Analysis (IGA).

Generalization and capacity of extensively large two-layered perceptrons.

PubMed

Rosen-Zvi, Michal; Engel, Andreas; Kanter, Ido

2002-09-01

The generalization ability and storage capacity of a treelike two-layered neural network with a number of hidden units scaling as the input dimension is examined. The mapping from the input to the hidden layer is via Boolean functions; the mapping from the hidden layer to the output is done by a perceptron. The analysis is within the replica framework where an order parameter characterizing the overlap between two networks in the combined space of Boolean functions and hidden-to-output couplings is introduced. The maximal capacity of such networks is found to scale linearly with the logarithm of the number of Boolean functions per hidden unit. The generalization process exhibits a first-order phase transition from poor to perfect learning for the case of discrete hidden-to-output couplings. The critical number of examples per input dimension, alpha(c), at which the transition occurs, again scales linearly with the logarithm of the number of Boolean functions. In the case of continuous hidden-to-output couplings, the generalization error decreases according to the same power law as for the perceptron, with the prefactor being different.

Shape functions for velocity interpolation in general hexahedral cells

USGS Publications Warehouse

Naff, R.L.; Russell, T.F.; Wilson, J.D.

2002-01-01

Numerical methods for grids with irregular cells require discrete shape functions to approximate the distribution of quantities across cells. For control-volume mixed finite-element (CVMFE) methods, vector shape functions approximate velocities and vector test functions enforce a discrete form of Darcy's law. In this paper, a new vector shape function is developed for use with irregular, hexahedral cells (trilinear images of cubes). It interpolates velocities and fluxes quadratically, because as shown here, the usual Piola-transformed shape functions, which interpolate linearly, cannot match uniform flow on general hexahedral cells. Truncation-error estimates for the shape function are demonstrated. CVMFE simulations of uniform and non-uniform flow with irregular meshes show first- and second-order convergence of fluxes in the L2 norm in the presence and absence of singularities, respectively.

47 CFR 10.500 - General requirements.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 47 Telecommunication 1 2010-10-01 2010-10-01 false General requirements. 10.500 Section 10.500 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL COMMERCIAL MOBILE ALERT SYSTEM Equipment Requirements § 10.500 General requirements. CMAS mobile device functionality is dependent on the capabilities of a...

Non-minimal Particle Creation from Asymptotic-de Sitter Inflation

NASA Astrophysics Data System (ADS)

Yusofi, E.; Mohsenzadeh, M.

2018-06-01

A general form of quasi-de Sitter(dS) modes is used to study the creation of particle during the inflation. Actually, by considering the general form of inflaton field equation as a function of the Hankel function index and by using the Planck 2015 constraint on spectral index, we obtain the possible new constraints for the values of coupling constant in the era with asymptotic-dS space-time. Then, we explicitly calculate the general form of expectation value of the created particles in terms of the Hankel function index and the conformal time. The correction terms in the number of created particles are very tiny in the early time but can have the significant effects in the later universe. Our result is general and at the early time limit confirm the conventional special results for the Minkowski and dS background.

Ambulatory cancer and US general population reference values and cutoff scores for the functional assessment of cancer therapy.

PubMed

Pearman, Timothy; Yanez, Betina; Peipert, John; Wortman, Katy; Beaumont, Jennifer; Cella, David

2014-09-15

Health-related quality of life (HRQOL) measures are commonly used in oncology research. Interest in their use for monitoring or screening is increasing. The Functional Assessment of Cancer Therapy (FACT) is one of the most widely used HRQOL instruments. Consequently, oncology researchers and practitioners have an increasing need for reference values for the Functional Assessment of Cancer Therapy-General (FACT-G) and its 7-item rapid version, the Functional Assessment of Cancer Therapy-General 7 (FACT-G7), to compare FACT scores across specific subgroups of patients in research trials and practice. The objectives of this study are to provide 1) reference values from a sample of the general US adult population and a sample of adults diagnosed with cancer and 2) cutoff scores for quality of life. A sample of the general US population (N = 1075) and a sample of patients with cancer from 12 studies (N = 5065) were analyzed. Cutoff scores were established using distribution- and anchor-based methods. Mean values for the cancer sample were analyzed by performance status, cancer type, and disease status. Also, t tests and established criteria for meaningful differences were used to compare values. FACT-G and FACT-G7 scores in the general US population sample and cancer sample were generally comparable. Among the sample of patients with cancer, FACT-G and FACT-G7 scores worsened with declining performance status and increasing disease status. These data will aid interpretation of the magnitude and meaning of FACT scores, and allow for comparisons of scores across studies. © 2014 American Cancer Society.

A unified stochastic formulation of dissipative quantum dynamics. I. Generalized hierarchical equations

NASA Astrophysics Data System (ADS)

Hsieh, Chang-Yu; Cao, Jianshu

2018-01-01

We extend a standard stochastic theory to study open quantum systems coupled to a generic quantum environment. We exemplify the general framework by studying a two-level quantum system coupled bilinearly to the three fundamental classes of non-interacting particles: bosons, fermions, and spins. In this unified stochastic approach, the generalized stochastic Liouville equation (SLE) formally captures the exact quantum dissipations when noise variables with appropriate statistics for different bath models are applied. Anharmonic effects of a non-Gaussian bath are precisely encoded in the bath multi-time correlation functions that noise variables have to satisfy. Starting from the SLE, we devise a family of generalized hierarchical equations by averaging out the noise variables and expand bath multi-time correlation functions in a complete basis of orthonormal functions. The general hierarchical equations constitute systems of linear equations that provide numerically exact simulations of quantum dynamics. For bosonic bath models, our general hierarchical equation of motion reduces exactly to an extended version of hierarchical equation of motion which allows efficient simulation for arbitrary spectral densities and temperature regimes. Similar efficiency and flexibility can be achieved for the fermionic bath models within our formalism. The spin bath models can be simulated with two complementary approaches in the present formalism. (I) They can be viewed as an example of non-Gaussian bath models and be directly handled with the general hierarchical equation approach given their multi-time correlation functions. (II) Alternatively, each bath spin can be first mapped onto a pair of fermions and be treated as fermionic environments within the present formalism.

New rules meet established sickness certification practice: A focus-group study on the introduction of functional assessments in Norwegian primary care

PubMed Central

Krohne, Kariann; Brage, Søren

2007-01-01

Objective To explore how general practitioners view and handle new standards for functional assessments in sickness certification practice. Design Qualitative study using focus group interviews. Data were analysed according to Giorgi's phenomenological approach and supported by theories on knowledge. Setting General practitioners from three neighbouring counties in Norway. Subjects Four focus groups with a total of 23 participants were recruited through the Norwegian Medical Association and its Continuous Medical Education system. Results The participants reported difficulties and reluctance to act in accordance with new functional assessment demands on both a practical and a conceptual level. In established sickness certification practice functional assessment was described as an unspoken part of the medical examination. After the introduction of formal, written functional assessments they identified problems of terminology, communication, and trust. Strategies were developed to circumvent these problems. Conclusions A gap was noticeable between the participants’ established practice and the new standards’ demand for a more theoretical and communicative functional assessment. The general lack of training, being confronted with new terminology, and increasingly high pressure to reduce sickness absences create an atmosphere of insecurity when assessing function. PMID:17846936

Local-scale Partitioning of Functional and Phylogenetic Beta Diversity in a Tropical Tree Assemblage.

PubMed

Yang, Jie; Swenson, Nathan G; Zhang, Guocheng; Ci, Xiuqin; Cao, Min; Sha, Liqing; Li, Jie; Ferry Slik, J W; Lin, Luxiang

2015-08-03

The relative degree to which stochastic and deterministic processes underpin community assembly is a central problem in ecology. Quantifying local-scale phylogenetic and functional beta diversity may shed new light on this problem. We used species distribution, soil, trait and phylogenetic data to quantify whether environmental distance, geographic distance or their combination are the strongest predictors of phylogenetic and functional beta diversity on local scales in a 20-ha tropical seasonal rainforest dynamics plot in southwest China. The patterns of phylogenetic and functional beta diversity were generally consistent. The phylogenetic and functional dissimilarity between subplots (10 × 10 m, 20 × 20 m, 50 × 50 m and 100 × 100 m) was often higher than that expected by chance. The turnover of lineages and species function within habitats was generally slower than that across habitats. Partitioning the variation in phylogenetic and functional beta diversity showed that environmental distance was generally a better predictor of beta diversity than geographic distance thereby lending relatively more support for deterministic environmental filtering over stochastic processes. Overall, our results highlight that deterministic processes play a stronger role than stochastic processes in structuring community composition in this diverse assemblage of tropical trees.

Expanded function allied dental personnel and dental practice productivity and efficiency.

PubMed

Beazoglou, Tryfon J; Chen, Lei; Lazar, Vickie F; Brown, L Jackson; Ray, Subhash C; Heffley, Dennis R; Berg, Rob; Bailit, Howard L

2012-08-01

This study examined the impact of expanded function allied dental personnel on the productivity and efficiency of general dental practices. Detailed practice financial and clinical data were obtained from a convenience sample of 154 general dental practices in Colorado. In this state, expanded function dental assistants can provide a wide range of reversible dental services/procedures, and dental hygienists can give local anesthesia. The survey identified practices that currently use expanded function allied dental personnel and the specific services/procedures delegated. Practice productivity was measured using patient visits, gross billings, and net income. Practice efficiency was assessed using a multivariate linear program, Data Envelopment Analysis. Sixty-four percent of the practices were found to use expanded function allied dental personnel, and on average they delegated 31.4 percent of delegatable services/procedures. Practices that used expanded function allied dental personnel treated more patients and had higher gross billings and net incomes than those practices that did not; the more services they delegated, the higher was the practice's productivity and efficiency. The effective use of expanded function allied dental personnel has the potential to substantially expand the capacity of general dental practices to treat more patients and to generate higher incomes for dental practices.

Generalized hamming networks and applications.

PubMed

Koutroumbas, Konstantinos; Kalouptsidis, Nicholas

2005-09-01

In this paper the classical Hamming network is generalized in various ways. First, for the Hamming maxnet, a generalized model is proposed, which covers under its umbrella most of the existing versions of the Hamming Maxnet. The network dynamics are time varying while the commonly used ramp function may be replaced by a much more general non-linear function. Also, the weight parameters of the network are time varying. A detailed convergence analysis is provided. A bound on the number of iterations required for convergence is derived and its distribution functions are given for the cases where the initial values of the nodes of the Hamming maxnet stem from the uniform and the peak distributions. Stabilization mechanisms aiming to prevent the node(s) with the maximum initial value diverging to infinity or decaying to zero are described. Simulations demonstrate the advantages of the proposed extension. Also, a rough comparison between the proposed generalized scheme as well as the original Hamming maxnet and its variants is carried out in terms of the time required for convergence, in hardware implementations. Finally, the other two parts of the Hamming network, namely the competitors generating module and the decoding module, are briefly considered in the framework of various applications such as classification/clustering, vector quantization and function optimization.

Inflammatory Profile of Awake Function-Controlled Craniotomy and Craniotomy under General Anesthesia

PubMed Central

Klimek, Markus; Hol, Jaap W.; Wens, Stephan; Heijmans-Antonissen, Claudia; Niehof, Sjoerd; Vincent, Arnaud J.; Klein, Jan; Zijlstra, Freek J.

2009-01-01

Background. Surgical stress triggers an inflammatory response and releases mediators into human plasma such as interleukins (ILs). Awake craniotomy and craniotomy performed under general anesthesia may be associated with different levels of stress. Our aim was to investigate whether those procedures cause different inflammatory responses. Methods. Twenty patients undergoing craniotomy under general anesthesia and 20 patients undergoing awake function-controlled craniotomy were included in this prospective, observational, two-armed study. Circulating levels of IL-6, IL-8, and IL-10 were determined pre-, peri-, and postoperatively in both patient groups. VAS scores for pain, anxiety, and stress were taken at four moments pre- and postoperatively to evaluate physical pain and mental duress. Results. Plasma IL-6 level significantly increased with time similarly in both groups. No significant plasma IL-8 and IL-10 change was observed in both experimental groups. The VAS pain score was significantly lower in the awake group compared to the anesthesia group at 12 hours postoperative. Postoperative anxiety and stress declined similarly in both groups. Conclusion. This study suggests that awake function-controlled craniotomy does not cause a significantly different inflammatory response than craniotomy performed under general anesthesia. It is also likely that function-controlled craniotomy does not cause a greater emotional challenge than tumor resection under general anesthesia. PMID:19536349

Pond tadpoles with generalized morphology: is it time to reconsider their functional roles in aquatic communities?

PubMed

Petranka, James W; Kennedy, Caroline A

1999-09-01

With rare exceptions, anuran larvae have traditionally been considered to occupy lower trophic levels in aquatic communities where they function as microphagous suspension feeders. This view is being challenged by studies showing that tadpoles with generalized morphology often function as macrophagous predators. Here, we review the literature concerning macrophagy by tadpoles and provide two additional examples involving generalized tadpoles. In the first, we demonstrate with laboratory and field experiments that wood frog (Rana sylvatica) tadpoles are major predators of macroinvertebrates in ponds. In the second, we show that green frog (R. clamitans) tadpoles can cause catastrophic reproductive failure of the wood frog via egg predation. These results and data from other studies challenge the assumption that generalized tadpoles function as filter-feeding omnivores, and question the general applicability of community organization models which assume that predation risk increases with pond permanence. We suggest that predation risk is greater in temporary ponds than in more permanent ponds for many organisms that are vulnerable to predation by tadpoles. This being so, a conditional model based upon interactions that are species-specific, life-stage-specific, and context-dependent may better explain community organization along hydrological gradients than models which assume that temporary ponds have few or no predators.

Multitime correlation functions in nonclassical stochastic processes

NASA Astrophysics Data System (ADS)

Krumm, F.; Sperling, J.; Vogel, W.

2016-06-01

A general method is introduced for verifying multitime quantum correlations through the characteristic function of the time-dependent P functional that generalizes the Glauber-Sudarshan P function. Quantum correlation criteria are derived which identify quantum effects for an arbitrary number of points in time. The Magnus expansion is used to visualize the impact of the required time ordering, which becomes crucial in situations when the interaction problem is explicitly time dependent. We show that the latter affects the multi-time-characteristic function and, therefore, the temporal evolution of the nonclassicality. As an example, we apply our technique to an optical parametric process with a frequency mismatch. The resulting two-time-characteristic function yields full insight into the two-time quantum correlation properties of such a system.

Response of discrete linear systems to forcing functions with inequality constraints.

NASA Technical Reports Server (NTRS)

Michalopoulos, C. D.; Riley, T. A.

1972-01-01

An analysis is made of the maximum response of discrete, linear mechanical systems to arbitrary forcing functions which lie within specified bounds. Primary attention is focused on the complete determination of the forcing function which will engender maximum displacement to any particular mass element of a multi-degree-of-freedom system. In general, the desired forcing function is found to be a bang-bang type function, i.e., a function which switches from the maximum to the minimum bound and vice-versa at certain instants of time. Examples of two-degree-of-freedom systems, with and without damping, are presented in detail. Conclusions are drawn concerning the effect of damping on the switching times and the general procedure for finding these times is discussed.

Transient response of multidegree-of-freedom linear systems to forcing functions with inequality constraints

NASA Technical Reports Server (NTRS)

Michalopoulos, C. D.

1974-01-01

Optimal control theory is applied to analyze the transient response of discrete linear systems to forcing functions with unknown time dependence but having known bounds. Particular attention is given to forcing functions which include: (1) maximum displacement of any given mass element, (2) maximum relative displacement of any two adjacent masses, and (3) maximum acceleration of a given mass. Linear mechanical systems with an arbitrary number of degrees of freedom and only one forcing function acting are considered. In the general case, the desired forcing function is found to be a function that switches from the upper-to-lower bound and vice-versa at certain moments of time. A general procedure for finding such switching times is set forth.

The advantage of flexible neuronal tunings in neural network models for motor learning

PubMed Central

Marongelli, Ellisha N.; Thoroughman, Kurt A.

2013-01-01

Human motor adaptation to novel environments is often modeled by a basis function network that transforms desired movement properties into estimated forces. This network employs a layer of nodes that have fixed broad tunings that generalize across the input domain. Learning is achieved by updating the weights of these nodes in response to training experience. This conventional model is unable to account for rapid flexibility observed in human spatial generalization during motor adaptation. However, added plasticity in the widths of the basis function tunings can achieve this flexibility, and several neurophysiological experiments have revealed flexibility in tunings of sensorimotor neurons. We found a model, Locally Weighted Projection Regression (LWPR), which uniquely possesses the structure of a basis function network in which both the weights and tuning widths of the nodes are updated incrementally during adaptation. We presented this LWPR model with training functions of different spatial complexities and monitored incremental updates to receptive field widths. An inverse pattern of dependence of receptive field adaptation on experienced error became evident, underlying both a relationship between generalization and complexity, and a unique behavior in which generalization always narrows after a sudden switch in environmental complexity. These results implicate a model that is flexible in both basis function widths and weights, like LWPR, as a viable alternative model for human motor adaptation that can account for previously observed plasticity in spatial generalization. This theory can be tested by using the behaviors observed in our experiments as novel hypotheses in human studies. PMID:23888141

Cross-Cultural adaptation of the General Functioning Scale of the Family

PubMed Central

Pires, Thiago; de Assis, Simone Gonçalves; Avanci, Joviana Quintes; Pesce, Renata Pires

2016-01-01

ABSTRACT OBJECTIVE To describe the process of cross-cultural adaptation of the General Functioning Scale of the Family, a subscale of the McMaster Family Assessment Device, for the Brazilian population. METHODS The General Functioning Scale of the Family was translated into Portuguese and administered to 500 guardians of children in the second grade of elementary school in public schools of Sao Gonçalo, Rio de Janeiro, Southeastern Brazil. The types of equivalences investigated were: conceptual and of items, semantic, operational, and measurement. The study involved discussions with experts, translations and back-translations of the instrument, and psychometric assessment. Reliability and validity studies were carried out by internal consistency testing (Cronbach’s alpha), Guttman split-half correlation model, Pearson correlation coefficient, and confirmatory factor analysis. Associations between General Functioning of the Family and variables theoretically associated with the theme (father’s or mother’s drunkenness and violence between parents) were estimated by odds ratio. RESULTS Semantic equivalence was between 90.0% and 100%. Cronbach’s alpha ranged from 0.79 to 0.81, indicating good internal consistency of the instrument. Pearson correlation coefficient ranged between 0.303 and 0.549. Statistical association was found between the general functioning of the family score and the theoretically related variables, as well as good fit quality of the confirmatory analysis model. CONCLUSIONS The results indicate the feasibility of administering the instrument to the Brazilian population, as it is easy to understand and a good measurement of the construct of interest. PMID:27355464

Multicomponent Program to Reduce Functional Decline in Frail Elderly People: A Cluster Controlled Trial.

PubMed

Ruikes, Franca G H; Zuidema, Sytse U; Akkermans, Reinier P; Assendelft, Willem J J; Schers, Henk J; Koopmans, Raymond T C M

2016-01-01

The increasing number of community-dwelling frail elderly people poses a challenge to general practice. We evaluated the effectiveness of a general practitioner-led extensive, multicomponent program integrating cure, care, and welfare for the prevention of functional decline. We performed a cluster controlled trial in 12 general practices in Nijmegen, the Netherlands. Community-dwelling frail elderly people aged ≥70 years were identified with the EASY-Care two-step older persons screening instrument. In 6 general practices, 287 frail elderly received care according to the CareWell primary care program. This consisted of proactive care planning, case management, medication reviews, and multidisciplinary team meetings with a general practitioner, practice and/or community nurse, elderly care physician, and social worker. In another 6 general practices, 249 participants received care as usual. The primary outcome was independence in functioning during (instrumental) activities of daily living (Katz-15 index). Secondary outcomes were quality of life [EuroQol (EQ5D+C) instrument], mental health and health-related social functioning (36-item RAND Short Form survey instrument), institutionalization, hospitalization, and mortality. Outcomes were assessed at baseline and at 12 months, and were analyzed with linear mixed-model analyses. A total of 204 participants (71.1%) in the intervention group and 165 participants (66.3%) in the control group completed the study. No differences between groups regarding independence in functioning and secondary outcomes were found. We found no evidence for the effectiveness of a multifaceted integrated care program in the prevention of adverse outcomes in community-dwelling frail elderly people. Large-scale implementation of this program is not advocated. © Copyright 2016 by the American Board of Family Medicine.

A randomized, single-blind cross-over design evaluating the effectiveness of an individually defined, targeted physical therapy approach in treatment of children with cerebral palsy.

PubMed

Franki, Inge; Van den Broeck, Christine; De Cat, Josse; Tijhuis, Wieke; Molenaers, Guy; Vanderstraeten, Guy; Desloovere, Kaat

2014-10-01

A pilot study to compare the effectiveness of an individual therapy program with the effects of a general physical therapy program. A randomized, single-blind cross-over design. Ten ambulant children with bilateral spastic cerebral palsy, age four to nine years. Participants were randomly assigned into a ten-week individually defined, targeted or a general program, followed by a cross-over. Evaluation was performed using the Gross Motor Function Measure-88 and three-dimensional gait analysis. General outcome parameters were Gross Motor Function Measure-88 scores, time and distance parameters, gait profile score and movement analysis profiles. Individual goal achievement was evaluated using z-scores for gait parameters and Goal Attainment Scale for gross motor function. No significant changes were observed regarding gross motor function. Only after individualized therapy, step- and stride-length increased significantly (p = 0.022; p = 0.017). Change in step-length was higher after the individualized program (p = 0.045). Within-group effects were found for the pelvis in transversal plane after the individualized program (p = 0.047) and in coronal plane after the general program (p = 0.047). Between-program differences were found for changes in the knee in sagittal plane, in the advantage of the individual program (p = 0.047). A median difference in z-score of 0.279 and 0.419 was measured after the general and individualized program, respectively. Functional goal attainment was higher after the individual therapy program compared with the general program (48 to 43.5). The results indicate slightly favorable effects towards the individualized program. To detect clinically significant changes, future studies require a minimal sample size of 72 to 90 participants. © The Author(s) 2014.

Research of generalized wavelet transformations of Haar correctness in remote sensing of the Earth

NASA Astrophysics Data System (ADS)

Kazaryan, Maretta; Shakhramanyan, Mihail; Nedkov, Roumen; Richter, Andrey; Borisova, Denitsa; Stankova, Nataliya; Ivanova, Iva; Zaharinova, Mariana

2017-10-01

In this paper, Haar's generalized wavelet functions are applied to the problem of ecological monitoring by the method of remote sensing of the Earth. We study generalized Haar wavelet series and suggest the use of Tikhonov's regularization method for investigating them for correctness. In the solution of this problem, an important role is played by classes of functions that were introduced and described in detail by I.M. Sobol for studying multidimensional quadrature formulas and it contains functions with rapidly convergent series of wavelet Haar. A theorem on the stability and uniform convergence of the regularized summation function of the generalized wavelet-Haar series of a function from this class with approximate coefficients is proved. The article also examines the problem of using orthogonal transformations in Earth remote sensing technologies for environmental monitoring. Remote sensing of the Earth allows to receive from spacecrafts information of medium, high spatial resolution and to conduct hyperspectral measurements. Spacecrafts have tens or hundreds of spectral channels. To process the images, the device of discrete orthogonal transforms, and namely, wavelet transforms, was used. The aim of the work is to apply the regularization method in one of the problems associated with remote sensing of the Earth and subsequently to process the satellite images through discrete orthogonal transformations, in particular, generalized Haar wavelet transforms. General methods of research. In this paper, Tikhonov's regularization method, the elements of mathematical analysis, the theory of discrete orthogonal transformations, and methods for decoding of satellite images are used. Scientific novelty. The task of processing of archival satellite snapshots (images), in particular, signal filtering, was investigated from the point of view of an incorrectly posed problem. The regularization parameters for discrete orthogonal transformations were determined.

Normal order and extended Wick theorem for a multiconfiguration reference wave function

NASA Astrophysics Data System (ADS)

Kutzelnigg, Werner; Mukherjee, Debashis

1997-07-01

A generalization of normal ordering and of Wick's theorem with respect to an arbitrary reference function Φ as some generalized "physical vacuum" is formulated in a different (but essentially equivalent) way than that suggested previously by one of the present authors. Guiding principles are that normal order operators with respect to any reference state must be expressible as linear combinations of those with respect to the genuine vacuum, that the vacuum expectation value of a normal order operator must vanish (with respect to the vacuum to which it is in normal order), and that the well-known formalism for a single Slater determinant as physical vacuum must be contained as a special case. The derivation is largely based on the concepts of "Quantum Chemistry in Fock space," which means that particle-number-conserving operators (excitation operators) play a central role. Nevertheless, the contraction rules in the frame of a generalized Wick theorem are derived, that hold for non-particle-number-conserving operators as well. The contraction rules are formulated and illustrated in terms of diagrams. The contractions involve the "residual n-particle density matrices" λ, which are the irreducible (non-factorizable) parts of the conventional n-particle density matrices γ, in the sense of a cumulant expansion for the density. A spinfree formulation is presented as well. The expression of the Hamiltonian in normal order with respect to a multiconfiguration reference function leads to a natural definition of a generalized Fock operator. MC-SCF-theory is easily worked out in this context. The paper concludes with a discussion of the excited configurations and the first-order interacting space, that underlies a perturbative coupled cluster type correction to the MCSCF function for an arbitrary reference function, and with general implications of the new formalism, that is related to "internally contracted multireference configuration interaction." The present generalization of normal ordering is not only valid for arbitrary reference functions, but also if the reference state is an ensemble state.

Conditionally Unbiased Bounded Influence Robust Regression with Applications to Generalized Linear Models.

DTIC Science & Technology

1987-03-01

some general results and definitions from robust statistics (see Hampel et. al.. 1986). The influence function of an M-Lstimator is IC (y.x.0) = D_...estimator is (4,T T T (\\cond(YXGB) . Yx(x,O.B) ) . where X~xO.) =x T T8 xT-lx 1/2 = x x v(x . b/(x B x) ) - B. The influence function of this...the influence function for (3.7) and (3.8) is equal to -. Eo[\\Pcond(y.X.,B)] -1 cond(Yx. ,B). (4.3) On the other hand, the influence function for the

Chaotic jumps in the generalized first adiabatic invariant in current sheets

NASA Technical Reports Server (NTRS)

Brittnacher, M. J.; Whipple, E. C.

1991-01-01

The present study examines how the changes in the generalized first adiabatic invariant J derived from the separatrix crossing theory can be incorporated into the drift variable approach to generating distribution functions. A method is proposed for determining distribution functions for an ensemble of particles following interaction with the tail current sheet by treating the interaction as a scattering problem characterized by changes in the invariant. Generalized drift velocities are obtained for a 1D tail configuration by using the generalized first invariant. The invariant remained constant except for the discrete changes caused by chaotic scattering as the particles cross the separatrix.

Generalized Dynamic Equations Related to Condensation and Freezing Processes

NASA Astrophysics Data System (ADS)

Wang, Xingrong; Huang, Yong

2018-01-01

The generalized thermodynamic equation related to condensation and freezing processes was derived by introducing the condensation and freezing probability function into the dynamic framework based on the statistical thermodynamic fluctuation theory. As a result, the physical mechanism of some weather phenomena covered by using δ(0,1) can in turn be studied and uncovered. From the generalized dynamic equations, the tendency equation of the generalized potential vorticity (GPV) is derived. From the discussion of tendency equation of GPV, in some very thin transitional areas, GPV is found nonconserved because of the introduction of the condensation and freezing probability function, even in frictionless and moist adiabatic air motion.

Flow assignment model for quantitative analysis of diverting bulk freight from road to railway

PubMed Central

Liu, Chang; Wang, Jiaxi; Xiao, Jie; Liu, Siqi; Wu, Jianping; Li, Jian

2017-01-01

Since railway transport possesses the advantage of high volume and low carbon emissions, diverting some freight from road to railway will help reduce the negative environmental impacts associated with transport. This paper develops a flow assignment model for quantitative analysis of diverting truck freight to railway. First, a general network which considers road transportation, railway transportation, handling and transferring is established according to all the steps in the whole transportation process. Then general functions which embody the factors which the shippers will pay attention to when choosing mode and path are formulated. The general functions contain the congestion cost on road, the capacity constraints of railways and freight stations. Based on the general network and general cost function, a user equilibrium flow assignment model is developed to simulate the flow distribution on the general network under the condition that all shippers choose transportation mode and path independently. Since the model is nonlinear and challenging, we adopt a method that uses tangent lines to constitute envelope curve to linearize it. Finally, a numerical example is presented to test the model and show the method of making quantitative analysis of bulk freight modal shift between road and railway. PMID:28771536

Supplemental Interscalene Blockade to General Anesthesia for Shoulder Arthroscopy: Effects on Fast Track Capability, Analgesic Quality, and Lung Function.

PubMed

Zoremba, Martin; Kratz, Thomas; Dette, Frank; Wulf, Hinnerk; Steinfeldt, Thorsten; Wiesmann, Thomas

2015-01-01

After shoulder surgery performed in patients with interscalene nerve block (without general anesthesia), fast track capability and postoperative pain management in the PACU are improved compared with general anesthesia alone. However, it is not known if these evidence-based benefits still exist when the interscalene block is combined with general anesthesia. We retrospectively analyzed a prospective cohort data set of 159 patients undergoing shoulder arthroscopy with general anesthesia alone (n = 60) or combined with an interscalene nerve block catheter (n = 99) for fast track capability time. Moreover, comparisons were made for VAS scores, analgesic consumption in the PACU, pain management, and lung function measurements. The groups did not differ in mean time to fast track capability (22 versus 22 min). Opioid consumption in PACU was significantly less in the interscalene group, who had significantly better VAS scores during PACU stay. Patients receiving interscalene blockade had a significantly impaired lung function postoperatively, although this did not affect postoperative recovery and had no impact on PACU times. The addition of interscalene block to general anesthesia for shoulder arthroscopy did not enhance fast track capability. Pain management and VAS scores were improved in the interscalene nerve block group.

Generalized Langevin equation with tempered memory kernel

NASA Astrophysics Data System (ADS)

Liemert, André; Sandev, Trifce; Kantz, Holger

2017-01-01

We study a generalized Langevin equation for a free particle in presence of a truncated power-law and Mittag-Leffler memory kernel. It is shown that in presence of truncation, the particle from subdiffusive behavior in the short time limit, turns to normal diffusion in the long time limit. The case of harmonic oscillator is considered as well, and the relaxation functions and the normalized displacement correlation function are represented in an exact form. By considering external time-dependent periodic force we obtain resonant behavior even in case of a free particle due to the influence of the environment on the particle movement. Additionally, the double-peak phenomenon in the imaginary part of the complex susceptibility is observed. It is obtained that the truncation parameter has a huge influence on the behavior of these quantities, and it is shown how the truncation parameter changes the critical frequencies. The normalized displacement correlation function for a fractional generalized Langevin equation is investigated as well. All the results are exact and given in terms of the three parameter Mittag-Leffler function and the Prabhakar generalized integral operator, which in the kernel contains a three parameter Mittag-Leffler function. Such kind of truncated Langevin equation motion can be of high relevance for the description of lateral diffusion of lipids and proteins in cell membranes.

Deorbitalization strategies for meta-generalized-gradient-approximation exchange-correlation functionals

NASA Astrophysics Data System (ADS)

Mejia-Rodriguez, Daniel; Trickey, S. B.

2017-11-01

We explore the simplification of widely used meta-generalized-gradient approximation (mGGA) exchange-correlation functionals to the Laplacian level of refinement by use of approximate kinetic-energy density functionals (KEDFs). Such deorbitalization is motivated by the prospect of reducing computational cost while recovering a strictly Kohn-Sham local potential framework (rather than the usual generalized Kohn-Sham treatment of mGGAs). A KEDF that has been rather successful in solid simulations proves to be inadequate for deorbitalization, but we produce other forms which, with parametrization to Kohn-Sham results (not experimental data) on a small training set, yield rather good results on standard molecular test sets when used to deorbitalize the meta-GGA made very simple, Tao-Perdew-Staroverov-Scuseria, and strongly constrained and appropriately normed functionals. We also study the difference between high-fidelity and best-performing deorbitalizations and discuss possible implications for use in ab initio molecular dynamics simulations of complicated condensed phase systems.

Thermoelectric efficiency of nanoscale devices in the linear regime

NASA Astrophysics Data System (ADS)

Bevilacqua, G.; Grosso, G.; Menichetti, G.; Pastori Parravicini, G.

2016-12-01

We study quantum transport through two-terminal nanoscale devices in contact with two particle reservoirs at different temperatures and chemical potentials. We discuss the general expressions controlling the electric charge current, heat currents, and the efficiency of energy transmutation in steady conditions in the linear regime. With focus in the parameter domain where the electron system acts as a power generator, we elaborate workable expressions for optimal efficiency and thermoelectric parameters of nanoscale devices. The general concepts are set at work in the paradigmatic cases of Lorentzian resonances and antiresonances, and the encompassing Fano transmission function: the treatments are fully analytic, in terms of the trigamma functions and Bernoulli numbers. From the general curves here reported describing transport through the above model transmission functions, useful guidelines for optimal efficiency and thermopower can be inferred for engineering nanoscale devices in energy regions where they show similar transmission functions.

Label-free functional nucleic acid sensors for detecting target agents

DOEpatents

Lu, Yi; Xiang, Yu

2015-01-13

A general methodology to design label-free fluorescent functional nucleic acid sensors using a vacant site approach and an abasic site approach is described. In one example, a method for designing label-free fluorescent functional nucleic acid sensors (e.g., those that include a DNAzyme, aptamer or aptazyme) that have a tunable dynamic range through the introduction of an abasic site (e.g., dSpacer) or a vacant site into the functional nucleic acids. Also provided is a general method for designing label-free fluorescent aptamer sensors based on the regulation of malachite green (MG) fluorescence. A general method for designing label-free fluorescent catalytic and molecular beacons (CAMBs) is also provided. The methods demonstrated here can be used to design many other label-free fluorescent sensors to detect a wide range of analytes. Sensors and methods of using the disclosed sensors are also provided.

Vibration analysis and transient response of a functionally graded piezoelectric curved beam with general boundary conditions

NASA Astrophysics Data System (ADS)

Su, Zhu; Jin, Guoyong; Ye, Tiangui

2016-06-01

The paper presents a unified solution for free and transient vibration analyses of a functionally graded piezoelectric curved beam with general boundary conditions within the framework of Timoshenko beam theory. The formulation is derived by means of the variational principle in conjunction with a modified Fourier series which consists of standard Fourier cosine series and supplemented functions. The mechanical and electrical properties of functionally graded piezoelectric materials (FGPMs) are assumed to vary continuously in the thickness direction and are estimated by Voigt’s rule of mixture. The convergence, accuracy and reliability of the present formulation are demonstrated by comparing the present solutions with those from the literature and finite element analysis. Numerous results for FGPM beams with different boundary conditions, geometrical parameters as well as material distributions are given. Moreover, forced vibration of the FGPM beams subjected to dynamic loads and general boundary conditions are also investigated.

Piracetam improves children's memory after general anaesthesia.

PubMed

Fesenko, Ułbołgan A

2009-01-01

Surgery and anaesthesia may account for postoperative complications including cognitive impairment. The purpose of the study was to assess the influence of general anaesthetics on children's memory and effectiveness of piracetam for prevention of postoperative cognitive dysfunction. The study included patients receiving different kinds of anaesthesia for various surgical procedures, randomly allocated to two groups. According to immediate postoperative treatment, the study group received intravenous piracetam 30 mg kg(-1) and the control group--placebo. The cognitive functions were examined preoperatively and within 10 consecutive postoperative days using the ten-word memory test. The study group consisted of 123 children, the control one--of 127. Declines in memory indexes were observed in all anaesthetized patients. The most injured function was long-term memory. The intravenous administration of piracetam improved this cognitive function. The study results confirm that general anaesthesia affects the memory function in children. Piracetam is effective for prevention of postoperative cognitive dysfunction after anaesthesia.

Increased Functional MEG Connectivity as a Hallmark of MRI-Negative Focal and Generalized Epilepsy.

PubMed

Li Hegner, Yiwen; Marquetand, Justus; Elshahabi, Adham; Klamer, Silke; Lerche, Holger; Braun, Christoph; Focke, Niels K

2018-05-15

Epilepsy is one of the most prevalent neurological diseases with a high morbidity. Accumulating evidence has shown that epilepsy is an archetypical neural network disorder. Here we developed a non-invasive cortical functional connectivity analysis based on magnetoencephalography (MEG) to assess commonalities and differences in the network phenotype in different epilepsy syndromes (non-lesional/cryptogenic focal and idiopathic/genetic generalized epilepsy). Thirty-seven epilepsy patients with normal structural brain anatomy underwent a 30-min resting state MEG measurement with eyes closed. We only analyzed interictal epochs without epileptiform discharges. The imaginary part of coherency was calculated as an indicator of cortical functional connectivity in five classical frequency bands. This connectivity measure was computed between all sources on individually reconstructed cortical surfaces that were surface-aligned to a common template. In comparison to healthy controls, both focal and generalized epilepsy patients showed widespread increased functional connectivity in several frequency bands, demonstrating the potential of elevated functional connectivity as a common pathophysiological hallmark in different epilepsy types. Furthermore, the comparison between focal and generalized epilepsies revealed increased network connectivity in bilateral mesio-frontal and motor regions specifically for the generalized epilepsy patients. Our study indicated that the surface-based normalization of MEG sources of individual brains enables the comparison of imaging findings across subjects and groups on a united platform, which leads to a straightforward and effective disclosure of pathological network characteristics in epilepsy. This approach may allow for the definition of more specific markers of different epilepsy syndromes, and increased MEG-based resting-state functional connectivity seems to be a common feature in MRI-negative epilepsy syndromes.