Approximate matching of regular expressions.
Myers, E W; Miller, W
1989-01-01
Given a sequence A and regular expression R, the approximate regular expression matching problem is to find a sequence matching R whose optimal alignment with A is the highest scoring of all such sequences. This paper develops an algorithm to solve the problem in time O(MN), where M and N are the lengths of A and R. Thus, the time requirement is asymptotically no worse than for the simpler problem of aligning two fixed sequences. Our method is superior to an earlier algorithm by Wagner and Seiferas in several ways. First, it treats real-valued costs, in addition to integer costs, with no loss of asymptotic efficiency. Second, it requires only O(N) space to deliver just the score of the best alignment. Finally, its structure permits implementation techniques that make it extremely fast in practice. We extend the method to accommodate gap penalties, as required for typical applications in molecular biology, and further refine it to search for sub-strings of A that strongly align with a sequence in R, as required for typical data base searches. We also show how to deliver an optimal alignment between A and R in only O(N + log M) space using O(MN log M) time. Finally, an O(MN(M + N) + N2log N) time algorithm is presented for alignment scoring schemes where the cost of a gap is an arbitrary increasing function of its length.
Finding the Best Quadratic Approximation of a Function
ERIC Educational Resources Information Center
Yang, Yajun; Gordon, Sheldon P.
2011-01-01
This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact…
Approximate analytic expression for the Skyrmions crystal
NASA Astrophysics Data System (ADS)
Grandi, Nicolás; Sturla, Mauricio
2018-01-01
We find approximate solutions for the two-dimensional nonlinear Σ-model with Dzyalioshinkii-Moriya term, representing magnetic Skyrmions. They are built in an analytic form, by pasting different approximate solutions found in different regions of space. We verify that our construction reproduces the phenomenology known from numerical solutions and Monte Carlo simulations, giving rise to a Skyrmion lattice at an intermediate range of magnetic field, flanked by spiral and spin-polarized phases for low and high magnetic fields, respectively.
Analytical approximations for spatial stochastic gene expression in single cells and tissues
Smith, Stephen; Cianci, Claudia; Grima, Ramon
2016-01-01
Gene expression occurs in an environment in which both stochastic and diffusive effects are significant. Spatial stochastic simulations are computationally expensive compared with their deterministic counterparts, and hence little is currently known of the significance of intrinsic noise in a spatial setting. Starting from the reaction–diffusion master equation (RDME) describing stochastic reaction–diffusion processes, we here derive expressions for the approximate steady-state mean concentrations which are explicit functions of the dimensionality of space, rate constants and diffusion coefficients. The expressions have a simple closed form when the system consists of one effective species. These formulae show that, even for spatially homogeneous systems, mean concentrations can depend on diffusion coefficients: this contradicts the predictions of deterministic reaction–diffusion processes, thus highlighting the importance of intrinsic noise. We confirm our theory by comparison with stochastic simulations, using the RDME and Brownian dynamics, of two models of stochastic and spatial gene expression in single cells and tissues. PMID:27146686
Goldstein, Darlene R
2006-10-01
Studies of gene expression using high-density short oligonucleotide arrays have become a standard in a variety of biological contexts. Of the expression measures that have been proposed to quantify expression in these arrays, multi-chip-based measures have been shown to perform well. As gene expression studies increase in size, however, utilizing multi-chip expression measures is more challenging in terms of computing memory requirements and time. A strategic alternative to exact multi-chip quantification on a full large chip set is to approximate expression values based on subsets of chips. This paper introduces an extrapolation method, Extrapolation Averaging (EA), and a resampling method, Partition Resampling (PR), to approximate expression in large studies. An examination of properties indicates that subset-based methods can perform well compared with exact expression quantification. The focus is on short oligonucleotide chips, but the same ideas apply equally well to any array type for which expression is quantified using an entire set of arrays, rather than for only a single array at a time. Software implementing Partition Resampling and Extrapolation Averaging is under development as an R package for the BioConductor project.
Approximate Expressions for the Period of a Simple Pendulum Using a Taylor Series Expansion
ERIC Educational Resources Information Center
Belendez, Augusto; Arribas, Enrique; Marquez, Andres; Ortuno, Manuel; Gallego, Sergi
2011-01-01
An approximate scheme for obtaining the period of a simple pendulum for large-amplitude oscillations is analysed and discussed. When students express the exact frequency or the period of a simple pendulum as a function of the oscillation amplitude, and they are told to expand this function in a Taylor series, they always do so using the…
NASA Technical Reports Server (NTRS)
Dutta, Soumitra
1988-01-01
A model for approximate spatial reasoning using fuzzy logic to represent the uncertainty in the environment is presented. Algorithms are developed which can be used to reason about spatial information expressed in the form of approximate linguistic descriptions similar to the kind of spatial information processed by humans. Particular attention is given to static spatial reasoning.
Monotone Boolean approximation
DOE Office of Scientific and Technical Information (OSTI.GOV)
Hulme, B.L.
1982-12-01
This report presents a theory of approximation of arbitrary Boolean functions by simpler, monotone functions. Monotone increasing functions can be expressed without the use of complements. Nonconstant monotone increasing functions are important in their own right since they model a special class of systems known as coherent systems. It is shown here that when Boolean expressions for noncoherent systems become too large to treat exactly, then monotone approximations are easily defined. The algorithms proposed here not only provide simpler formulas but also produce best possible upper and lower monotone bounds for any Boolean function. This theory has practical application formore » the analysis of noncoherent fault trees and event tree sequences.« less
Mauda, R.; Pinchas, M.
2014-01-01
Recently a new blind equalization method was proposed for the 16QAM constellation input inspired by the maximum entropy density approximation technique with improved equalization performance compared to the maximum entropy approach, Godard's algorithm, and others. In addition, an approximated expression for the minimum mean square error (MSE) was obtained. The idea was to find those Lagrange multipliers that bring the approximated MSE to minimum. Since the derivation of the obtained MSE with respect to the Lagrange multipliers leads to a nonlinear equation for the Lagrange multipliers, the part in the MSE expression that caused the nonlinearity in the equation for the Lagrange multipliers was ignored. Thus, the obtained Lagrange multipliers were not those Lagrange multipliers that bring the approximated MSE to minimum. In this paper, we derive a new set of Lagrange multipliers based on the nonlinear expression for the Lagrange multipliers obtained from minimizing the approximated MSE with respect to the Lagrange multipliers. Simulation results indicate that for the high signal to noise ratio (SNR) case, a faster convergence rate is obtained for a channel causing a high initial intersymbol interference (ISI) while the same equalization performance is obtained for an easy channel (initial ISI low). PMID:24723813
Drug effects on responses to emotional facial expressions: recent findings
Miller, Melissa A.; Bershad, Anya K.; de Wit, Harriet
2016-01-01
Many psychoactive drugs increase social behavior and enhance social interactions, which may, in turn, increase their attractiveness to users. Although the psychological mechanisms by which drugs affect social behavior are not fully understood, there is some evidence that drugs alter the perception of emotions in others. Drugs can affect the ability to detect, attend to, and respond to emotional facial expressions, which in turn may influence their use in social settings. Either increased reactivity to positive expressions or decreased response to negative expressions may facilitate social interaction. This article reviews evidence that psychoactive drugs alter the processing of emotional facial expressions using subjective, behavioral, and physiological measures. The findings lay the groundwork for better understanding how drugs alter social processing and social behavior more generally. PMID:26226144
Drug effects on responses to emotional facial expressions: recent findings.
Miller, Melissa A; Bershad, Anya K; de Wit, Harriet
2015-09-01
Many psychoactive drugs increase social behavior and enhance social interactions, which may, in turn, increase their attractiveness to users. Although the psychological mechanisms by which drugs affect social behavior are not fully understood, there is some evidence that drugs alter the perception of emotions in others. Drugs can affect the ability to detect, attend to, and respond to emotional facial expressions, which in turn may influence their use in social settings. Either increased reactivity to positive expressions or decreased response to negative expressions may facilitate social interaction. This article reviews evidence that psychoactive drugs alter the processing of emotional facial expressions using subjective, behavioral, and physiological measures. The findings lay the groundwork for better understanding how drugs alter social processing and social behavior more generally.
Padé Approximant and Minimax Rational Approximation in Standard Cosmology
NASA Astrophysics Data System (ADS)
Zaninetti, Lorenzo
2016-02-01
The luminosity distance in the standard cosmology as given by $\\Lambda$CDM and consequently the distance modulus for supernovae can be defined by the Pad\\'e approximant. A comparison with a known analytical solution shows that the Pad\\'e approximant for the luminosity distance has an error of $4\\%$ at redshift $= 10$. A similar procedure for the Taylor expansion of the luminosity distance gives an error of $4\\%$ at redshift $=0.7 $; this means that for the luminosity distance, the Pad\\'e approximation is superior to the Taylor series. The availability of an analytical expression for the distance modulus allows applying the Levenberg--Marquardt method to derive the fundamental parameters from the available compilations for supernovae. A new luminosity function for galaxies derived from the truncated gamma probability density function models the observed luminosity function for galaxies when the observed range in absolute magnitude is modeled by the Pad\\'e approximant. A comparison of $\\Lambda$CDM with other cosmologies is done adopting a statistical point of view.
Quirks of Stirling's Approximation
ERIC Educational Resources Information Center
Macrae, Roderick M.; Allgeier, Benjamin M.
2013-01-01
Stirling's approximation to ln "n"! is typically introduced to physical chemistry students as a step in the derivation of the statistical expression for the entropy. However, naive application of this approximation leads to incorrect conclusions. In this article, the problem is first illustrated using a familiar "toy…
Cosmological applications of Padé approximant
NASA Astrophysics Data System (ADS)
Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan
2014-01-01
As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation.
Analytical approximations for the collapse of an empty spherical bubble.
Obreschkow, D; Bruderer, M; Farhat, M
2012-06-01
The Rayleigh equation 3/2R+RR+pρ(-1)=0 with initial conditions R(0)=R(0), R(0)=0 models the collapse of an empty spherical bubble of radius R(T) in an ideal, infinite liquid with far-field pressure p and density ρ. The solution for r≡R/R(0) as a function of time t≡T/T(c), where R(T(c))≡0, is independent of R(0), p, and ρ. While no closed-form expression for r(t) is known, we find that r(0)(t)=(1-t(2))(2/5) approximates r(t) with an error below 1%. A systematic development in orders of t(2) further yields the 0.001% approximation r(*)(t)=r(0)(t)[1-a(1)Li(2.21)(t(2))], where a(1)≈-0.01832099 is a constant and Li is the polylogarithm. The usefulness of these approximations is demonstrated by comparison to high-precision cavitation data obtained in microgravity.
Finding approximate gene clusters with Gecko 3.
Winter, Sascha; Jahn, Katharina; Wehner, Stefanie; Kuchenbecker, Leon; Marz, Manja; Stoye, Jens; Böcker, Sebastian
2016-11-16
Gene-order-based comparison of multiple genomes provides signals for functional analysis of genes and the evolutionary process of genome organization. Gene clusters are regions of co-localized genes on genomes of different species. The rapid increase in sequenced genomes necessitates bioinformatics tools for finding gene clusters in hundreds of genomes. Existing tools are often restricted to few (in many cases, only two) genomes, and often make restrictive assumptions such as short perfect conservation, conserved gene order or monophyletic gene clusters. We present Gecko 3, an open-source software for finding gene clusters in hundreds of bacterial genomes, that comes with an easy-to-use graphical user interface. The underlying gene cluster model is intuitive, can cope with low degrees of conservation as well as misannotations and is complemented by a sound statistical evaluation. To evaluate the biological benefit of Gecko 3 and to exemplify our method, we search for gene clusters in a dataset of 678 bacterial genomes using Synechocystis sp. PCC 6803 as a reference. We confirm detected gene clusters reviewing the literature and comparing them to a database of operons; we detect two novel clusters, which were confirmed by publicly available experimental RNA-Seq data. The computational analysis is carried out on a laptop computer in <40 min. © The Author(s) 2016. Published by Oxford University Press on behalf of Nucleic Acids Research.
NASA Astrophysics Data System (ADS)
Christenson, J. G.; Austin, R. A.; Phillips, R. J.
2018-05-01
The phonon Boltzmann transport equation is used to analyze model problems in one and two spatial dimensions, under transient and steady-state conditions. New, explicit solutions are obtained by using the P1 and P3 approximations, based on expansions in spherical harmonics, and are compared with solutions from the discrete ordinates method. For steady-state energy transfer, it is shown that analytic expressions derived using the P1 and P3 approximations agree quantitatively with the discrete ordinates method, in some cases for large Knudsen numbers, and always for Knudsen numbers less than unity. However, for time-dependent energy transfer, the PN solutions differ qualitatively from converged solutions obtained by the discrete ordinates method. Although they correctly capture the wave-like behavior of energy transfer at short times, the P1 and P3 approximations rely on one or two wave velocities, respectively, yielding abrupt, step-changes in temperature profiles that are absent when the angular dependence of the phonon velocities is captured more completely. It is shown that, with the gray approximation, the P1 approximation is formally equivalent to the so-called "hyperbolic heat equation." Overall, these results support the use of the PN approximation to find solutions to the phonon Boltzmann transport equation for steady-state conditions. Such solutions can be useful in the design and analysis of devices that involve heat transfer at nanometer length scales, where continuum-scale approaches become inaccurate.
Sparse approximation problem: how rapid simulated annealing succeeds and fails
NASA Astrophysics Data System (ADS)
Obuchi, Tomoyuki; Kabashima, Yoshiyuki
2016-03-01
Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an overcomplete basis is termed the sparse approximation. In this paper, we apply simulated annealing, a metaheuristic algorithm for general optimization problems, to sparse approximation in the situation where the given data have a planted sparse representation and noise is present. The result in the noiseless case shows that our simulated annealing works well in a reasonable parameter region: the planted solution is found fairly rapidly. This is true even in the case where a common relaxation of the sparse approximation problem, the G-relaxation, is ineffective. On the other hand, when the dimensionality of the data is close to the number of non-zero components, another metastable state emerges, and our algorithm fails to find the planted solution. This phenomenon is associated with a first-order phase transition. In the case of very strong noise, it is no longer meaningful to search for the planted solution. In this situation, our algorithm determines a solution with close-to-minimum distortion fairly quickly.
Approximate Bayesian evaluations of measurement uncertainty
NASA Astrophysics Data System (ADS)
Possolo, Antonio; Bodnar, Olha
2018-04-01
The Guide to the Expression of Uncertainty in Measurement (GUM) includes formulas that produce an estimate of a scalar output quantity that is a function of several input quantities, and an approximate evaluation of the associated standard uncertainty. This contribution presents approximate, Bayesian counterparts of those formulas for the case where the output quantity is a parameter of the joint probability distribution of the input quantities, also taking into account any information about the value of the output quantity available prior to measurement expressed in the form of a probability distribution on the set of possible values for the measurand. The approximate Bayesian estimates and uncertainty evaluations that we present have a long history and illustrious pedigree, and provide sufficiently accurate approximations in many applications, yet are very easy to implement in practice. Differently from exact Bayesian estimates, which involve either (analytical or numerical) integrations, or Markov Chain Monte Carlo sampling, the approximations that we describe involve only numerical optimization and simple algebra. Therefore, they make Bayesian methods widely accessible to metrologists. We illustrate the application of the proposed techniques in several instances of measurement: isotopic ratio of silver in a commercial silver nitrate; odds of cryptosporidiosis in AIDS patients; height of a manometer column; mass fraction of chromium in a reference material; and potential-difference in a Zener voltage standard.
Odic, Darko; Lisboa, Juan Valle; Eisinger, Robert; Olivera, Magdalena Gonzalez; Maiche, Alejandro; Halberda, Justin
2016-01-01
What is the relationship between our intuitive sense of number (e.g., when estimating how many marbles are in a jar), and our intuitive sense of other quantities, including time (e.g., when estimating how long it has been since we last ate breakfast)? Recent work in cognitive, developmental, comparative psychology, and computational neuroscience has suggested that our representations of approximate number, time, and spatial extent are fundamentally linked and constitute a "generalized magnitude system". But, the shared behavioral and neural signatures between number, time, and space may alternatively be due to similar encoding and decision-making processes, rather than due to shared domain-general representations. In this study, we investigate the relationship between approximate number and time in a large sample of 6-8 year-old children in Uruguay by examining how individual differences in the precision of number and time estimation correlate with school mathematics performance. Over four testing days, each child completed an approximate number discrimination task, an approximate time discrimination task, a digit span task, and a large battery of symbolic math tests. We replicate previous reports showing that symbolic math abilities correlate with approximate number precision and extend those findings by showing that math abilities also correlate with approximate time precision. But, contrary to approximate number and time sharing common representations, we find that each of these dimensions uniquely correlates with formal math: approximate number correlates more strongly with formal math compared to time and continues to correlate with math even when precision in time and individual differences in working memory are controlled for. These results suggest that there are important differences in the mental representations of approximate number and approximate time and further clarify the relationship between quantity representations and mathematics. Copyright
Approximate Model of Zone Sedimentation
NASA Astrophysics Data System (ADS)
Dzianik, František
2011-12-01
The process of zone sedimentation is affected by many factors that are not possible to express analytically. For this reason, the zone settling is evaluated in practice experimentally or by application of an empirical mathematical description of the process. The paper presents the development of approximate model of zone settling, i.e. the general function which should properly approximate the behaviour of the settling process within its entire range and at the various conditions. Furthermore, the specification of the model parameters by the regression analysis of settling test results is shown. The suitability of the model is reviewed by graphical dependencies and by statistical coefficients of correlation. The approximate model could by also useful on the simplification of process design of continual settling tanks and thickeners.
NASA Astrophysics Data System (ADS)
Wu, Dongmei; Wang, Zhongcheng
2006-03-01
According to Mickens [R.E. Mickens, Comments on a Generalized Galerkin's method for non-linear oscillators, J. Sound Vib. 118 (1987) 563], the general HB (harmonic balance) method is an approximation to the convergent Fourier series representation of the periodic solution of a nonlinear oscillator and not an approximation to an expansion in terms of a small parameter. Consequently, for a nonlinear undamped Duffing equation with a driving force Bcos(ωx), to find a periodic solution when the fundamental frequency is identical to ω, the corresponding Fourier series can be written as y˜(x)=∑n=1m acos[(2n-1)ωx]. How to calculate the coefficients of the Fourier series efficiently with a computer program is still an open problem. For HB method, by substituting approximation y˜(x) into force equation, expanding the resulting expression into a trigonometric series, then letting the coefficients of the resulting lowest-order harmonic be zero, one can obtain approximate coefficients of approximation y˜(x) [R.E. Mickens, Comments on a Generalized Galerkin's method for non-linear oscillators, J. Sound Vib. 118 (1987) 563]. But for nonlinear differential equations such as Duffing equation, it is very difficult to construct higher-order analytical approximations, because the HB method requires solving a set of algebraic equations for a large number of unknowns with very complex nonlinearities. To overcome the difficulty, forty years ago, Urabe derived a computational method for Duffing equation based on Galerkin procedure [M. Urabe, A. Reiter, Numerical computation of nonlinear forced oscillations by Galerkin's procedure, J. Math. Anal. Appl. 14 (1966) 107-140]. Dooren obtained an approximate solution of the Duffing oscillator with a special set of parameters by using Urabe's method [R. van Dooren, Stabilization of Cowell's classic finite difference method for numerical integration, J. Comput. Phys. 16 (1974) 186-192]. In this paper, in the frame of the general HB method
Born approximation in linear-time invariant system
NASA Astrophysics Data System (ADS)
Gumjudpai, Burin
2017-09-01
An alternative way of finding the LTI’s solution with the Born approximation, is investigated. We use Born approximation in the LTI and in the transformed LTI in form of Helmholtz equation. General solution are considered as infinite series or Feynman graph. Slow-roll approximation are explored. Transforming the LTI system into Helmholtz equation, approximated general solution can be found for any given forms of force with its initial value.
More on approximations of Poisson probabilities
DOE Office of Scientific and Technical Information (OSTI.GOV)
Kao, C
1980-05-01
Calculation of Poisson probabilities frequently involves calculating high factorials, which becomes tedious and time-consuming with regular calculators. The usual way to overcome this difficulty has been to find approximations by making use of the table of the standard normal distribution. A new transformation proposed by Kao in 1978 appears to perform better for this purpose than traditional transformations. In the present paper several approximation methods are stated and compared numerically, including an approximation method that utilizes a modified version of Kao's transformation. An approximation based on a power transformation was found to outperform those based on the square-root type transformationsmore » as proposed in literature. The traditional Wilson-Hilferty approximation and Makabe-Morimura approximation are extremely poor compared with this approximation. 4 tables. (RWR)« less
Spline approximation, Part 1: Basic methodology
NASA Astrophysics Data System (ADS)
Ezhov, Nikolaj; Neitzel, Frank; Petrovic, Svetozar
2018-04-01
In engineering geodesy point clouds derived from terrestrial laser scanning or from photogrammetric approaches are almost never used as final results. For further processing and analysis a curve or surface approximation with a continuous mathematical function is required. In this paper the approximation of 2D curves by means of splines is treated. Splines offer quite flexible and elegant solutions for interpolation or approximation of "irregularly" distributed data. Depending on the problem they can be expressed as a function or as a set of equations that depend on some parameter. Many different types of splines can be used for spline approximation and all of them have certain advantages and disadvantages depending on the approximation problem. In a series of three articles spline approximation is presented from a geodetic point of view. In this paper (Part 1) the basic methodology of spline approximation is demonstrated using splines constructed from ordinary polynomials and splines constructed from truncated polynomials. In the forthcoming Part 2 the notion of B-spline will be explained in a unique way, namely by using the concept of convex combinations. The numerical stability of all spline approximation approaches as well as the utilization of splines for deformation detection will be investigated on numerical examples in Part 3.
Surface expression of the Chicxulub crater
Pope, K O; Ocampo, A C; Kinsland, G L; Smith, R
1996-06-01
Analyses of geomorphic, soil, and topographic data from the northern Yucatan Peninsula, Mexico, confirm that the buried Chicxulub impact crater has a distinct surface expression and that carbonate sedimentation throughout the Cenozoic has been influenced by the crater. Late Tertiary sedimentation was mostly restricted to the region within the buried crater, and a semicircular moat existed until at least Pliocene time. The topographic expression of the crater is a series of features concentric with the crater. The most prominent is an approximately 83-km-radius trough or moat containing sinkholes (the Cenote ring). Early Tertiary surfaces rise abruptly outside the moat and form a stepped topography with an outer trough and ridge crest at radii of approximately 103 and approximately 129 km, respectively. Two discontinuous troughs lie within the moat at radii of approximately 41 and approximately 62 km. The low ridge between the inner troughs corresponds to the buried peak ring. The moat corresponds to the outer edge of the crater floor demarcated by a major ring fault. The outer trough and the approximately 62-km-radius inner trough also mark buried ring faults. The ridge crest corresponds to the topographic rim of the crater as modified by postimpact processes. These interpretations support previous findings that the principal impact basin has a diameter of approximately 180 km, but concentric, low-relief slumping extends well beyond this diameter and the eroded crater rim may extend to a diameter of approximately 260 km.
The Quantum Approximation Optimization Algorithm for MaxCut: A Fermionic View
NASA Technical Reports Server (NTRS)
Wang, Zhihui; Hadfield, Stuart; Jiang, Zhang; Rieffel, Eleanor G.
2017-01-01
Farhi et al. recently proposed a class of quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA), for approximately solving combinatorial optimization problems. A level-p QAOA circuit consists of steps in which a classical Hamiltonian, derived from the cost function, is applied followed by a mixing Hamiltonian. The 2p times for which these two Hamiltonians are applied are the parameters of the algorithm. As p increases, however, the parameter search space grows quickly. The success of the QAOA approach will depend, in part, on finding effective parameter-setting strategies. Here, we analytically and numerically study parameter setting for QAOA applied to MAXCUT. For level-1 QAOA, we derive an analytical expression for a general graph. In principle, expressions for higher p could be derived, but the number of terms quickly becomes prohibitive. For a special case of MAXCUT, the Ring of Disagrees, or the 1D antiferromagnetic ring, we provide an analysis for arbitrarily high level. Using a Fermionic representation, the evolution of the system under QAOA translates into quantum optimal control of an ensemble of independent spins. This treatment enables us to obtain analytical expressions for the performance of QAOA for any p. It also greatly simplifies numerical search for the optimal values of the parameters. By exploring symmetries, we identify a lower-dimensional sub-manifold of interest; the search effort can be accordingly reduced. This analysis also explains an observed symmetry in the optimal parameter values. Further, we numerically investigate the parameter landscape and show that it is a simple one in the sense of having no local optima.
NASA Astrophysics Data System (ADS)
Long, Yin; Zhang, Xiao-Jun; Wang, Kui
2018-05-01
In this paper, convergence and approximate calculation of average degree under different network sizes for decreasing random birth-and-death networks (RBDNs) are studied. First, we find and demonstrate that the average degree is convergent in the form of power law. Meanwhile, we discover that the ratios of the back items to front items of convergent reminder are independent of network link number for large network size, and we theoretically prove that the limit of the ratio is a constant. Moreover, since it is difficult to calculate the analytical solution of the average degree for large network sizes, we adopt numerical method to obtain approximate expression of the average degree to approximate its analytical solution. Finally, simulations are presented to verify our theoretical results.
Impulse approximation in nuclear pion production reactions: Absence of a one-body operator
DOE Office of Scientific and Technical Information (OSTI.GOV)
Bolton, Daniel R.; Miller, Gerald A.
2011-06-15
The impulse approximation of pion production reactions is studied by developing a relativistic formalism, consistent with that used to define the nucleon-nucleon potential. For plane wave initial states we find that the usual one-body (1B) expression O{sub 1B} is replaced by O{sub 2B}=-iK(m{sub {pi}}/2)O{sub 1B}/m{sub {pi}}, where K(m{sub {pi}}/2) is the sum of all irreducible contributions to nucleon-nucleon scattering with energy transfer of m{sub {pi}}/2. We show that O{sub 2B}{approx_equal}O{sub 1B} for plane wave initial states. For distorted waves, we find that the usual operator is replaced with a sum of two-body operators that are well approximated by the operatormore » O{sub 2B}. Our new formalism solves the (previously ignored) problem of energy transfer forbidding a one-body impulse operator. Using a purely one pion exchange deuteron, the net result is that the impulse amplitude for np{yields}d{pi}{sup 0} at threshold is enhanced by a factor of approximately two. This amplitude is added to the larger ''rescattering'' amplitude and, although experimental data remain in disagreement, the theoretical prediction of the threshold cross section is brought closer to (and in agreement with) the data.« less
Finding gene regulatory network candidates using the gene expression knowledge base.
Venkatesan, Aravind; Tripathi, Sushil; Sanz de Galdeano, Alejandro; Blondé, Ward; Lægreid, Astrid; Mironov, Vladimir; Kuiper, Martin
2014-12-10
Network-based approaches for the analysis of large-scale genomics data have become well established. Biological networks provide a knowledge scaffold against which the patterns and dynamics of 'omics' data can be interpreted. The background information required for the construction of such networks is often dispersed across a multitude of knowledge bases in a variety of formats. The seamless integration of this information is one of the main challenges in bioinformatics. The Semantic Web offers powerful technologies for the assembly of integrated knowledge bases that are computationally comprehensible, thereby providing a potentially powerful resource for constructing biological networks and network-based analysis. We have developed the Gene eXpression Knowledge Base (GeXKB), a semantic web technology based resource that contains integrated knowledge about gene expression regulation. To affirm the utility of GeXKB we demonstrate how this resource can be exploited for the identification of candidate regulatory network proteins. We present four use cases that were designed from a biological perspective in order to find candidate members relevant for the gastrin hormone signaling network model. We show how a combination of specific query definitions and additional selection criteria derived from gene expression data and prior knowledge concerning candidate proteins can be used to retrieve a set of proteins that constitute valid candidates for regulatory network extensions. Semantic web technologies provide the means for processing and integrating various heterogeneous information sources. The GeXKB offers biologists such an integrated knowledge resource, allowing them to address complex biological questions pertaining to gene expression. This work illustrates how GeXKB can be used in combination with gene expression results and literature information to identify new potential candidates that may be considered for extending a gene regulatory network.
Uniform analytic approximation of Wigner rotation matrices
NASA Astrophysics Data System (ADS)
Hoffmann, Scott E.
2018-02-01
We derive the leading asymptotic approximation, for low angle θ, of the Wigner rotation matrix elements, dm1m2 j(θ ) , uniform in j, m1, and m2. The result is in terms of a Bessel function of integer order. We numerically investigate the error for a variety of cases and find that the approximation can be useful over a significant range of angles. This approximation has application in the partial wave analysis of wavepacket scattering.
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.
DOE Office of Scientific and Technical Information (OSTI.GOV)
Traytak, Sergey D., E-mail: sergtray@mail.ru; Le STUDIUM; Semenov Institute of Chemical Physics RAS, 4 Kosygina St., 117977 Moscow
The anisotropic 3D equation describing the pointlike particles diffusion in slender impermeable tubes of revolution with cross section smoothly depending on the longitudinal coordinate is the object of our study. We use singular perturbations approach to find the rigorous asymptotic expression for the local particles concentration as an expansion in the ratio of the characteristic transversal and longitudinal diffusion relaxation times. The corresponding leading-term approximation is a generalization of well-known Fick-Jacobs approximation. This result allowed us to delineate the conditions on temporal and spatial scales under which the Fick-Jacobs approximation is valid. A striking analogy between solution of our problemmore » and the method of inner-outer expansions for low Knudsen numbers gas kinetic theory is established. With the aid of this analogy we clarify the physical and mathematical meaning of the obtained results.« less
NASA Astrophysics Data System (ADS)
Walker, David M.; Allingham, David; Lee, Heung Wing Joseph; Small, Michael
2010-02-01
Small world network models have been effective in capturing the variable behaviour of reported case data of the SARS coronavirus outbreak in Hong Kong during 2003. Simulations of these models have previously been realized using informed “guesses” of the proposed model parameters and tested for consistency with the reported data by surrogate analysis. In this paper we attempt to provide statistically rigorous parameter distributions using Approximate Bayesian Computation sampling methods. We find that such sampling schemes are a useful framework for fitting parameters of stochastic small world network models where simulation of the system is straightforward but expressing a likelihood is cumbersome.
Approximate geodesic distances reveal biologically relevant structures in microarray data.
Nilsson, Jens; Fioretos, Thoas; Höglund, Mattias; Fontes, Magnus
2004-04-12
Genome-wide gene expression measurements, as currently determined by the microarray technology, can be represented mathematically as points in a high-dimensional gene expression space. Genes interact with each other in regulatory networks, restricting the cellular gene expression profiles to a certain manifold, or surface, in gene expression space. To obtain knowledge about this manifold, various dimensionality reduction methods and distance metrics are used. For data points distributed on curved manifolds, a sensible distance measure would be the geodesic distance along the manifold. In this work, we examine whether an approximate geodesic distance measure captures biological similarities better than the traditionally used Euclidean distance. We computed approximate geodesic distances, determined by the Isomap algorithm, for one set of lymphoma and one set of lung cancer microarray samples. Compared with the ordinary Euclidean distance metric, this distance measure produced more instructive, biologically relevant, visualizations when applying multidimensional scaling. This suggests the Isomap algorithm as a promising tool for the interpretation of microarray data. Furthermore, the results demonstrate the benefit and importance of taking nonlinearities in gene expression data into account.
Double power series method for approximating cosmological perturbations
NASA Astrophysics Data System (ADS)
Wren, Andrew J.; Malik, Karim A.
2017-04-01
We introduce a double power series method for finding approximate analytical solutions for systems of differential equations commonly found in cosmological perturbation theory. The method was set out, in a noncosmological context, by Feshchenko, Shkil' and Nikolenko (FSN) in 1966, and is applicable to cases where perturbations are on subhorizon scales. The FSN method is essentially an extension of the well known Wentzel-Kramers-Brillouin (WKB) method for finding approximate analytical solutions for ordinary differential equations. The FSN method we use is applicable well beyond perturbation theory to solve systems of ordinary differential equations, linear in the derivatives, that also depend on a small parameter, which here we take to be related to the inverse wave-number. We use the FSN method to find new approximate oscillating solutions in linear order cosmological perturbation theory for a flat radiation-matter universe. Together with this model's well-known growing and decaying Mészáros solutions, these oscillating modes provide a complete set of subhorizon approximations for the metric potential, radiation and matter perturbations. Comparison with numerical solutions of the perturbation equations shows that our approximations can be made accurate to within a typical error of 1%, or better. We also set out a heuristic method for error estimation. A Mathematica notebook which implements the double power series method is made available online.
NASA Astrophysics Data System (ADS)
Adhikari, Satyabrata
2018-04-01
Structural physical approximation (SPA) has been exploited to approximate nonphysical operation such as partial transpose. It has already been studied in the context of detection of entanglement and found that if the minimum eigenvalue of SPA to partial transpose is less than 2/9 then the two-qubit state is entangled. We find application of SPA to partial transpose in the estimation of the optimal singlet fraction. We show that the optimal singlet fraction can be expressed in terms of the minimum eigenvalue of SPA to partial transpose. We also show that the optimal singlet fraction can be realized using Hong-Ou-Mandel interferometry with only two detectors. Further we have shown that the generated hybrid entangled state between a qubit and a binary coherent state can be used as a resource state in quantum teleportation.
Spline approximations for nonlinear hereditary control systems
NASA Technical Reports Server (NTRS)
Daniel, P. L.
1982-01-01
A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.
NASA Astrophysics Data System (ADS)
Ivliev, S. V.
2017-12-01
For calculation of short laser pulse absorption in metal the imaginary part of permittivity, which is simply related to the conductivity, is required. Currently to find the static and dynamic conductivity the Kubo-Greenwood formula is most commonly used. It describes the electromagnetic energy absorption in the one-electron approach. In the present study, this formula is derived directly from the expression for the permittivity expression in the random phase approximation, which in fact is equivalent to the method of the mean field. The detailed analysis of the role of electron-electron interaction in the calculation of the matrix elements of the velocity operator is given. It is shown that in the one-electron random phase approximation the single-particle conductive electron wave functions in the field of fixed ions should be used. The possibility of considering the exchange and correlation effects by means of an amendment to a local function field is discussed.
Lognormal Approximations of Fault Tree Uncertainty Distributions.
El-Shanawany, Ashraf Ben; Ardron, Keith H; Walker, Simon P
2018-01-26
Fault trees are used in reliability modeling to create logical models of fault combinations that can lead to undesirable events. The output of a fault tree analysis (the top event probability) is expressed in terms of the failure probabilities of basic events that are input to the model. Typically, the basic event probabilities are not known exactly, but are modeled as probability distributions: therefore, the top event probability is also represented as an uncertainty distribution. Monte Carlo methods are generally used for evaluating the uncertainty distribution, but such calculations are computationally intensive and do not readily reveal the dominant contributors to the uncertainty. In this article, a closed-form approximation for the fault tree top event uncertainty distribution is developed, which is applicable when the uncertainties in the basic events of the model are lognormally distributed. The results of the approximate method are compared with results from two sampling-based methods: namely, the Monte Carlo method and the Wilks method based on order statistics. It is shown that the closed-form expression can provide a reasonable approximation to results obtained by Monte Carlo sampling, without incurring the computational expense. The Wilks method is found to be a useful means of providing an upper bound for the percentiles of the uncertainty distribution while being computationally inexpensive compared with full Monte Carlo sampling. The lognormal approximation method and Wilks's method appear attractive, practical alternatives for the evaluation of uncertainty in the output of fault trees and similar multilinear models. © 2018 Society for Risk Analysis.
Exact and approximate stochastic simulation of intracellular calcium dynamics.
Wieder, Nicolas; Fink, Rainer H A; Wegner, Frederic von
2011-01-01
In simulations of chemical systems, the main task is to find an exact or approximate solution of the chemical master equation (CME) that satisfies certain constraints with respect to computation time and accuracy. While Brownian motion simulations of single molecules are often too time consuming to represent the mesoscopic level, the classical Gillespie algorithm is a stochastically exact algorithm that provides satisfying results in the representation of calcium microdomains. Gillespie's algorithm can be approximated via the tau-leap method and the chemical Langevin equation (CLE). Both methods lead to a substantial acceleration in computation time and a relatively small decrease in accuracy. Elimination of the noise terms leads to the classical, deterministic reaction rate equations (RRE). For complex multiscale systems, hybrid simulations are increasingly proposed to combine the advantages of stochastic and deterministic algorithms. An often used exemplary cell type in this context are striated muscle cells (e.g., cardiac and skeletal muscle cells). The properties of these cells are well described and they express many common calcium-dependent signaling pathways. The purpose of the present paper is to provide an overview of the aforementioned simulation approaches and their mutual relationships in the spectrum ranging from stochastic to deterministic algorithms.
Fostering Formal Commutativity Knowledge with Approximate Arithmetic
Hansen, Sonja Maria; Haider, Hilde; Eichler, Alexandra; Godau, Claudia; Frensch, Peter A.; Gaschler, Robert
2015-01-01
How can we enhance the understanding of abstract mathematical principles in elementary school? Different studies found out that nonsymbolic estimation could foster subsequent exact number processing and simple arithmetic. Taking the commutativity principle as a test case, we investigated if the approximate calculation of symbolic commutative quantities can also alter the access to procedural and conceptual knowledge of a more abstract arithmetic principle. Experiment 1 tested first graders who had not been instructed about commutativity in school yet. Approximate calculation with symbolic quantities positively influenced the use of commutativity-based shortcuts in formal arithmetic. We replicated this finding with older first graders (Experiment 2) and third graders (Experiment 3). Despite the positive effect of approximation on the spontaneous application of commutativity-based shortcuts in arithmetic problems, we found no comparable impact on the application of conceptual knowledge of the commutativity principle. Overall, our results show that the usage of a specific arithmetic principle can benefit from approximation. However, the findings also suggest that the correct use of certain procedures does not always imply conceptual understanding. Rather, the conceptual understanding of commutativity seems to lag behind procedural proficiency during elementary school. PMID:26560311
Radiative transfer in falling snow: A two-stream approximation
NASA Astrophysics Data System (ADS)
Koh, Gary
1989-04-01
Light transmission measurements through falling snow have produced results unexplainable by single scattering arguments. A two-stream approximation to radiative transfer is used to derive an analytical expression that describes the effects of multiple scattering as a function of the snow optical depth and the snow asymmetry parameter. The approximate solution is simple and it may be as accurate as the exact solution for describing the transmission measurements within the limits of experimental uncertainties.
On approximate formulas for the electrostatic force between two conducting spheres
NASA Astrophysics Data System (ADS)
Sliško, Josip; Brito-Orta, Raúl A.
1998-04-01
A series expression for the electrostatic force between two charged conducting spheres having equal radii and charges is derived using the method of electrical images. This expression is a special case of that for two spheres with arbitrary charges and radii, found by Maxwell using zonal harmonics. Keeping in mind the use of approximate formulas for the interpretation of classroom measurements of the electrostatic force between spheres, we comment on two incorrect approximate formulas and examine the contribution of the first few non-Coulomb terms of the correct formula by comparing with values obtained using a computational approach.
Rational trigonometric approximations using Fourier series partial sums
NASA Technical Reports Server (NTRS)
Geer, James F.
1993-01-01
A class of approximations (S(sub N,M)) to a periodic function f which uses the ideas of Pade, or rational function, approximations based on the Fourier series representation of f, rather than on the Taylor series representation of f, is introduced and studied. Each approximation S(sub N,M) is the quotient of a trigonometric polynomial of degree N and a trigonometric polynomial of degree M. The coefficients in these polynomials are determined by requiring that an appropriate number of the Fourier coefficients of S(sub N,M) agree with those of f. Explicit expressions are derived for these coefficients in terms of the Fourier coefficients of f. It is proven that these 'Fourier-Pade' approximations converge point-wise to (f(x(exp +))+f(x(exp -)))/2 more rapidly (in some cases by a factor of 1/k(exp 2M)) than the Fourier series partial sums on which they are based. The approximations are illustrated by several examples and an application to the solution of an initial, boundary value problem for the simple heat equation is presented.
Quantum approximate optimization algorithm for MaxCut: A fermionic view
NASA Astrophysics Data System (ADS)
Wang, Zhihui; Hadfield, Stuart; Jiang, Zhang; Rieffel, Eleanor G.
2018-02-01
Farhi et al. recently proposed a class of quantum algorithms, the quantum approximate optimization algorithm (QAOA), for approximately solving combinatorial optimization problems (E. Farhi et al., arXiv:1411.4028;
Approximation Of Multi-Valued Inverse Functions Using Clustering And Sugeno Fuzzy Inference
NASA Technical Reports Server (NTRS)
Walden, Maria A.; Bikdash, Marwan; Homaifar, Abdollah
1998-01-01
Finding the inverse of a continuous function can be challenging and computationally expensive when the inverse function is multi-valued. Difficulties may be compounded when the function itself is difficult to evaluate. We show that we can use fuzzy-logic approximators such as Sugeno inference systems to compute the inverse on-line. To do so, a fuzzy clustering algorithm can be used in conjunction with a discriminating function to split the function data into branches for the different values of the forward function. These data sets are then fed into a recursive least-squares learning algorithm that finds the proper coefficients of the Sugeno approximators; each Sugeno approximator finds one value of the inverse function. Discussions about the accuracy of the approximation will be included.
Variational Gaussian approximation for Poisson data
NASA Astrophysics Data System (ADS)
Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen
2018-02-01
The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.
CMB-lensing beyond the Born approximation
DOE Office of Scientific and Technical Information (OSTI.GOV)
Marozzi, Giovanni; Fanizza, Giuseppe; Durrer, Ruth
2016-09-01
We investigate the weak lensing corrections to the cosmic microwave background temperature anisotropies considering effects beyond the Born approximation. To this aim, we use the small deflection angle approximation, to connect the lensed and unlensed power spectra, via expressions for the deflection angles up to third order in the gravitational potential. While the small deflection angle approximation has the drawback to be reliable only for multipoles ℓ ∼< 2500, it allows us to consistently take into account the non-Gaussian nature of cosmological perturbation theory beyond the linear level. The contribution to the lensed temperature power spectrum coming from the non-Gaussianmore » nature of the deflection angle at higher order is a new effect which has not been taken into account in the literature so far. It turns out to be the leading contribution among the post-Born lensing corrections. On the other hand, the effect is smaller than corrections coming from non-linearities in the matter power spectrum, and its imprint on CMB lensing is too small to be seen in present experiments.« less
Local approximation of a metapopulation's equilibrium.
Barbour, A D; McVinish, R; Pollett, P K
2018-04-18
We consider the approximation of the equilibrium of a metapopulation model, in which a finite number of patches are randomly distributed over a bounded subset [Formula: see text] of Euclidean space. The approximation is good when a large number of patches contribute to the colonization pressure on any given unoccupied patch, and when the quality of the patches varies little over the length scale determined by the colonization radius. If this is the case, the equilibrium probability of a patch at z being occupied is shown to be close to [Formula: see text], the equilibrium occupation probability in Levins's model, at any point [Formula: see text] not too close to the boundary, if the local colonization pressure and extinction rates appropriate to z are assumed. The approximation is justified by giving explicit upper and lower bounds for the occupation probabilities, expressed in terms of the model parameters. Since the patches are distributed randomly, the occupation probabilities are also random, and we complement our bounds with explicit bounds on the probability that they are satisfied at all patches simultaneously.
A Survey of Techniques for Approximate Computing
Mittal, Sparsh
2016-03-18
Approximate computing trades off computation quality with the effort expended and as rising performance demands confront with plateauing resource budgets, approximate computing has become, not merely attractive, but even imperative. Here, we present a survey of techniques for approximate computing (AC). We discuss strategies for finding approximable program portions and monitoring output quality, techniques for using AC in different processing units (e.g., CPU, GPU and FPGA), processor components, memory technologies etc., and programming frameworks for AC. Moreover, we classify these techniques based on several key characteristics to emphasize their similarities and differences. Finally, the aim of this paper is tomore » provide insights to researchers into working of AC techniques and inspire more efforts in this area to make AC the mainstream computing approach in future systems.« less
Partially Coherent Scattering in Stellar Chromospheres. Part 4; Analytic Wing Approximations
NASA Technical Reports Server (NTRS)
Gayley, K. G.
1993-01-01
Simple analytic expressions are derived to understand resonance-line wings in stellar chromospheres and similar astrophysical plasmas. The results are approximate, but compare well with accurate numerical simulations. The redistribution is modeled using an extension of the partially coherent scattering approximation (PCS) which we term the comoving-frame partially coherent scattering approximation (CPCS). The distinction is made here because Doppler diffusion is included in the coherent/noncoherent decomposition, in a form slightly improved from the earlier papers in this series.
On the convergence of local approximations to pseudodifferential operators with applications
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas
1994-01-01
We consider the approximation of a class pseudodifferential operators by sequences of operators which can be expressed as compositions of differential operators and their inverses. We show that the error in such approximations can be bounded in terms of L(1) error in approximating a convolution kernel, and use this fact to develop convergence results. Our main result is a finite time convergence analysis of the Engquist-Majda Pade approximants to the square root of the d'Alembertian. We also show that no spatially local approximation to this operator can be convergent uniformly in time. We propose some temporally local but spatially nonlocal operators with better long time behavior. These are based on Laguerre and exponential series.
Approximate reasoning using terminological models
NASA Technical Reports Server (NTRS)
Yen, John; Vaidya, Nitin
1992-01-01
Term Subsumption Systems (TSS) form a knowledge-representation scheme in AI that can express the defining characteristics of concepts through a formal language that has a well-defined semantics and incorporates a reasoning mechanism that can deduce whether one concept subsumes another. However, TSS's have very limited ability to deal with the issue of uncertainty in knowledge bases. The objective of this research is to address issues in combining approximate reasoning with term subsumption systems. To do this, we have extended an existing AI architecture (CLASP) that is built on the top of a term subsumption system (LOOM). First, the assertional component of LOOM has been extended for asserting and representing uncertain propositions. Second, we have extended the pattern matcher of CLASP for plausible rule-based inferences. Third, an approximate reasoning model has been added to facilitate various kinds of approximate reasoning. And finally, the issue of inconsistency in truth values due to inheritance is addressed using justification of those values. This architecture enhances the reasoning capabilities of expert systems by providing support for reasoning under uncertainty using knowledge captured in TSS. Also, as definitional knowledge is explicit and separate from heuristic knowledge for plausible inferences, the maintainability of expert systems could be improved.
Hamilton's Principle and Approximate Solutions to Problems in Classical Mechanics
ERIC Educational Resources Information Center
Schlitt, D. W.
1977-01-01
Shows how to use the Ritz method for obtaining approximate solutions to problems expressed in variational form directly from the variational equation. Application of this method to classical mechanics is given. (MLH)
Transcriptional regulation of IGF-I expression in skeletal muscle
NASA Technical Reports Server (NTRS)
McCall, G. E.; Allen, D. L.; Haddad, F.; Baldwin, K. M.
2003-01-01
The present study investigated the role of transcription in the regulation of insulin-like growth factor (IGF)-I expression in skeletal muscle. RT-PCR was used to determine endogenous expression of IGF-I pre-mRNA and mRNA in control (Con) and functionally overloaded (FO) rat plantaris. The transcriptional activities of five different-length IGF-I promoter fragments controlling transcription of a firefly luciferase (FLuc) reporter gene were tested in vitro by transfection of myoblasts or in vivo during FO by direct gene transfer into the plantaris. Increased endogenous IGF-I gene transcription during 7 days of plantaris FO was evidenced by an approximately 140-160% increase (P < 0.0001) in IGF-I pre-mRNA (a transcriptional marker). IGF-I mRNA expression also increased by approximately 90% (P < 0.0001), and it was correlated (R = 0.93; P < 0.0001) with the pre-mRNA increases. The three longest IGF-I exon 1 promoters induced reporter gene expression in proliferating C2C12 and L6E9 myoblasts. In differentiated L6E9 myotubes, promoter activity increased approximately two- to threefold over myoblasts. Overexpression of calcineurin and MyoD increased the activity of the -852/+192 promoter in C2C12 myotubes by approximately 5- and approximately 18-fold, respectively. However, FO did not induce these exogenous promoter fragments. Nevertheless, the present findings are consistent with the hypothesis that the IGF-I gene is transcriptionally regulated during muscle hypertrophy in vivo as evidenced by the induction of the endogenous IGF-I pre-mRNA during plantaris FO. The exon 1 promoter region of the IGF-I gene is sufficient to direct inducible expression in vitro; however, an in vivo response to FO may require elements outside the -852/+346 region of the exon 1 IGF-I promoter or features inherent to the endogenous IGF-I gene.
Origin of Quantum Criticality in Yb-Al-Au Approximant Crystal and Quasicrystal
NASA Astrophysics Data System (ADS)
Watanabe, Shinji; Miyake, Kazumasa
2016-06-01
To get insight into the mechanism of emergence of unconventional quantum criticality observed in quasicrystal Yb15Al34Au51, the approximant crystal Yb14Al35Au51 is analyzed theoretically. By constructing a minimal model for the approximant crystal, the heavy quasiparticle band is shown to emerge near the Fermi level because of strong correlation of 4f electrons at Yb. We find that charge-transfer mode between 4f electron at Yb on the 3rd shell and 3p electron at Al on the 4th shell in Tsai-type cluster is considerably enhanced with almost flat momentum dependence. The mode-coupling theory shows that magnetic as well as valence susceptibility exhibits χ ˜ T-0.5 for zero-field limit and is expressed as a single scaling function of the ratio of temperature to magnetic field T/B over four decades even in the approximant crystal when some condition is satisfied by varying parameters, e.g., by applying pressure. The key origin is clarified to be due to strong locality of the critical Yb-valence fluctuation and small Brillouin zone reflecting the large unit cell, giving rise to the extremely-small characteristic energy scale. This also gives a natural explanation for the quantum criticality in the quasicrystal corresponding to the infinite limit of the unit-cell size.
DOE Office of Scientific and Technical Information (OSTI.GOV)
Lestrange, Patrick J.; Egidi, Franco; Li, Xiaosong, E-mail: xsli@uw.edu
2015-12-21
The interaction between a quantum mechanical system and plane wave light is usually modeled within the electric dipole approximation. This assumes that the intensity of the incident field is constant over the length of the system and transition probabilities are described in terms of the electric dipole transition moment. For short wavelength spectroscopies, such as X-ray absorption, the electric dipole approximation often breaks down. Higher order multipoles are then included to describe transition probabilities. The square of the magnetic dipole and electric quadrupole are often included, but this results in an origin-dependent expression for the oscillator strength. The oscillator strengthmore » can be made origin-independent if all terms through the same order in the wave vector are retained. We will show the consequences and potential pitfalls of using either of these two expressions. It is shown that the origin-dependent expression may violate the Thomas-Reiche-Kuhn sum rule and the origin-independent expression can result in negative transition probabilities.« less
Lestrange, Patrick J; Egidi, Franco; Li, Xiaosong
2015-12-21
The interaction between a quantum mechanical system and plane wave light is usually modeled within the electric dipole approximation. This assumes that the intensity of the incident field is constant over the length of the system and transition probabilities are described in terms of the electric dipole transition moment. For short wavelength spectroscopies, such as X-ray absorption, the electric dipole approximation often breaks down. Higher order multipoles are then included to describe transition probabilities. The square of the magnetic dipole and electric quadrupole are often included, but this results in an origin-dependent expression for the oscillator strength. The oscillator strength can be made origin-independent if all terms through the same order in the wave vector are retained. We will show the consequences and potential pitfalls of using either of these two expressions. It is shown that the origin-dependent expression may violate the Thomas-Reiche-Kuhn sum rule and the origin-independent expression can result in negative transition probabilities.
NASA Astrophysics Data System (ADS)
Lestrange, Patrick J.; Egidi, Franco; Li, Xiaosong
2015-12-01
The interaction between a quantum mechanical system and plane wave light is usually modeled within the electric dipole approximation. This assumes that the intensity of the incident field is constant over the length of the system and transition probabilities are described in terms of the electric dipole transition moment. For short wavelength spectroscopies, such as X-ray absorption, the electric dipole approximation often breaks down. Higher order multipoles are then included to describe transition probabilities. The square of the magnetic dipole and electric quadrupole are often included, but this results in an origin-dependent expression for the oscillator strength. The oscillator strength can be made origin-independent if all terms through the same order in the wave vector are retained. We will show the consequences and potential pitfalls of using either of these two expressions. It is shown that the origin-dependent expression may violate the Thomas-Reiche-Kuhn sum rule and the origin-independent expression can result in negative transition probabilities.
NASA Technical Reports Server (NTRS)
Laurenson, R. M.; Baumgarten, J. R.
1975-01-01
An approximation technique has been developed for determining the transient response of a nonlinear dynamic system. The nonlinearities in the system which has been considered appear in the system's dissipation function. This function was expressed as a second order polynomial in the system's velocity. The developed approximation is an extension of the classic Kryloff-Bogoliuboff technique. Two examples of the developed approximation are presented for comparative purposes with other approximation methods.
NASA Astrophysics Data System (ADS)
Leilaeioun, Mehdi; Holman, Zachary C.
2016-09-01
An approximate expression proposed by Green predicts the maximum obtainable fill factor (FF) of a solar cell from its open-circuit voltage (Voc). The expression was originally suggested for silicon solar cells that behave according to a single-diode model and, in addition to Voc, it requires an ideality factor as input. It is now commonly applied to silicon cells by assuming a unity ideality factor—even when the cells are not in low injection—as well as to non-silicon cells. Here, we evaluate the accuracy of the expression in several cases. In particular, we calculate the recombination-limited FF and Voc of hypothetical silicon solar cells from simulated lifetime curves, and compare the exact FF to that obtained with the approximate expression using assumed ideality factors. Considering cells with a variety of recombination mechanisms, wafer doping densities, and photogenerated current densities reveals the range of conditions under which the approximate expression can safely be used. We find that the expression is unable to predict FF generally: For a typical silicon solar cell under one-sun illumination, the error is approximately 6% absolute with an assumed ideality factor of 1. Use of the expression should thus be restricted to cells under very low or very high injection.
Approximate matching of structured motifs in DNA sequences.
El-Mabrouk, Nadia; Raffinot, Mathieu; Duchesne, Jean-Eudes; Lajoie, Mathieu; Luc, Nicolas
2005-04-01
Several methods have been developed for identifying more or less complex RNA structures in a genome. All these methods are based on the search for conserved primary and secondary sub-structures. In this paper, we present a simple formal representation of a helix, which is a combination of sequence and folding constraints, as a constrained regular expression. This representation allows us to develop a well-founded algorithm that searches for all approximate matches of a helix in a genome. The algorithm is based on an alignment graph constructed from several copies of a pushdown automaton, arranged one on top of another. This is a first attempt to take advantage of the possibilities of pushdown automata in the context of approximate matching. The worst time complexity is O(krpn), where k is the error threshold, n the size of the genome, p the size of the secondary expression, and r its number of union symbols. We then extend the algorithm to search for pseudo-knots and secondary structures containing an arbitrary number of helices.
Finding Groups in Gene Expression Data
2005-01-01
The vast potential of the genomic insight offered by microarray technologies has led to their widespread use since they were introduced a decade ago. Application areas include gene function discovery, disease diagnosis, and inferring regulatory networks. Microarray experiments enable large-scale, high-throughput investigations of gene activity and have thus provided the data analyst with a distinctive, high-dimensional field of study. Many questions in this field relate to finding subgroups of data profiles which are very similar. A popular type of exploratory tool for finding subgroups is cluster analysis, and many different flavors of algorithms have been used and indeed tailored for microarray data. Cluster analysis, however, implies a partitioning of the entire data set, and this does not always match the objective. Sometimes pattern discovery or bump hunting tools are more appropriate. This paper reviews these various tools for finding interesting subgroups. PMID:16046827
Testing the Ginzburg-Landau approximation for three-flavor crystalline color superconductivity
DOE Office of Scientific and Technical Information (OSTI.GOV)
Mannarelli, Massimo; Sharma, Rishi; Rajagopal, Krishna
2006-06-01
It is an open challenge to analyze the crystalline color superconducting phases that may arise in cold dense, but not asymptotically dense, three-flavor quark matter. At present the only approximation within which it seems possible to compare the free energies of the myriad possible crystal structures is the Ginzburg-Landau approximation. Here, we test this approximation on a particularly simple 'crystal' structure in which there are only two condensates
Approximate analytical solution for induction heating of solid cylinders
Jankowski, Todd Andrew; Pawley, Norma Helen; Gonzales, Lindsey Michal; ...
2015-10-20
An approximate solution to the mathematical model for induction heating of a solid cylinder in a cylindrical induction coil is presented here. The coupled multiphysics model includes equations describing the electromagnetic field in the heated object, a heat transfer simulation to determine temperature of the heated object, and an AC circuit simulation of the induction heating power supply. A multiple-scale perturbation method is used to solve the multiphysics model. The approximate analytical solution yields simple closed-form expressions for the electromagnetic field and heat generation rate in the solid cylinder, for the equivalent impedance of the associated tank circuit, and formore » the frequency response of a variable frequency power supply driving the tank circuit. The solution developed here is validated by comparing predicted power supply frequency to both experimental measurements and calculated values from finite element analysis for heating of graphite cylinders in an induction furnace. The simple expressions from the analytical solution clearly show the functional dependence of the power supply frequency on the material properties of the load and the geometrical characteristics of the furnace installation. In conclusion, the expressions developed here provide physical insight into observations made during load signature analysis of induction heating.« less
libFLASM: a software library for fixed-length approximate string matching.
Ayad, Lorraine A K; Pissis, Solon P P; Retha, Ahmad
2016-11-10
Approximate string matching is the problem of finding all factors of a given text that are at a distance at most k from a given pattern. Fixed-length approximate string matching is the problem of finding all factors of a text of length n that are at a distance at most k from any factor of length ℓ of a pattern of length m. There exist bit-vector techniques to solve the fixed-length approximate string matching problem in time [Formula: see text] and space [Formula: see text] under the edit and Hamming distance models, where w is the size of the computer word; as such these techniques are independent of the distance threshold k or the alphabet size. Fixed-length approximate string matching is a generalisation of approximate string matching and, hence, has numerous direct applications in computational molecular biology and elsewhere. We present and make available libFLASM, a free open-source C++ software library for solving fixed-length approximate string matching under both the edit and the Hamming distance models. Moreover we describe how fixed-length approximate string matching is applied to solve real problems by incorporating libFLASM into established applications for multiple circular sequence alignment as well as single and structured motif extraction. Specifically, we describe how it can be used to improve the accuracy of multiple circular sequence alignment in terms of the inferred likelihood-based phylogenies; and we also describe how it is used to efficiently find motifs in molecular sequences representing regulatory or functional regions. The comparison of the performance of the library to other algorithms show how it is competitive, especially with increasing distance thresholds. Fixed-length approximate string matching is a generalisation of the classic approximate string matching problem. We present libFLASM, a free open-source C++ software library for solving fixed-length approximate string matching. The extensive experimental results presented here
Analytic approximation for random muffin-tin alloys
DOE Office of Scientific and Technical Information (OSTI.GOV)
Mills, R.; Gray, L.J.; Kaplan, T.
1983-03-15
The methods introduced in a previous paper under the name of ''traveling-cluster approximation'' (TCA) are applied, in a multiple-scattering approach, to the case of a random muffin-tin substitutional alloy. This permits the iterative part of a self-consistent calculation to be carried out entirely in terms of on-the-energy-shell scattering amplitudes. Off-shell components of the mean resolvent, needed for the calculation of spectral functions, are obtained by standard methods involving single-site scattering wave functions. The single-site TCA is just the usual coherent-potential approximation, expressed in a form particularly suited for iteration. A fixed-point theorem is proved for the general t-matrix TCA, ensuringmore » convergence upon iteration to a unique self-consistent solution with the physically essential Herglotz properties.« less
Best uniform approximation to a class of rational functions
NASA Astrophysics Data System (ADS)
Zheng, Zhitong; Yong, Jun-Hai
2007-10-01
We explicitly determine the best uniform polynomial approximation to a class of rational functions of the form 1/(x-c)2+K(a,b,c,n)/(x-c) on [a,b] represented by their Chebyshev expansion, where a, b, and c are real numbers, n-1 denotes the degree of the best approximating polynomial, and K is a constant determined by a, b, c, and n. Our result is based on the explicit determination of a phase angle [eta] in the representation of the approximation error by a trigonometric function. Moreover, we formulate an ansatz which offers a heuristic strategies to determine the best approximating polynomial to a function represented by its Chebyshev expansion. Combined with the phase angle method, this ansatz can be used to find the best uniform approximation to some more functions.
Approximation for limit cycles and their isochrons.
Demongeot, Jacques; Françoise, Jean-Pierre
2006-12-01
Local analysis of trajectories of dynamical systems near an attractive periodic orbit displays the notion of asymptotic phase and isochrons. These notions are quite useful in applications to biosciences. In this note, we give an expression for the first approximation of equations of isochrons in the setting of perturbations of polynomial Hamiltonian systems. This method can be generalized to perturbations of systems that have a polynomial integral factor (like the Lotka-Volterra equation).
Pérez-Cárceles, M D; Sibón, A; Vizcaya, M A; Osuna, E; Gómez-Zapata, M; Luna, A; Martínez-Díaz, F
2008-09-01
The histopathological alterations that permit the diagnosis of death by asphyxia are very unspecific, although pulmonary alterations are of great importance in this respect. The postmortem diagnosis of drowning, particularly, continues to be one of the most difficult in forensic pathology. The aim of this study is to jointly evaluate microscopic findings and immunohistochemical surfactant protein A (SP-A) expression in the upper and lower lobes of lungs in different causes of death, and their possible application to the diagnosis of drowning. We studied 120 cadavers from subjects with a mean age of 48.73 years (SD 19.45; range 2-86 years), and with a mean post-mortem interval of 30 hours (SD 39.59; range 3-216 hours). According to the scene, cause and circumstances of death, and autopsy findings, cases were classified into groups as follows: (a) drowning (n=47); (b) other asphyxia (n=44) and (c) other causes (n=29). In the upper and lower lobes of lungs, histological studies of H&E staining and immunohistochemical surfactant protein A expression were made. The presence and severity of congestion, haemorrhage and oedema, together with immunohistochemical SP-A expression, may have a diagnostic value in differentiating asphyxia and drowning from other causes of death, and drowning from other types of asphyxia. Our findings suggest that both lobes should be investigated to establish the diagnosis, although the findings in the upper lobe might be the most important for differentiating the exact cause of death.
Finding Meaning in Written Emotional Expression by Family Caregivers of Persons With Dementia.
Butcher, Howard K; Gordon, Jean K; Ko, Ji Woon; Perkhounkova, Yelena; Cho, Jun Young; Rinner, Andrew; Lutgendorf, Susan
2016-12-01
This study tested the effect of written emotional expression on the ability to find meaning in caregiving and the effects of finding meaning on emotional state and psychological burden in 91 dementia family caregivers. In a pretest-posttest design, participants were randomly assigned to either an experimental or a comparison group. Experimental caregivers (n = 57) wrote about their deepest thoughts and feelings about caring for a family member with dementia, whereas those in the comparison group (n = 34) wrote about nonemotional topics. Results showed enhanced meaning-making abilities in experimental participants relative to comparison participants, particularly for those who used more positive emotion words. Improved meaning-making ability was in turn associated with psychological benefits at posttest, but experimental participants did not show significantly more benefit than comparison participants. We explore the mediating roles of the meaning-making process as well as some of the background characteristics of the individual caregivers and their caregiving environments. © The Author(s) 2016.
Differential global gene expression in red and white skeletal muscle
NASA Technical Reports Server (NTRS)
Campbell, W. G.; Gordon, S. E.; Carlson, C. J.; Pattison, J. S.; Hamilton, M. T.; Booth, F. W.
2001-01-01
The differences in gene expression among the fiber types of skeletal muscle have long fascinated scientists, but for the most part, previous experiments have only reported differences of one or two genes at a time. The evolving technology of global mRNA expression analysis was employed to determine the potential differential expression of approximately 3,000 mRNAs between the white quad (white muscle) and the red soleus muscle (mixed red muscle) of female ICR mice (30-35 g). Microarray analysis identified 49 mRNA sequences that were differentially expressed between white and mixed red skeletal muscle, including newly identified differential expressions between muscle types. For example, the current findings increase the number of known, differentially expressed mRNAs for transcription factors/coregulators by nine and signaling proteins by three. The expanding knowledge of the diversity of mRNA expression between white and mixed red muscle suggests that there could be quite a complex regulation of phenotype between muscles of different fiber types.
Highly Accurate Analytical Approximate Solution to a Nonlinear Pseudo-Oscillator
NASA Astrophysics Data System (ADS)
Wu, Baisheng; Liu, Weijia; Lim, C. W.
2017-07-01
A second-order Newton method is presented to construct analytical approximate solutions to a nonlinear pseudo-oscillator in which the restoring force is inversely proportional to the dependent variable. The nonlinear equation is first expressed in a specific form, and it is then solved in two steps, a predictor and a corrector step. In each step, the harmonic balance method is used in an appropriate manner to obtain a set of linear algebraic equations. With only one simple second-order Newton iteration step, a short, explicit, and highly accurate analytical approximate solution can be derived. The approximate solutions are valid for all amplitudes of the pseudo-oscillator. Furthermore, the method incorporates second-order Taylor expansion in a natural way, and it is of significant faster convergence rate.
A test of the adhesion approximation for gravitational clustering
NASA Technical Reports Server (NTRS)
Melott, Adrian L.; Shandarin, Sergei; Weinberg, David H.
1993-01-01
We quantitatively compare a particle implementation of the adhesion approximation to fully non-linear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel-dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel-dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate than that from ZA or TZA, (b) the error in the phase angle of Fourier components is worse than that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.
A test of the adhesion approximation for gravitational clustering
NASA Technical Reports Server (NTRS)
Melott, Adrian L.; Shandarin, Sergei F.; Weinberg, David H.
1994-01-01
We quantitatively compare a particle implementation of the adhesion approximation to fully nonlinear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel'dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel'dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate that that from ZA to TZA, (b) the error in the phase angle of Fourier components is worse that that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.
A new approximate sum rule for bulk alloy properties
NASA Technical Reports Server (NTRS)
Bozzolo, Guillermo; Ferrante, John
1991-01-01
A new, approximate sum rule is introduced for determining bulk properties of multicomponent systems, in terms of the pure components properties. This expression is applied for the study of lattice parameters, cohesive energies, and bulk moduli of binary alloys. The correct experimental trends (i.e., departure from average values) are predicted in all cases.
Elastic scattering of virtual photons via a quark loop in the double-logarithmic approximation
NASA Astrophysics Data System (ADS)
Ermolaev, B. I.; Ivanov, D. Yu.; Troyan, S. I.
2018-04-01
We calculate the amplitude of elastic photon-photon scattering via a single quark loop in the double-logarithmic approximation, presuming all external photons to be off-shell and unpolarized. At the same time we account for the running coupling effects. We consider this process in the forward kinematics at arbitrary relations between t and the external photon virtualities. We obtain explicit expressions for the photon-photon scattering amplitudes in all double-logarithmic kinematic regions. Then we calculate the small-x asymptotics of the obtained amplitudes and compare them with the parent amplitudes, thereby fixing the applicability regions of the asymptotics, i.e., fixing the applicability region for the nonvacuum Reggeons. We find that these Reggeons should be used at x <10-8 only.
Revised Thomas-Fermi approximation for singular potentials
NASA Astrophysics Data System (ADS)
Dufty, James W.; Trickey, S. B.
2016-08-01
Approximations for the many-fermion free-energy density functional that include the Thomas-Fermi (TF) form for the noninteracting part lead to singular densities for singular external potentials (e.g., attractive Coulomb). This limitation of the TF approximation is addressed here by a formal map of the exact Euler equation for the density onto an equivalent TF form characterized by a modified Kohn-Sham potential. It is shown to be a "regularized" version of the Kohn-Sham potential, tempered by convolution with a finite-temperature response function. The resulting density is nonsingular, with the equilibrium properties obtained from the total free-energy functional evaluated at this density. This new representation is formally exact. Approximate expressions for the regularized potential are given to leading order in a nonlocality parameter, and the limiting behavior at high and low temperatures is described. The noninteracting part of the free energy in this approximation is the usual Thomas-Fermi functional. These results generalize and extend to finite temperatures the ground-state regularization by R. G. Parr and S. Ghosh [Proc. Natl. Acad. Sci. U.S.A. 83, 3577 (1986), 10.1073/pnas.83.11.3577] and by L. R. Pratt, G. G. Hoffman, and R. A. Harris [J. Chem. Phys. 88, 1818 (1988), 10.1063/1.454105] and formally systematize the finite-temperature regularization given by the latter authors.
Approximate effective nonlinear coefficient of second-harmonic generation in KTiOPO(4).
Asaumi, K
1993-10-20
A simplified approximate expression for the effective nonlinear coefficient of type-II second-harmonicgeneration in KTiOPO(4) was obtained by observing that the difference between the refractive indices n(x) and n(y) is 1 order of magnitude smaller than the difference between n(z) and n(y) (or n(x)). The agreement of this approximate equation with the true definition is good, with a maximum discrepancy of 4%.
New Hardness Results for Diophantine Approximation
NASA Astrophysics Data System (ADS)
Eisenbrand, Friedrich; Rothvoß, Thomas
We revisit simultaneous Diophantine approximation, a classical problem from the geometry of numbers which has many applications in algorithms and complexity. The input to the decision version of this problem consists of a rational vector α ∈ ℚ n , an error bound ɛ and a denominator bound N ∈ ℕ + . One has to decide whether there exists an integer, called the denominator Q with 1 ≤ Q ≤ N such that the distance of each number Q ·α i to its nearest integer is bounded by ɛ. Lagarias has shown that this problem is NP-complete and optimization versions have been shown to be hard to approximate within a factor n c/ loglogn for some constant c > 0. We strengthen the existing hardness results and show that the optimization problem of finding the smallest denominator Q ∈ ℕ + such that the distances of Q·α i to the nearest integer are bounded by ɛ is hard to approximate within a factor 2 n unless {textrm{P}} = NP.
Geometrical-optics approximation of forward scattering by gradient-index spheres.
Li, Xiangzhen; Han, Xiang'e; Li, Renxian; Jiang, Huifen
2007-08-01
By means of geometrical optics we present an approximation method for acceleration of the computation of the scattering intensity distribution within a forward angular range (0-60 degrees ) for gradient-index spheres illuminated by a plane wave. The incident angle of reflected light is determined by the scattering angle, thus improving the approximation accuracy. The scattering angle and the optical path length are numerically integrated by a general-purpose integrator. With some special index models, the scattering angle and the optical path length can be expressed by a unique function and the calculation is faster. This method is proved effective for transparent particles with size parameters greater than 50. It fails to give good approximation results at scattering angles whose refractive rays are in the backward direction. For different index models, the geometrical-optics approximation is effective only for forward angles, typically those less than 60 degrees or when the refractive-index difference of a particle is less than a certain value.
Correlation Energies from the Two-Component Random Phase Approximation.
Kühn, Michael
2014-02-11
The correlation energy within the two-component random phase approximation accounting for spin-orbit effects is derived. The resulting plasmon equation is rewritten-analogously to the scalar relativistic case-in terms of the trace of two Hermitian matrices for (Kramers-restricted) closed-shell systems and then represented as an integral over imaginary frequency using the resolution of the identity approximation. The final expression is implemented in the TURBOMOLE program suite. The code is applied to the computation of equilibrium distances and vibrational frequencies of heavy diatomic molecules. The efficiency is demonstrated by calculation of the relative energies of the Oh-, D4h-, and C5v-symmetric isomers of Pb6. Results within the random phase approximation are obtained based on two-component Kohn-Sham reference-state calculations, using effective-core potentials. These values are finally compared to other two-component and scalar relativistic methods, as well as experimental data.
On Born approximation in black hole scattering
NASA Astrophysics Data System (ADS)
Batic, D.; Kelkar, N. G.; Nowakowski, M.
2011-12-01
A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner-Nordström and Reissner-Nordström-de Sitter backgrounds is considered. In particular, explicit formulae in terms of transcendental functions for the scattering of massless scalar particles off black holes are derived within a Born approximation. It is shown that the conditions on the existence of the Born integral forbid a straightforward extraction of the quasi normal modes using the Born approximation for the scattering amplitude. Such a method has been used in literature. We suggest a novel, well defined method, to extract the large imaginary part of quasinormal modes via the Coulomb-like phase shift. Furthermore, we compare the numerically evaluated exact scattering amplitude with the Born one to find that the approximation is not very useful for the scattering of massless scalar, electromagnetic as well as gravitational waves from black holes.
New approximate orientation averaging of the water molecule interacting with the thermal neutron
DOE Office of Scientific and Technical Information (OSTI.GOV)
Markovic, M.I.; Minic, D.M.; Rakic, A.D.
1992-02-01
This paper reports that exactly describing the time of thermal neutron collisions with water molecules, orientation averaging is performed by an exact method (EOA{sub k}) and four approximate methods (two well known and two less known). Expressions for the microscopic scattering kernel are developed. The two well-known approximate orientation averaging methods are Krieger-Nelkin (K-N) and Koppel-Young (K-Y). The results obtained by one of the two proposed approximate orientation averaging methods agree best with the corresponding results obtained by EOA{sub k}. The largest discrepancies between the EOA{sub k} results and the results of the approximate methods are obtained using the well-knowmore » K-N approximate orientation averaging method.« less
Inverse eigenproblem for R-symmetric matrices and their approximation
NASA Astrophysics Data System (ADS)
Yuan, Yongxin
2009-11-01
Let be a nontrivial involution, i.e., R=R-1[not equal to]±In. We say that is R-symmetric if RGR=G. The set of all -symmetric matrices is denoted by . In this paper, we first give the solvability condition for the following inverse eigenproblem (IEP): given a set of vectors in and a set of complex numbers , find a matrix such that and are, respectively, the eigenvalues and eigenvectors of A. We then consider the following approximation problem: Given an n×n matrix , find such that , where is the solution set of IEP and ||[dot operator]|| is the Frobenius norm. We provide an explicit formula for the best approximation solution by means of the canonical correlation decomposition.
Flexible Approximation Model Approach for Bi-Level Integrated System Synthesis
NASA Technical Reports Server (NTRS)
Sobieszczanski-Sobieski, Jaroslaw; Kim, Hongman; Ragon, Scott; Soremekun, Grant; Malone, Brett
2004-01-01
Bi-Level Integrated System Synthesis (BLISS) is an approach that allows design problems to be naturally decomposed into a set of subsystem optimizations and a single system optimization. In the BLISS approach, approximate mathematical models are used to transfer information from the subsystem optimizations to the system optimization. Accurate approximation models are therefore critical to the success of the BLISS procedure. In this paper, new capabilities that are being developed to generate accurate approximation models for BLISS procedure will be described. The benefits of using flexible approximation models such as Kriging will be demonstrated in terms of convergence characteristics and computational cost. An approach of dealing with cases where subsystem optimization cannot find a feasible design will be investigated by using the new flexible approximation models for the violated local constraints.
Approximated analytical solution to an Ebola optimal control problem
NASA Astrophysics Data System (ADS)
Hincapié-Palacio, Doracelly; Ospina, Juan; Torres, Delfim F. M.
2016-11-01
An analytical expression for the optimal control of an Ebola problem is obtained. The analytical solution is found as a first-order approximation to the Pontryagin Maximum Principle via the Euler-Lagrange equation. An implementation of the method is given using the computer algebra system Maple. Our analytical solutions confirm the results recently reported in the literature using numerical methods.
Mean-field approximation for spacing distribution functions in classical systems
NASA Astrophysics Data System (ADS)
González, Diego Luis; Pimpinelli, Alberto; Einstein, T. L.
2012-01-01
We propose a mean-field method to calculate approximately the spacing distribution functions p(n)(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p(n)(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.
Lindén, Fredrik; Cederquist, Henrik; Zettergren, Henning
2016-11-21
We present exact analytical solutions for charge transfer reactions between two arbitrarily charged hard dielectric spheres. These solutions, and the corresponding exact ones for sphere-sphere interaction energies, include sums that describe polarization effects to infinite orders in the inverse of the distance between the sphere centers. In addition, we show that these exact solutions may be approximated by much simpler analytical expressions that are useful for many practical applications. This is exemplified through calculations of Langevin type cross sections for forming a compound system of two colliding spheres and through calculations of electron transfer cross sections. We find that it is important to account for dielectric properties and finite sphere sizes in such calculations, which for example may be useful for describing the evolution, growth, and dynamics of nanometer sized dielectric objects such as molecular clusters or dust grains in different environments including astrophysical ones.
Approximate scaling properties of RNA free energy landscapes
NASA Technical Reports Server (NTRS)
Baskaran, S.; Stadler, P. F.; Schuster, P.
1996-01-01
RNA free energy landscapes are analysed by means of "time-series" that are obtained from random walks restricted to excursion sets. The power spectra, the scaling of the jump size distribution, and the scaling of the curve length measured with different yard stick lengths are used to describe the structure of these "time series". Although they are stationary by construction, we find that their local behavior is consistent with both AR(1) and self-affine processes. Random walks confined to excursion sets (i.e., with the restriction that the fitness value exceeds a certain threshold at each step) exhibit essentially the same statistics as free random walks. We find that an AR(1) time series is in general approximately self-affine on timescales up to approximately the correlation length. We present an empirical relation between the correlation parameter rho of the AR(1) model and the exponents characterizing self-affinity.
Multimodal far-field acoustic radiation pattern: An approximate equation
NASA Technical Reports Server (NTRS)
Rice, E. J.
1977-01-01
The far-field sound radiation theory for a circular duct was studied for both single mode and multimodal inputs. The investigation was intended to develop a method to determine the acoustic power produced by turbofans as a function of mode cut-off ratio. With reasonable simplifying assumptions the single mode radiation pattern was shown to be reducible to a function of mode cut-off ratio only. With modal cut-off ratio as the dominant variable, multimodal radiation patterns can be reduced to a simple explicit expression. This approximate expression provides excellent agreement with an exact calculation of the sound radiation pattern using equal acoustic power per mode.
Accuracy of the adiabatic-impulse approximation for closed and open quantum systems
NASA Astrophysics Data System (ADS)
Tomka, Michael; Campos Venuti, Lorenzo; Zanardi, Paolo
2018-03-01
We study the adiabatic-impulse approximation (AIA) as a tool to approximate the time evolution of quantum states when driven through a region of small gap. Such small-gap regions are a common situation in adiabatic quantum computing and having reliable approximations is important in this context. The AIA originates from the Kibble-Zurek theory applied to continuous quantum phase transitions. The Kibble-Zurek mechanism was developed to predict the power-law scaling of the defect density across a continuous quantum phase transition. Instead, here we quantify the accuracy of the AIA via the trace norm distance with respect to the exact evolved state. As expected, we find that for short times or fast protocols, the AIA outperforms the simple adiabatic approximation. However, for large times or slow protocols, the situation is actually reversed and the AIA provides a worse approximation. Nevertheless, we found a variation of the AIA that can perform better than the adiabatic one. This counterintuitive modification consists in crossing the region of small gap twice. Our findings are illustrated by several examples of driven closed and open quantum systems.
Is Approximate Number Precision a Stable Predictor of Math Ability?
ERIC Educational Resources Information Center
Libertus, Melissa E.; Feigenson, Lisa; Halberda, Justin
2013-01-01
Previous research shows that children's ability to estimate numbers of items using their Approximate Number System (ANS) predicts later math ability. To more closely examine the predictive role of early ANS acuity on later abilities, we assessed the ANS acuity, math ability, and expressive vocabulary of preschoolers twice, six months apart. We…
A New Closed Form Approximation for BER for Optical Wireless Systems in Weak Atmospheric Turbulence
NASA Astrophysics Data System (ADS)
Kaushik, Rahul; Khandelwal, Vineet; Jain, R. C.
2018-04-01
Weak atmospheric turbulence condition in an optical wireless communication (OWC) is captured by log-normal distribution. The analytical evaluation of average bit error rate (BER) of an OWC system under weak turbulence is intractable as it involves the statistical averaging of Gaussian Q-function over log-normal distribution. In this paper, a simple closed form approximation for BER of OWC system under weak turbulence is given. Computation of BER for various modulation schemes is carried out using proposed expression. The results obtained using proposed expression compare favorably with those obtained using Gauss-Hermite quadrature approximation and Monte Carlo Simulations.
Lockhart, Nicole C; Weil, Carol J; Carithers, Latarsha J; Koester, Susan E; Little, A Roger; Volpi, Simona; Moore, Helen M; Berkman, Benjamin E
2018-06-14
The active debate about the return of incidental or secondary findings in research has primarily focused on return to research participants, or in some cases, family members. Particular attention has been paid to return of genomic findings. Yet, research may generate other types of findings that warrant consideration for return, including findings related to the pathology of donated biospecimens. In the case of deceased biospecimen donors who are also organ and/or tissue transplant donors, pathology incidental findings may be relevant not to family members, but to potential organ or tissue transplant recipients. This paper will describe the ethical implications of pathology incidental findings in the Genotype-Tissue Expression (GTEx) project, the process for developing a consensus approach as to if/when such findings should be returned, possible implications for other research projects collecting postmortem tissues and how the scenario encountered in GTEx fits into the larger return of results/incidental findings debate. © Article author(s) (or their employer(s) unless otherwise stated in the text of the article) 2018. All rights reserved. No commercial use is permitted unless otherwise expressly granted.
Low rank approximation in G 0W 0 calculations
Shao, MeiYue; Lin, Lin; Yang, Chao; ...
2016-06-04
The single particle energies obtained in a Kohn-Sham density functional theory (DFT) calculation are generally known to be poor approximations to electron excitation energies that are measured in tr ansport, tunneling and spectroscopic experiments such as photo-emission spectroscopy. The correction to these energies can be obtained from the poles of a single particle Green’s function derived from a many-body perturbation theory. From a computational perspective, the accuracy and efficiency of such an approach depends on how a self energy term that properly accounts for dynamic screening of electrons is approximated. The G 0W 0 approximation is a widely used techniquemore » in which the self energy is expressed as the convolution of a noninteracting Green’s function (G 0) and a screened Coulomb interaction (W 0) in the frequency domain. The computational cost associated with such a convolution is high due to the high complexity of evaluating W 0 at multiple frequencies. In this paper, we discuss how the cost of G 0W 0 calculation can be reduced by constructing a low rank approximation to the frequency dependent part of W 0 . In particular, we examine the effect of such a low rank approximation on the accuracy of the G 0W 0 approximation. We also discuss how the numerical convolution of G 0 and W 0 can be evaluated efficiently and accurately by using a contour deformation technique with an appropriate choice of the contour.« less
Harmonic-phase path-integral approximation of thermal quantum correlation functions
NASA Astrophysics Data System (ADS)
Robertson, Christopher; Habershon, Scott
2018-03-01
We present an approximation to the thermal symmetric form of the quantum time-correlation function in the standard position path-integral representation. By transforming to a sum-and-difference position representation and then Taylor-expanding the potential energy surface of the system to second order, the resulting expression provides a harmonic weighting function that approximately recovers the contribution of the phase to the time-correlation function. This method is readily implemented in a Monte Carlo sampling scheme and provides exact results for harmonic potentials (for both linear and non-linear operators) and near-quantitative results for anharmonic systems for low temperatures and times that are likely to be relevant to condensed phase experiments. This article focuses on one-dimensional examples to provide insights into convergence and sampling properties, and we also discuss how this approximation method may be extended to many-dimensional systems.
Mean-field approximation for spacing distribution functions in classical systems.
González, Diego Luis; Pimpinelli, Alberto; Einstein, T L
2012-01-01
We propose a mean-field method to calculate approximately the spacing distribution functions p((n))(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p((n))(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed. © 2012 American Physical Society
Approximate Dynamic Programming: Combining Regional and Local State Following Approximations.
Deptula, Patryk; Rosenfeld, Joel A; Kamalapurkar, Rushikesh; Dixon, Warren E
2018-06-01
An infinite-horizon optimal regulation problem for a control-affine deterministic system is solved online using a local state following (StaF) kernel and a regional model-based reinforcement learning (R-MBRL) method to approximate the value function. Unlike traditional methods such as R-MBRL that aim to approximate the value function over a large compact set, the StaF kernel approach aims to approximate the value function in a local neighborhood of the state that travels within a compact set. In this paper, the value function is approximated using a state-dependent convex combination of the StaF-based and the R-MBRL-based approximations. As the state enters a neighborhood containing the origin, the value function transitions from being approximated by the StaF approach to the R-MBRL approach. Semiglobal uniformly ultimately bounded (SGUUB) convergence of the system states to the origin is established using a Lyapunov-based analysis. Simulation results are provided for two, three, six, and ten-state dynamical systems to demonstrate the scalability and performance of the developed method.
Correlation energy functional within the GW -RPA: Exact forms, approximate forms, and challenges
NASA Astrophysics Data System (ADS)
Ismail-Beigi, Sohrab
2010-05-01
In principle, the Luttinger-Ward Green’s-function formalism allows one to compute simultaneously the total energy and the quasiparticle band structure of a many-body electronic system from first principles. We present approximate and exact expressions for the correlation energy within the GW -random-phase approximation that are more amenable to computation and allow for developing efficient approximations to the self-energy operator and correlation energy. The exact form is a sum over differences between plasmon and interband energies. The approximate forms are based on summing over screened interband transitions. We also demonstrate that blind extremization of such functionals leads to unphysical results: imposing physical constraints on the allowed solutions (Green’s functions) is necessary. Finally, we present some relevant numerical results for atomic systems.
Direct application of Padé approximant for solving nonlinear differential equations.
Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Garcia-Gervacio, Jose Luis; Huerta-Chua, Jesus; Morales-Mendoza, Luis Javier; Gonzalez-Lee, Mario
2014-01-01
This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. 34L30.
Ise, Hirohiko; Nikaido, Toshio; Negishi, Naoki; Sugihara, Nobuhiro; Suzuki, Fumitaka; Akaike, Toshihiro; Ikeda, Uichi
2004-08-01
Development of a reliable method of isolating highly proliferative potential hepatocytes provides information crucial to progress in the field of hepatocyte transplantation. The aim of this study was to develop reliable hepatocyte transplantation using highly proliferative, eg, progenitor-like hepatocytes, based on asialoglycoprotein receptor (ASGPR) expression levels for hepatocyte transplantation. We have previously reported that mouse hepatocytes with low ASGPR expression levels have highly proliferative potential and can be used as progenitor-like hepatocytes. We therefore fractionated F344 male rat hepatocytes expressing low and high levels of ASGPR and determined the liver repopulation capacity of hepatocytes according to low and high ASGPR expression in the liver. Next, 2 x 10(5) cells of each type were transplanted into female liver regenerative model dipeptidyl peptidase-deficient rats, and we estimated the rate of liver repopulation by the transplanted hepatocytes in the host liver, as determined by recognition of the Sry gene on the Y-chromosome. At 60 days after hepatocyte transplantation, the transplanted hepatocytes occupied approximately 76% of the total hepatocyte mass in the case of the transplantation of hepatocytes with low ASGPR expression, but accounted for approximately 12% and 17% of the mass in the case of the transplantation of hepatocytes with high ASGPR expression and unfractionated hepatocytes, respectively. In conclusion, these findings suggest that hepatocytes with low ASGPR expression can result in normal liver function and a high repopulation capacity in vivo. These results provide insight into development of a strategy for effective liver repopulation using transplanted hepatocytes.
Countably QC-Approximating Posets
Mao, Xuxin; Xu, Luoshan
2014-01-01
As a generalization of countably C-approximating posets, the concept of countably QC-approximating posets is introduced. With the countably QC-approximating property, some characterizations of generalized completely distributive lattices and generalized countably approximating posets are given. The main results are as follows: (1) a complete lattice is generalized completely distributive if and only if it is countably QC-approximating and weakly generalized countably approximating; (2) a poset L having countably directed joins is generalized countably approximating if and only if the lattice σ c(L)op of all σ-Scott-closed subsets of L is weakly generalized countably approximating. PMID:25165730
Approximations for column effect in airplane wing spars
NASA Technical Reports Server (NTRS)
Warner, Edward P; Short, Mac
1927-01-01
The significance attaching to "column effect" in airplane wing spars has been increasingly realized with the passage of time, but exact computations of the corrections to bending moment curves resulting from the existence of end loads are frequently omitted because of the additional labor involved in an analysis by rigorously correct methods. The present report represents an attempt to provide for approximate column effect corrections that can be graphically or otherwise expressed so as to be applied with a minimum of labor. Curves are plotted giving approximate values of the correction factors for single and two bay trusses of varying proportions and with various relationships between axial and lateral loads. It is further shown from an analysis of those curves that rough but useful approximations can be obtained from Perry's formula for corrected bending moment, with the assumed distance between points of inflection arbitrarily modified in accordance with rules given in the report. The discussion of general rules of variation of bending stress with axial load is accompanied by a study of the best distribution of the points of support along a spar for various conditions of loading.
Exponential Approximations Using Fourier Series Partial Sums
NASA Technical Reports Server (NTRS)
Banerjee, Nana S.; Geer, James F.
1997-01-01
The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.
Capacitor-Chain Successive-Approximation ADC
NASA Technical Reports Server (NTRS)
Cunningham, Thomas
2003-01-01
A proposed successive-approximation analog-to-digital converter (ADC) would contain a capacitively terminated chain of identical capacitor cells. Like a conventional successive-approximation ADC containing a bank of binary-scaled capacitors, the proposed ADC would store an input voltage on a sample-and-hold capacitor and would digitize the stored input voltage by finding the closest match between this voltage and a capacitively generated sum of binary fractions of a reference voltage (Vref). However, the proposed capacitor-chain ADC would offer two major advantages over a conventional binary-scaled-capacitor ADC: (1) In a conventional ADC that digitizes to n bits, the largest capacitor (representing the most significant bit) must have 2(exp n-1) times as much capacitance, and hence, approximately 2(exp n-1) times as much area as does the smallest capacitor (representing the least significant bit), so that the total capacitor area must be 2(exp n) times that of the smallest capacitor. In the proposed capacitor-chain ADC, there would be three capacitors per cell, each approximately equal to the smallest capacitor in the conventional ADC, and there would be one cell per bit. Therefore, the total capacitor area would be only about 3(exp n) times that of the smallest capacitor. The net result would be that the proposed ADC could be considerably smaller than the conventional ADC. (2) Because of edge effects, parasitic capacitances, and manufacturing tolerances, it is difficult to make capacitor banks in which the values of capacitance are scaled by powers of 2 to the required precision. In contrast, because all the capacitors in the proposed ADC would be identical, the problem of precise binary scaling would not arise.
Compensation for intracellular environment in expression levels of mammalian circadian clock genes
Matsumura, Ritsuko; Okamoto, Akihiko; Node, Koichi; Akashi, Makoto
2014-01-01
The circadian clock is driven by transcriptional oscillation of clock genes in almost all body cells. To investigate the effect of cell type-specific intracellular environment on the circadian machinery, we examined gene expression profiles in five peripheral tissues. As expected, the phase relationship between expression rhythms of nine clock genes was similar in all tissues examined. We also compared relative expression levels of clock genes among tissues, and unexpectedly found that quantitative variation remained within an approximately three-fold range, which was substantially smaller than that of metabolic housekeeping genes. Interestingly, circadian gene expression was little affected even when fibroblasts were cultured with different concentrations of serum. Together, these findings support a hypothesis that expression levels of clock genes are quantitatively compensated for the intracellular environment, such as redox potential and metabolite composition. However, more comprehensive studies are required to reach definitive conclusions. PMID:24504324
Posed versus spontaneous facial expressions are modulated by opposite cerebral hemispheres.
Ross, Elliott D; Pulusu, Vinay K
2013-05-01
Clinical research has indicated that the left face is more expressive than the right face, suggesting that modulation of facial expressions is lateralized to the right hemisphere. The findings, however, are controversial because the results explain, on average, approximately 4% of the data variance. Using high-speed videography, we sought to determine if movement-onset asymmetry was a more powerful research paradigm than terminal movement asymmetry. The results were very robust, explaining up to 70% of the data variance. Posed expressions began overwhelmingly on the right face whereas spontaneous expressions began overwhelmingly on the left face. This dichotomy was most robust for upper facial expressions. In addition, movement-onset asymmetries did not predict terminal movement asymmetries, which were not significantly lateralized. The results support recent neuroanatomic observations that upper versus lower facial movements have different forebrain motor representations and recent behavioral constructs that posed versus spontaneous facial expressions are modulated preferentially by opposite cerebral hemispheres and that spontaneous facial expressions are graded rather than non-graded movements. Published by Elsevier Ltd.
ERK1/2 mediates glucose-regulated POMC gene expression in hypothalamic neurons.
Zhang, Juan; Zhou, Yunting; Chen, Cheng; Yu, Feiyuan; Wang, Yun; Gu, Jiang; Ma, Lian; Ho, Guyu
2015-04-01
Hypothalamic glucose-sensing neurons regulate the expression of genes encoding feeding-related neuropetides POMC, AgRP, and NPY - the key components governing metabolic homeostasis. AMP-activated protein kinase (AMPK) is postulated to be the molecular mediator relaying glucose signals to regulate the expression of these neuropeptides. Whether other signaling mediator(s) plays a role is not clear. In this study, we investigated the role of ERK1/2 using primary hypothalamic neurons as the model system. The primary neurons were differentiated from hypothalamic progenitor cells. The differentiated neurons possessed the characteristic neuronal cell morphology and expressed neuronal post-mitotic markers as well as leptin-regulated orexigenic POMC and anorexigenic AgRP/NPY genes. Treatment of cells with glucose dose-dependently increased POMC and decreased AgRP/NPY expression with a concurrent suppression of AMPK phosphorylation. In addition, glucose treatment dose-dependently increased the ERK1/2 phosphorylation. Blockade of ERK1/2 activity with its specific inhibitor PD98059 partially (approximately 50%) abolished glucose-induced POMC expression, but had little effect on AgRP/NPY expression. Conversely, blockade of AMPK activity with its specific inhibitor produced a partial (approximately 50%) reversion of low-glucose-suppressed POMC expression, but almost completely blunted the low-glucose-induced AgRP/NPY expression. The results indicate that ERK1/2 mediated POMC but not AgRP/NPY expression. Confirming the in vitro findings, i.c.v. administration of PD98059 in rats similarly attenuated glucose-induced POMC expression in the hypothalamus, but again had little effect on AgRP/NPY expression. The results are indicative of a novel role of ERK1/2 in glucose-regulated POMC expression and offer new mechanistic insights into hypothalamic glucose sensing. © 2015 Society for Endocrinology.
A Space-Saving Approximation Algorithm for Grammar-Based Compression
NASA Astrophysics Data System (ADS)
Sakamoto, Hiroshi; Maruyama, Shirou; Kida, Takuya; Shimozono, Shinichi
A space-efficient approximation algorithm for the grammar-based compression problem, which requests for a given string to find a smallest context-free grammar deriving the string, is presented. For the input length n and an optimum CFG size g, the algorithm consumes only O(g log g) space and O(n log*n) time to achieve O((log*n)log n) approximation ratio to the optimum compression, where log*n is the maximum number of logarithms satisfying log log…log n > 1. This ratio is thus regarded to almost O(log n), which is the currently best approximation ratio. While g depends on the string, it is known that g =Ω(log n) and g=\\\\Omega(\\\\log n) and g=O\\\\left(\\\\frac{n}{log_kn}\\\\right) for strings from k-letter alphabet[12].
Phonons in random alloys: The itinerant coherent-potential approximation
NASA Astrophysics Data System (ADS)
Ghosh, Subhradip; Leath, P. L.; Cohen, Morrel H.
2002-12-01
We present the itinerant coherent-potential approximation (ICPA), an analytic, translationally invariant, and tractable form of augmented-space-based multiple-scattering theory18 in a single-site approximation for harmonic phonons in realistic random binary alloys with mass and force-constant disorder. We provide expressions for quantities needed for comparison with experimental structure factors such as partial and average spectral functions and derive the sum rules associated with them. Numerical results are presented for Ni55Pd45 and Ni50Pt50 alloys which serve as test cases, the former for weak force-constant disorder and the latter for strong. We present results on dispersion curves and disorder-induced widths. Direct comparisons with the single-site coherent potential approximation (CPA) and experiment are made which provide insight into the physics of force-constant changes in random alloys. The CPA accounts well for the weak force-constant disorder case but fails for strong force-constant disorder where the ICPA succeeds.
The TSP-approach to approximate solving the m-Cycles Cover Problem
NASA Astrophysics Data System (ADS)
Gimadi, Edward Kh.; Rykov, Ivan; Tsidulko, Oxana
2016-10-01
In the m-Cycles Cover problem it is required to find a collection of m vertex-disjoint cycles that covers all vertices of the graph and the total weight of edges in the cover is minimum (or maximum). The problem is a generalization of the Traveling salesmen problem. It is strongly NP-hard. We discuss a TSP-approach that gives polynomial approximate solutions for this problem. It transforms an approximation TSP algorithm into an approximation m-CCP algorithm. In this paper we present a number of successful transformations with proven performance guarantees for the obtained solutions.
Estimating proportions in petrographic mixing equations by least-squares approximation.
Bryan, W B; Finger, L W; Chayes, F
1969-02-28
Petrogenetic hypotheses involving fractional crystallization, assimilation, or mixing of magmas may be expressed and tested as problems in leastsquares approximation. The calculation uses all of the data and yields a unique solution for each model, thus avoiding the ambiguity inherent in graphical or trial-and-error procedures. The compositional change in the 1960 lavas of Kilauea Volcano, Hawaii, is used to illustrate the method of calculation.
Approximate symmetries of Hamiltonians
NASA Astrophysics Data System (ADS)
Chubb, Christopher T.; Flammia, Steven T.
2017-08-01
We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.
Optimal causal inference: estimating stored information and approximating causal architecture.
Still, Susanne; Crutchfield, James P; Ellison, Christopher J
2010-09-01
We introduce an approach to inferring the causal architecture of stochastic dynamical systems that extends rate-distortion theory to use causal shielding--a natural principle of learning. We study two distinct cases of causal inference: optimal causal filtering and optimal causal estimation. Filtering corresponds to the ideal case in which the probability distribution of measurement sequences is known, giving a principled method to approximate a system's causal structure at a desired level of representation. We show that in the limit in which a model-complexity constraint is relaxed, filtering finds the exact causal architecture of a stochastic dynamical system, known as the causal-state partition. From this, one can estimate the amount of historical information the process stores. More generally, causal filtering finds a graded model-complexity hierarchy of approximations to the causal architecture. Abrupt changes in the hierarchy, as a function of approximation, capture distinct scales of structural organization. For nonideal cases with finite data, we show how the correct number of the underlying causal states can be found by optimal causal estimation. A previously derived model-complexity control term allows us to correct for the effect of statistical fluctuations in probability estimates and thereby avoid overfitting.
DOE Office of Scientific and Technical Information (OSTI.GOV)
Tobias, Benjamin John
A series approximation has been derived for the transport of optical photons within a cylindrically symmetric light pipe and applied to the task of evaluating both the origin and angular distribution of light reaching the output plane. This analytic expression finds particular utility in first-pass photonic design applications since it may be evaluated at a very modest computational cost and is readily parameterized for relevant design constraints. It has been applied toward quantitative exploration of various scintillation crystal preparations and their impact on both quantum efficiency and noise, reproducing sensible dependencies and providing physical justification for certain gamma ray cameramore » design choices.« less
Description of high-power laser radiation in the paraxial approximation
DOE Office of Scientific and Technical Information (OSTI.GOV)
Milant'ev, V P; Karnilovich, S P; Shaar, Ya N
2015-11-30
We consider the feasibility of an adequate description of a laser pulse of arbitrary shape within the framework of the paraxial approximation. In this approximation, using a parabolic equation and an expansion in the small parameter, expressions are obtained for the field of a sufficiently intense laser radiation given in the form of axially symmetric Hermite – Gaussian beams of arbitrary mode and arbitrary polarisation. It is shown that in the case of sufficiently short pulses, corrections to the transverse components of the laser field are the first-order rather than the secondorder quantities in the expansion in the small parameter.more » The peculiarities of the description of higher-mode Hermite – Gaussian beams are outlined. (light wave transformation)« less
NASA Technical Reports Server (NTRS)
Omidvar, K.
1971-01-01
Expressions for the excitation cross section of the highly excited states of the hydrogenlike atoms by fast charged particles have been derived in the dipole approximation of the semiclassical impact parameter and the Born approximations, making use of a formula for the asymptotic expansion of the oscillator strength of the hydrogenlike atoms given by Menzel. When only the leading term in the asymptotic expansion is retained, the expression for the cross section becomes identical to the expression obtained by the method of the classical collision and correspondence principle given by Percival and Richards. Comparisons are made between the Bethe coefficients obtained here and the Bethe coefficients of the Born approximation for transitions where the Born calculation is available. Satisfactory agreement is obtained only for n yields n + 1 transitions, with n the principal quantum number of the excited state.
Plasma Physics Approximations in Ares
DOE Office of Scientific and Technical Information (OSTI.GOV)
Managan, R. A.
Lee & More derived analytic forms for the transport properties of a plasma. Many hydro-codes use their formulae for electrical and thermal conductivity. The coefficients are complex functions of Fermi-Dirac integrals, F n( μ/θ ), the chemical potential, μ or ζ = ln(1+e μ/θ ), and the temperature, θ = kT. Since these formulae are expensive to compute, rational function approximations were fit to them. Approximations are also used to find the chemical potential, either μ or ζ . The fits use ζ as the independent variable instead of μ/θ . New fits are provided for A α (ζmore » ),A β (ζ ), ζ, f(ζ ) = (1 + e -μ/θ)F 1/2(μ/θ), F 1/2'/F 1/2, F c α, and F c β. In each case the relative error of the fit is minimized since the functions can vary by many orders of magnitude. The new fits are designed to exactly preserve the limiting values in the non-degenerate and highly degenerate limits or as ζ→ 0 or ∞. The original fits due to Lee & More and George Zimmerman are presented for comparison.« less
Montes-Perez, J; Cruz-Vera, A; Herrera, J N
2011-12-01
This work presents the full analytic expressions for the thermodynamic properties and the static structure factor for a hard sphere plus 1-Yukawa fluid within the mean spherical approximation. To obtain these properties of the fluid type Yukawa analytically it was necessary to solve an equation of fourth order for the scaling parameter on a large scale. The physical root of this equation was determined by imposing physical conditions. The results of this work are obtained from seminal papers of Blum and Høye. We show that is not necessary the use the series expansion to solve the equation for the scaling parameter. We applied our theoretical result to find the thermodynamic and the static structure factor for krypton. Our results are in good agreement with those obtained in an experimental form or by simulation using the Monte Carlo method.
Thermally Driven One-Fluid Electron-Proton Solar Wind: Eight-Moment Approximation
NASA Astrophysics Data System (ADS)
Olsen, Espen Lyngdal; Leer, Egil
1996-05-01
In an effort to improve the "classical" solar wind model, we study an eight-moment approximation hydrodynamic solar wind model, in which the full conservation equation for the heat conductive flux is solved together with the conservation equations for mass, momentum, and energy. We consider two different cases: In one model the energy flux needed to drive the solar wind is supplied as heat flux from a hot coronal base, where both the density and temperature are specified. In the other model, the corona is heated. In that model, the coronal base density and temperature are also specified, but the temperature increases outward from the coronal base due to a specified energy flux that is dissipated in the corona. The eight-moment approximation solutions are compared with the results from a "classical" solar wind model in which the collision-dominated gas expression for the heat conductive flux is used. It is shown that the "classical" expression for the heat conductive flux is generally not valid in the solar wind. In collisionless regions of the flow, the eight-moment approximation gives a larger thermalization of the heat conductive flux than the models using the collision-dominated gas approximation for the heat flux, but the heat flux is still larger than the "saturation heat flux." This leads to a breakdown of the electron distribution function, which turns negative in the collisionless region of the flow. By increasing the interaction between the electrons, the heat flux is reduced, and a reasonable shape is obtained on the distribution function. By solving the full set of equations consistent with the eight-moment distribution function for the electrons, we are thus able to draw inferences about the validity of the eight-moment description of the solar wind as well as the validity of the very commonly used collision-dominated gas approximation for the heat conductive flux in the solar wind.
Localization and stationary phase approximation on supermanifolds
NASA Astrophysics Data System (ADS)
Zakharevich, Valentin
2017-08-01
Given an odd vector field Q on a supermanifold M and a Q-invariant density μ on M, under certain compactness conditions on Q, the value of the integral ∫Mμ is determined by the value of μ on any neighborhood of the vanishing locus N of Q. We present a formula for the integral in the case where N is a subsupermanifold which is appropriately non-degenerate with respect to Q. In the process, we discuss the linear algebra necessary to express our result in a coordinate independent way. We also extend the stationary phase approximation and the Morse-Bott lemma to supermanifolds.
Hsiao, K K; Groth, D; Scott, M; Yang, S L; Serban, H; Rapp, D; Foster, D; Torchia, M; Dearmond, S J; Prusiner, S B
1994-01-01
Two lines of transgenic (Tg) mice expressing high (H) levels of the mutant P101L prion protein (PrP) developed a neurologic illness and central nervous system pathology indistinguishable from experimental murine scrapie; these mice were designated Tg(MoPrP-P101L)H. Brain homogenates from Tg(MoPrP-P101L)H mice were inoculated intracerebrally into CD-1 Swiss mice, Syrian hamsters, and Tg196 mice, Tg mice expressing the MoPrP-P101L transgene at low levels. None of the CD-1 mice developed central nervous system dysfunction, whereas approximately 10% of hamsters and approximately 40% of the Tg196 mice manifested neurologic signs between 117 and 639 days after inoculation. Serial transmission of neurodegeneration in Tg196 mice and Syrian hamsters was initiated with brain extracts, producing incubation times of approximately 400 and approximately 75 days, respectively. Although the Tg(MoPrP-P101L)H mice appear to accumulate only low levels of infections prions in their brains, the serial transmission of disease to inoculated recipients argues that prion formation occurs de novo in the brains of these uninoculated animals. These Tg mouse studies, taken together with similar findings in humans dying of inherited prion diseases, provide additional evidence that prions lack a foreign nucleic acid. Images PMID:7916462
Dissociation between exact and approximate addition in developmental dyslexia.
Yang, Xiujie; Meng, Xiangzhi
2016-09-01
Previous research has suggested that number sense and language are involved in number representation and calculation, in which number sense supports approximate arithmetic, and language permits exact enumeration and calculation. Meanwhile, individuals with dyslexia have a core deficit in phonological processing. Based on these findings, we thus hypothesized that children with dyslexia may exhibit exact calculation impairment while doing mental arithmetic. The reaction time and accuracy while doing exact and approximate addition with symbolic Arabic digits and non-symbolic visual arrays of dots were compared between typically developing children and children with dyslexia. Reaction time analyses did not reveal any differences across two groups of children, the accuracies, interestingly, revealed a distinction of approximation and exact addition across two groups of children. Specifically, two groups of children had no differences in approximation. Children with dyslexia, however, had significantly lower accuracy in exact addition in both symbolic and non-symbolic tasks than that of typically developing children. Moreover, linguistic performances were selectively associated with exact calculation across individuals. These results suggested that children with dyslexia have a mental arithmetic deficit specifically in the realm of exact calculation, while their approximation ability is relatively intact. Copyright © 2016 Elsevier Ltd. All rights reserved.
NASA Astrophysics Data System (ADS)
Barlow, Nathaniel S.; Weinstein, Steven J.; Faber, Joshua A.
2017-07-01
An accurate closed-form expression is provided to predict the bending angle of light as a function of impact parameter for equatorial orbits around Kerr black holes of arbitrary spin. This expression is constructed by assuring that the weak- and strong-deflection limits are explicitly satisfied while maintaining accuracy at intermediate values of impact parameter via the method of asymptotic approximants (Barlow et al 2017 Q. J. Mech. Appl. Math. 70 21-48). To this end, the strong deflection limit for a prograde orbit around an extremal black hole is examined, and the full non-vanishing asymptotic behavior is determined. The derived approximant may be an attractive alternative to computationally expensive elliptical integrals used in black hole simulations.
Mars Express recent findings and future plans
NASA Astrophysics Data System (ADS)
Titov, Dmitrij; Bibring, Jean-Pierre; Cardesin, Alejandro; Duxbury, Thomas; Forget, Francois; Giuranna, Marco; González-Galindo, Francisco; Holmström, Mats; Jaumann, Ralf; Määttänen, Anni; Martin, Patrick; Montmessin, Franck; Orosei, Roberto; Pätzold, Martin; Plaut, Jeffrey; MEx SGS Team
2017-04-01
Mars Express remains one of ESA's most scientifically productive missions whose publication record now exceeds 1000 papers. Characterization of geological processes on a local-to-regional scale by HRSC, OMEGA and partner experiments on NASA spacecraft has allowed constraining land-forming processes in space and time. Recent results suggest episodic geological activity as well as the presence of large bodies of liquid water in several provinces (e.g. Eridania Planum, Terra Chimeria) in the early and middle Amazonian epoch and formation of vast sedimentary plains north of the Hellas basin. Mars Express observations and experimental teams provided an essential contribution to the selection of the Mars-2020 landing sites. More than a decade-long record of atmospheric parameters such as temperature, dust loading, water vapor and ozone abundance, water ice and CO2 clouds distribution, collected by SPICAM, PFS and OMEGA spectrometers as well as subsequent modeling have provided key contributions to our understanding of the martian climate. The ASPERA-3 observations of ion escape covering a complete solar cycle have revealed important dependencies of the atmospheric erosion rate on parameters of the solar wind and EUV flux. Structure of the ionosphere sounded by the MARSIS radar and the MaRS radio science experiment was found to be significantly affected by the solar activity, the crustal magnetic field, as well as by the influx of meteorite and cometary dust. MARSIS and ASPERA-3 observations suggest that the sunlit ionosphere over the regions with strong crustal fields is denser and extends to higher altitudes as compared to the regions with no crustal anomalies. The ionospheric plasma expands to higher altitudes where it contacts with the solar wind plasma. Reconnection of solar magnetic field lines carried by the solar wind with field lines of crustal origin opens channels through which the ionospheric plasma escapes to space, producing strong and narrow cavities in the
Mullighan, C G; Kennedy, A; Zhou, X; Radtke, I; Phillips, L A; Shurtleff, S A; Downing, J R
2007-09-01
Somatic mutations in nucleophosmin (NPM1) occur in approximately 35% of adult acute myeloid leukemia (AML). To assess the frequency of NPM1 mutations in pediatric AML, we sequenced NPM1 in the diagnostic blasts from 93 pediatric AML patients. Six cases harbored NPM1 mutations, with each case lacking common cytogenetic abnormalities. To explore the phenotype of the AMLs with NPM1 mutations, gene expression profiles were obtained using Affymetrix U133A microarrays. NPM1 mutations were associated with increased expression of multiple homeobox genes including HOXA9, A10, B2, B6 and MEIS1. As dysregulated homeobox gene expression is also a feature of MLL-rearranged leukemia, the gene expression signatures of NPM1-mutated and MLL-rearranged leukemias were compared. Significant differences were identified between these leukemia subtypes including the expression of different HOX genes, with NPM1-mutated AML showing higher levels of expression of HOXB2, B3, B6 and D4. These results confirm recent reports of perturbed HOX expression in NPM1-mutated adult AML, and provide the first evidence that the NPM1-mutated signature is distinct from MLL-rearranged AML. These findings suggest that mutated NPM1 leads to dysregulated HOX expression via a different mechanism than MLL rearrangement.
An Extension of the Krieger-Li-Iafrate Approximation to the Optimized-Effective-Potential Method
DOE Office of Scientific and Technical Information (OSTI.GOV)
Wilson, B.G.
1999-11-11
The Krieger-Li-Iafrate approximation can be expressed as the zeroth order result of an unstable iterative method for solving the integral equation form of the optimized-effective-potential method. By pre-conditioning the iterate a first order correction can be obtained which recovers the bulk of quantal oscillations missing in the zeroth order approximation. A comparison of calculated total energies are given with Krieger-Li-Iafrate, Local Density Functional, and Hyper-Hartree-Fock results for non-relativistic atoms and ions.
Combinatorial approximation algorithms for MAXCUT using random walks.
DOE Office of Scientific and Technical Information (OSTI.GOV)
Seshadhri, Comandur; Kale, Satyen
We give the first combinatorial approximation algorithm for MaxCut that beats the trivial 0.5 factor by a constant. The main partitioning procedure is very intuitive, natural, and easily described. It essentially performs a number of random walks and aggregates the information to provide the partition. We can control the running time to get an approximation factor-running time tradeoff. We show that for any constant b > 1.5, there is an {tilde O}(n{sup b}) algorithm that outputs a (0.5 + {delta})-approximation for MaxCut, where {delta} = {delta}(b) is some positive constant. One of the components of our algorithm is a weakmore » local graph partitioning procedure that may be of independent interest. Given a starting vertex i and a conductance parameter {phi}, unless a random walk of length {ell} = O(log n) starting from i mixes rapidly (in terms of {phi} and {ell}), we can find a cut of conductance at most {phi} close to the vertex. The work done per vertex found in the cut is sublinear in n.« less
Thermal effects and sudden decay approximation in the curvaton scenario
DOE Office of Scientific and Technical Information (OSTI.GOV)
Kitajima, Naoya; Takesako, Tomohiro; Yokoyama, Shuichiro
2014-10-01
We study the impact of a temperature-dependent curvaton decay rate on the primordial curvature perturbation generated in the curvaton scenario. Using the familiar sudden decay approximation, we obtain an analytical expression for the curvature perturbation after the decay of the curvaton. We then investigate numerically the evolution of the background and of the perturbations during the decay. We first show that the instantaneous transfer coefficient, related to the curvaton energy fraction at the decay, can be extended into a more general parameter, which depends on the net transfer of the curvaton energy into radiation energy or, equivalently, on the totalmore » entropy ratio after the complete curvaton decay. We then compute the curvature perturbation and compare this result with the sudden decay approximation prediction.« less
Approximate inference on planar graphs using loop calculus and belief progagation
DOE Office of Scientific and Technical Information (OSTI.GOV)
Chertkov, Michael; Gomez, Vicenc; Kappen, Hilbert
We introduce novel results for approximate inference on planar graphical models using the loop calculus framework. The loop calculus (Chertkov and Chernyak, 2006b) allows to express the exact partition function Z of a graphical model as a finite sum of terms that can be evaluated once the belief propagation (BP) solution is known. In general, full summation over all correction terms is intractable. We develop an algorithm for the approach presented in Chertkov et al. (2008) which represents an efficient truncation scheme on planar graphs and a new representation of the series in terms of Pfaffians of matrices. We analyzemore » in detail both the loop series and the Pfaffian series for models with binary variables and pairwise interactions, and show that the first term of the Pfaffian series can provide very accurate approximations. The algorithm outperforms previous truncation schemes of the loop series and is competitive with other state-of-the-art methods for approximate inference.« less
Improvements in the Approximate Formulae for the Period of the Simple Pendulum
ERIC Educational Resources Information Center
Turkyilmazoglu, M.
2010-01-01
This paper is concerned with improvements in some exact formulae for the period of the simple pendulum problem. Two recently presented formulae are re-examined and refined rationally, yielding more accurate approximate periods. Based on the improved expressions here, a particular new formula is proposed for the period. It is shown that the derived…
NASA Technical Reports Server (NTRS)
Dutta, Soumitra
1988-01-01
Much of human reasoning is approximate in nature. Formal models of reasoning traditionally try to be precise and reject the fuzziness of concepts in natural use and replace them with non-fuzzy scientific explicata by a process of precisiation. As an alternate to this approach, it has been suggested that rather than regard human reasoning processes as themselves approximating to some more refined and exact logical process that can be carried out with mathematical precision, the essence and power of human reasoning is in its capability to grasp and use inexact concepts directly. This view is supported by the widespread fuzziness of simple everyday terms (e.g., near tall) and the complexity of ordinary tasks (e.g., cleaning a room). Spatial reasoning is an area where humans consistently reason approximately with demonstrably good results. Consider the case of crossing a traffic intersection. We have only an approximate idea of the locations and speeds of various obstacles (e.g., persons and vehicles), but we nevertheless manage to cross such traffic intersections without any harm. The details of our mental processes which enable us to carry out such intricate tasks in such apparently simple manner are not well understood. However, it is that we try to incorporate such approximate reasoning techniques in our computer systems. Approximate spatial reasoning is very important for intelligent mobile agents (e.g., robots), specially for those operating in uncertain or unknown or dynamic domains.
Weber's gravitational force as static weak field approximation
NASA Astrophysics Data System (ADS)
Tiandho, Yuant
2016-02-01
Weber's gravitational force (WGF) is one of gravitational model that can accommodate a non-static system because it depends not only on the distance but also on the velocity and the acceleration. Unlike Newton's law of gravitation, WGF can predict the anomalous of Mercury and gravitational bending of light near massive object very well. Then, some researchers use WGF as an alternative model of gravitation and propose a new mechanics theory namely the relational mechanics theory. However, currently we have known that the theory of general relativity which proposed by Einstein can explain gravity with very accurate. Through the static weak field approximation for the non-relativistic object, we also have known that the theory of general relativity will reduce to Newton's law of gravity. In this work, we expand the static weak field approximation that compatible with relativistic object and we obtain a force equation which correspond to WGF. Therefore, WGF is more precise than Newton's gravitational law. The static-weak gravitational field that we used is a solution of the Einstein's equation in the vacuum that satisfy the linear field approximation. The expression of WGF with ξ = 1 and satisfy the requirement of energy conservation are obtained after resolving the geodesic equation. By this result, we can conclude that WGF can be derived from the general relativity.
Differential TRPV1 and TRPV2 Channel Expression in Dental Pulp
Gibbs, J.L.; Melnyk, J.L.; Basbaum, A.I.
2011-01-01
Hypersensitivity to thermal and mechanical stimuli can occur in painful pulpitis. To explore the neuro-anatomical basis of heat and mechanical sensitivity, we evaluated expression of TRPV1 (heat) and TRPV2 (heat/mechanical) channels in the cell bodies and terminal arborizations of neurons that innervate the dental pulp (DP) and periodontal tissues (PDL). We report that ~50% of trigeminal ganglion (TG) neurons retrogradely labeled from the DP express TRPV2, and this was significantly greater than the general expression of this channel in the TG (15%) and slightly more than what is expressed in the PDL by retrograde labeling (40%). The TRPV1 receptor, however, was less prevalent in neurons innervating the DP than their general expression in the TG (17% vs. 26%) and was more extensively expressed in neurons innervating the PDL (26%). Co-labeling studies showed that 70% of neurons that innervate the DP are myelinated. Approximately 1/3 of the retrogradely labeled neurons from the DP were calcitonin-gene-related-peptide-positive (peptide-expressing), but very few expressed the IB4 marker of non-peptidergic unmyelinated afferents. These findings suggest that the DP has a unique neurochemical innervation with regard to TRP receptor expression, which has significant implications for the mechanisms contributing to odontogenic pain and management strategies. PMID:21406609
Differential TRPV1 and TRPV2 channel expression in dental pulp.
Gibbs, J L; Melnyk, J L; Basbaum, A I
2011-06-01
Hypersensitivity to thermal and mechanical stimuli can occur in painful pulpitis. To explore the neuro-anatomical basis of heat and mechanical sensitivity, we evaluated expression of TRPV1 (heat) and TRPV2 (heat/mechanical) channels in the cell bodies and terminal arborizations of neurons that innervate the dental pulp (DP) and periodontal tissues (PDL). We report that ~50% of trigeminal ganglion (TG) neurons retrogradely labeled from the DP express TRPV2, and this was significantly greater than the general expression of this channel in the TG (15%) and slightly more than what is expressed in the PDL by retrograde labeling (40%). The TRPV1 receptor, however, was less prevalent in neurons innervating the DP than their general expression in the TG (17% vs. 26%) and was more extensively expressed in neurons innervating the PDL (26%). Co-labeling studies showed that 70% of neurons that innervate the DP are myelinated. Approximately 1/3 of the retrogradely labeled neurons from the DP were calcitonin-gene-related-peptide-positive (peptide-expressing), but very few expressed the IB4 marker of non-peptidergic unmyelinated afferents. These findings suggest that the DP has a unique neurochemical innervation with regard to TRP receptor expression, which has significant implications for the mechanisms contributing to odontogenic pain and management strategies.
Feltus, F Alex; Ficklin, Stephen P; Gibson, Scott M; Smith, Melissa C
2013-06-05
In genomics, highly relevant gene interaction (co-expression) networks have been constructed by finding significant pair-wise correlations between genes in expression datasets. These networks are then mined to elucidate biological function at the polygenic level. In some cases networks may be constructed from input samples that measure gene expression under a variety of different conditions, such as for different genotypes, environments, disease states and tissues. When large sets of samples are obtained from public repositories it is often unmanageable to associate samples into condition-specific groups, and combining samples from various conditions has a negative effect on network size. A fixed significance threshold is often applied also limiting the size of the final network. Therefore, we propose pre-clustering of input expression samples to approximate condition-specific grouping of samples and individual network construction of each group as a means for dynamic significance thresholding. The net effect is increase sensitivity thus maximizing the total co-expression relationships in the final co-expression network compendium. A total of 86 Arabidopsis thaliana co-expression networks were constructed after k-means partitioning of 7,105 publicly available ATH1 Affymetrix microarray samples. We term each pre-sorted network a Gene Interaction Layer (GIL). Random Matrix Theory (RMT), an un-supervised thresholding method, was used to threshold each of the 86 networks independently, effectively providing a dynamic (non-global) threshold for the network. The overall gene count across all GILs reached 19,588 genes (94.7% measured gene coverage) and 558,022 unique co-expression relationships. In comparison, network construction without pre-sorting of input samples yielded only 3,297 genes (15.9%) and 129,134 relationships. in the global network. Here we show that pre-clustering of microarray samples helps approximate condition-specific networks and allows for dynamic
2013-01-01
Background In genomics, highly relevant gene interaction (co-expression) networks have been constructed by finding significant pair-wise correlations between genes in expression datasets. These networks are then mined to elucidate biological function at the polygenic level. In some cases networks may be constructed from input samples that measure gene expression under a variety of different conditions, such as for different genotypes, environments, disease states and tissues. When large sets of samples are obtained from public repositories it is often unmanageable to associate samples into condition-specific groups, and combining samples from various conditions has a negative effect on network size. A fixed significance threshold is often applied also limiting the size of the final network. Therefore, we propose pre-clustering of input expression samples to approximate condition-specific grouping of samples and individual network construction of each group as a means for dynamic significance thresholding. The net effect is increase sensitivity thus maximizing the total co-expression relationships in the final co-expression network compendium. Results A total of 86 Arabidopsis thaliana co-expression networks were constructed after k-means partitioning of 7,105 publicly available ATH1 Affymetrix microarray samples. We term each pre-sorted network a Gene Interaction Layer (GIL). Random Matrix Theory (RMT), an un-supervised thresholding method, was used to threshold each of the 86 networks independently, effectively providing a dynamic (non-global) threshold for the network. The overall gene count across all GILs reached 19,588 genes (94.7% measured gene coverage) and 558,022 unique co-expression relationships. In comparison, network construction without pre-sorting of input samples yielded only 3,297 genes (15.9%) and 129,134 relationships. in the global network. Conclusions Here we show that pre-clustering of microarray samples helps approximate condition
Quantum cognition based on an ambiguous representation derived from a rough set approximation.
Gunji, Yukio-Pegio; Sonoda, Kohei; Basios, Vasileios
2016-03-01
Over the last years, in a series papers by Arecchi and others, a model for the cognitive processes involved in decision making has been proposed and investigated. The key element of this model is the expression of apprehension and judgment, basic cognitive process of decision making, as an inverse Bayes inference classifying the information content of neuron spike trains. It has been shown that for successive plural stimuli this inference, equipped with basic non-algorithmic jumps, is affected by quantum-like characteristics. We show here that such a decision making process is related consistently with an ambiguous representation by an observer within a universe of discourse. In our work the ambiguous representation of an object or a stimuli is defined as a pair of maps from objects of a set to their representations, where these two maps are interrelated in a particular structure. The a priori and a posteriori hypotheses in Bayes inference are replaced by the upper and lower approximations, correspondingly, for the initial data sets that are derived with respect to each map. Upper and lower approximations herein are defined in the context of "rough set" analysis. The inverse Bayes inference is implemented by the lower approximations with respect to the one map and for the upper approximation with respect to the other map for a given data set. We show further that, due to the particular structural relation between the two maps, the logical structure of such combined approximations can only be expressed as an orthomodular lattice and therefore can be represented by a quantum rather than a Boolean logic. To our knowledge, this is the first investigation aiming to reveal the concrete logic structure of inverse Bayes inference in cognitive processes. Copyright © 2016. Published by Elsevier Ireland Ltd.
Strong washout approximation to resonant leptogenesis
DOE Office of Scientific and Technical Information (OSTI.GOV)
Garbrecht, Björn; Gautier, Florian; Klaric, Juraj, E-mail: garbrecht@tum.de, E-mail: florian.gautier@tum.de, E-mail: juraj.klaric@tum.de
We show that the effective decay asymmetry for resonant Leptogenesis in the strong washout regime with two sterile neutrinos and a single active flavour can in wide regions of parameter space be approximated by its late-time limit ε=Xsin(2φ)/(X{sup 2}+sin{sup 2}φ), where X=8πΔ/(|Y{sub 1}|{sup 2}+|Y{sub 2}|{sup 2}), Δ=4(M{sub 1}-M{sub 2})/(M{sub 1}+M{sub 2}), φ=arg(Y{sub 2}/Y{sub 1}), and M{sub 1,2}, Y{sub 1,2} are the masses and Yukawa couplings of the sterile neutrinos. This approximation in particular extends to parametric regions where |Y{sub 1,2}|{sup 2}>> Δ, i.e. where the width dominates the mass splitting. We generalise the formula for the effective decay asymmetry to themore » case of several flavours of active leptons and demonstrate how this quantity can be used to calculate the lepton asymmetry for phenomenological scenarios that are in agreement with the observed neutrino oscillations. We establish analytic criteria for the validity of the late-time approximation for the decay asymmetry and compare these with numerical results that are obtained by solving for the mixing and the oscillations of the sterile neutrinos. For phenomenologically viable models with two sterile neutrinos, we find that the flavoured effective late-time decay asymmetry can be applied throughout parameter space.« less
Demidenko, Eugene
2017-09-01
The exact density distribution of the nonlinear least squares estimator in the one-parameter regression model is derived in closed form and expressed through the cumulative distribution function of the standard normal variable. Several proposals to generalize this result are discussed. The exact density is extended to the estimating equation (EE) approach and the nonlinear regression with an arbitrary number of linear parameters and one intrinsically nonlinear parameter. For a very special nonlinear regression model, the derived density coincides with the distribution of the ratio of two normally distributed random variables previously obtained by Fieller (1932), unlike other approximations previously suggested by other authors. Approximations to the density of the EE estimators are discussed in the multivariate case. Numerical complications associated with the nonlinear least squares are illustrated, such as nonexistence and/or multiple solutions, as major factors contributing to poor density approximation. The nonlinear Markov-Gauss theorem is formulated based on the near exact EE density approximation.
Computational Modeling of Proteins based on Cellular Automata: A Method of HP Folding Approximation.
Madain, Alia; Abu Dalhoum, Abdel Latif; Sleit, Azzam
2018-06-01
The design of a protein folding approximation algorithm is not straightforward even when a simplified model is used. The folding problem is a combinatorial problem, where approximation and heuristic algorithms are usually used to find near optimal folds of proteins primary structures. Approximation algorithms provide guarantees on the distance to the optimal solution. The folding approximation approach proposed here depends on two-dimensional cellular automata to fold proteins presented in a well-studied simplified model called the hydrophobic-hydrophilic model. Cellular automata are discrete computational models that rely on local rules to produce some overall global behavior. One-third and one-fourth approximation algorithms choose a subset of the hydrophobic amino acids to form H-H contacts. Those algorithms start with finding a point to fold the protein sequence into two sides where one side ignores H's at even positions and the other side ignores H's at odd positions. In addition, blocks or groups of amino acids fold the same way according to a predefined normal form. We intend to improve approximation algorithms by considering all hydrophobic amino acids and folding based on the local neighborhood instead of using normal forms. The CA does not assume a fixed folding point. The proposed approach guarantees one half approximation minus the H-H endpoints. This lower bound guaranteed applies to short sequences only. This is proved as the core and the folds of the protein will have two identical sides for all short sequences.
High-Dimensional Function Approximation With Neural Networks for Large Volumes of Data.
Andras, Peter
2018-02-01
Approximation of high-dimensional functions is a challenge for neural networks due to the curse of dimensionality. Often the data for which the approximated function is defined resides on a low-dimensional manifold and in principle the approximation of the function over this manifold should improve the approximation performance. It has been show that projecting the data manifold into a lower dimensional space, followed by the neural network approximation of the function over this space, provides a more precise approximation of the function than the approximation of the function with neural networks in the original data space. However, if the data volume is very large, the projection into the low-dimensional space has to be based on a limited sample of the data. Here, we investigate the nature of the approximation error of neural networks trained over the projection space. We show that such neural networks should have better approximation performance than neural networks trained on high-dimensional data even if the projection is based on a relatively sparse sample of the data manifold. We also find that it is preferable to use a uniformly distributed sparse sample of the data for the purpose of the generation of the low-dimensional projection. We illustrate these results considering the practical neural network approximation of a set of functions defined on high-dimensional data including real world data as well.
ɛ-connectedness, finite approximations, shape theory and coarse graining in hyperspaces
NASA Astrophysics Data System (ADS)
Alonso-Morón, Manuel; Cuchillo-Ibanez, Eduardo; Luzón, Ana
2008-12-01
We use upper semifinite hyperspaces of compacta to describe ε-connectedness and to compute homology from finite approximations. We find a new connection between ε-connectedness and the so-called Shape Theory. We construct a geodesically complete R-tree, by means of ε-components at different resolutions, whose behavior at infinite captures the topological structure of the space of components of a given compact metric space. We also construct inverse sequences of finite spaces using internal finite approximations of compact metric spaces. These sequences can be converted into inverse sequences of polyhedra and simplicial maps by means of what we call the Alexandroff-McCord correspondence. This correspondence allows us to relate upper semifinite hyperspaces of finite approximation with the Vietoris-Rips complexes of such approximations at different resolutions. Two motivating examples are included in the introduction. We propose this procedure as a different mathematical foundation for problems on data analysis. This process is intrinsically related to the methodology of shape theory. This paper reinforces Robins’s idea of using methods from shape theory to compute homology from finite approximations.
Structural Reliability Analysis and Optimization: Use of Approximations
NASA Technical Reports Server (NTRS)
Grandhi, Ramana V.; Wang, Liping
1999-01-01
This report is intended for the demonstration of function approximation concepts and their applicability in reliability analysis and design. Particularly, approximations in the calculation of the safety index, failure probability and structural optimization (modification of design variables) are developed. With this scope in mind, extensive details on probability theory are avoided. Definitions relevant to the stated objectives have been taken from standard text books. The idea of function approximations is to minimize the repetitive use of computationally intensive calculations by replacing them with simpler closed-form equations, which could be nonlinear. Typically, the approximations provide good accuracy around the points where they are constructed, and they need to be periodically updated to extend their utility. There are approximations in calculating the failure probability of a limit state function. The first one, which is most commonly discussed, is how the limit state is approximated at the design point. Most of the time this could be a first-order Taylor series expansion, also known as the First Order Reliability Method (FORM), or a second-order Taylor series expansion (paraboloid), also known as the Second Order Reliability Method (SORM). From the computational procedure point of view, this step comes after the design point identification; however, the order of approximation for the probability of failure calculation is discussed first, and it is denoted by either FORM or SORM. The other approximation of interest is how the design point, or the most probable failure point (MPP), is identified. For iteratively finding this point, again the limit state is approximated. The accuracy and efficiency of the approximations make the search process quite practical for analysis intensive approaches such as the finite element methods; therefore, the crux of this research is to develop excellent approximations for MPP identification and also different
The evolution of voids in the adhesion approximation
NASA Astrophysics Data System (ADS)
Sahni, Varun; Sathyaprakah, B. S.; Shandarin, Sergei F.
1994-08-01
We apply the adhesion approximation to study the formation and evolution of voids in the universe. Our simulations-carried out using 1283 particles in a cubical box with side 128 Mpc-indicate that the void spectrum evolves with time and that the mean void size in the standard Cosmic Background Explorer Satellite (COBE)-normalized cold dark matter (CDM) model with H50 = 1 scals approximately as bar D(z) = bar Dzero/(1+2)1/2, where bar Dzero approximately = 10.5 Mpc. Interestingly, we find a strong correlation between the sizes of voids and the value of the primordial gravitational potential at void centers. This observation could in principle, pave the way toward reconstructing the form of the primordial potential from a knowledge of the observed void spectrum. Studying the void spectrum at different cosmological epochs, for spectra with a built in k-space cutoff we find that the number of voids in a representative volume evolves with time. The mean number of voids first increases until a maximum value is reached (indicating that the formation of cellular structure is complete), and then begins to decrease as clumps and filaments erge leading to hierarchical clustering and the subsequent elimination of small voids. The cosmological epoch characterizing the completion of cellular structure occurs when the length scale going nonlinear approaches the mean distance between peaks of the gravitaional potential. A central result of this paper is that voids can be populated by substructure such as mini-sheets and filaments, which run through voids. The number of such mini-pancakes that pass through a given void can be measured by the genus characteristic of an individual void which is an indicator of the topology of a given void in intial (Lagrangian) space. Large voids have on an average a larger measure than smaller voids indicating more substructure within larger voids relative to smaller ones. We find that the topology of individual voids is strongly epoch dependent
Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations
DOE Office of Scientific and Technical Information (OSTI.GOV)
Verde, Licia; Jimenez, Raul; Alvarez-Gaume, Luis
2013-06-01
We provide an exact expression for the multi-variate joint probability distribution function of non-Gaussian fields primordially arising from local transformations of a Gaussian field. This kind of non-Gaussianity is generated in many models of inflation. We apply our expression to the non-Gaussianity estimation from Cosmic Microwave Background maps and the halo mass function where we obtain analytical expressions. We also provide analytic approximations and their range of validity. For the Cosmic Microwave Background we give a fast way to compute the PDF which is valid up to more than 7σ for f{sub NL} values (both true and sampled) not ruledmore » out by current observations, which consists of expressing the PDF as a combination of bispectrum and trispectrum of the temperature maps. The resulting expression is valid for any kind of non-Gaussianity and is not limited to the local type. The above results may serve as the basis for a fully Bayesian analysis of the non-Gaussianity parameter.« less
Validity of the Born approximation for beyond Gaussian weak lensing observables
Petri, Andrea; Haiman, Zoltan; May, Morgan
2017-06-06
Accurate forward modeling of weak lensing (WL) observables from cosmological parameters is necessary for upcoming galaxy surveys. Because WL probes structures in the nonlinear regime, analytical forward modeling is very challenging, if not impossible. Numerical simulations of WL features rely on ray tracing through the outputs of N-body simulations, which requires knowledge of the gravitational potential and accurate solvers for light ray trajectories. A less accurate procedure, based on the Born approximation, only requires knowledge of the density field, and can be implemented more efficiently and at a lower computational cost. In this work, we use simulations to show thatmore » deviations of the Born-approximated convergence power spectrum, skewness and kurtosis from their fully ray-traced counterparts are consistent with the smallest nontrivial O(Φ 3) post-Born corrections (so-called geodesic and lens-lens terms). Our results imply a cancellation among the larger O(Φ 4) (and higher order) terms, consistent with previous analytic work. We also find that cosmological parameter bias induced by the Born-approximated power spectrum is negligible even for a LSST-like survey, once galaxy shape noise is considered. When considering higher order statistics such as the κ skewness and kurtosis, however, we find significant bias of up to 2.5σ. Using the LensTools software suite, we show that the Born approximation saves a factor of 4 in computing time with respect to the full ray tracing in reconstructing the convergence.« less
Validity of the Born approximation for beyond Gaussian weak lensing observables
NASA Astrophysics Data System (ADS)
Petri, Andrea; Haiman, Zoltán; May, Morgan
2017-06-01
Accurate forward modeling of weak lensing (WL) observables from cosmological parameters is necessary for upcoming galaxy surveys. Because WL probes structures in the nonlinear regime, analytical forward modeling is very challenging, if not impossible. Numerical simulations of WL features rely on ray tracing through the outputs of N -body simulations, which requires knowledge of the gravitational potential and accurate solvers for light ray trajectories. A less accurate procedure, based on the Born approximation, only requires knowledge of the density field, and can be implemented more efficiently and at a lower computational cost. In this work, we use simulations to show that deviations of the Born-approximated convergence power spectrum, skewness and kurtosis from their fully ray-traced counterparts are consistent with the smallest nontrivial O (Φ3) post-Born corrections (so-called geodesic and lens-lens terms). Our results imply a cancellation among the larger O (Φ4) (and higher order) terms, consistent with previous analytic work. We also find that cosmological parameter bias induced by the Born-approximated power spectrum is negligible even for a LSST-like survey, once galaxy shape noise is considered. When considering higher order statistics such as the κ skewness and kurtosis, however, we find significant bias of up to 2.5 σ . Using the LensTools software suite, we show that the Born approximation saves a factor of 4 in computing time with respect to the full ray tracing in reconstructing the convergence.
Noise in gene expression is coupled to growth rate
Keren, Leeat; van Dijk, David; Weingarten-Gabbay, Shira; Davidi, Dan; Jona, Ghil; Weinberger, Adina; Milo, Ron; Segal, Eran
2015-01-01
Genetically identical cells exposed to the same environment display variability in gene expression (noise), with important consequences for the fidelity of cellular regulation and biological function. Although population average gene expression is tightly coupled to growth rate, the effects of changes in environmental conditions on expression variability are not known. Here, we measure the single-cell expression distributions of approximately 900 Saccharomyces cerevisiae promoters across four environmental conditions using flow cytometry, and find that gene expression noise is tightly coupled to the environment and is generally higher at lower growth rates. Nutrient-poor conditions, which support lower growth rates, display elevated levels of noise for most promoters, regardless of their specific expression values. We present a simple model of noise in expression that results from having an asynchronous population, with cells at different cell-cycle stages, and with different partitioning of the cells between the stages at different growth rates. This model predicts non-monotonic global changes in noise at different growth rates as well as overall higher variability in expression for cell-cycle–regulated genes in all conditions. The consistency between this model and our data, as well as with noise measurements of cells growing in a chemostat at well-defined growth rates, suggests that cell-cycle heterogeneity is a major contributor to gene expression noise. Finally, we identify gene and promoter features that play a role in gene expression noise across conditions. Our results show the existence of growth-related global changes in gene expression noise and suggest their potential phenotypic implications. PMID:26355006
On the validity of the use of a localized approximation for helical beams. I. Formal aspects
NASA Astrophysics Data System (ADS)
Gouesbet, Gérard; André Ambrosio, Leonardo
2018-03-01
The description of an electromagnetic beam for use in light scattering theories may be carried out by using an expansion over vector spherical wave functions with expansion coefficients expressed in terms of Beam Shape Coefficients (BSCs). A celebrated method to evaluate these BSCs has been the use of localized approximations (with several existing variants). We recently established that the use of any existing localized approximation is of limited validity in the case of Bessel and Mathieu beams. In the present paper, we address a warning against the use of any existing localized approximation in the case of helical beams. More specifically, we demonstrate that a procedure used to validate any existing localized approximation fails in the case of helical beams. Numerical computations in a companion paper will confirm that existing localized approximations are of limited validity in the case of helical beams.
Relaxation approximation in the theory of shear turbulence
NASA Technical Reports Server (NTRS)
Rubinstein, Robert
1995-01-01
Leslie's perturbative treatment of the direct interaction approximation for shear turbulence (Modern Developments in the Theory of Turbulence, 1972) is applied to derive a time dependent model for the Reynolds stresses. The stresses are decomposed into tensor components which satisfy coupled linear relaxation equations; the present theory therefore differs from phenomenological Reynolds stress closures in which the time derivatives of the stresses are expressed in terms of the stresses themselves. The theory accounts naturally for the time dependence of the Reynolds normal stress ratios in simple shear flow. The distortion of wavenumber space by the mean shear plays a crucial role in this theory.
NASA Technical Reports Server (NTRS)
Ito, K.
1984-01-01
The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A charactristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.
Some remarks concerning the centrifugal term approximation
NASA Astrophysics Data System (ADS)
Ferreira, F. J. S.; Bezerra, V. B.
2017-10-01
We generalize the Pekeris approximation for the centrifugal term potential, l/(l +1 ) r2 , and use this to obtain the solutions of the radial Schrödinger equation for the arbitrary angular quantum number, l, of the Hulthén potential. We also obtain the expressions for the bound state energies corresponding to this potential and calculate their values for different states and compare with other results presented in the literature. We also consider some models of physical potentials, namely, the Eckart potential, the Poschl-Teller potentials, the Rosen-Morse potential, the Woods-Saxon potential, and the Manning-Rosen potential. Thus, following straightforward the example corresponding to the Hulthén potential, we show what the radial solutions and the energy spectra for these potentials are.
Analytical approximation for the Einstein-dilaton-Gauss-Bonnet black hole metric
NASA Astrophysics Data System (ADS)
Kokkotas, K. D.; Konoplya, R. A.; Zhidenko, A.
2017-09-01
We construct an analytical approximation for the numerical black hole metric of P. Kanti et al. [Phys. Rev. D 54, 5049 (1996), 10.1103/PhysRevD.54.5049] in the four-dimensional Einstein-dilaton-Gauss-Bonnet (EdGB) theory. The continued fraction expansion in terms of a compactified radial coordinate, used here, converges slowly when the dilaton coupling approaches its extremal values, but for a black hole far from the extremal state, the analytical formula has a maximal relative error of a fraction of one percent already within the third order of the continued fraction expansion. The suggested analytical representation of the numerical black hole metric is relatively compact and a good approximation in the whole space outside the black hole event horizon. Therefore, it can serve in the same way as an exact solution when analyzing particles' motion, perturbations, quasinormal modes, Hawking radiation, accreting disks, and many other problems in the vicinity of a black hole. In addition, we construct the approximate analytical expression for the dilaton field.
Approximate Dispersion Relations for Waves on Arbitrary Shear Flows
NASA Astrophysics Data System (ADS)
Ellingsen, S. À.; Li, Y.
2017-12-01
An approximate dispersion relation is derived and presented for linear surface waves atop a shear current whose magnitude and direction can vary arbitrarily with depth. The approximation, derived to first order of deviation from potential flow, is shown to produce good approximations at all wavelengths for a wide range of naturally occuring shear flows as well as widely used model flows. The relation reduces in many cases to a 3-D generalization of the much used approximation by Skop (1987), developed further by Kirby and Chen (1989), but is shown to be more robust, succeeding in situations where the Kirby and Chen model fails. The two approximations incur the same numerical cost and difficulty. While the Kirby and Chen approximation is excellent for a wide range of currents, the exact criteria for its applicability have not been known. We explain the apparently serendipitous success of the latter and derive proper conditions of applicability for both approximate dispersion relations. Our new model has a greater range of applicability. A second order approximation is also derived. It greatly improves accuracy, which is shown to be important in difficult cases. It has an advantage over the corresponding second-order expression proposed by Kirby and Chen that its criterion of accuracy is explicitly known, which is not currently the case for the latter to our knowledge. Our second-order term is also arguably significantly simpler to implement, and more physically transparent, than its sibling due to Kirby and Chen.
Approximation and inference methods for stochastic biochemical kinetics—a tutorial review
NASA Astrophysics Data System (ADS)
Schnoerr, David; Sanguinetti, Guido; Grima, Ramon
2017-03-01
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the chemical master equation. Despite its simple structure, no analytic solutions to the chemical master equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics.
Bonanno, George A; Colak, Deniz M; Keltner, Dacher; Shiota, Michelle N; Papa, Anthony; Noll, Jennie G; Putnam, Frank W; Trickett, Penelope K
2007-11-01
Positive emotions promote adjustment to aversive life events. However, evolutionary theory and empirical research on trauma disclosure suggest that in the context of stigmatized events, expressing positive emotions might incur social costs. To test this thesis, the authors coded genuine (Duchenne) smiling and laughter and also non-Duchenne smiling from videotapes of late-adolescent and young adult women, approximately half with documented histories of childhood sexual abuse (CSA), as they described the most distressing event of their lives. Consistent with previous studies, genuine positive emotional expression was generally associated with better social adjustment two years later. However, as anticipated, CSA survivors who expressed positive emotion in the context of describing a past CSA experience had poorer long-term social adjustment, whereas CSA survivors who expressed positive emotion while describing a nonabuse experience had improved social adjustment. These findings suggest that the benefits of positive emotional expression may often be context specific.
Approximating quantum many-body wave functions using artificial neural networks
NASA Astrophysics Data System (ADS)
Cai, Zi; Liu, Jinguo
2018-01-01
In this paper, we demonstrate the expressibility of artificial neural networks (ANNs) in quantum many-body physics by showing that a feed-forward neural network with a small number of hidden layers can be trained to approximate with high precision the ground states of some notable quantum many-body systems. We consider the one-dimensional free bosons and fermions, spinless fermions on a square lattice away from half-filling, as well as frustrated quantum magnetism with a rapidly oscillating ground-state characteristic function. In the latter case, an ANN with a standard architecture fails, while that with a slightly modified one successfully learns the frustration-induced complex sign rule in the ground state and approximates the ground states with high precisions. As an example of practical use of our method, we also perform the variational method to explore the ground state of an antiferromagnetic J1-J2 Heisenberg model.
CONTRIBUTIONS TO RATIONAL APPROXIMATION,
Some of the key results of linear Chebyshev approximation theory are extended to generalized rational functions. Prominent among these is Haar’s...linear theorem which yields necessary and sufficient conditions for uniqueness. Some new results in the classic field of rational function Chebyshev...Furthermore a Weierstrass type theorem is proven for rational Chebyshev approximation. A characterization theorem for rational trigonometric Chebyshev approximation in terms of sign alternation is developed. (Author)
NASA Astrophysics Data System (ADS)
Khatami, Ehsan; Macridin, Alexandru; Jarrell, Mark
2008-03-01
Recently, several authors have employed the ``glue" approximation for the Cuprates in which the full pairing vertex is approximated by the spin susceptibility. We study this approximation using Quantum Monte Carlo Dynamical Cluster Approximation methods on a 2D Hubbard model. By considering a reasonable finite value for the next nearest neighbor hopping, we find that this ``glue" approximation, in the current form, does not capture the correct pairing symmetry. Here, d-wave is not the leading pairing symmetry while it is the dominant symmetry using the ``exact" QMC results. We argue that the sensitivity of this approximation to the band structure changes leads to this inconsistency and that this form of interaction may not be the appropriate description of the pairing mechanism in Cuprates. We suggest improvements to this approximation which help to capture the the essential features of the QMC data.
Expression of recombinant sea urchin cellulase SnEG54 using mammalian cell lines.
Okumura, Fumihiko; Kameda, Hiroyuki; Ojima, Takao; Hatakeyama, Shigetsugu
2010-05-07
We previously identified the cellulase SnEG54 from Japanese purple sea urchin Strongylocentrotus nudus, the molecular mass of which is about 54kDa on SDS-PAGE. It is difficult to express and purify a recombinant cellulase protein using bacteria such as Escherichia coli or yeast. In this study, we generated mammalian expression vectors encoding SnEG54 to transiently express SnEG54 in mammalian cells. Both SnEG54 expressed in mammalian cells and SnEG54 released into the culture supernatant showed hydrolytic activity toward carboxymethyl cellulose. By using a retroviral expression system, we also established a mammalian cell line that constitutively produces SnEG54. Unexpectedly, SnEG54 released into the culture medium was not stable, and the peak time showing the highest concentration was approximately 1-2days after seeding into fresh culture media. These findings suggest that non-mammalian sea urchin cellulase can be generated in human cell lines but that recombinant SnEG54 is unstable in culture medium due to an unidentified mechanism. Copyright (c) 2010 Elsevier Inc. All rights reserved.
Actin expression in trypanosomatids (Euglenozoa: Kinetoplastea)
Souza, Ligia Cristina Kalb; Pinho, Rosana Elisa Gonçalves Gonçalves; Lima, Carla Vanessa de Paula; Fragoso, Stênio Perdigão; Soares, Maurilio José
2013-01-01
Heteroxenic and monoxenic trypanosomatids were screened for the presence of actin using a mouse polyclonal antibody produced against the entire sequence of the Trypanosoma cruzi actin gene, encoding a 41.9 kDa protein. Western blot analysis showed that this antibody reacted with a polypeptide of approximately 42 kDa in the whole-cell lysates of parasites targeting mammals (T. cruzi, Trypanosoma brucei and Leishmania major), insects (Angomonas deanei, Crithidia fasciculata, Herpetomonas samuelpessoai and Strigomonas culicis) and plants (Phytomonas serpens). A single polypeptide of approximately 42 kDa was detected in the whole-cell lysates of T. cruzi cultured epimastigotes, metacyclic trypomastigotes and amastigotes at similar protein expression levels. Confocal microscopy showed that actin was expressed throughout the cytoplasm of all the tested trypanosomatids. These data demonstrate that actin expression is widespread in trypanosomatids. PMID:23903980
Approximate Genealogies Under Genetic Hitchhiking
Pfaffelhuber, P.; Haubold, B.; Wakolbinger, A.
2006-01-01
The rapid fixation of an advantageous allele leads to a reduction in linked neutral variation around the target of selection. The genealogy at a neutral locus in such a selective sweep can be simulated by first generating a random path of the advantageous allele's frequency and then a structured coalescent in this background. Usually the frequency path is approximated by a logistic growth curve. We discuss an alternative method that approximates the genealogy by a random binary splitting tree, a so-called Yule tree that does not require first constructing a frequency path. Compared to the coalescent in a logistic background, this method gives a slightly better approximation for identity by descent during the selective phase and a much better approximation for the number of lineages that stem from the founder of the selective sweep. In applications such as the approximation of the distribution of Tajima's D, the two approximation methods perform equally well. For relevant parameter ranges, the Yule approximation is faster. PMID:17182733
The HSP terminator of Arabidopsis thaliana increases gene expression in plant cells.
Nagaya, Shingo; Kawamura, Kazue; Shinmyo, Atsuhiko; Kato, Ko
2010-02-01
To express a foreign gene in plants effectively, a good expression system is required. Here we describe the identification of a transcriptional terminator that supports increased levels of expression. The terminators of several Arabidopsis genes were examined in transfected Arabidopsis T87 protoplasts. The heat shock protein 18.2 (HSP) terminator was the most effective in supporting increased levels of expression. The HSP terminator increases mRNA levels of both transiently and stably expressed transgenes approximately 2-fold more than the NOS (nopaline synthase) terminator. When combined with the HSP terminator, a translational enhancer increased gene expression levels approximately 60- to 100-fold in transgenic plants.
Solving Math Problems Approximately: A Developmental Perspective
Ganor-Stern, Dana
2016-01-01
Although solving arithmetic problems approximately is an important skill in everyday life, little is known about the development of this skill. Past research has shown that when children are asked to solve multi-digit multiplication problems approximately, they provide estimates that are often very far from the exact answer. This is unfortunate as computation estimation is needed in many circumstances in daily life. The present study examined 4th graders, 6th graders and adults’ ability to estimate the results of arithmetic problems relative to a reference number. A developmental pattern was observed in accuracy, speed and strategy use. With age there was a general increase in speed, and an increase in accuracy mainly for trials in which the reference number was close to the exact answer. The children tended to use the sense of magnitude strategy, which does not involve any calculation but relies mainly on an intuitive coarse sense of magnitude, while the adults used the approximated calculation strategy which involves rounding and multiplication procedures, and relies to a greater extent on calculation skills and working memory resources. Importantly, the children were less accurate than the adults, but were well above chance level. In all age groups performance was enhanced when the reference number was smaller (vs. larger) than the exact answer and when it was far (vs. close) from it, suggesting the involvement of an approximate number system. The results suggest the existence of an intuitive sense of magnitude for the results of arithmetic problems that might help children and even adults with difficulties in math. The present findings are discussed in the context of past research reporting poor estimation skills among children, and the conditions that might allow using children estimation skills in an effective manner. PMID:27171224
The evolution of voids in the adhesion approximation
NASA Technical Reports Server (NTRS)
Sahni, Varun; Sathyaprakah, B. S.; Shandarin, Sergei F.
1994-01-01
We apply the adhesion approximation to study the formation and evolution of voids in the universe. Our simulations-carried out using 128(exp 3) particles in a cubical box with side 128 Mpc-indicate that the void spectrum evolves with time and that the mean void size in the standard Cosmic Background Explorer Satellite (COBE)-normalized cold dark matter (CDM) model with H(sub 50) = 1 scals approximately as bar D(z) = bar D(sub zero)/(1+2)(exp 1/2), where bar D(sub zero) approximately = 10.5 Mpc. Interestingly, we find a strong correlation between the sizes of voids and the value of the primordial gravitational potential at void centers. This observation could in principle, pave the way toward reconstructing the form of the primordialpotential from a knowledge of the observed void spectrum. Studying the void spectrum at different cosmological epochs, for spectra with a built in k-space cutoff we find that the number of voids in a representative volume evolves with time. The mean number of voids first increases until a maximum value is reached (indicating that the formation of cellular structure is complete), and then begins to decrease as clumps and filaments erge leading to hierarchical clustering and the subsequent elimination of small voids. The cosmological epoch characterizing the completion of cellular structure occurs when the length scale going nonlinear approaches the mean distance between peaks of the gravitaional potential. A central result of this paper is that voids can be populated by substructure such as mini-sheets and filaments, which run through voids. The number of such mini-pancakes that pass through a given void can be measured by the genus characteristic of an individual void which is an indicator of the topology of a given void in intial (Lagrangian) space. Large voids have on an average a larger measure than smaller voids indicating more substructure within larger voids relative to smaller ones. We find that the topology of individual voids is
NASA Technical Reports Server (NTRS)
Connor, J. N. L.; Curtis, P. R.; Farrelly, D.
1984-01-01
Methods that can be used in the numerical implementation of the uniform swallowtail approximation are described. An explicit expression for that approximation is presented to the lowest order, showing that there are three problems which must be overcome in practice before the approximation can be applied to any given problem. It is shown that a recently developed quadrature method can be used for the accurate numerical evaluation of the swallowtail canonical integral and its partial derivatives. Isometric plots of these are presented to illustrate some of their properties. The problem of obtaining the arguments of the swallowtail integral from an analytical function of its argument is considered, describing two methods of solving this problem. The asymptotic evaluation of the butterfly canonical integral is addressed.
Approximate kernel competitive learning.
Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang
2015-03-01
Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches. Copyright © 2014 Elsevier Ltd. All rights reserved.
Born-Oppenheimer approximation for a singular system
NASA Astrophysics Data System (ADS)
Akbas, Haci; Turgut, O. Teoman
2018-01-01
We discuss a simple singular system in one dimension, two heavy particles interacting with a light particle via an attractive contact interaction and not interacting among themselves. It is natural to apply the Born-Oppenheimer approximation to this problem. We present a detailed discussion of this approach; the advantage of this simple model is that one can estimate the error terms self-consistently. Moreover, a Fock space approach to this problem is presented where an expansion can be proposed to get higher order corrections. A slight modification of the same problem in which the light particle is relativistic is discussed in a later section by neglecting pair creation processes. Here, the second quantized description is more challenging, but with some care, one can recover the first order expression exactly.
Noise in gene expression is coupled to growth rate.
Keren, Leeat; van Dijk, David; Weingarten-Gabbay, Shira; Davidi, Dan; Jona, Ghil; Weinberger, Adina; Milo, Ron; Segal, Eran
2015-12-01
Genetically identical cells exposed to the same environment display variability in gene expression (noise), with important consequences for the fidelity of cellular regulation and biological function. Although population average gene expression is tightly coupled to growth rate, the effects of changes in environmental conditions on expression variability are not known. Here, we measure the single-cell expression distributions of approximately 900 Saccharomyces cerevisiae promoters across four environmental conditions using flow cytometry, and find that gene expression noise is tightly coupled to the environment and is generally higher at lower growth rates. Nutrient-poor conditions, which support lower growth rates, display elevated levels of noise for most promoters, regardless of their specific expression values. We present a simple model of noise in expression that results from having an asynchronous population, with cells at different cell-cycle stages, and with different partitioning of the cells between the stages at different growth rates. This model predicts non-monotonic global changes in noise at different growth rates as well as overall higher variability in expression for cell-cycle-regulated genes in all conditions. The consistency between this model and our data, as well as with noise measurements of cells growing in a chemostat at well-defined growth rates, suggests that cell-cycle heterogeneity is a major contributor to gene expression noise. Finally, we identify gene and promoter features that play a role in gene expression noise across conditions. Our results show the existence of growth-related global changes in gene expression noise and suggest their potential phenotypic implications. © 2015 Keren et al.; Published by Cold Spring Harbor Laboratory Press.
Baek, A-Hyong; Jeon, Eun-Yeong; Lee, Sun-Mee; Park, Jin-Byung
2015-05-01
We demonstrated for the first time that the archaeal chaperones (i.e., γ-prefoldin and thermosome) can stabilize enzyme activity in vivo. Ricinoleic acid biotransformation activity of recombinant Escherichia coli expressing Micrococcus luteus alcohol dehydrogenase and the Pseudomonas putida KT2440 Baeyer-Villiger monooxygenase improved significantly with co-expression of γ-prefoldin or recombinant themosome originating from the deep-sea hyperthermophile archaea Methanocaldococcus jannaschii. Furthermore, the degree of enhanced activity was dependent on the expression levels of the chaperones. For example, whole-cell biotransformation activity was highest at 12 µmol/g dry cells/min when γ-prefoldin expression level was approximately 46% of the theoretical maximum. This value was approximately two-fold greater than that in E. coli, where the γ-prefoldin expression level was zero or set to the theoretical maximum. Therefore, it was assumed that the expression levels of chaperones must be optimized to achieve maximum biotransformation activity in whole-cell biocatalysts. © 2014 Wiley Periodicals, Inc.
Variational extension of the mean spherical approximation to arbitrary dimensions
NASA Astrophysics Data System (ADS)
Velázquez, Esov S.; Blum, Lesser; Frisch, Harry L.
1997-10-01
We generalize a variational principle for the mean spherical approximation for a system of charged hard spheres in 3D to arbitrary dimensions. We first construct a free energy variational trial function from the Debye-Hückel excess charging internal energy at a finite concentration and an entropy obtained at the zero-concentration limit by thermodynamic integration. In three dimensions the minimization of this expression with respect to the screening parameter leads to the mean spherical approximation, usually obtained by solution of the Ornstein-Zernike equation. This procedure, which interpolates naturally between the zero concentration/coupling limit and the high-concentration/ coupling limit, is extended to arbitrary dimensions. We conjecture that this result is also equivalent to the MSA as originally defined, although a technical proof of this point is left for the future. The Onsager limit T ΔS MSA / ΔE MSA → 0 for infinite concentration/coupling is satisfied for all d ≠ 2, while for d=2 this limit is 1.
Jablonski-Momeni, Anahita; Jablonski, Boris; Lippe, Nikola
2017-01-01
Apart from the visual detection of caries, X-rays can be taken for detection of approximal lesions. The Proxi head of VistaCam iX intraoral camera system uses near-infrared light (NIR) to enable caries detection in approximal surfaces. The aim of this study was to evaluate the performance of the NIR for the detection of approximal enamel lesions by comparison with radiographic findings. One hundred ninety-three approximal surfaces from 18 patients were examined visually and using digital radiographs for presence or absence of enamel lesions. Then digital images of each surface were produced using the near-infrared light. Correlation between methods was assessed using Spearman's rank correlation coefficient ( r s ). Agreement between radiographic and NIR findings was calculated using the kappa coefficient. McNemar's test was used to analyse differences between the radiographic and NIR findings ( α =0.05). Moderate correlation was found between all detection methods ( r s =0.33-0.50, P <0.0001). Agreement between the radiographic and NIR findings was moderate ( κ =0.50, 95% CI=0.37-0.62) for the distinction between sound surfaces and enamel caries. No significant differences were found between the findings ( P =0.07). Radiographs and NIR were found to be comparable for the detection of enamel lesions in permanent teeth.
Liao, Jin-sheng; Ding, Xiao-yi; Xu, Shun-liang
2015-05-01
To investigate the mRNA and protein expression levels of S100A8 and S100A9 in giant cell tumor (GCT) of bone, and its relation with radiological findings and biological behavior. Forty three patient with GCT of bone admitted in Ruijin Hospital Shanghai Jiaotong University School of Medicine from January 2009 to June 2012 were enrolled in the study. The expression levels of S100A8 and S100A9 mRNA and protein were detected by using semiquantitative RT-PCR and Western blotting in 43 specimens of GCT and 6 specimens of normal bone marrow. The CT and MRI findings of patients were retrospectively reviewed, its relation with tissue expression of S100A8 and S100A9 was analyzed. Among 43 GCT cases 40 showed positive expression of S100A8 and S100A9 mRNA and protein, and the expression levels were significantly higher than those in normal bone marrow P<0.05). The expression level of S100A8 protein was significantly different in bone GCT with different composition ratio on MRI (P<0.05).The expression level of S100A9 protein was significantly different in GCT with different degree of bone destruction on CT scan (P<0.05). The expression of S100A8 and S100A9 mRNA and protein is up-regulated in GCT of bone. The expression of S100A8 and S100A9 is associated with the real composition ratio and the degree of bone destruction, respectively, indicating that S100A8 and S100A9 may be involved in the biological behavior of bone GCT.
Training the approximate number system improves math proficiency.
Park, Joonkoo; Brannon, Elizabeth M
2013-10-01
Humans and nonhuman animals share an approximate number system (ANS) that permits estimation and rough calculation of quantities without symbols. Recent studies show a correlation between the acuity of the ANS and performance in symbolic math throughout development and into adulthood, which suggests that the ANS may serve as a cognitive foundation for the uniquely human capacity for symbolic math. Such a proposition leads to the untested prediction that training aimed at improving ANS performance will transfer to improvement in symbolic-math ability. In the two experiments reported here, we showed that ANS training on approximate addition and subtraction of arrays of dots selectively improved symbolic addition and subtraction. This finding strongly supports the hypothesis that complex math skills are fundamentally linked to rudimentary preverbal quantitative abilities and provides the first direct evidence that the ANS and symbolic math may be causally related. It also raises the possibility that interventions aimed at the ANS could benefit children and adults who struggle with math.
Padé approximations for Painlevé I and II transcendents
NASA Astrophysics Data System (ADS)
Novokshenov, V. Yu.
2009-06-01
We use a version of the Fair-Luke algorithm to find the Padé approximate solutions of the Painlevé I and II equations. We find the distributions of poles for the well-known Ablowitz-Segur and Hastings-McLeod solutions of the Painlevé II equation. We show that the Boutroux tritronquée solution of the Painleé I equation has poles only in the critical sector of the complex plane. The algorithm allows checking other analytic properties of the Painlevé transcendents, such as the asymptotic behavior at infinity in the complex plane.
Linear Approximation to Optimal Control Allocation for Rocket Nozzles with Elliptical Constraints
NASA Technical Reports Server (NTRS)
Orr, Jeb S.; Wall, Johnm W.
2011-01-01
In this paper we present a straightforward technique for assessing and realizing the maximum control moment effectiveness for a launch vehicle with multiple constrained rocket nozzles, where elliptical deflection limits in gimbal axes are expressed as an ensemble of independent quadratic constraints. A direct method of determining an approximating ellipsoid that inscribes the set of attainable angular accelerations is derived. In the case of a parameterized linear generalized inverse, the geometry of the attainable set is computationally expensive to obtain but can be approximated to a high degree of accuracy with the proposed method. A linear inverse can then be optimized to maximize the volume of the true attainable set by maximizing the volume of the approximating ellipsoid. The use of a linear inverse does not preclude the use of linear methods for stability analysis and control design, preferred in practice for assessing the stability characteristics of the inertial and servoelastic coupling appearing in large boosters. The present techniques are demonstrated via application to the control allocation scheme for a concept heavy-lift launch vehicle.
Husimi-cactus approximation study on the diluted spin ice
NASA Astrophysics Data System (ADS)
Otsuka, Hiromi; Okabe, Yutaka; Nefedev, Konstantin
2018-04-01
We investigate dilution effects on the classical spin-ice materials such as Ho2Ti2O7 and Dy2Ti2O7 . In particular, we derive a formula of the thermodynamic quantities as functions of the temperature and a nonmagnetic ion concentration based on a Husimi-cactus approximation. We find that the formula predicts a dilution-induced crossover from the cooperative to the conventional paramagnets in a ground state, and that it also reproduces the "generalized Pauling's entropy" given by Ke et al. To verify the formula from a numerical viewpoint, we compare these results with Monte Carlo simulation calculation data, and then find good agreement for all parameter values.
Laplace transform homotopy perturbation method for the approximation of variational problems.
Filobello-Nino, U; Vazquez-Leal, H; Rashidi, M M; Sedighi, H M; Perez-Sesma, A; Sandoval-Hernandez, M; Sarmiento-Reyes, A; Contreras-Hernandez, A D; Pereyra-Diaz, D; Hoyos-Reyes, C; Jimenez-Fernandez, V M; Huerta-Chua, J; Castro-Gonzalez, F; Laguna-Camacho, J R
2016-01-01
This article proposes the application of Laplace Transform-Homotopy Perturbation Method and some of its modifications in order to find analytical approximate solutions for the linear and nonlinear differential equations which arise from some variational problems. As case study we will solve four ordinary differential equations, and we will show that the proposed solutions have good accuracy, even we will obtain an exact solution. In the sequel, we will see that the square residual error for the approximate solutions, belongs to the interval [0.001918936920, 0.06334882582], which confirms the accuracy of the proposed methods, taking into account the complexity and difficulty of variational problems.
Super-sample covariance approximations and partial sky coverage
NASA Astrophysics Data System (ADS)
Lacasa, Fabien; Lima, Marcos; Aguena, Michel
2018-04-01
Super-sample covariance (SSC) is the dominant source of statistical error on large scale structure (LSS) observables for both current and future galaxy surveys. In this work, we concentrate on the SSC of cluster counts, also known as sample variance, which is particularly useful for the self-calibration of the cluster observable-mass relation; our approach can similarly be applied to other observables, such as galaxy clustering and lensing shear. We first examined the accuracy of two analytical approximations proposed in the literature for the flat sky limit, finding that they are accurate at the 15% and 30-35% level, respectively, for covariances of counts in the same redshift bin. We then developed a harmonic expansion formalism that allows for the prediction of SSC in an arbitrary survey mask geometry, such as large sky areas of current and future surveys. We show analytically and numerically that this formalism recovers the full sky and flat sky limits present in the literature. We then present an efficient numerical implementation of the formalism, which allows fast and easy runs of covariance predictions when the survey mask is modified. We applied our method to a mask that is broadly similar to the Dark Energy Survey footprint, finding a non-negligible negative cross-z covariance, i.e. redshift bins are anti-correlated. We also examined the case of data removal from holes due to, for example bright stars, quality cuts, or systematic removals, and find that this does not have noticeable effects on the structure of the SSC matrix, only rescaling its amplitude by the effective survey area. These advances enable analytical covariances of LSS observables to be computed for current and future galaxy surveys, which cover large areas of the sky where the flat sky approximation fails.
Calculation of light delay for coupled microrings by FDTD technique and Padé approximation.
Huang, Yong-Zhen; Yang, Yue-De
2009-11-01
The Padé approximation with Baker's algorithm is compared with the least-squares Prony method and the generalized pencil-of-functions (GPOF) method for calculating mode frequencies and mode Q factors for coupled optical microdisks by FDTD technique. Comparisons of intensity spectra and the corresponding mode frequencies and Q factors show that the Padé approximation can yield more stable results than the Prony and the GPOF methods, especially the intensity spectrum. The results of the Prony method and the GPOF method are greatly influenced by the selected number of resonant modes, which need to be optimized during the data processing, in addition to the length of the time response signal. Furthermore, the Padé approximation is applied to calculate light delay for embedded microring resonators from complex transmission spectra obtained by the Padé approximation from a FDTD output. The Prony and the GPOF methods cannot be applied to calculate the transmission spectra, because the transmission signal obtained by the FDTD simulation cannot be expressed as a sum of damped complex exponentials.
Non-symbolic approximate arithmetic training improves math performance in preschoolers.
Park, Joonkoo; Bermudez, Vanessa; Roberts, Rachel C; Brannon, Elizabeth M
2016-12-01
Math proficiency at early school age is an important predictor of later academic achievement. Thus, an important goal for society should be to improve math readiness in preschool-age children, especially in low-income children who typically arrive in kindergarten with less mathematical competency than their higher income peers. The majority of existing research-based math intervention programs target symbolic verbal number concepts in young children. However, very little attention has been paid to the preverbal intuitive ability to approximately represent numerical quantity, which is hypothesized to be an important foundation for full-fledged mathematical thinking. Here, we tested the hypothesis that repeated engagement of non-symbolic approximate addition and subtraction of large arrays of items results in improved math skills in very young children, an idea that stems from our previous studies in adults. In the current study, 3- to 5-year-olds showed selective improvements in math skills after multiple days of playing a tablet-based non-symbolic approximate arithmetic game compared with children who played a memory game. These findings, collectively with our previous reports, suggest that mental manipulation of approximate numerosities provides an important tool for improving math readiness, even in preschoolers who have yet to master the meaning of number words. Copyright © 2016 Elsevier Inc. All rights reserved.
Non-symbolic approximate arithmetic training improves math performance in preschoolers
Park, Joonkoo; Bermudez, Vanessa; Roberts, Rachel C.; Brannon, Elizabeth M.
2016-01-01
Math proficiency in early school age is an important predictor of later academic achievement. Thus, an important goal for society should be to improve math readiness in pre-school age children, especially in low-income children who typically arrive in kindergarten with less mathematical competency than their higher-income peers. The majority of existing research-based math intervention programs target symbolic, verbal number concepts in young children. However, very little attention has been paid to the preverbal, intuitive ability to approximately represent numerical quantity, which is hypothesized to be an important foundation for full-fledged mathematical thinking. Here, we test the hypothesis that repeated engagement of non-symbolic approximate addition and subtraction of large array of items results in improved math skills in very young children, an idea that stems from our previous studies in adults. Three to five year-old children showed selective improvements in math skills after multiple days of playing a tablet-based non-symbolic approximate arithmetic game compared to children who played a memory game. These findings, collectively with our previous reports, suggest that mental manipulation of approximate numerosities provides an important tool for improving math readiness, even in preschoolers who have yet to master the meaning of number words. PMID:27596808
Corrections to the thin wall approximation in general relativity
NASA Technical Reports Server (NTRS)
Garfinkle, David; Gregory, Ruth
1989-01-01
The question is considered whether the thin wall formalism of Israel applies to the gravitating domain walls of a lambda phi(exp 4) theory. The coupled Einstein-scalar equations that describe the thick gravitating wall are expanded in powers of the thickness of the wall. The solutions of the zeroth order equations reproduce the results of the usual Israel thin wall approximation for domain walls. The solutions of the first order equations provide corrections to the expressions for the stress-energy of the wall and to the Israel thin wall equations. The modified thin wall equations are then used to treat the motion of spherical and planar domain walls.
Producing approximate answers to database queries
NASA Technical Reports Server (NTRS)
Vrbsky, Susan V.; Liu, Jane W. S.
1993-01-01
We have designed and implemented a query processor, called APPROXIMATE, that makes approximate answers available if part of the database is unavailable or if there is not enough time to produce an exact answer. The accuracy of the approximate answers produced improves monotonically with the amount of data retrieved to produce the result. The exact answer is produced if all of the needed data are available and query processing is allowed to continue until completion. The monotone query processing algorithm of APPROXIMATE works within the standard relational algebra framework and can be implemented on a relational database system with little change to the relational architecture. We describe here the approximation semantics of APPROXIMATE that serves as the basis for meaningful approximations of both set-valued and single-valued queries. We show how APPROXIMATE is implemented to make effective use of semantic information, provided by an object-oriented view of the database, and describe the additional overhead required by APPROXIMATE.
Structural optimization with approximate sensitivities
NASA Technical Reports Server (NTRS)
Patnaik, S. N.; Hopkins, D. A.; Coroneos, R.
1994-01-01
Computational efficiency in structural optimization can be enhanced if the intensive computations associated with the calculation of the sensitivities, that is, gradients of the behavior constraints, are reduced. Approximation to gradients of the behavior constraints that can be generated with small amount of numerical calculations is proposed. Structural optimization with these approximate sensitivities produced correct optimum solution. Approximate gradients performed well for different nonlinear programming methods, such as the sequence of unconstrained minimization technique, method of feasible directions, sequence of quadratic programming, and sequence of linear programming. Structural optimization with approximate gradients can reduce by one third the CPU time that would otherwise be required to solve the problem with explicit closed-form gradients. The proposed gradient approximation shows potential to reduce intensive computation that has been associated with traditional structural optimization.
Analytical expressions for the evolution of many-body quantum systems quenched far from equilibrium
NASA Astrophysics Data System (ADS)
Santos, Lea F.; Torres-Herrera, E. Jonathan
2017-12-01
Possible strategies to describe analytically the dynamics of many-body quantum systems out of equilibrium include the use of solvable models and of full random matrices. None of the two approaches represent actual realistic systems, but they serve as references for the studies of these ones. We take the second path and obtain analytical expressions for the survival probability, density imbalance, and out-of-time-ordered correlator. Using these findings, we then propose an approximate expression that matches very well numerical results for the evolution of realistic finite quantum systems that are strongly chaotic and quenched far from equilibrium. In the case of the survival probability, the expression proposed covers all different time scales, from the moment the system is taken out of equilibrium to the moment it reaches a new equilibrium. The realistic systems considered are described by one-dimensional spin-1/2 models.
Mean-field approximation for the Sznajd model in complex networks
NASA Astrophysics Data System (ADS)
Araújo, Maycon S.; Vannucchi, Fabio S.; Timpanaro, André M.; Prado, Carmen P. C.
2015-02-01
This paper studies the Sznajd model for opinion formation in a population connected through a general network. A master equation describing the time evolution of opinions is presented and solved in a mean-field approximation. Although quite simple, this approximation allows us to capture the most important features regarding the steady states of the model. When spontaneous opinion changes are included, a discontinuous transition from consensus to polarization can be found as the rate of spontaneous change is increased. In this case we show that a hybrid mean-field approach including interactions between second nearest neighbors is necessary to estimate correctly the critical point of the transition. The analytical prediction of the critical point is also compared with numerical simulations in a wide variety of networks, in particular Barabási-Albert networks, finding reasonable agreement despite the strong approximations involved. The same hybrid approach that made it possible to deal with second-order neighbors could just as well be adapted to treat other problems such as epidemic spreading or predator-prey systems.
Jablonski-Momeni, Anahita; Jablonski, Boris; Lippe, Nikola
2017-01-01
Objectives/Aims: Apart from the visual detection of caries, X-rays can be taken for detection of approximal lesions. The Proxi head of VistaCam iX intraoral camera system uses near-infrared light (NIR) to enable caries detection in approximal surfaces. The aim of this study was to evaluate the performance of the NIR for the detection of approximal enamel lesions by comparison with radiographic findings. Materials and methods: One hundred ninety-three approximal surfaces from 18 patients were examined visually and using digital radiographs for presence or absence of enamel lesions. Then digital images of each surface were produced using the near-infrared light. Correlation between methods was assessed using Spearman’s rank correlation coefficient (rs). Agreement between radiographic and NIR findings was calculated using the kappa coefficient. McNemar’s test was used to analyse differences between the radiographic and NIR findings (α=0.05). Results: Moderate correlation was found between all detection methods (rs=0.33–0.50, P<0.0001). Agreement between the radiographic and NIR findings was moderate (κ=0.50, 95% CI=0.37–0.62) for the distinction between sound surfaces and enamel caries. No significant differences were found between the findings (P=0.07). Conclusion: Radiographs and NIR were found to be comparable for the detection of enamel lesions in permanent teeth. PMID:29607082
Kondo necklace model in approximants of Fibonacci chains
NASA Astrophysics Data System (ADS)
Reyes, Daniel; Tarazona, H.; Cuba-Supanta, G.; Landauro, C. V.; Espinoza, R.; Quispe-Marcatoma, J.
2017-11-01
The low energy behavior of the one dimensional Kondo necklace model with structural aperiodicity is studied using a representation for the localized and conduction electron spins, in terms of local Kondo singlet and triplet operators at zero temperature. A decoupling scheme on the double time Green's functions is used to find the dispersion relation for the excitations of the system. We determine the dependence between the structural aperiodicity modulation and the spin gap in a Fibonacci approximant chain at zero temperature and in the paramagnetic side of the phase diagram.
Bounded-Degree Approximations of Stochastic Networks
DOE Office of Scientific and Technical Information (OSTI.GOV)
Quinn, Christopher J.; Pinar, Ali; Kiyavash, Negar
2017-06-01
We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify optimal and near-optimal approximations in terms of Kullback-Leibler divergence. The user-chosen sparsity trades off the quality of the approximation against visual conciseness and computational tractability. One class of approximations contains graphs with speci ed in-degrees. Another class additionally requires that the graph is connected. For both classes, we propose algorithms to identify the optimal approximations and also near-optimal approximations, using a novel relaxation of submodularity. We also propose algorithms to identifymore » the r-best approximations among these classes, enabling robust decision making.« less
Prediction of gene expression with cis-SNPs using mixed models and regularization methods.
Zeng, Ping; Zhou, Xiang; Huang, Shuiping
2017-05-11
It has been shown that gene expression in human tissues is heritable, thus predicting gene expression using only SNPs becomes possible. The prediction of gene expression can offer important implications on the genetic architecture of individual functional associated SNPs and further interpretations of the molecular basis underlying human diseases. We compared three types of methods for predicting gene expression using only cis-SNPs, including the polygenic model, i.e. linear mixed model (LMM), two sparse models, i.e. Lasso and elastic net (ENET), and the hybrid of LMM and sparse model, i.e. Bayesian sparse linear mixed model (BSLMM). The three kinds of prediction methods have very different assumptions of underlying genetic architectures. These methods were evaluated using simulations under various scenarios, and were applied to the Geuvadis gene expression data. The simulations showed that these four prediction methods (i.e. Lasso, ENET, LMM and BSLMM) behaved best when their respective modeling assumptions were satisfied, but BSLMM had a robust performance across a range of scenarios. According to R 2 of these models in the Geuvadis data, the four methods performed quite similarly. We did not observe any clustering or enrichment of predictive genes (defined as genes with R 2 ≥ 0.05) across the chromosomes, and also did not see there was any clear relationship between the proportion of the predictive genes and the proportion of genes in each chromosome. However, an interesting finding in the Geuvadis data was that highly predictive genes (e.g. R 2 ≥ 0.30) may have sparse genetic architectures since Lasso, ENET and BSLMM outperformed LMM for these genes; and this observation was validated in another gene expression data. We further showed that the predictive genes were enriched in approximately independent LD blocks. Gene expression can be predicted with only cis-SNPs using well-developed prediction models and these predictive genes were enriched in
Limitations of shallow nets approximation.
Lin, Shao-Bo
2017-10-01
In this paper, we aim at analyzing the approximation abilities of shallow networks in reproducing kernel Hilbert spaces (RKHSs). We prove that there is a probability measure such that the achievable lower bound for approximating by shallow nets can be realized for all functions in balls of reproducing kernel Hilbert space with high probability, which is different with the classical minimax approximation error estimates. This result together with the existing approximation results for deep nets shows the limitations for shallow nets and provides a theoretical explanation on why deep nets perform better than shallow nets. Copyright © 2017 Elsevier Ltd. All rights reserved.
Libertus, Melissa E; Odic, Darko; Feigenson, Lisa; Halberda, Justin
2016-10-01
Children can represent number in at least two ways: by using their non-verbal, intuitive approximate number system (ANS) and by using words and symbols to count and represent numbers exactly. Furthermore, by the time they are 5years old, children can map between the ANS and number words, as evidenced by their ability to verbally estimate numbers of items without counting. How does the quality of the mapping between approximate and exact numbers relate to children's math abilities? The role of the ANS-number word mapping in math competence remains controversial for at least two reasons. First, previous work has not examined the relation between verbal estimation and distinct subtypes of math abilities. Second, previous work has not addressed how distinct components of verbal estimation-mapping accuracy and variability-might each relate to math performance. Here, we addressed these gaps by measuring individual differences in ANS precision, verbal number estimation, and formal and informal math abilities in 5- to 7-year-old children. We found that verbal estimation variability, but not estimation accuracy, predicted formal math abilities, even when controlling for age, expressive vocabulary, and ANS precision, and that it mediated the link between ANS precision and overall math ability. These findings suggest that variability in the ANS-number word mapping may be especially important for formal math abilities. Copyright © 2016 Elsevier Inc. All rights reserved.
Quantitative molecular orbital energies within a G0W0 approximation
NASA Astrophysics Data System (ADS)
Sharifzadeh, S.; Tamblyn, I.; Doak, P.; Darancet, P. T.; Neaton, J. B.
2012-09-01
Using many-body perturbation theory within a G 0 W 0 approximation, with a plane wave basis set and using a starting point based on density functional theory within the generalized gradient approximation, we explore routes for computing the ionization potential (IP), electron affinity (EA), and fundamental gap of three gas-phase molecules — benzene, thiophene, and (1,4) diamino-benzene — and compare with experiments. We examine the dependence of the IP and fundamental gap on the number of unoccupied states used to represent the dielectric function and the self energy, as well as the dielectric function plane-wave cutoff. We find that with an effective completion strategy for approximating the unoccupied subspace, and a well converged dielectric function kinetic energy cutoff, the computed IPs and EAs are in excellent quantitative agreement with available experiment (within 0.2 eV), indicating that a one-shot G 0 W 0 approach can be very accurate for calculating addition/removal energies of small organic molecules.
Typical performance of approximation algorithms for NP-hard problems
NASA Astrophysics Data System (ADS)
Takabe, Satoshi; Hukushima, Koji
2016-11-01
Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with the presentation of a theoretical framework. Herein, three approximation algorithms are examined: linear-programming relaxation, loopy-belief propagation, and the leaf-removal algorithm. The former two algorithms are analyzed using a statistical-mechanical technique, whereas the average-case analysis of the last one is conducted using the generating function method. These algorithms have a threshold in the typical performance with increasing average degree of the random graph, below which they find true optimal solutions with high probability. Our study reveals that there exist only three cases, determined by the order of the typical performance thresholds. In addition, we provide some conditions for classification of the graph ensembles and demonstrate explicitly some examples for the difference in thresholds.
The chemokine receptor CXCR3 and its splice variant are expressed in human airway epithelial cells.
Kelsen, Steven G; Aksoy, Mark O; Yang, Yi; Shahabuddin, Syed; Litvin, Judith; Safadi, Fayez; Rogers, Thomas J
2004-09-01
Activation of the chemokine receptor CXCR3 by its cognate ligands induces several differentiated cellular responses important to the growth and migration of a variety of hematopoietic and structural cells. In the human respiratory tract, human airway epithelial cells (HAEC) release the CXCR3 ligands Mig/CXCL9, IP-10/CXCL10, and I-TAC/CXCL11. Simultaneous expression of CXCR3 by HAEC would have important implications for the processes of airway inflammation and repair. Accordingly, in the present study we sought to determine whether HAEC also express the classic CXCR3 chemokine receptor CXCR3-A and its splice variant CXCR3-B and hence may respond in autocrine fashion to its ligands. We found that cultured HAEC (16-HBE and tracheocytes) constitutively expressed CXCR3 mRNA and protein. CXCR3 mRNA levels assessed by expression array were approximately 35% of beta-actin expression. In contrast, CCR3, CCR4, CCR5, CCR8, and CX3CR1 were <5% beta-actin. Both CXCR3-A and -B were expressed. Furthermore, tracheocytes freshly harvested by bronchoscopy stained positively for CXCR3 by immunofluorescence microscopy, and 68% of cytokeratin-positive tracheocytes (i.e., the epithelial cell population) were positive for CXCR3 by flow cytometry. In 16-HBE cells, CXCR3 receptor density was approximately 78,000 receptors/cell when assessed by competitive displacement of 125I-labeled IP-10/CXCL10. Finally, CXCR3 ligands induced chemotactic responses and actin reorganization in 16-HBE cells. These findings indicate constitutive expression by HAEC of a functional CXC chemokine receptor, CXCR3. Our data suggest the possibility that autocrine activation of CXCR3 expressed by HAEC may contribute to airway inflammation and remodeling in obstructive lung disease by regulating HAEC migration.
NASA Astrophysics Data System (ADS)
Popov, Vladislav; Lavrinenko, Andrei V.; Novitsky, Andrey
2018-03-01
In this paper, we elaborate on the operator effective medium approximation developed recently in Popov et al. [Phys. Rev. B 94, 085428 (2016), 10.1103/PhysRevB.94.085428] to get insight into the surface polariton excitation at the interface of a multilayer hyperbolic metamaterial (HMM). In particular, we find that HMMs with bilayer unit cells support the TE- and TM-polarized surface waves beyond the Maxwell Garnett approximation due to the spatial dispersion interpreted as effective magnetoelectric coupling. The latter is also responsible for the dependence of surface wave propagation on the order of layers in the unit cell. Elimination of the magnetoelectric coupling in three-layer unit cells complying with inversion symmetry restores the qualitative regularity of the Maxwell Garnett approximation, as well as strongly suppresses the influence of the order of layers in the unit cell.
Transverse signal decay under the weak field approximation: Theory and validation.
Berman, Avery J L; Pike, G Bruce
2018-07-01
To derive an expression for the transverse signal time course from systems in the motional narrowing regime, such as water diffusing in blood. This was validated in silico and experimentally with ex vivo blood samples. A closed-form solution (CFS) for transverse signal decay under any train of refocusing pulses was derived using the weak field approximation. The CFS was validated via simulations of water molecules diffusing in the presence of spherical perturbers, with a range of sizes and under various pulse sequences. The CFS was compared with more conventional fits assuming monoexponential decay, including chemical exchange, using ex vivo blood Carr-Purcell-Meiboom-Gill data. From simulations, the CFS was shown to be valid in the motional narrowing regime and partially into the intermediate dephasing regime, with increased accuracy with increasing Carr-Purcell-Meiboom-Gill refocusing rate. In theoretical calculations of the CFS, fitting for the transverse relaxation rate (R 2 ) gave excellent agreement with the weak field approximation expression for R 2 for Carr-Purcell-Meiboom-Gill sequences, but diverged for free induction decay. These same results were confirmed in the ex vivo analysis. Transverse signal decay in the motional narrowing regime can be accurately described analytically. This theory has applications in areas such as tissue iron imaging, relaxometry of blood, and contrast agent imaging. Magn Reson Med 80:341-350, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.
Approximate circuits for increased reliability
DOE Office of Scientific and Technical Information (OSTI.GOV)
Hamlet, Jason R.; Mayo, Jackson R.
2015-08-18
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the referencemore » circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.« less
Investigation of approximate models of experimental temperature characteristics of machines
NASA Astrophysics Data System (ADS)
Parfenov, I. V.; Polyakov, A. N.
2018-05-01
This work is devoted to the investigation of various approaches to the approximation of experimental data and the creation of simulation mathematical models of thermal processes in machines with the aim of finding ways to reduce the time of their field tests and reducing the temperature error of the treatments. The main methods of research which the authors used in this work are: the full-scale thermal testing of machines; realization of various approaches at approximation of experimental temperature characteristics of machine tools by polynomial models; analysis and evaluation of modelling results (model quality) of the temperature characteristics of machines and their derivatives up to the third order in time. As a result of the performed researches, rational methods, type, parameters and complexity of simulation mathematical models of thermal processes in machine tools are proposed.
DOE Office of Scientific and Technical Information (OSTI.GOV)
Liu, Fang, E-mail: fliu@lsec.cc.ac.cn; Lin, Lin, E-mail: linlin@math.berkeley.edu; Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720
We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite trapezoidal rule. We also discuss the benefit ofmore » using different self energy expressions to perform the numerical convolution at different frequencies.« less
NASA Astrophysics Data System (ADS)
Wang, Jing; Yang, Tianyu; Staskevich, Gennady; Abbe, Brian
2017-04-01
This paper studies the cooperative control problem for a class of multiagent dynamical systems with partially unknown nonlinear system dynamics. In particular, the control objective is to solve the state consensus problem for multiagent systems based on the minimisation of certain cost functions for individual agents. Under the assumption that there exist admissible cooperative controls for such class of multiagent systems, the formulated problem is solved through finding the optimal cooperative control using the approximate dynamic programming and reinforcement learning approach. With the aid of neural network parameterisation and online adaptive learning, our method renders a practically implementable approximately adaptive neural cooperative control for multiagent systems. Specifically, based on the Bellman's principle of optimality, the Hamilton-Jacobi-Bellman (HJB) equation for multiagent systems is first derived. We then propose an approximately adaptive policy iteration algorithm for multiagent cooperative control based on neural network approximation of the value functions. The convergence of the proposed algorithm is rigorously proved using the contraction mapping method. The simulation results are included to validate the effectiveness of the proposed algorithm.
Extending the Fellegi-Sunter probabilistic record linkage method for approximate field comparators.
DuVall, Scott L; Kerber, Richard A; Thomas, Alun
2010-02-01
Probabilistic record linkage is a method commonly used to determine whether demographic records refer to the same person. The Fellegi-Sunter method is a probabilistic approach that uses field weights based on log likelihood ratios to determine record similarity. This paper introduces an extension of the Fellegi-Sunter method that incorporates approximate field comparators in the calculation of field weights. The data warehouse of a large academic medical center was used as a case study. The approximate comparator extension was compared with the Fellegi-Sunter method in its ability to find duplicate records previously identified in the data warehouse using different demographic fields and matching cutoffs. The approximate comparator extension misclassified 25% fewer pairs and had a larger Welch's T statistic than the Fellegi-Sunter method for all field sets and matching cutoffs. The accuracy gain provided by the approximate comparator extension grew as less information was provided and as the matching cutoff increased. Given the ubiquity of linkage in both clinical and research settings, the incremental improvement of the extension has the potential to make a considerable impact.
NASA Astrophysics Data System (ADS)
Chen, Zhixiang; Fu, Bin
This paper is our third step towards developing a theory of testing monomials in multivariate polynomials and concentrates on two problems: (1) How to compute the coefficients of multilinear monomials; and (2) how to find a maximum multilinear monomial when the input is a ΠΣΠ polynomial. We first prove that the first problem is #P-hard and then devise a O *(3 n s(n)) upper bound for this problem for any polynomial represented by an arithmetic circuit of size s(n). Later, this upper bound is improved to O *(2 n ) for ΠΣΠ polynomials. We then design fully polynomial-time randomized approximation schemes for this problem for ΠΣ polynomials. On the negative side, we prove that, even for ΠΣΠ polynomials with terms of degree ≤ 2, the first problem cannot be approximated at all for any approximation factor ≥ 1, nor "weakly approximated" in a much relaxed setting, unless P=NP. For the second problem, we first give a polynomial time λ-approximation algorithm for ΠΣΠ polynomials with terms of degrees no more a constant λ ≥ 2. On the inapproximability side, we give a n (1 - ɛ)/2 lower bound, for any ɛ> 0, on the approximation factor for ΠΣΠ polynomials. When the degrees of the terms in these polynomials are constrained as ≤ 2, we prove a 1.0476 lower bound, assuming Pnot=NP; and a higher 1.0604 lower bound, assuming the Unique Games Conjecture.
Gorodkin, Jan; Cirera, Susanna; Hedegaard, Jakob; Gilchrist, Michael J; Panitz, Frank; Jørgensen, Claus; Scheibye-Knudsen, Karsten; Arvin, Troels; Lumholdt, Steen; Sawera, Milena; Green, Trine; Nielsen, Bente J; Havgaard, Jakob H; Rosenkilde, Carina; Wang, Jun; Li, Heng; Li, Ruiqiang; Liu, Bin; Hu, Songnian; Dong, Wei; Li, Wei; Yu, Jun; Wang, Jian; Stærfeldt, Hans-Henrik; Wernersson, Rasmus; Madsen, Lone B; Thomsen, Bo; Hornshøj, Henrik; Bujie, Zhan; Wang, Xuegang; Wang, Xuefei; Bolund, Lars; Brunak, Søren; Yang, Huanming; Bendixen, Christian; Fredholm, Merete
2007-01-01
Background Knowledge of the structure of gene expression is essential for mammalian transcriptomics research. We analyzed a collection of more than one million porcine expressed sequence tags (ESTs), of which two-thirds were generated in the Sino-Danish Pig Genome Project and one-third are from public databases. The Sino-Danish ESTs were generated from one normalized and 97 non-normalized cDNA libraries representing 35 different tissues and three developmental stages. Results Using the Distiller package, the ESTs were assembled to roughly 48,000 contigs and 73,000 singletons, of which approximately 25% have a high confidence match to UniProt. Approximately 6,000 new porcine gene clusters were identified. Expression analysis based on the non-normalized libraries resulted in the following findings. The distribution of cluster sizes is scaling invariant. Brain and testes are among the tissues with the greatest number of different expressed genes, whereas tissues with more specialized function, such as developing liver, have fewer expressed genes. There are at least 65 high confidence housekeeping gene candidates and 876 cDNA library-specific gene candidates. We identified differential expression of genes between different tissues, in particular brain/spinal cord, and found patterns of correlation between genes that share expression in pairs of libraries. Finally, there was remarkable agreement in expression between specialized tissues according to Gene Ontology categories. Conclusion This EST collection, the largest to date in pig, represents an essential resource for annotation, comparative genomics, assembly of the pig genome sequence, and further porcine transcription studies. PMID:17407547
DOE Office of Scientific and Technical Information (OSTI.GOV)
Bauer, Jaroslaw H.
2011-03-15
In the recent work of Vanne and Saenz [Phys. Rev. A 75, 063403 (2007)] the quasistatic limit of the velocity gauge strong-field approximation describing the ionization rate of atomic or molecular systems exposed to linearly polarized laser fields was derived. It was shown that in the low-frequency limit the ionization rate is proportional to the laser frequency {omega} (for a constant intensity of the laser field). In the present work I show that for circularly polarized laser fields the ionization rate is proportional to {omega}{sup 4} for H(1s) and H(2s) atoms, to {omega}{sup 6} for H(2p{sub x}) and H(2p{sub y})more » atoms, and to {omega}{sup 8} for H(2p{sub z}) atoms. The analytical expressions for asymptotic ionization rates (which become nearly accurate in the limit {omega}{yields}0) contain no summations over multiphoton contributions. For very low laser frequencies (optical or infrared) these expressions usually remain with an order-of-magnitude agreement with the velocity gauge strong-field approximation.« less
Choice of phase in the CS and IOS approximation
DOE Office of Scientific and Technical Information (OSTI.GOV)
Snider, R.F.
1982-04-01
With the recognition that the angular momentum representations of unit position and momentum directional states must have different but uniquely related phases, the previously presented expression of scattering amplitude in terms of IOS angle dependent phase shifts must be modified. This resolves a major disagreement between IOS and close coupled degeneracy averaged differential cross sections. It is found that the phase factors appearing in the differential cross section have nothing to do with any particular choice of decoupling parameter. As a consequence, the differential cross section is relatively insensitive to the choice of CS decoupling parameter. The phase relations obtainedmore » are also in agreement with those deduced from the Born approximation.« less
Approximate Model Checking of PCTL Involving Unbounded Path Properties
NASA Astrophysics Data System (ADS)
Basu, Samik; Ghosh, Arka P.; He, Ru
We study the problem of applying statistical methods for approximate model checking of probabilistic systems against properties encoded as
Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.
Talaei, Behzad; Jagannathan, Sarangapani; Singler, John
2018-04-01
This paper develops a near optimal boundary control method for distributed parameter systems governed by uncertain linear 1-D parabolic partial differential equations (PDE) by using approximate dynamic programming. A quadratic surface integral is proposed to express the optimal cost functional for the infinite-dimensional state space. Accordingly, the Hamilton-Jacobi-Bellman (HJB) equation is formulated in the infinite-dimensional domain without using any model reduction. Subsequently, a neural network identifier is developed to estimate the unknown spatially varying coefficient in PDE dynamics. Novel tuning law is proposed to guarantee the boundedness of identifier approximation error in the PDE domain. A radial basis network (RBN) is subsequently proposed to generate an approximate solution for the optimal surface kernel function online. The tuning law for near optimal RBN weights is created, such that the HJB equation error is minimized while the dynamics are identified and closed-loop system remains stable. Ultimate boundedness (UB) of the closed-loop system is verified by using the Lyapunov theory. The performance of the proposed controller is successfully confirmed by simulation on an unstable diffusion-reaction process.
Mueller, Silke M; Schiebener, Johannes; Delazer, Margarete; Brand, Matthias
2018-01-22
Many decision situations in everyday life involve mathematical considerations. In decisions under objective risk, i.e., when explicit numeric information is available, executive functions and abilities to handle exact numbers and ratios are predictors of objectively advantageous choices. Although still debated, exact numeric abilities, e.g., normative calculation skills, are assumed to be related to approximate number processing skills. The current study investigates the effects of approximative numeric abilities on decision making under objective risk. Participants (N = 153) performed a paradigm measuring number-comparison, quantity-estimation, risk-estimation, and decision-making skills on the basis of rapid dot comparisons. Additionally, a risky decision-making task with exact numeric information was administered, as well as tasks measuring executive functions and exact numeric abilities, e.g., mental calculation and ratio processing skills, were conducted. Approximative numeric abilities significantly predicted advantageous decision making, even beyond the effects of executive functions and exact numeric skills. Especially being able to make accurate risk estimations seemed to contribute to superior choices. We recommend approximation skills and approximate number processing to be subject of future investigations on decision making under risk.
Sandfort, Theo G M; Bos, Henny; Reddy, Vasu
2018-02-20
Unlike studies conducted in Western countries, two studies among Black South African men who have sex with men (MSM) found no support for the association between gender nonconformity and mental distress, even though gender-nonconforming men experienced more discrimination and discrimination was associated with mental distress (Cook, Sandfort, Nel, & Rich, 2013; Sandfort, Bos, Knox, & Reddy, 2016). In Sandfort et al., gender nonconformity was assessed as a continuous variable, validated by comparing scores between a categorical assessment of gender presentation (masculine, feminine, no preference). Using the same dataset, we further explored this topic by (1) testing differences between gender expression groups in sexual minority stressors, resilience factors, and mental distress; (2) testing whether the impact of elevated discrimination in the feminine group was counterbalanced by lower scores on other stressors or higher scores on resilience factors; and (3) exploring whether relationships of stressors and resilience factors with mental distress varied between gender expression groups. Controlling for demographics, we found several differences between the gender expression groups in the stressors and resilience factors, but not in mental distress. We found no support for the idea that the lack of differences in mental distress between the gender expression groups was a consequence of factors working in opposite directions. However, internalized homophobia had a differential impact on depression in feminine men compared to masculine men. In our discussion of these findings, we explored the meaning of our participants' self-categorization as it might relate to gender instead of sexual identities.
The Linear Mixing Approximation for Planetary Ices
NASA Astrophysics Data System (ADS)
Bethkenhagen, M.; Meyer, E. R.; Hamel, S.; Nettelmann, N.; French, M.; Scheibe, L.; Ticknor, C.; Collins, L. A.; Kress, J. D.; Fortney, J. J.; Redmer, R.
2017-12-01
We investigate the validity of the widely used linear mixing approximation for the equations of state (EOS) of planetary ices, which are thought to dominate the interior of the ice giant planets Uranus and Neptune. For that purpose we perform density functional theory molecular dynamics simulations using the VASP code.[1] In particular, we compute 1:1 binary mixtures of water, ammonia, and methane, as well as their 2:1:4 ternary mixture at pressure-temperature conditions typical for the interior of Uranus and Neptune.[2,3] In addition, a new ab initio EOS for methane is presented. The linear mixing approximation is verified for the conditions present inside Uranus ranging up to 10 Mbar based on the comprehensive EOS data set. We also calculate the diffusion coefficients for the ternary mixture along different Uranus interior profiles and compare them to the values of the pure compounds. We find that deviations of the linear mixing approximation from the real mixture are generally small; for the EOS they fall within about 4% uncertainty while the diffusion coefficients deviate up to 20% . The EOS of planetary ices are applied to adiabatic models of Uranus. It turns out that a deep interior of almost pure ices is consistent with the gravity field data, in which case the planet becomes rather cold (T core ˜ 4000 K). [1] G. Kresse and J. Hafner, Physical Review B 47, 558 (1993). [2] R. Redmer, T.R. Mattsson, N. Nettelmann and M. French, Icarus 211, 798 (2011). [3] N. Nettelmann, K. Wang, J. J. Fortney, S. Hamel, S. Yellamilli, M. Bethkenhagen and R. Redmer, Icarus 275, 107 (2016).
Approximating a DSM-5 Diagnosis of PTSD Using DSM-IV Criteria
Rosellini, Anthony J.; Stein, Murray B.; Colpe, Lisa J.; Heeringa, Steven G.; Petukhova, Maria V.; Sampson, Nancy A.; Schoenbaum, Michael; Ursano, Robert J.; Kessler, Ronald C.
2015-01-01
Background Diagnostic criteria for DSM-5 posttraumatic stress disorder (PTSD) are in many ways similar to DSM-IV criteria, raising the possibility that it might be possible to closely approximate DSM-5 diagnoses using DSM-IV symptoms. If so, the resulting transformation rules could be used to pool research data based on the two criteria sets. Methods The Pre-Post Deployment Study (PPDS) of the Army Study to Assess Risk and Resilience in Servicemembers (Army STARRS) administered a blended 30-day DSM-IV and DSM-5 PTSD symptom assessment based on the civilian PTSD Checklist for DSM-IV (PCL-C) and the PTSD Checklist for DSM-5 (PCL-5). This assessment was completed by 9,193 soldiers from three US Army Brigade Combat Teams approximately three months after returning from Afghanistan. PCL-C items were used to operationalize conservative and broad approximations of DSM-5 PTSD diagnoses. The operating characteristics of these approximations were examined compared to diagnoses based on actual DSM-5 criteria. Results The estimated 30-day prevalence of DSM-5 PTSD based on conservative (4.3%) and broad (4.7%) approximations of DSM-5 criteria using DSM-IV symptom assessments were similar to estimates based on actual DSM-5 criteria (4.6%). Both approximations had excellent sensitivity (92.6-95.5%), specificity (99.6-99.9%), total classification accuracy (99.4-99.6%), and area under the receiver operating characteristic curve (0.96-0.98). Conclusions DSM-IV symptoms can be used to approximate DSM-5 diagnoses of PTSD among recently-deployed soldiers, making it possible to recode symptom-level data from earlier DSM-IV studies to draw inferences about DSM-5 PTSD. However, replication is needed in broader trauma-exposed samples to evaluate the external validity of this finding. PMID:25845710
NASA Astrophysics Data System (ADS)
Gritsenko, O. V.; van Gisbergen, S. J. A.; Görling, A.; Baerends, E. J.
2000-11-01
Time-dependent density functional theory (TDDFT) is applied for calculation of the excitation energies of the dissociating H2 molecule. The standard TDDFT method of adiabatic local density approximation (ALDA) totally fails to reproduce the potential curve for the lowest excited singlet 1Σu+ state of H2. Analysis of the eigenvalue problem for the excitation energies as well as direct derivation of the exchange-correlation (xc) kernel fxc(r,r',ω) shows that ALDA fails due to breakdown of its simple spatially local approximation for the kernel. The analysis indicates a complex structure of the function fxc(r,r',ω), which is revealed in a different behavior of the various matrix elements K1c,1cxc (between the highest occupied Kohn-Sham molecular orbital ψ1 and virtual MOs ψc) as a function of the bond distance R(H-H). The effect of nonlocality of fxc(r,r') is modeled by using different expressions for the corresponding matrix elements of different orbitals. Asymptotically corrected ALDA (ALDA-AC) expressions for the matrix elements K12,12xc(στ) are proposed, while for other matrix elements the standard ALDA expressions are retained. This approach provides substantial improvement over the standard ALDA. In particular, the ALDA-AC curve for the lowest singlet excitation qualitatively reproduces the shape of the exact curve. It displays a minimum and approaches a relatively large positive energy at large R(H-H). ALDA-AC also produces a substantial improvement for the calculated lowest triplet excitation, which is known to suffer from the triplet instability problem of the restricted KS ground state. Failure of the ALDA for the excitation energies is related to the failure of the local density as well as generalized gradient approximations to reproduce correctly the polarizability of dissociating H2. The expression for the response function χ is derived to show the origin of the field-counteracting term in the xc potential, which is lacking in the local density
Josselyn, Sheena A; Köhler, Stefan; Frankland, Paul W
2015-09-01
Many attempts have been made to localize the physical trace of a memory, or engram, in the brain. However, until recently, engrams have remained largely elusive. In this Review, we develop four defining criteria that enable us to critically assess the recent progress that has been made towards finding the engram. Recent 'capture' studies use novel approaches to tag populations of neurons that are active during memory encoding, thereby allowing these engram-associated neurons to be manipulated at later times. We propose that findings from these capture studies represent considerable progress in allowing us to observe, erase and express the engram.
Biochemical simulations: stochastic, approximate stochastic and hybrid approaches.
Pahle, Jürgen
2009-01-01
Computer simulations have become an invaluable tool to study the sometimes counterintuitive temporal dynamics of (bio-)chemical systems. In particular, stochastic simulation methods have attracted increasing interest recently. In contrast to the well-known deterministic approach based on ordinary differential equations, they can capture effects that occur due to the underlying discreteness of the systems and random fluctuations in molecular numbers. Numerous stochastic, approximate stochastic and hybrid simulation methods have been proposed in the literature. In this article, they are systematically reviewed in order to guide the researcher and help her find the appropriate method for a specific problem.
Biochemical simulations: stochastic, approximate stochastic and hybrid approaches
2009-01-01
Computer simulations have become an invaluable tool to study the sometimes counterintuitive temporal dynamics of (bio-)chemical systems. In particular, stochastic simulation methods have attracted increasing interest recently. In contrast to the well-known deterministic approach based on ordinary differential equations, they can capture effects that occur due to the underlying discreteness of the systems and random fluctuations in molecular numbers. Numerous stochastic, approximate stochastic and hybrid simulation methods have been proposed in the literature. In this article, they are systematically reviewed in order to guide the researcher and help her find the appropriate method for a specific problem. PMID:19151097
Approximations, idealizations and 'experiments' at the physics-biology interface.
Rowbottom, Darrell P
2011-06-01
This paper, which is based on recent empirical research at the University of Leeds, the University of Edinburgh, and the University of Bristol, presents two difficulties which arise when condensed matter physicists interact with molecular biologists: (1) the former use models which appear to be too coarse-grained, approximate and/or idealized to serve a useful scientific purpose to the latter; and (2) the latter have a rather narrower view of what counts as an experiment, particularly when it comes to computer simulations, than the former. It argues that these findings are related; that computer simulations are considered to be undeserving of experimental status, by molecular biologists, precisely because of the idealizations and approximations that they involve. The complexity of biological systems is a key factor. The paper concludes by critically examining whether the new research programme of 'systems biology' offers a genuine alternative to the modelling strategies used by physicists. It argues that it does not. Copyright © 2010 Elsevier Ltd. All rights reserved.
Approximating the Qualitative Vickrey Auction by a Negotiation Protocol
NASA Astrophysics Data System (ADS)
Hindriks, Koen V.; Tykhonov, Dmytro; de Weerdt, Mathijs
A result of Bulow and Klemperer has suggested that auctions may be a better tool to obtain an efficient outcome than negotiation. For example, some auction mechanisms can be shown to be efficient and strategy-proof. However, they generally also require that the preferences of at least one side of the auction are publicly known. However, sometimes it is very costly, impossible, or undesirable to publicly announce such preferences. It thus is interesting to find methods that do not impose this constraint but still approximate the outcome of the auction. In this paper we show that a multi-round multi-party negotiation protocol may be used to this end if the negotiating agents are capable of learning opponent preferences. The latter condition can be met by current state of the art negotiation technology. We show that this protocol approximates the theoretical outcome predicted by a so-called Qualitative Vickrey auction mechanism (even) on a complex multi-issue domain.
Combining global and local approximations
NASA Technical Reports Server (NTRS)
Haftka, Raphael T.
1991-01-01
A method based on a linear approximation to a scaling factor, designated the 'global-local approximation' (GLA) method, is presented and shown capable of extending the range of usefulness of derivative-based approximations to a more refined model. The GLA approach refines the conventional scaling factor by means of a linearly varying, rather than constant, scaling factor. The capabilities of the method are demonstrated for a simple beam example with a crude and more refined FEM model.
Libertus, Melissa E.; Odic, Darko; Feigenson, Lisa; Halberda, Justin
2016-01-01
Children can represent number in at least two ways: by using their non-verbal, intuitive Approximate Number System (ANS), and by using words and symbols to count and represent numbers exactly. Further, by the time they are five years old, children can map between the ANS and number words, as evidenced by their ability to verbally estimate numbers of items without counting. How does the quality of the mapping between approximate and exact numbers relate to children’s math abilities? The role of the ANS-number word mapping in math competence remains controversial for at least two reasons. First, previous work has not examined the relation between verbal estimation and distinct subtypes of math abilities. Second, previous work has not addressed how distinct components of verbal estimation – mapping accuracy and variability – might each relate to math performance. Here, we address these gaps by measuring individual differences in ANS precision, verbal number estimation, and formal and informal math abilities in 5- to 7-year-old children. We found that verbal estimation variability, but not estimation accuracy, predicted formal math abilities even when controlling for age, expressive vocabulary, and ANS precision, and that it mediated the link between ANS precision and overall math ability. These findings suggest that variability in the ANS-number word mapping may be especially important for formal math abilities. PMID:27348475
Yang, Jian-Rong; Maclean, Calum J; Park, Chungoo; Zhao, Huabin; Zhang, Jianzhi
2017-09-01
It is commonly, although not universally, accepted that most intra and interspecific genome sequence variations are more or less neutral, whereas a large fraction of organism-level phenotypic variations are adaptive. Gene expression levels are molecular phenotypes that bridge the gap between genotypes and corresponding organism-level phenotypes. Yet, it is unknown whether natural variations in gene expression levels are mostly neutral or adaptive. Here we address this fundamental question by genome-wide profiling and comparison of gene expression levels in nine yeast strains belonging to three closely related Saccharomyces species and originating from five different ecological environments. We find that the transcriptome-based clustering of the nine strains approximates the genome sequence-based phylogeny irrespective of their ecological environments. Remarkably, only ∼0.5% of genes exhibit similar expression levels among strains from a common ecological environment, no greater than that among strains with comparable phylogenetic relationships but different environments. These and other observations strongly suggest that most intra and interspecific variations in yeast gene expression levels result from the accumulation of random mutations rather than environmental adaptations. This finding has profound implications for understanding the driving force of gene expression evolution, genetic basis of phenotypic adaptation, and general role of stochasticity in evolution. © The Author 2017. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution.
The Epoch of Disk Formation: z is Approximately l to Today
NASA Technical Reports Server (NTRS)
Kassin, Susan; Gardner, Jonathan; Weiner, Ben; Faber, Sandra
2012-01-01
We present data on galaxy kinematics, morphologies, and star-formation rates over 0.1 less than z less than 1.2 for approximately 500 blue galaxies. These data show how systems like our own Milky-Way have come into being. At redshifts around 1, about half the age of the Universe ago, Milky-Way mass galaxies were different beasts than today. They had a significant amount of disturbed motions, disturbed morphologies, shallower potential wells, higher specific star-formation rates, and likely higher gas fractions. Since redshift approximately 1, galaxies have decreased in disturbed motions, increased in rotation velocity and potential well depth, become more well-ordered morphologically, and decreased in specific star-formation rate. We find interrelationships between these measurements. Galaxy kinematics are correlated with morphology and specific star-formation rate such that galaxies with the fastest rotation velocities and the least amounts of disturbed motions have the most well-ordered morphologies and the lowest specific star-formation rates. The converse is true. Moreover, we find that the rate at which galaxies become more well-ordered kinematically (i.e., increased rotation velocity, decreased disturbed motions) and morphologically is directly proportional to their stellar mass.
Programmed Death-ligand 1 Expression in Upper Tract Urothelial Carcinoma.
Skala, Stephanie L; Liu, Tzu-Ying; Udager, Aaron M; Weizer, Alon Z; Montgomery, Jeffrey S; Palapattu, Ganesh S; Siddiqui, Javed; Cao, Xuhong; Fields, Kristina; Abugharib, Ahmed E; Soliman, Moaaz; Hafez, Khaled S; Miller, David; Lee, Cheryl T; Alva, Ajjai; Chinnaiyan, Arul M; Morgan, Todd M; Spratt, Daniel E; Jiang, Hui; Mehra, Rohit
2017-10-01
Urothelial carcinoma (UC) is the most common malignancy of the urinary tract. Upper tract (renal pelvis and ureter) urothelial carcinomas (UTUC) account for approximately 5% of UCs but a significant subset are invasive and associated with poor clinical outcomes. To evaluate programmed death-ligand 1 (PD-L1) expression in UTUC. UTUC cases from 1997-2016 were retrospectively identified from the surgical pathology database at a single large academic institution. The cohort included 149 cases: 27 low-grade and 24 high-grade pathologic T (pT)a, 29 pT1, 23 pT2, 38 pT3, and eight pT4. PD-L1 immunohistochemistry (IHC) was performed on representative whole tumor sections using anti-PD-L1 primary antibody clone 5H1. PD-L1 expression was evaluated using a previously established cut-off for positivity (≥ 5% membranous staining). Association between PD-L1 IHC expression and clinicopathologic parameters was examined with Fisher's exact test; the effect of PD-L1 expression on cancer-specific mortality was assessed using the Cox proportional hazard model. Approximately one-third (32.7%) of invasive primary UTUC and 23.5% of all primary UTUC (invasive and noninvasive tumors) demonstrated positive PD-L1 expression. Positive PD-L1 expression was associated with high histologic grade, high pathologic stage, and angiolymphatic invasion. Cancer-specific survival was not significantly associated with positive PD-L1 expression using a 5% cut-off. Study limitations include the retrospective nature and the fact that PD-L1 expression by IHC is an imperfect surrogate for response to therapy. Positive PD-L1 expression in approximately one-third of primary invasive UTUC and association with high-risk clinicopathologic features provide a rational basis for further investigation of PD-L1-based immunotherapeutics in these patients. Upper tract urothelial carcinoma is often associated with poor clinical outcome. While current treatment options for advanced upper tract urothelial carcinoma are
DOE Office of Scientific and Technical Information (OSTI.GOV)
Lewis, E.R.; Schwartz, S.
2010-03-15
Light scattering by aerosols plays an important role in Earth’s radiative balance, and quantification of this phenomenon is important in understanding and accounting for anthropogenic influences on Earth’s climate. Light scattering by an aerosol particle is determined by its radius and index of refraction, and for aerosol particles that are hygroscopic, both of these quantities vary with relative humidity RH. Here exact expressions are derived for the dependences of the radius ratio (relative to the volume-equivalent dry radius) and index of refraction on RH for aqueous solutions of single solutes. Both of these quantities depend on the apparent molal volumemore » of the solute in solution and on the practical osmotic coefficient of the solution, which in turn depend on concentration and thus implicitly on RH. Simple but accurate approximations are also presented for the RH dependences of both radius ratio and index of refraction for several atmospherically important inorganic solutes over the entire range of RH values for which these substances can exist as solution drops. For all substances considered, the radius ratio is accurate to within a few percent, and the index of refraction to within ~0.02, over this range of RH. Such parameterizations will be useful in radiation transfer models and climate models.« less
Reproduction of exact solutions of Lipkin model by nonlinear higher random-phase approximation
NASA Astrophysics Data System (ADS)
Terasaki, J.; Smetana, A.; Šimkovic, F.; Krivoruchenko, M. I.
2017-10-01
It is shown that the random-phase approximation (RPA) method with its nonlinear higher generalization, which was previously considered as approximation except for a very limited case, reproduces the exact solutions of the Lipkin model. The nonlinear higher RPA is based on an equation nonlinear on eigenvectors and includes many-particle-many-hole components in the creation operator of the excited states. We demonstrate the exact character of solutions analytically for the particle number N = 2 and numerically for N = 8. This finding indicates that the nonlinear higher RPA is equivalent to the exact Schrödinger equation.
ERIC Educational Resources Information Center
Sofronas, Kimberly S.; DeFranco, Thomas C.; Swaminathan, Hariharan; Gorgievski, Nicholas; Vinsonhaler, Charles; Wiseman, Brianna; Escolas, Samuel
2015-01-01
This paper discusses findings from a research study designed to investigate calculus instructors' perceptions of approximation as a central concept and possible unifying thread of the first-year calculus. The study also examines the role approximation plays in participants' self-reported instructional practices. A survey was administered to 279…
Qi, Xiao-Hua; Xu, Xue-Wen; Lin, Xiao-Jian; Zhang, Wen-Jie; Chen, Xue-Hao
2012-03-01
High-throughput tag-sequencing (Tag-seq) analysis based on the Solexa Genome Analyzer platform was applied to analyze the gene expression profiling of cucumber plant at 5 time points over a 24h period of waterlogging treatment. Approximately 5.8 million total clean sequence tags per library were obtained with 143013 distinct clean tag sequences. Approximately 23.69%-29.61% of the distinct clean tags were mapped unambiguously to the unigene database, and 53.78%-60.66% of the distinct clean tags were mapped to the cucumber genome database. Analysis of the differentially expressed genes revealed that most of the genes were down-regulated in the waterlogging stages, and the differentially expressed genes mainly linked to carbon metabolism, photosynthesis, reactive oxygen species generation/scavenging, and hormone synthesis/signaling. Finally, quantitative real-time polymerase chain reaction using nine genes independently verified the tag-mapped results. This present study reveals the comprehensive mechanisms of waterlogging-responsive transcription in cucumber. Copyright © 2011 Elsevier Inc. All rights reserved.
How Good Are Statistical Models at Approximating Complex Fitness Landscapes?
du Plessis, Louis; Leventhal, Gabriel E.; Bonhoeffer, Sebastian
2016-01-01
Fitness landscapes determine the course of adaptation by constraining and shaping evolutionary trajectories. Knowledge of the structure of a fitness landscape can thus predict evolutionary outcomes. Empirical fitness landscapes, however, have so far only offered limited insight into real-world questions, as the high dimensionality of sequence spaces makes it impossible to exhaustively measure the fitness of all variants of biologically meaningful sequences. We must therefore revert to statistical descriptions of fitness landscapes that are based on a sparse sample of fitness measurements. It remains unclear, however, how much data are required for such statistical descriptions to be useful. Here, we assess the ability of regression models accounting for single and pairwise mutations to correctly approximate a complex quasi-empirical fitness landscape. We compare approximations based on various sampling regimes of an RNA landscape and find that the sampling regime strongly influences the quality of the regression. On the one hand it is generally impossible to generate sufficient samples to achieve a good approximation of the complete fitness landscape, and on the other hand systematic sampling schemes can only provide a good description of the immediate neighborhood of a sequence of interest. Nevertheless, we obtain a remarkably good and unbiased fit to the local landscape when using sequences from a population that has evolved under strong selection. Thus, current statistical methods can provide a good approximation to the landscape of naturally evolving populations. PMID:27189564
Locus ceruleus control of state-dependent gene expression.
Cirelli, Chiara; Tononi, Giulio
2004-06-09
Wakefulness and sleep are accompanied by changes in behavior and neural activity, as well as by the upregulation of different functional categories of genes. However, the mechanisms responsible for such state-dependent changes in gene expression are unknown. Here we investigate to what extent state-dependent changes in gene expression depend on the central noradrenergic (NA) system, which is active in wakefulness and reduces its firing during sleep. We measured the levels of approximately 5000 transcripts expressed in the cerebral cortex of control rats and in rats pretreated with DSP-4 [N-(2-chloroethyl)-N-ethyl-2-bromobenzylamine], a neurotoxin that removes the noradrenergic innervation of the cortex. We found that NA depletion reduces the expression of approximately 20% of known wakefulness-related transcripts. Most of these transcripts are involved in synaptic plasticity and in the cellular response to stress. In contrast, NA depletion increased the expression of the sleep-related gene encoding the translation elongation factor 2. These results indicate that the activity of the central NA system during wakefulness modulates neuronal transcription to favor synaptic potentiation and counteract cellular stress, whereas its inactivity during sleep may play a permissive role to enhance brain protein synthesis.
Mutant calreticulin-expressing cells induce monocyte hyperreactivity through a paracrine mechanism
Garbati, Michael R.; Welgan, Catherine A.; Landefeld, Sally H.; Newell, Laura F.; Agarwal, Anupriya; Dunlap, Jennifer B.; Chourasia, Tapan K.; Lee, Hyunjung; Elferich, Johannes; Traer, Elie; Rattray, Rogan; Cascio, Michael J.; Press, Richard D.; Bagby, Grover C.; Tyner, Jeffrey W.; Druker, Brian J.; Dao, Kim-Hien T.
2016-01-01
Mutations in the calreticulin gene (CALR) were recently identified in approximately 70–80% of patients with JAK2-V617F-negative essential thrombocytosis and primary myelofibrosis. All frameshift mutations generate a recurring novel C-terminus. Here we provide evidence that mutant calreticulin does not accumulate efficiently in cells and is abnormally enriched in the nucleus and extracellular space compared to wildtype calreticulin. The main determinant of these findings is the loss of the calcium-binding and KDEL domains. Expression of type I mutant CALR in Ba/F3 cells confers minimal IL-3-independent growth. Interestingly, expression of type I and type II mutant CALR in a non-hematopoietic cell line does not directly activate JAK/STAT signaling compared to JAK2-V617F expression. These results led us to investigate paracrine mechanisms of JAK/STAT activation. Here we show that conditioned media from cells expressing type I mutant CALR exaggerate cytokine production from normal monocytes with or without treatment with a toll-like receptor agonist. These effects are not dependent on the novel C-terminus. These studies offer novel insights into the mechanism of JAK/STAT activation in patients with JAK2-V617F-negative essential thrombocytosis and primary myelofibrosis. PMID:26573090
Analytical expression for the exit probability of the q -voter model in one dimension
NASA Astrophysics Data System (ADS)
Timpanaro, André M.; Galam, Serge
2015-07-01
We present in this paper an approximation that is able to give an analytical expression for the exit probability of the q -voter model in one dimension. This expression gives a better fit for the more recent data about simulations in large networks [A. M. Timpanaro and C. P. C. do Prado, Phys. Rev. E 89, 052808 (2014), 10.1103/PhysRevE.89.052808] and as such departs from the expression ρ/qρq+(1-ρ ) q found in papers that investigated small networks only [R. Lambiotte and S. Redner, Europhys. Lett. 82, 18007 (2008), 10.1209/0295-5075/82/18007; P. Przybyła et al., Phys. Rev. E 84, 031117 (2011), 10.1103/PhysRevE.84.031117; F. Slanina et al., Europhys. Lett. 82, 18006 (2008), 10.1209/0295-5075/82/18006]. The approximation consists in assuming a large separation on the time scales at which active groups of agents convince inactive ones and the time taken in the competition between active groups. Some interesting findings are that for q =2 we still have ρ/2ρ2+(1-ρ ) 2 as the exit probability and for q >2 we can obtain a lower-order approximation of the form ρ/sρs+(1-ρ ) s with s varying from q for low values of q to q -1/2 for large values of q . As such, this work can also be seen as a deduction for why the exit probability ρ/qρq+(1-ρ ) q gives a good fit, without relying on mean-field arguments or on the assumption that only the first step is nondeterministic, as q and q -1/2 will give very similar results when q →∞ .
Testing approximations for non-linear gravitational clustering
NASA Technical Reports Server (NTRS)
Coles, Peter; Melott, Adrian L.; Shandarin, Sergei F.
1993-01-01
The accuracy of various analytic approximations for following the evolution of cosmological density fluctuations into the nonlinear regime is investigated. The Zel'dovich approximation is found to be consistently the best approximation scheme. It is extremely accurate for power spectra characterized by n = -1 or less; when the approximation is 'enhanced' by truncating highly nonlinear Fourier modes the approximation is excellent even for n = +1. The performance of linear theory is less spectrum-dependent, but this approximation is less accurate than the Zel'dovich one for all cases because of the failure to treat dynamics. The lognormal approximation generally provides a very poor fit to the spatial pattern.
Formalizing Neurath's ship: Approximate algorithms for online causal learning.
Bramley, Neil R; Dayan, Peter; Griffiths, Thomas L; Lagnado, David A
2017-04-01
Higher-level cognition depends on the ability to learn models of the world. We can characterize this at the computational level as a structure-learning problem with the goal of best identifying the prevailing causal relationships among a set of relata. However, the computational cost of performing exact Bayesian inference over causal models grows rapidly as the number of relata increases. This implies that the cognitive processes underlying causal learning must be substantially approximate. A powerful class of approximations that focuses on the sequential absorption of successive inputs is captured by the Neurath's ship metaphor in philosophy of science, where theory change is cast as a stochastic and gradual process shaped as much by people's limited willingness to abandon their current theory when considering alternatives as by the ground truth they hope to approach. Inspired by this metaphor and by algorithms for approximating Bayesian inference in machine learning, we propose an algorithmic-level model of causal structure learning under which learners represent only a single global hypothesis that they update locally as they gather evidence. We propose a related scheme for understanding how, under these limitations, learners choose informative interventions that manipulate the causal system to help elucidate its workings. We find support for our approach in the analysis of 3 experiments. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
Judelson, Howard S; Ah-Fong, Audrey M V; Aux, George; Avrova, Anna O; Bruce, Catherine; Cakir, Cahid; da Cunha, Luis; Grenville-Briggs, Laura; Latijnhouwers, Maita; Ligterink, Wilco; Meijer, Harold J G; Roberts, Samuel; Thurber, Carrie S; Whisson, Stephen C; Birch, Paul R J; Govers, Francine; Kamoun, Sophien; van West, Pieter; Windass, John
2008-04-01
Much of the pathogenic success of Phytophthora infestans, the potato and tomato late blight agent, relies on its ability to generate from mycelia large amounts of sporangia, which release zoospores that encyst and form infection structures. To better understand these stages, Affymetrix GeneChips based on 15,650 unigenes were designed and used to profile the life cycle. Approximately half of P. infestans genes were found to exhibit significant differential expression between developmental transitions, with approximately (1)/(10) being stage-specific and most changes occurring during zoosporogenesis. Quantitative reverse-transcription polymerase chain reaction assays confirmed the robustness of the array results and showed that similar patterns of differential expression were obtained regardless of whether hyphae were from laboratory media or infected tomato. Differentially expressed genes encode potential cellular regulators, especially protein kinases; metabolic enzymes such as those involved in glycolysis, gluconeogenesis, or the biosynthesis of amino acids or lipids; regulators of DNA synthesis; structural proteins, including predicted flagellar proteins; and pathogenicity factors, including cell-wall-degrading enzymes, RXLR effector proteins, and enzymes protecting against plant defense responses. Curiously, some stage-specific transcripts do not appear to encode functional proteins. These findings reveal many new aspects of oomycete biology, as well as potential targets for crop protection chemicals.
NASA Astrophysics Data System (ADS)
Castro, Manuel J.; Gallardo, José M.; Marquina, Antonio
2017-10-01
We present recent advances in PVM (Polynomial Viscosity Matrix) methods based on internal approximations to the absolute value function, and compare them with Chebyshev-based PVM solvers. These solvers only require a bound on the maximum wave speed, so no spectral decomposition is needed. Another important feature of the proposed methods is that they are suitable to be written in Jacobian-free form, in which only evaluations of the physical flux are used. This is particularly interesting when considering systems for which the Jacobians involve complex expressions, e.g., the relativistic magnetohydrodynamics (RMHD) equations. On the other hand, the proposed Jacobian-free solvers have also been extended to the case of approximate DOT (Dumbser-Osher-Toro) methods, which can be regarded as simple and efficient approximations to the classical Osher-Solomon method, sharing most of it interesting features and being applicable to general hyperbolic systems. To test the properties of our schemes a number of numerical experiments involving the RMHD equations are presented, both in one and two dimensions. The obtained results are in good agreement with those found in the literature and show that our schemes are robust and accurate, running stable under a satisfactory time step restriction. It is worth emphasizing that, although this work focuses on RMHD, the proposed schemes are suitable to be applied to general hyperbolic systems.
Photogrammetric Processing of Planetary Linear Pushbroom Images Based on Approximate Orthophotos
NASA Astrophysics Data System (ADS)
Geng, X.; Xu, Q.; Xing, S.; Hou, Y. F.; Lan, C. Z.; Zhang, J. J.
2018-04-01
It is still a great challenging task to efficiently produce planetary mapping products from orbital remote sensing images. There are many disadvantages in photogrammetric processing of planetary stereo images, such as lacking ground control information and informative features. Among which, image matching is the most difficult job in planetary photogrammetry. This paper designs a photogrammetric processing framework for planetary remote sensing images based on approximate orthophotos. Both tie points extraction for bundle adjustment and dense image matching for generating digital terrain model (DTM) are performed on approximate orthophotos. Since most of planetary remote sensing images are acquired by linear scanner cameras, we mainly deal with linear pushbroom images. In order to improve the computational efficiency of orthophotos generation and coordinates transformation, a fast back-projection algorithm of linear pushbroom images is introduced. Moreover, an iteratively refined DTM and orthophotos scheme was adopted in the DTM generation process, which is helpful to reduce search space of image matching and improve matching accuracy of conjugate points. With the advantages of approximate orthophotos, the matching results of planetary remote sensing images can be greatly improved. We tested the proposed approach with Mars Express (MEX) High Resolution Stereo Camera (HRSC) and Lunar Reconnaissance Orbiter (LRO) Narrow Angle Camera (NAC) images. The preliminary experimental results demonstrate the feasibility of the proposed approach.
Approximate method of variational Bayesian matrix factorization/completion with sparse prior
NASA Astrophysics Data System (ADS)
Kawasumi, Ryota; Takeda, Koujin
2018-05-01
We derive the analytical expression of a matrix factorization/completion solution by the variational Bayes method, under the assumption that the observed matrix is originally the product of low-rank, dense and sparse matrices with additive noise. We assume the prior of a sparse matrix is a Laplace distribution by taking matrix sparsity into consideration. Then we use several approximations for the derivation of a matrix factorization/completion solution. By our solution, we also numerically evaluate the performance of a sparse matrix reconstruction in matrix factorization, and completion of a missing matrix element in matrix completion.
Finding minimum-quotient cuts in planar graphs
DOE Office of Scientific and Technical Information (OSTI.GOV)
Park, J.K.; Phillips, C.A.
Given a graph G = (V, E) where each vertex v {element_of} V is assigned a weight w(v) and each edge e {element_of} E is assigned a cost c(e), the quotient of a cut partitioning the vertices of V into sets S and {bar S} is c(S, {bar S})/min{l_brace}w(S), w(S){r_brace}, where c(S, {bar S}) is the sum of the costs of the edges crossing the cut and w(S) and w({bar S}) are the sum of the weights of the vertices in S and {bar S}, respectively. The problem of finding a cut whose quotient is minimum for a graph hasmore » in recent years attracted considerable attention, due in large part to the work of Rao and Leighton and Rao. They have shown that an algorithm (exact or approximation) for the minimum-quotient-cut problem can be used to obtain an approximation algorithm for the more famous minimumb-balanced-cut problem, which requires finding a cut (S,{bar S}) minimizing c(S,{bar S}) subject to the constraint bW {le} w(S) {le} (1 {minus} b)W, where W is the total vertex weight and b is some fixed balance in the range 0 < b {le} {1/2}. Unfortunately, the minimum-quotient-cut problem is strongly NP-hard for general graphs, and the best polynomial-time approximation algorithm known for the general problem guarantees only a cut whose quotient is at mostO(lg n) times optimal, where n is the size of the graph. However, for planar graphs, the minimum-quotient-cut problem appears more tractable, as Rao has developed several efficient approximation algorithms for the planar version of the problem capable of finding a cut whose quotient is at most some constant times optimal. In this paper, we improve Rao`s algorithms, both in terms of accuracy and speed. As our first result, we present two pseudopolynomial-time exact algorithms for the planar minimum-quotient-cut problem. As Rao`s most accurate approximation algorithm for the problem -- also a pseudopolynomial-time algorithm -- guarantees only a 1.5-times-optimal cut, our algorithms represent a significant advance.« less
Finding minimum-quotient cuts in planar graphs
DOE Office of Scientific and Technical Information (OSTI.GOV)
Park, J.K.; Phillips, C.A.
Given a graph G = (V, E) where each vertex v [element of] V is assigned a weight w(v) and each edge e [element of] E is assigned a cost c(e), the quotient of a cut partitioning the vertices of V into sets S and [bar S] is c(S, [bar S])/min[l brace]w(S), w(S)[r brace], where c(S, [bar S]) is the sum of the costs of the edges crossing the cut and w(S) and w([bar S]) are the sum of the weights of the vertices in S and [bar S], respectively. The problem of finding a cut whose quotient is minimummore » for a graph has in recent years attracted considerable attention, due in large part to the work of Rao and Leighton and Rao. They have shown that an algorithm (exact or approximation) for the minimum-quotient-cut problem can be used to obtain an approximation algorithm for the more famous minimumb-balanced-cut problem, which requires finding a cut (S,[bar S]) minimizing c(S,[bar S]) subject to the constraint bW [le] w(S) [le] (1 [minus] b)W, where W is the total vertex weight and b is some fixed balance in the range 0 < b [le] [1/2]. Unfortunately, the minimum-quotient-cut problem is strongly NP-hard for general graphs, and the best polynomial-time approximation algorithm known for the general problem guarantees only a cut whose quotient is at mostO(lg n) times optimal, where n is the size of the graph. However, for planar graphs, the minimum-quotient-cut problem appears more tractable, as Rao has developed several efficient approximation algorithms for the planar version of the problem capable of finding a cut whose quotient is at most some constant times optimal. In this paper, we improve Rao's algorithms, both in terms of accuracy and speed. As our first result, we present two pseudopolynomial-time exact algorithms for the planar minimum-quotient-cut problem. As Rao's most accurate approximation algorithm for the problem -- also a pseudopolynomial-time algorithm -- guarantees only a 1.5-times-optimal cut, our algorithms represent a significant advance.« less
NASA Astrophysics Data System (ADS)
Horowitz, Jordan M.
2015-07-01
The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.
Horowitz, Jordan M
2015-07-28
The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.
On beam models and their paraxial approximation
NASA Astrophysics Data System (ADS)
Waters, W. J.; King, B.
2018-01-01
We derive focused laser pulse solutions to the electromagnetic wave equation in vacuum. After reproducing beam and pulse expressions for the well-known paraxial Gaussian and axicon cases, we apply the method to analyse a laser beam with Lorentzian transverse momentum distribution. Whilst a paraxial approach has some success close to the focal axis and within a Rayleigh range of the focal spot, we find that it incorrectly predicts the transverse fall-off typical of a Lorentzian. Our vector-potential approach is particularly relevant to calculation of quantum electrodynamical processes in weak laser pulse backgrounds.
Approximate flavor symmetries in the lepton sector
DOE Office of Scientific and Technical Information (OSTI.GOV)
Rasin, A.; Silva, J.P.
1994-01-01
Approximate flavor symmetries in the quark sector have been used as a handle on physics beyond the standard model. Because of the great interest in neutrino masses and mixings and the wealth of existing and proposed neutrino experiments it is important to extend this analysis to the leptonic sector. We show that in the seesaw mechanism the neutrino masses and mixing angles do not depend on the details of the right-handed neutrino flavor symmetry breaking, and are related by a simple formula. We propose several [ital Ansa]$[ital uml]---[ital tze] which relate different flavor symmetry-breaking parameters and find that the MSWmore » solution to the solar neutrino problem is always easily fit. Further, the [nu][sub [mu]-][nu][sub [tau
An approximate solution for interlaminar stresses in laminated composites: Applied mechanics program
NASA Technical Reports Server (NTRS)
Rose, Cheryl A.; Herakovich, Carl T.
1992-01-01
An approximate solution for interlaminar stresses in finite width, laminated composites subjected to uniform extensional, and bending loads is presented. The solution is based upon the principle of minimum complementary energy and an assumed, statically admissible stress state, derived by considering local material mismatch effects and global equilibrium requirements. The stresses in each layer are approximated by polynomial functions of the thickness coordinate, multiplied by combinations of exponential functions of the in-plane coordinate, expressed in terms of fourteen unknown decay parameters. Imposing the stationary condition of the laminate complementary energy with respect to the unknown variables yields a system of fourteen non-linear algebraic equations for the parameters. Newton's method is implemented to solve this system. Once the parameters are known, the stresses can be easily determined at any point in the laminate. Results are presented for through-thickness and interlaminar stress distributions for angle-ply, cross-ply (symmetric and unsymmetric laminates), and quasi-isotropic laminates subjected to uniform extension and bending. It is shown that the solution compares well with existing finite element solutions and represents an improved approximate solution for interlaminar stresses, primarily at interfaces where global equilibrium is satisfied by the in-plane stresses, but large local mismatch in properties requires the presence of interlaminar stresses.
Computational gene expression profiling under salt stress reveals patterns of co-expression
Sanchita; Sharma, Ashok
2016-01-01
Plants respond differently to environmental conditions. Among various abiotic stresses, salt stress is a condition where excess salt in soil causes inhibition of plant growth. To understand the response of plants to the stress conditions, identification of the responsible genes is required. Clustering is a data mining technique used to group the genes with similar expression. The genes of a cluster show similar expression and function. We applied clustering algorithms on gene expression data of Solanum tuberosum showing differential expression in Capsicum annuum under salt stress. The clusters, which were common in multiple algorithms were taken further for analysis. Principal component analysis (PCA) further validated the findings of other cluster algorithms by visualizing their clusters in three-dimensional space. Functional annotation results revealed that most of the genes were involved in stress related responses. Our findings suggest that these algorithms may be helpful in the prediction of the function of co-expressed genes. PMID:26981411
Onaindia, Arantza; Martínez, Nerea; Montes-Moreno, Santiago; Almaraz, Carmen; Rodríguez-Pinilla, Socorro M; Cereceda, Laura; Revert, Jose B; Ortega, César; Tardio, Antoni; González, Lucía; García, Sonia; Camacho, Francisca I; González-Vela, Carmen; Piris, Miguel A
2016-03-01
CD30 expression in peripheral T-cell lymphoma (PTCL) and angioimmunoblastic T-cell lymphoma (AITL) is currently of great interest because therapy targeting CD30 is of clinical benefit, but the clinical and therapeutic relevance of CD30 expression in these neoplasms still remains uncertain. The aim of this study was to better quantify CD30 expression in AITL and PTCL-not otherwise specified (NOS). The secondary objective was to determine whether CD30 cells exhibit a B-cell or a T-cell phenotype. Gene expression profiling was studied in a series of 37 PTCL cases demonstrating a continuous spectrum of TNFRSF8 expression. This prompted us to study CD30 immunohistochemical (IHC) expression and mRNA levels by reverse transcription polymerase chain reaction (RT-PCR) in a different series of 51 cases (43 AITLs and 8 PTCL-NOSs) in routine samples. Double stainings with PAX5/CD30, CD3/CD30, and LEF1/CD30 were performed to study the phenotype of CD30 cells. Most (90%) of the cases showed some level of CD30 expression by IHC (1% to 95%); these levels were high (>50% of tumoral cells) in 14% of cases. CD30 expression was not detected in 10% of the cases. Quantitative RT-PCR results largely confirmed these findings, demonstrating a moderately strong correlation between global CD30 IHC and mRNA levels (r=0.65, P=1.75e-7). Forty-four of the positive cases (98%) contained CD30-positive B cells (PAX5), whereas atypical CD30-positive T cells were detected in 42 cases (93%). In conclusion, our data show that most AITL and PTCL-NOS cases express CD30, exhibiting very variable levels of CD30 expression that may be measured by IHC or RT-PCR techniques.
A new approximation of Fermi-Dirac integrals of order 1/2 for degenerate semiconductor devices
NASA Astrophysics Data System (ADS)
AlQurashi, Ahmed; Selvakumar, C. R.
2018-06-01
There had been tremendous growth in the field of Integrated circuits (ICs) in the past fifty years. Scaling laws mandated both lateral and vertical dimensions to be reduced and a steady increase in doping densities. Most of the modern semiconductor devices have invariably heavily doped regions where Fermi-Dirac Integrals are required. Several attempts have been devoted to developing analytical approximations for Fermi-Dirac Integrals since numerical computations of Fermi-Dirac Integrals are difficult to use in semiconductor devices, although there are several highly accurate tabulated functions available. Most of these analytical expressions are not sufficiently suitable to be employed in semiconductor device applications due to their poor accuracy, the requirement of complicated calculations, and difficulties in differentiating and integrating. A new approximation has been developed for the Fermi-Dirac integrals of the order 1/2 by using Prony's method and discussed in this paper. The approximation is accurate enough (Mean Absolute Error (MAE) = 0.38%) and easy enough to be used in semiconductor device equations. The new approximation of Fermi-Dirac Integrals is applied to a more generalized Einstein Relation which is an important relation in semiconductor devices.
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).
HSP70 reduces chronic hypoxia-induced neural suppression via regulating expression of syntaxin.
Fei, Guanghe; Guo, Conghui; Sun, Hong-Shuo; Feng, Zhong-Ping
2008-01-01
Long-term exposure to modest hypoxia conditions may result in neural dysfunction; however, the involvement of presynaptic proteins has not been tested directly. Here, we reported that adult snails, Lymnaea stagnalis, developed a slow righting movement after placement in low O2 (approximately 5%) for 4 days. Semi-quantitative Western blot analysis showed that hypoxia induced heat shock protein 70 (HSP70) up-regulation and a reduction of syntaxin I. The inducible HSP70 occurs within 6 hours preceding the down-regulation of syntaxin I, suggesting that HSP70 may be involved in regulation of syntaxin expression. Injecting directly double-stranded RNAs (dsRNA) into the center ganglia region, we found that dsRNA HSP70, not the scrambled RNA, prevented the hypoxia-induced HSP70 expression, enhanced the hypoxia-dependent down-regulation of syntaxin I, and aggravated motor suppression. We thus provided the first evidence that early induction of HSP70 by chronic hypoxia is critical for maintaining expression levels of presynaptic proteins and neural function. These findings implicate a new molecular mechanism underlying chronic hypoxia-induced neurobehavioral adaptation and impairment.
GEM-TREND: a web tool for gene expression data mining toward relevant network discovery
Feng, Chunlai; Araki, Michihiro; Kunimoto, Ryo; Tamon, Akiko; Makiguchi, Hiroki; Niijima, Satoshi; Tsujimoto, Gozoh; Okuno, Yasushi
2009-01-01
Background DNA microarray technology provides us with a first step toward the goal of uncovering gene functions on a genomic scale. In recent years, vast amounts of gene expression data have been collected, much of which are available in public databases, such as the Gene Expression Omnibus (GEO). To date, most researchers have been manually retrieving data from databases through web browsers using accession numbers (IDs) or keywords, but gene-expression patterns are not considered when retrieving such data. The Connectivity Map was recently introduced to compare gene expression data by introducing gene-expression signatures (represented by a set of genes with up- or down-regulated labels according to their biological states) and is available as a web tool for detecting similar gene-expression signatures from a limited data set (approximately 7,000 expression profiles representing 1,309 compounds). In order to support researchers to utilize the public gene expression data more effectively, we developed a web tool for finding similar gene expression data and generating its co-expression networks from a publicly available database. Results GEM-TREND, a web tool for searching gene expression data, allows users to search data from GEO using gene-expression signatures or gene expression ratio data as a query and retrieve gene expression data by comparing gene-expression pattern between the query and GEO gene expression data. The comparison methods are based on the nonparametric, rank-based pattern matching approach of Lamb et al. (Science 2006) with the additional calculation of statistical significance. The web tool was tested using gene expression ratio data randomly extracted from the GEO and with in-house microarray data, respectively. The results validated the ability of GEM-TREND to retrieve gene expression entries biologically related to a query from GEO. For further analysis, a network visualization interface is also provided, whereby genes and gene annotations
GEM-TREND: a web tool for gene expression data mining toward relevant network discovery.
Feng, Chunlai; Araki, Michihiro; Kunimoto, Ryo; Tamon, Akiko; Makiguchi, Hiroki; Niijima, Satoshi; Tsujimoto, Gozoh; Okuno, Yasushi
2009-09-03
DNA microarray technology provides us with a first step toward the goal of uncovering gene functions on a genomic scale. In recent years, vast amounts of gene expression data have been collected, much of which are available in public databases, such as the Gene Expression Omnibus (GEO). To date, most researchers have been manually retrieving data from databases through web browsers using accession numbers (IDs) or keywords, but gene-expression patterns are not considered when retrieving such data. The Connectivity Map was recently introduced to compare gene expression data by introducing gene-expression signatures (represented by a set of genes with up- or down-regulated labels according to their biological states) and is available as a web tool for detecting similar gene-expression signatures from a limited data set (approximately 7,000 expression profiles representing 1,309 compounds). In order to support researchers to utilize the public gene expression data more effectively, we developed a web tool for finding similar gene expression data and generating its co-expression networks from a publicly available database. GEM-TREND, a web tool for searching gene expression data, allows users to search data from GEO using gene-expression signatures or gene expression ratio data as a query and retrieve gene expression data by comparing gene-expression pattern between the query and GEO gene expression data. The comparison methods are based on the nonparametric, rank-based pattern matching approach of Lamb et al. (Science 2006) with the additional calculation of statistical significance. The web tool was tested using gene expression ratio data randomly extracted from the GEO and with in-house microarray data, respectively. The results validated the ability of GEM-TREND to retrieve gene expression entries biologically related to a query from GEO. For further analysis, a network visualization interface is also provided, whereby genes and gene annotations are dynamically
Kreienkamp, Amelia B.; Liu, Lucy Y.; Minkara, Mona S.; Knepley, Matthew G.; Bardhan, Jaydeep P.; Radhakrishnan, Mala L.
2013-01-01
We analyze and suggest improvements to a recently developed approximate continuum-electrostatic model for proteins. The model, called BIBEE/I (boundary-integral based electrostatics estimation with interpolation), was able to estimate electrostatic solvation free energies to within a mean unsigned error of 4% on a test set of more than 600 proteins—a significant improvement over previous BIBEE models. In this work, we tested the BIBEE/I model for its capability to predict residue-by-residue interactions in protein–protein binding, using the widely studied model system of trypsin and bovine pancreatic trypsin inhibitor (BPTI). Finding that the BIBEE/I model performs surprisingly less well in this task than simpler BIBEE models, we seek to explain this behavior in terms of the models’ differing spectral approximations of the exact boundary-integral operator. Calculations of analytically solvable systems (spheres and tri-axial ellipsoids) suggest two possibilities for improvement. The first is a modified BIBEE/I approach that captures the asymptotic eigenvalue limit correctly, and the second involves the dipole and quadrupole modes for ellipsoidal approximations of protein geometries. Our analysis suggests that fast, rigorous approximate models derived from reduced-basis approximation of boundary-integral equations might reach unprecedented accuracy, if the dipole and quadrupole modes can be captured quickly for general shapes. PMID:24466561
Ise, H; Sugihara, N; Negishi, N; Nikaido, T; Akaike, T
2001-07-13
Development of a reliable method to isolate highly proliferative potential hepatocytes will provide insight into the molecular mechanisms of liver regeneration, as well as proving crucial for the development of a biohybrid artificial liver. The aim of this study is to isolate highly proliferative, e.g., progenitor-like, hepatocytes. To this end, we fractionated hepatocytes expressing low and high levels of the asialoglycoprotein receptor (ASGP-R) based on the difference in their adhesion to poly[N-p-vinylbenzyl-O-beta-d-galactopyranosyl-(1-->4)-d-gluconamide] (PVLA), and examined the proliferative activity and gene expression of these fractionated hepatocytes. The results showed that approximately 0.5 to 1% of the total number of hepatocytes, which showed low adhesion to PVLA, expressed low levels of the ASGP-R, while the rest of hepatocyte population with high adhesion to PVLA expressed high levels of the ASGP-R. Interestingly hepatocytes with low ASGP-R expression levels had much higher DNA synthesizing activity (i.e., are much more proliferative) than those with high ASGP-R expression levels. Moreover, hepatocytes with low ASGP-R expression levels expressed higher levels of epidermal growth factor receptor (EGF-R), CD29 (beta1 integrin) and CD49f (alpha6 integrin) and lower levels of glutamine synthetase than those with high ASGP-R expression. These findings suggested that hepatocytes with low adhesion to PVLA due to their low ASGP-R expression could be potential candidates for progenitor-like hepatocytes due to their high proliferative capacity; hence, the low expression of the ASGP-R could be a unique marker for progenitor hepatocytes. The isolation of hepatocytes with different functional phenotypes using PVLA may provide a new research tool for a better understanding of the biology of hepatocytes and the mechanisms regulating their proliferation and differentiation in health and disease. Copyright 2001 Academic Press.
The shifted harmonic approximation and asymptotic SU(2) and SU(1,1) Clebsch-Gordan coefficients
NASA Astrophysics Data System (ADS)
Rowe, D. J.; de Guise, Hubert
2010-12-01
Clebsch-Gordan coefficients of SU(2) and SU(1,1) are defined as eigenfunctions of a linear operator acting on the tensor product of the Hilbert spaces for two irreps of these groups. The shifted harmonic approximation is then used to solve these equations in asymptotic limits in which these eigenfunctions approach harmonic oscillator wavefunctions and thereby derive asymptotic expressions for these Clebsch-Gordan coefficients.
Exact and approximate solutions to the oblique shock equations for real-time applications
NASA Technical Reports Server (NTRS)
Hartley, T. T.; Brandis, R.; Mossayebi, F.
1991-01-01
The derivation of exact solutions for determining the characteristics of an oblique shock wave in a supersonic flow is investigated. Specifically, an explicit expression for the oblique shock angle in terms of the free stream Mach number, the centerbody deflection angle, and the ratio of the specific heats, is derived. A simpler approximate solution is obtained and compared to the exact solution. The primary objectives of obtaining these solutions is to provide a fast algorithm that can run in a real time environment.
An Approximate Approach to Automatic Kernel Selection.
Ding, Lizhong; Liao, Shizhong
2016-02-02
Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.
Technical Note: Approximate Bayesian parameterization of a complex tropical forest model
NASA Astrophysics Data System (ADS)
Hartig, F.; Dislich, C.; Wiegand, T.; Huth, A.
2013-08-01
Inverse parameter estimation of process-based models is a long-standing problem in ecology and evolution. A key problem of inverse parameter estimation is to define a metric that quantifies how well model predictions fit to the data. Such a metric can be expressed by general cost or objective functions, but statistical inversion approaches are based on a particular metric, the probability of observing the data given the model, known as the likelihood. Deriving likelihoods for dynamic models requires making assumptions about the probability for observations to deviate from mean model predictions. For technical reasons, these assumptions are usually derived without explicit consideration of the processes in the simulation. Only in recent years have new methods become available that allow generating likelihoods directly from stochastic simulations. Previous applications of these approximate Bayesian methods have concentrated on relatively simple models. Here, we report on the application of a simulation-based likelihood approximation for FORMIND, a parameter-rich individual-based model of tropical forest dynamics. We show that approximate Bayesian inference, based on a parametric likelihood approximation placed in a conventional MCMC, performs well in retrieving known parameter values from virtual field data generated by the forest model. We analyze the results of the parameter estimation, examine the sensitivity towards the choice and aggregation of model outputs and observed data (summary statistics), and show results from using this method to fit the FORMIND model to field data from an Ecuadorian tropical forest. Finally, we discuss differences of this approach to Approximate Bayesian Computing (ABC), another commonly used method to generate simulation-based likelihood approximations. Our results demonstrate that simulation-based inference, which offers considerable conceptual advantages over more traditional methods for inverse parameter estimation, can
Technical Note: Approximate Bayesian parameterization of a process-based tropical forest model
NASA Astrophysics Data System (ADS)
Hartig, F.; Dislich, C.; Wiegand, T.; Huth, A.
2014-02-01
Inverse parameter estimation of process-based models is a long-standing problem in many scientific disciplines. A key question for inverse parameter estimation is how to define the metric that quantifies how well model predictions fit to the data. This metric can be expressed by general cost or objective functions, but statistical inversion methods require a particular metric, the probability of observing the data given the model parameters, known as the likelihood. For technical and computational reasons, likelihoods for process-based stochastic models are usually based on general assumptions about variability in the observed data, and not on the stochasticity generated by the model. Only in recent years have new methods become available that allow the generation of likelihoods directly from stochastic simulations. Previous applications of these approximate Bayesian methods have concentrated on relatively simple models. Here, we report on the application of a simulation-based likelihood approximation for FORMIND, a parameter-rich individual-based model of tropical forest dynamics. We show that approximate Bayesian inference, based on a parametric likelihood approximation placed in a conventional Markov chain Monte Carlo (MCMC) sampler, performs well in retrieving known parameter values from virtual inventory data generated by the forest model. We analyze the results of the parameter estimation, examine its sensitivity to the choice and aggregation of model outputs and observed data (summary statistics), and demonstrate the application of this method by fitting the FORMIND model to field data from an Ecuadorian tropical forest. Finally, we discuss how this approach differs from approximate Bayesian computation (ABC), another method commonly used to generate simulation-based likelihood approximations. Our results demonstrate that simulation-based inference, which offers considerable conceptual advantages over more traditional methods for inverse parameter estimation
Khanum, Saeeda; Hanif, Rubina; Spelke, Elizabeth S; Berteletti, Ilaria; Hyde, Daniel C
2016-01-01
Current theories of numerical cognition posit that uniquely human symbolic number abilities connect to an early developing cognitive system for representing approximate numerical magnitudes, the approximate number system (ANS). In support of this proposal, recent laboratory-based training experiments with U.S. children show enhanced performance on symbolic addition after brief practice comparing or adding arrays of dots without counting: tasks that engage the ANS. Here we explore the nature and generality of this effect through two brief training experiments. In Experiment 1, elementary school children in Pakistan practiced either a non-symbolic numerical addition task or a line-length addition task with no numerical content, and then were tested on symbolic addition. After training, children in the numerical training group completed the symbolic addition test faster than children in the line length training group, suggesting a causal role of brief, non-symbolic numerical training on exact, symbolic addition. These findings replicate and extend the core findings of a recent U.S. laboratory-based study to non-Western children tested in a school setting, attesting to the robustness and generalizability of the observed training effects. Experiment 2 tested whether ANS training would also enhance the consistency of performance on a symbolic number line task. Over several analyses of the data there was some evidence that approximate number training enhanced symbolic number line placements relative to control conditions. Together, the findings suggest that engagement of the ANS through brief training procedures enhances children's immediate attention to number and engagement with symbolic number tasks.
Khanum, Saeeda; Hanif, Rubina; Spelke, Elizabeth S.; Berteletti, Ilaria; Hyde, Daniel C.
2016-01-01
Current theories of numerical cognition posit that uniquely human symbolic number abilities connect to an early developing cognitive system for representing approximate numerical magnitudes, the approximate number system (ANS). In support of this proposal, recent laboratory-based training experiments with U.S. children show enhanced performance on symbolic addition after brief practice comparing or adding arrays of dots without counting: tasks that engage the ANS. Here we explore the nature and generality of this effect through two brief training experiments. In Experiment 1, elementary school children in Pakistan practiced either a non-symbolic numerical addition task or a line-length addition task with no numerical content, and then were tested on symbolic addition. After training, children in the numerical training group completed the symbolic addition test faster than children in the line length training group, suggesting a causal role of brief, non-symbolic numerical training on exact, symbolic addition. These findings replicate and extend the core findings of a recent U.S. laboratory-based study to non-Western children tested in a school setting, attesting to the robustness and generalizability of the observed training effects. Experiment 2 tested whether ANS training would also enhance the consistency of performance on a symbolic number line task. Over several analyses of the data there was some evidence that approximate number training enhanced symbolic number line placements relative to control conditions. Together, the findings suggest that engagement of the ANS through brief training procedures enhances children's immediate attention to number and engagement with symbolic number tasks. PMID:27764117
NASA Astrophysics Data System (ADS)
Zhang, Li-qiang; Ma, Ting-ting; Yu, Chang-shui
2018-03-01
The computability of the quantifier of a given quantum resource is the essential challenge in the resource theory and the inevitable bottleneck for its application. Here we focus on the measurement-induced nonlocality and present a redefinition in terms of the skew information subject to a broken observable. It is shown that the obtained quantity possesses an obvious operational meaning, can tackle the noncontractivity of the measurement-induced nonlocality and has analytic expressions for pure states, (2 ⊗d )-dimensional quantum states, and some particular high-dimensional quantum states. Most importantly, an inverse approximate joint diagonalization algorithm, due to its simplicity, high efficiency, stability, and state independence, is presented to provide almost-analytic expressions for any quantum state, which can also shed light on other aspects in physics. To illustrate applications as well as demonstrate the validity of the algorithm, we compare the analytic and numerical expressions of various examples and show their perfect consistency.
Approximate error conjugation gradient minimization methods
Kallman, Jeffrey S
2013-05-21
In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems.
DOE Office of Scientific and Technical Information (OSTI.GOV)
Horowitz, Jordan M., E-mail: jordan.horowitz@umb.edu
The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochasticmore » thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.« less
NASA Astrophysics Data System (ADS)
Lauvergnat, David; Nauts, André; Justum, Yves; Chapuisat, Xavier
2001-04-01
The harmonic adiabatic approximation (HADA), an efficient and accurate quantum method to calculate highly excited vibrational levels of molecular systems, is presented. It is well-suited to applications to "floppy molecules" with a rather large number of atoms (N>3). A clever choice of internal coordinates naturally suggests their separation into active, slow, or large amplitude coordinates q', and inactive, fast, or small amplitude coordinates q″, which leads to an adiabatic (or Born-Oppenheimer-type) approximation (ADA), i.e., the total wave function is expressed as a product of active and inactive total wave functions. However, within the framework of the ADA, potential energy data concerning the inactive coordinates q″ are required. To reduce this need, a minimum energy domain (MED) is defined by minimizing the potential energy surface (PES) for each value of the active variables q', and a quadratic or harmonic expansion of the PES, based on the MED, is used (MED harmonic potential). In other words, the overall picture is that of a harmonic valley about the MED. In the case of only one active variable, we have a minimum energy path (MEP) and a MEP harmonic potential. The combination of the MED harmonic potential and the adiabatic approximation (harmonic adiabatic approximation: HADA) greatly reduces the size of the numerical computations, so that rather large molecules can be studied. In the present article however, the HADA is applied to our benchmark molecule HCN/CNH, to test the validity of the method. Thus, the HADA vibrational energy levels are compared and are in excellent agreement with the ADA calculations (adiabatic approximation with the full PES) of Light and Bačić [J. Chem. Phys. 87, 4008 (1987)]. Furthermore, the exact harmonic results (exact calculations without the adiabatic approximation but with the MEP harmonic potential) are compared to the exact calculations (without any sort of approximation). In addition, we compare the densities of
Hashmi, Atif Ali; Naz, Samreen; Hashmi, Shumaila Kanwal; Hussain, Zubaida Fida; Irfan, Muhammad; Bakar, Syed Muhammad Abu; Faridi, Naveen; Khan, Amir; Edhi, Muhammad Muzzammil
2018-06-08
Cytokeratin 5/6 and Cytokeratin 8/18 are basal and luminal markers of breast cancer and they have pathological and prognostic significance in breast cancer. We performed Cytokeratin 5/6 and CK8/18 immunohistochemistry on 150 cases of triple negative breast cancers and association with various clinicopathological features was evaluated. Positive CK5/6 expression was noted in 8% (12 cases) of TNBC while 2.4% (4 cases) showed focal positive (< 10%) and 89.3% (134) were negative with CK5/6. Complete loss of CK8/18 expression was seen in 4.7% (7 cases) while 32.7% (49 cases) revealed focal loss of CK8/18 and 62.7% (94 cases) showed intact normal expression of CK8/18. No significant association of CK5/6 and CK8/18 with various clinicopathological parameters was observed. We found a low expression of basal cytokeratin (CK5/6) in TNBC our studied population, while loss/altered expression of CK8/18 in approximately 38% of TNBC. Although no prognostic relevance of these finding was noted in our study, however these findings are different from those reported in literature in other parts of the world. Therefore we suggest a more through immunohistochemical and genomic profiling of TNBC in our population for better understanding of this disease in this part of the world.
Haltom, Kate E.; Mulvenna, Catherine M.; Lieberman, Matthew D.; Stanton, Annette L.
2013-01-01
The current study assessed main effects and moderators (including emotional expressiveness, emotional processing and ambivalence over emotional expression) of the effects of expressive writing in a sample of healthy adults. Young adult participants (N = 116) were randomly assigned to write for 20 minutes on four occasions about deepest thoughts and feelings regarding their most stressful/traumatic event in the past five years (expressive writing) or about a control topic (control). Dependent variables were indicators of anxiety, depression, and physical symptoms. No significant effects of writing condition were evident on anxiety, depressive symptoms, or physical symptoms. Emotional expressiveness emerged as a significant moderator of anxiety outcomes, however. Within the expressive writing group, participants high in expressiveness evidenced a significant reduction in anxiety at three-month follow-up, and participants low in expressiveness showed a significant increase in anxiety. Expressiveness did not predict change in anxiety in the control group. These findings on anxiety are consistent with the matching hypothesis, which suggests that matching a person’s naturally elected coping approach with an assigned intervention is beneficial. These findings also suggest that expressive writing about a stressful event may be contraindicated for individuals who do not typically express emotions. PMID:23742666
A distributed-memory approximation algorithm for maximum weight perfect bipartite matching
DOE Office of Scientific and Technical Information (OSTI.GOV)
Azad, Ariful; Buluc, Aydin; Li, Xiaoye S.
We design and implement an efficient parallel approximation algorithm for the problem of maximum weight perfect matching in bipartite graphs, i.e. the problem of finding a set of non-adjacent edges that covers all vertices and has maximum weight. This problem differs from the maximum weight matching problem, for which scalable approximation algorithms are known. It is primarily motivated by finding good pivots in scalable sparse direct solvers before factorization where sequential implementations of maximum weight perfect matching algorithms, such as those available in MC64, are widely used due to the lack of scalable alternatives. To overcome this limitation, we proposemore » a fully parallel distributed memory algorithm that first generates a perfect matching and then searches for weightaugmenting cycles of length four in parallel and iteratively augments the matching with a vertex disjoint set of such cycles. For most practical problems the weights of the perfect matchings generated by our algorithm are very close to the optimum. An efficient implementation of the algorithm scales up to 256 nodes (17,408 cores) on a Cray XC40 supercomputer and can solve instances that are too large to be handled by a single node using the sequential algorithm.« less
Yoneda, Norihide; Matsui, Osamu; Ikeno, Hiroshi; Inoue, Dai; Yoshida, Kotaro; Kitao, Azusa; Kozaka, Kazuto; Kobayashi, Satoshi; Gabata, Toshifumi; Ikeda, Hiroko; Nakamura, Keishi; Ohta, Tetsuo
2015-10-01
We report a female case of sinusoidal obstruction syndrome (SOS) diagnosed pathologically after chemotherapy (Pmab+m-FOLFOX6) for ascending colon cancer with multiple liver metastases, focusing on the findings of gadoxetic acid-enhanced MRI (EOB-MRI) and the organic anion transporting polypeptide 1B3 (OATP1B3) expression of in the liver. The patient was a 75-year-old female. She had received chemotherapy (Pmab+m-FOLFOX6) as six cycles for preoperative chemotherapy. After the preoperative chemotherapy, tumor sizes of hepatic metastases were reduced and hepatobiliary phase of EOB-MRI clearly depicted diffuse reticular hypointensity in the background liver. On the other hand, dynamic CT and/or other sequences of EOB-MRI did not show definite abnormality in the background liver. After the operation, this patient was pathologically confirmed as SOS demonstrating centrilobular congestion, sinusoidal dilatation, and perisinusoidal fibrosis. In normal liver parenchyma, OATP1B3 (uptake transporter of the EOB-MRI) expression is observed predominantly in centrilobular hepatocytes (zone 3). On the other hand, OATP1B3 expression was remarkably reduced because of the damages in the centrilobular (zone 3) hepatocytes in this SOS case. This indicated that EOB-MRI might be extremely sensitive in diagnosing SOS in its early stage.
Estimates of the absolute error and a scheme for an approximate solution to scheduling problems
NASA Astrophysics Data System (ADS)
Lazarev, A. A.
2009-02-01
An approach is proposed for estimating absolute errors and finding approximate solutions to classical NP-hard scheduling problems of minimizing the maximum lateness for one or many machines and makespan is minimized. The concept of a metric (distance) between instances of the problem is introduced. The idea behind the approach is, given the problem instance, to construct another instance for which an optimal or approximate solution can be found at the minimum distance from the initial instance in the metric introduced. Instead of solving the original problem (instance), a set of approximating polynomially/pseudopolynomially solvable problems (instances) are considered, an instance at the minimum distance from the given one is chosen, and the resulting schedule is then applied to the original instance.
NASA Technical Reports Server (NTRS)
Merrill, W. C.
1978-01-01
The Routh approximation technique for reducing the complexity of system models was applied in the frequency domain to a 16th order, state variable model of the F100 engine and to a 43d order, transfer function model of a launch vehicle boost pump pressure regulator. The results motivate extending the frequency domain formulation of the Routh method to the time domain in order to handle the state variable formulation directly. The time domain formulation was derived and a characterization that specifies all possible Routh similarity transformations was given. The characterization was computed by solving two eigenvalue-eigenvector problems. The application of the time domain Routh technique to the state variable engine model is described, and some results are given. Additional computational problems are discussed, including an optimization procedure that can improve the approximation accuracy by taking advantage of the transformation characterization.
Expression of eukaryotic polypeptides in chloroplasts
Mayfield, Stephen P.
2013-06-04
The present invention relates to a gene expression system in eukaryotic and prokaryotic cells, preferably plant cells and intact plants. In particular, the invention relates to an expression system having a RB47 binding site upstream of a translation initiation site for regulation of translation mediated by binding of RB47 protein, a member of the poly(A) binding protein family. Regulation is further effected by RB60, a protein disulfide isomerase. The expression system is capable of functioning in the nuclear/cytoplasm of cells and in the chloroplast of plants. Translation regulation of a desired molecule is enhanced approximately 100 fold over that obtained without RB47 binding site activation.
Approximate stresses in 2-D flat elastic contact fretting problems
NASA Astrophysics Data System (ADS)
Urban, Michael Rene
Fatigue results from the cyclic loading of a solid body. If the body subject to fatigue is in contact with another body and relative sliding motion occurs between these two bodies, then rubbing surface damage can accelerate fatigue failure. The acceleration of fatigue failure is especially important if the relative motion between the two bodies results in surface damage without excessive surface removal via wear. The situation just described is referred to as fretting fatigue. Understanding of fretting fatigue is greatly enhanced if the stress state associated with fretting can be characterized. For Hertzian contact, this can readily be done. Unfortunately, simple stress formulae are not available for flat body contact. The primary result of the present research is the development of a new, reasonably accurate, approximate closed form expression for 2-dimensional contact stresses which has been verified using finite element modeling. This expression is also combined with fracture mechanics to provide a simple method of determining when a crack is long enough to no longer be affected by the contact stress field. Lower bounds on fatigue life can then easily be calculated using fracture mechanics. This closed form expression can also be used to calculate crack propagation within the contact stress field. The problem of determining the cycles required to generate an initial crack and what to choose as an initial crack size is unresolved as it is in non-fretting fatigue.
A simple, approximate model of parachute inflation
DOE Office of Scientific and Technical Information (OSTI.GOV)
Macha, J.M.
1992-11-01
A simple, approximate model of parachute inflation is described. The model is based on the traditional, practical treatment of the fluid resistance of rigid bodies in nonsteady flow, with appropriate extensions to accommodate the change in canopy inflated shape. Correlations for the steady drag and steady radial force as functions of the inflated radius are required as input to the dynamic model. In a novel approach, the radial force is expressed in terms of easily obtainable drag and reefing fine tension measurements. A series of wind tunnel experiments provides the needed correlations. Coefficients associated with the added mass of fluidmore » are evaluated by calibrating the model against an extensive and reliable set of flight data. A parameter is introduced which appears to universally govern the strong dependence of the axial added mass coefficient on motion history. Through comparisons with flight data, the model is shown to realistically predict inflation forces for ribbon and ringslot canopies over a wide range of sizes and deployment conditions.« less
A simple, approximate model of parachute inflation
DOE Office of Scientific and Technical Information (OSTI.GOV)
Macha, J.M.
1992-01-01
A simple, approximate model of parachute inflation is described. The model is based on the traditional, practical treatment of the fluid resistance of rigid bodies in nonsteady flow, with appropriate extensions to accommodate the change in canopy inflated shape. Correlations for the steady drag and steady radial force as functions of the inflated radius are required as input to the dynamic model. In a novel approach, the radial force is expressed in terms of easily obtainable drag and reefing fine tension measurements. A series of wind tunnel experiments provides the needed correlations. Coefficients associated with the added mass of fluidmore » are evaluated by calibrating the model against an extensive and reliable set of flight data. A parameter is introduced which appears to universally govern the strong dependence of the axial added mass coefficient on motion history. Through comparisons with flight data, the model is shown to realistically predict inflation forces for ribbon and ringslot canopies over a wide range of sizes and deployment conditions.« less
Analysis of corrections to the eikonal approximation
NASA Astrophysics Data System (ADS)
Hebborn, C.; Capel, P.
2017-11-01
Various corrections to the eikonal approximations are studied for two- and three-body nuclear collisions with the goal to extend the range of validity of this approximation to beam energies of 10 MeV/nucleon. Wallace's correction does not improve much the elastic-scattering cross sections obtained at the usual eikonal approximation. On the contrary, a semiclassical approximation that substitutes the impact parameter by a complex distance of closest approach computed with the projectile-target optical potential efficiently corrects the eikonal approximation. This opens the possibility to analyze data measured down to 10 MeV/nucleon within eikonal-like reaction models.
Expression analysis of NOS family and HSP genes during thermal stress in goat ( Capra hircus)
NASA Astrophysics Data System (ADS)
Yadav, Vijay Pratap; Dangi, Satyaveer Singh; Chouhan, Vikrant Singh; Gupta, Mahesh; Dangi, Saroj K.; Singh, Gyanendra; Maurya, Vijay Prakash; Kumar, Puneet; Sarkar, Mihir
2016-03-01
Approximately 50 genes other than heat shock protein (HSP) expression changes during thermal stress. These genes like nitric oxide synthase (NOS) need proper attention and investigation to find out their possible role in the adaptation to thermal stress in animals. So, the present study was undertaken to demonstrate the expressions of inducible form type II NOS (iNOS), endothelial type III NOS (eNOS), constitutively expressed enzyme NOS (cNOS), HSP70, and HSP90 in peripheral blood mononuclear cells (PBMCs) during different seasons in Barbari goats. Real-time polymerase chain reaction, western blot, and immunocytochemistry were applied to investigate messenger RNA (mRNA) expression, protein expression, and immunolocalization of examined factors. The mRNA and protein expressions of iNOS, eNOS, cNOS, HSP70, and HSP90 were significantly higher ( P < 0.05) during peak summer, and iNOS and eNOS expressions were also observed to be significantly higher ( P < 0.05) during peak winter season as compared with moderate season. The iNOS, eNOS, cNOS, HSP70, and HSP90 were mainly localized in plasma membrane and cytoplasm of PBMCs. To conclude, data generated in the present study indicate the possible involvement of the NOS family genes in amelioration of thermal stress so as to maintain cellular integrity and homeostasis in goats.
NASA Technical Reports Server (NTRS)
Adamczyk, J. L.
1974-01-01
An approximate solution is reported for the unsteady aerodynamic response of an infinite swept wing encountering a vertical oblique gust in a compressible stream. The approximate expressions are of closed form and do not require excessive computer storage or computation time, and further, they are in good agreement with the results of exact theory. This analysis is used to predict the unsteady aerodynamic response of a helicopter rotor blade encountering the trailing vortex from a previous blade. Significant effects of three dimensionality and compressibility are evident in the results obtained. In addition, an approximate solution for the unsteady aerodynamic forces associated with the pitching or plunging motion of a two dimensional airfoil in a subsonic stream is presented. The mathematical form of this solution approaches the incompressible solution as the Mach number vanishes, the linear transonic solution as the Mach number approaches one, and the solution predicted by piston theory as the reduced frequency becomes large.
Sun, Wenqing; Chen, Lei; Tuya, Wulan; He, Yong; Zhu, Rihong
2013-12-01
Chebyshev and Legendre polynomials are frequently used in rectangular pupils for wavefront approximation. Ideally, the dataset completely fits with the polynomial basis, which provides the full-pupil approximation coefficients and the corresponding geometric aberrations. However, if there are horizontal translation and scaling, the terms in the original polynomials will become the linear combinations of the coefficients of the other terms. This paper introduces analytical expressions for two typical situations after translation and scaling. With a small translation, first-order Taylor expansion could be used to simplify the computation. Several representative terms could be selected as inputs to compute the coefficient changes before and after translation and scaling. Results show that the outcomes of the analytical solutions and the approximated values under discrete sampling are consistent. With the computation of a group of randomly generated coefficients, we contrasted the changes under different translation and scaling conditions. The larger ratios correlate the larger deviation from the approximated values to the original ones. Finally, we analyzed the peak-to-valley (PV) and root mean square (RMS) deviations from the uses of the first-order approximation and the direct expansion under different translation values. The results show that when the translation is less than 4%, the most deviated 5th term in the first-order 1D-Legendre expansion has a PV deviation less than 7% and an RMS deviation less than 2%. The analytical expressions and the computed results under discrete sampling given in this paper for the multiple typical function basis during translation and scaling in the rectangular areas could be applied in wavefront approximation and analysis.
Stibinger, Jakub
2017-05-01
The research was focused on approximation of clogging in a leachate collection system in municipal solid waste landfill in Osecna, situated near the location Osecna, region Liberec, Northern Bohemia, Czech Republic, by analysis of numerical experiment results. To approximate the clogging of the leachate collection system after fifteen years of landfill operation (1995-2009) were successfully tested modified De Zeeuw-Hellinga transient drainage theory. This procedure allows application of the reduction factors to express clogging of the leachate collection system in Osecna landfill. The results proved that the modified De Zeeuw-Hellinga method with reduction factors can serve as a good tool for clogging approximation in a leachate collection system in Osecna landfill. Copyright © 2016 Elsevier Ltd. All rights reserved.
Approximations of Two-Attribute Utility Functions
1976-09-01
preferred to") be a bina-zy relation on the set • of simple probability measures or ’gambles’ defined on a set T of consequences. Throughout this study it...simplifying independence assumptions. Although there are several approaches to this problem, the21 present study will focus on approximations of u... study will elicit additional interest in the topic. 2. REMARKS ON APPROXIMATION THEORY This section outlines a few basic ideas of approximation theory
Heterologous expression of Trametes versicolor laccase in Saccharomyces cerevisiae.
Iimura, Yosuke; Sonoki, Tomonori; Habe, Hiroshi
2018-01-01
Laccase is used in various industrial fields, and it has been the subject of numerous studies. Trametes versicolor laccase has one of the highest redox potentials among the various forms of this enzyme. In this study, we optimized the expression of laccase in Saccharomyces cerevisiae. Optimizing the culture conditions resulted in an improvement in the expression level, and approximately 45 U/L of laccase was functionally secreted in the culture. The recombinant laccase was found to be a heavily hypermannosylated glycoprotein, and the molecular weight of the carbohydrate chain was approximately 60 kDa. These hypermannosylated glycans lowered the substrate affinity, but the optimum pH and thermo-stability were not changed by these hypermannosylated glycans. This functional expression system described here will aid in molecular evolutionary studies conducted to generate new variants of laccase. Copyright © 2017 Elsevier Inc. All rights reserved.
A circannual clock drives expression of genes central for seasonal reproduction.
Sáenz de Miera, Cristina; Monecke, Stefanie; Bartzen-Sprauer, Julien; Laran-Chich, Marie-Pierre; Pévet, Paul; Hazlerigg, David G; Simonneaux, Valérie
2014-07-07
Animals living in temperate zones anticipate seasonal environmental changes to adapt their biological functions, especially reproduction and metabolism. Two main physiological mechanisms have evolved for this adaptation: intrinsic long-term timing mechanisms with an oscillating period of approximately 1 year, driven by a circannual clock [1], and synchronization of biological rhythms to the sidereal year using day length (photoperiod) [2]. In mammals, the pineal hormone melatonin relays photoperiodic information to the hypothalamus to control seasonal physiology through well-defined mechanisms [3-6]. In contrast, little is known about how the circannual clock drives endogenous changes in seasonal functions. The aim of this study was to determine whether genes involved in photoperiodic time measurement (TSHβ and Dio2) and central control of reproduction (Rfrp and Kiss1) display circannual rhythms in expression under constant conditions. Male European hamsters, deprived of seasonal time cues by pinealectomy and maintenance in constant photoperiod, were selected when expressing a subjective summer or subjective winter state in their circannual cycle of body weight, temperature, and testicular size. TSHβ expression in the pars tuberalis (PT) displayed a robust circannual variation with highest level in the subjective summer state, which was positively correlated with hypothalamic Dio2 and Rfrp expression. The negative sex steroid feedback was found to act specifically on arcuate Kiss1 expression. Our findings reveal TSH as a circannual output of the PT, which in turn regulates hypothalamic neurons controlling reproductive activity. Therefore, both the circannual and the melatonin signals converge on PT TSHβ expression to synchronize seasonal biological activity. Copyright © 2014 Elsevier Ltd. All rights reserved.
Thin airfoil theory based on approximate solution of the transonic flow equation
NASA Technical Reports Server (NTRS)
Spreiter, John R; Alksne, Alberta Y
1957-01-01
A method is presented for the approximate solution of the nonlinear equations transonic flow theory. Solutions are found for two-dimensional flows at a Mach number of 1 and for purely subsonic and purely supersonic flows. Results are obtained in closed analytic form for a large and significant class of nonlifting airfoils. At a Mach number of 1 general expressions are given for the pressure distribution on an airfoil of specified geometry and for the shape of an airfoil having a prescribed pressure distribution. Extensive comparisons are made with available data, particularly for a Mach number of 1, and with existing solutions.
Single-particle properties of the Hubbard model in a novel three-pole approximation
NASA Astrophysics Data System (ADS)
Di Ciolo, Andrea; Avella, Adolfo
2018-05-01
We study the 2D Hubbard model using the Composite Operator Method within a novel three-pole approximation. Motivated by the long-standing experimental puzzle of the single-particle properties of the underdoped cuprates, we include in the operatorial basis, together with the usual Hubbard operators, a field describing the electronic transitions dressed by the nearest-neighbor spin fluctuations, which play a crucial role in the unconventional behavior of the Fermi surface and of the electronic dispersion. Then, we adopt this approximation to study the single-particle properties in the strong coupling regime and find an unexpected behavior of the van Hove singularity that can be seen as a precursor of a pseudogap regime.
NASA Technical Reports Server (NTRS)
Tal-Ezer, Hillel
1987-01-01
During the process of solving a mathematical model numerically, there is often a need to operate on a vector v by an operator which can be expressed as f(A) while A is NxN matrix (ex: exp(A), sin(A), A sup -1). Except for very simple matrices, it is impractical to construct the matrix f(A) explicitly. Usually an approximation to it is used. In the present research, an algorithm is developed which uses a polynomial approximation to f(A). It is reduced to a problem of approximating f(z) by a polynomial in z while z belongs to the domain D in the complex plane which includes all the eigenvalues of A. This problem of approximation is approached by interpolating the function f(z) in a certain set of points which is known to have some maximal properties. The approximation thus achieved is almost best. Implementing the algorithm to some practical problem is described. Since a solution to a linear system Ax = b is x= A sup -1 b, an iterative solution to it can be regarded as a polynomial approximation to f(A) = A sup -1. Implementing the algorithm in this case is also described.
Theory and application of an approximate model of saltwater upconing in aquifers
McElwee, C.; Kemblowski, M.
1990-01-01
Motion and mixing of salt water and fresh water are vitally important for water-resource development throughout the world. An approximate model of saltwater upconing in aquifers is developed, which results in three non-linear coupled equations for the freshwater zone, the saltwater zone, and the transition zone. The description of the transition zone uses the concept of a boundary layer. This model invokes some assumptions to give a reasonably tractable model, considerably better than the sharp interface approximation but considerably simpler than a fully three-dimensional model with variable density. We assume the validity of the Dupuit-Forchheimer approximation of horizontal flow in each layer. Vertical hydrodynamic dispersion into the base of the transition zone is assumed and concentration of the saltwater zone is assumed constant. Solute in the transition zone is assumed to be moved by advection only. Velocity and concentration are allowed to vary vertically in the transition zone by using shape functions. Several numerical techniques can be used to solve the model equations, and simple analytical solutions can be useful in validating the numerical solution procedures. We find that the model equations can be solved with adequate accuracy using the procedures presented. The approximate model is applied to the Smoky Hill River valley in central Kansas. This model can reproduce earlier sharp interface results as well as evaluate the importance of hydrodynamic dispersion for feeding salt water to the river. We use a wide range of dispersivity values and find that unstable upconing always occurs. Therefore, in this case, hydrodynamic dispersion is not the only mechanism feeding salt water to the river. Calculations imply that unstable upconing and hydrodynamic dispersion could be equally important in transporting salt water. For example, if groundwater flux to the Smoky Hill River were only about 40% of its expected value, stable upconing could exist where
NASA Astrophysics Data System (ADS)
Lisienko, V. G.; Malikov, G. K.; Titaev, A. A.
2014-12-01
The paper presents a new simple-to-use expression to calculate the total emissivity of a mixture of gases CO2 and H2O used for modeling heat transfer by radiation in industrial furnaces. The accuracy of this expression is evaluated using the exponential wide band model. It is found that the time taken to calculate the total emissivity in this expression is 1.5 times less than in other approximation methods.
Energy conservation - A test for scattering approximations
NASA Technical Reports Server (NTRS)
Acquista, C.; Holland, A. C.
1980-01-01
The roles of the extinction theorem and energy conservation in obtaining the scattering and absorption cross sections for several light scattering approximations are explored. It is shown that the Rayleigh, Rayleigh-Gans, anomalous diffraction, geometrical optics, and Shifrin approximations all lead to reasonable values of the cross sections, while the modified Mie approximation does not. Further examination of the modified Mie approximation for the ensembles of nonspherical particles reveals additional problems with that method.
DOE Office of Scientific and Technical Information (OSTI.GOV)
Shirdel-Havar, A. H., E-mail: Amir.hushang.shirdel@gmail.com; Masoudian Saadabad, R.
2015-03-21
Based on ballistic-diffusive approximation, a method is presented to model heat transfer in nanocomposites containing metal nanoparticles. This method provides analytical expression for the temperature dynamics of metallic nanoparticles embedded in a dielectric medium. In this study, nanoparticles are considered as spherical shells, so that Boltzmann equation is solved using ballistic-diffusive approximation to calculate the electron and lattice thermal dynamics in gold nanoparticles, while thermal exchange between the particles is taken into account. The model was used to investigate the influence of particle size and metal concentration of the medium on the electron and lattice thermal dynamics. It is shownmore » that these two parameters are crucial in determining the nanocomposite thermal behavior. Our results showed that the heat transfer rate from nanoparticles to the matrix decreases as the nanoparticle size increases. On the other hand, increasing the metal concentration of the medium can also decrease the heat transfer rate.« less
Application of the N-quantum approximation to the proton radius problem
NASA Astrophysics Data System (ADS)
Cowen, Steven
This thesis is organized into three parts: 1. Introduction and bound state calculations of electronic and muonic hydrogen, 2. Bound states in motion, and 3.Treatment of soft photons. In the first part, we apply the N-Quantum Approximation (NQA) to electronic and muonic hydrogen and search for any new corrections to energy levels that could account for the 0.31 meV discrepancy of the proton radius problem. We derive a bound state equation and compare our numerical solutions and wave functions to those of the Dirac equation. We find NQA Lamb shift diagrams and calculate the associated energy shift contributions. We do not find any new corrections large enough to account for the discrepancy. In part 2, we discuss the effects of motion on bound states using the NQA. We find classical Lorentz contraction of the lowest order NQA wave function. Finally, in part 3, we develop a clothing transformation for interacting fields in order to produce the correct asymptotic limits. We find the clothing eliminates a trilinear interacting Hamiltonian term and produces a quadrilinear soft photon interaction term.
Recognition of computerized facial approximations by familiar assessors.
Richard, Adam H; Monson, Keith L
2017-11-01
Studies testing the effectiveness of facial approximations typically involve groups of participants who are unfamiliar with the approximated individual(s). This limitation requires the use of photograph arrays including a picture of the subject for comparison to the facial approximation. While this practice is often necessary due to the difficulty in obtaining a group of assessors who are familiar with the approximated subject, it may not accurately simulate the thought process of the target audience (friends and family members) in comparing a mental image of the approximated subject to the facial approximation. As part of a larger process to evaluate the effectiveness and best implementation of the ReFace facial approximation software program, the rare opportunity arose to conduct a recognition study using assessors who were personally acquainted with the subjects of the approximations. ReFace facial approximations were generated based on preexisting medical scans, and co-workers of the scan donors were tested on whether they could accurately pick out the approximation of their colleague from arrays of facial approximations. Results from the study demonstrated an overall poor recognition performance (i.e., where a single choice within a pool is not enforced) for individuals who were familiar with the approximated subjects. Out of 220 recognition tests only 10.5% resulted in the assessor selecting the correct approximation (or correctly choosing not to make a selection when the array consisted only of foils), an outcome that was not significantly different from the 9% random chance rate. When allowed to select multiple approximations the assessors felt resembled the target individual, the overall sensitivity for ReFace approximations was 16.0% and the overall specificity was 81.8%. These results differ markedly from the results of a previous study using assessors who were unfamiliar with the approximated subjects. Some possible explanations for this disparity in
Consistent Yokoya-Chen Approximation to Beamstrahlung(LCC-0010)
DOE Office of Scientific and Technical Information (OSTI.GOV)
Peskin, M
2004-04-22
I reconsider the Yokoya-Chen approximate evolution equation for beamstrahlung and modify it slightly to generate simple, consistent analytical approximations for the electron and photon energy spectra. I compare these approximations to previous ones, and to simulation data.I reconsider the Yokoya-Chen approximate evolution equation for beamstrahlung and modify it slightly to generate simple, consistent analytical approximations for the electron and photon energy spectra. I compare these approximations to previous ones, and to simulation data.
Use of mRNA expression signatures to discover small molecule inhibitors of skeletal muscle atrophy
Adams, Christopher M.; Ebert, Scott M.; Dyle, Michael C.
2017-01-01
Purpose of review Here, we discuss a recently developed experimental strategy for discovering small molecules with potential to prevent and treat skeletal muscle atrophy. Recent findings Muscle atrophy involves and requires widespread changes in skeletal muscle gene expression, which generate complex but measurable patterns of positive and negative changes in skeletal muscle mRNA levels (a.k.a. mRNA expression signatures of muscle atrophy). Many bioactive small molecules generate their own characteristic mRNA expression signatures, and by identifying small molecules whose signatures approximate mirror images of muscle atrophy signatures, one may identify small molecules with potential to prevent and/or reverse muscle atrophy. Unlike a conventional drug discovery approach, this strategy does not rely on a predefined molecular target but rather exploits the complexity of muscle atrophy to identify small molecules that counter the entire spectrum of pathological changes in atrophic muscle. We discuss how this strategy has been used to identify two natural compounds, ursolic acid and tomatidine, that reduce muscle atrophy and improve skeletal muscle function. Summary Discovery strategies based on mRNA expression signatures can elucidate new approaches for preserving and restoring muscle mass and function. PMID:25807353
Study of multiband disordered systems using the typical medium dynamical cluster approximation
DOE Office of Scientific and Technical Information (OSTI.GOV)
Zhang, Yi; Terletska, Hanna; Moore, C.
We generalize the typical medium dynamical cluster approximation to multiband disordered systems. Using our extended formalism, we perform a systematic study of the nonlocal correlation effects induced by disorder on the density of states and the mobility edge of the three-dimensional two-band Anderson model. We include interband and intraband hopping and an intraband disorder potential. Our results are consistent with those obtained by the transfer matrix and the kernel polynomial methods. We also apply the method to K xFe 2-ySe 2 with Fe vacancies. Despite the strong vacancy disorder and anisotropy, we find the material is not an Anderson insulator.more » Moreover our results demonstrate the application of the typical medium dynamical cluster approximation method to study Anderson localization in real materials.« less
Study of multiband disordered systems using the typical medium dynamical cluster approximation
Zhang, Yi; Terletska, Hanna; Moore, C.; ...
2015-11-06
We generalize the typical medium dynamical cluster approximation to multiband disordered systems. Using our extended formalism, we perform a systematic study of the nonlocal correlation effects induced by disorder on the density of states and the mobility edge of the three-dimensional two-band Anderson model. We include interband and intraband hopping and an intraband disorder potential. Our results are consistent with those obtained by the transfer matrix and the kernel polynomial methods. We also apply the method to K xFe 2-ySe 2 with Fe vacancies. Despite the strong vacancy disorder and anisotropy, we find the material is not an Anderson insulator.more » Moreover our results demonstrate the application of the typical medium dynamical cluster approximation method to study Anderson localization in real materials.« less
Approximating natural connectivity of scale-free networks based on largest eigenvalue
NASA Astrophysics Data System (ADS)
Tan, S.-Y.; Wu, J.; Li, M.-J.; Lu, X.
2016-06-01
It has been recently proposed that natural connectivity can be used to efficiently characterize the robustness of complex networks. The natural connectivity has an intuitive physical meaning and a simple mathematical formulation, which corresponds to an average eigenvalue calculated from the graph spectrum. However, as a network model close to the real-world system that widely exists, the scale-free network is found difficult to obtain its spectrum analytically. In this article, we investigate the approximation of natural connectivity based on the largest eigenvalue in both random and correlated scale-free networks. It is demonstrated that the natural connectivity of scale-free networks can be dominated by the largest eigenvalue, which can be expressed asymptotically and analytically to approximate natural connectivity with small errors. Then we show that the natural connectivity of random scale-free networks increases linearly with the average degree given the scaling exponent and decreases monotonically with the scaling exponent given the average degree. Moreover, it is found that, given the degree distribution, the more assortative a scale-free network is, the more robust it is. Experiments in real networks validate our methods and results.
Two-layer interfacial flows beyond the Boussinesq approximation: a Hamiltonian approach
NASA Astrophysics Data System (ADS)
Camassa, R.; Falqui, G.; Ortenzi, G.
2017-02-01
The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler system for two-layer stratified flows in an infinite two-dimensional channel. The Hamiltonian structure of the averaged equations is obtained directly from that of the Euler equations through the process of Hamiltonian reduction. Long-wave asymptotics together with the Boussinesq approximation of neglecting the fluids’ inertia is then applied to reduce the leading order vertically averaged equations to the shallow-water Airy system, albeit in a non-trivial way. The full non-Boussinesq system for the dispersionless limit can then be viewed as a deformation of this well known equation. In a perturbative study of this deformation, a family of approximate constants of the motion are explicitly constructed and used to find local solutions of the evolution equations by means of hodograph-like formulae.
Exponential approximations in optimal design
NASA Technical Reports Server (NTRS)
Belegundu, A. D.; Rajan, S. D.; Rajgopal, J.
1990-01-01
One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.
Analyzing the errors of DFT approximations for compressed water systems
NASA Astrophysics Data System (ADS)
Alfè, D.; Bartók, A. P.; Csányi, G.; Gillan, M. J.
2014-07-01
We report an extensive study of the errors of density functional theory (DFT) approximations for compressed water systems. The approximations studied are based on the widely used PBE and BLYP exchange-correlation functionals, and we characterize their errors before and after correction for 1- and 2-body errors, the corrections being performed using the methods of Gaussian approximation potentials. The errors of the uncorrected and corrected approximations are investigated for two related types of water system: first, the compressed liquid at temperature 420 K and density 1.245 g/cm3 where the experimental pressure is 15 kilobars; second, thermal samples of compressed water clusters from the trimer to the 27-mer. For the liquid, we report four first-principles molecular dynamics simulations, two generated with the uncorrected PBE and BLYP approximations and a further two with their 1- and 2-body corrected counterparts. The errors of the simulations are characterized by comparing with experimental data for the pressure, with neutron-diffraction data for the three radial distribution functions, and with quantum Monte Carlo (QMC) benchmarks for the energies of sets of configurations of the liquid in periodic boundary conditions. The DFT errors of the configuration samples of compressed water clusters are computed using QMC benchmarks. We find that the 2-body and beyond-2-body errors in the liquid are closely related to similar errors exhibited by the clusters. For both the liquid and the clusters, beyond-2-body errors of DFT make a substantial contribution to the overall errors, so that correction for 1- and 2-body errors does not suffice to give a satisfactory description. For BLYP, a recent representation of 3-body energies due to Medders, Babin, and Paesani [J. Chem. Theory Comput. 9, 1103 (2013)] gives a reasonably good way of correcting for beyond-2-body errors, after which the remaining errors are typically 0.5 mEh ≃ 15 meV/monomer for the liquid and the
Analyzing the errors of DFT approximations for compressed water systems
DOE Office of Scientific and Technical Information (OSTI.GOV)
Alfè, D.; London Centre for Nanotechnology, UCL, London WC1H 0AH; Thomas Young Centre, UCL, London WC1H 0AH
We report an extensive study of the errors of density functional theory (DFT) approximations for compressed water systems. The approximations studied are based on the widely used PBE and BLYP exchange-correlation functionals, and we characterize their errors before and after correction for 1- and 2-body errors, the corrections being performed using the methods of Gaussian approximation potentials. The errors of the uncorrected and corrected approximations are investigated for two related types of water system: first, the compressed liquid at temperature 420 K and density 1.245 g/cm{sup 3} where the experimental pressure is 15 kilobars; second, thermal samples of compressed watermore » clusters from the trimer to the 27-mer. For the liquid, we report four first-principles molecular dynamics simulations, two generated with the uncorrected PBE and BLYP approximations and a further two with their 1- and 2-body corrected counterparts. The errors of the simulations are characterized by comparing with experimental data for the pressure, with neutron-diffraction data for the three radial distribution functions, and with quantum Monte Carlo (QMC) benchmarks for the energies of sets of configurations of the liquid in periodic boundary conditions. The DFT errors of the configuration samples of compressed water clusters are computed using QMC benchmarks. We find that the 2-body and beyond-2-body errors in the liquid are closely related to similar errors exhibited by the clusters. For both the liquid and the clusters, beyond-2-body errors of DFT make a substantial contribution to the overall errors, so that correction for 1- and 2-body errors does not suffice to give a satisfactory description. For BLYP, a recent representation of 3-body energies due to Medders, Babin, and Paesani [J. Chem. Theory Comput. 9, 1103 (2013)] gives a reasonably good way of correcting for beyond-2-body errors, after which the remaining errors are typically 0.5 mE{sub h} ≃ 15 meV/monomer for the
DOE Office of Scientific and Technical Information (OSTI.GOV)
Zillich, Robert E., E-mail: robert.zillich@jku.at
2015-11-15
We construct an accurate imaginary time propagator for path integral Monte Carlo simulations for heterogeneous systems consisting of a mixture of atoms and molecules. We combine the pair density approximation, which is highly accurate but feasible only for the isotropic interactions between atoms, with the Takahashi–Imada approximation for general interactions. We present finite temperature simulations results for energy and structure of molecules–helium clusters X{sup 4}He{sub 20} (X=HCCH and LiH) which show a marked improvement over the Trotter approximation which has a 2nd-order time step bias. We show that the 4th-order corrections of the Takahashi–Imada approximation can also be applied perturbativelymore » to a 2nd-order simulation.« less
Katao, Kazuo; Honma, Reiko; Kato, Satoko; Watanabe, Shinya; Imai, Jun-ichi
2011-01-01
Platinum is recognized as a harmless metal and is widely used in many industrial products. Recent studies have proposed that platinum in the form of nanoparticles has antioxidant properties, suggesting potential uses for platinum nanoparticles as additives in foods and cosmetics, with direct exposure consequences for humans. However, the influence of platinum nanoparticles on humans has not been sufficiently evaluated, thus far. Therefore, to investigate the influence of platinum nanoparticles on a living body, we comprehensively examined the expression profiles of genes obtained from 25 organs and tissues of rats after oral administration of platinum nanoparticles by gavage. Comparative analysis revealed that the expression levels of 18 genes were altered in 12 organs and tissues after the administration (approximately 0.17% of all the genes examined). Of the tissues examined, those of the glandular stomach, which were most directly exposed to the orally administered platinum nanoparticles, showed altered expression levels of genes associated with inflammation. In subcutaneous adipose tissue, the expression levels of genes whose products exhibited ATPase activity were altered. Real-time reverse transcription polymerase chain reaction (real-time RT-PCR) analysis confirmed the alteration in the expression levels of these genes in these 2 different tissues. Our findings indicate that orally administered platinum nanoparticles do not have a marked effect on systemic gene expression levels, except on a small number of genes expressed in rat tissues, including peripheral tissues indirectly exposed to the orally administered nanoparticles.
Better approximation guarantees for job-shop scheduling
DOE Office of Scientific and Technical Information (OSTI.GOV)
Goldberg, L.A.; Paterson, M.; Srinivasan, A.
1997-06-01
Job-shop scheduling is a classical NP-hard problem. Shmoys, Stein & Wein presented the first polynomial-time approximation algorithm for this problem that has a good (polylogarithmic) approximation guarantee. We improve the approximation guarantee of their work, and present further improvements for some important NP-hard special cases of this problem (e.g., in the preemptive case where machines can suspend work on operations and later resume). We also present NC algorithms with improved approximation guarantees for some NP-hard special cases.
A Dictionary of Hindi Verbal Expressions (Hindi-English). Final Report.
ERIC Educational Resources Information Center
Bahl, Kali Charan, Comp.
This dictionary covers approximately 28,277 verbal expressions in modern standard Hindi and their rendered English equivalents. The study lists longer verbal expressions which are generally matched by single verbs in English. The lexicographer notes that the majority of entries in this dictionary do not appear in their present form in most other…
Continuous approximation for interaction energy of adamantane encapsulated inside carbon nanotubes
NASA Astrophysics Data System (ADS)
Baowan, Duangkamon; Hill, James M.; Bacsa, Wolfgang
2018-02-01
The interaction energy for two adjacent adamantane molecules and that of adamantane molecules encapsulated inside carbon nanotubes are investigated considering only dipole-dipole induced interaction. The Lennard-Jones potential and the continuous approximation are utilised to derive analytical expressions for these interaction energies. The equilibrium distance 3.281 Å between two adamantane molecules is determined. The smallest carbon nanotube radius b0 that can encapsulate the adamantane molecule and the radius of the tube bmax that gives the maximum suction energy, linearly depend on the adamantane radius, are calculated. For larger diameter tubes, the off axis position has been calculated, and equilibrium distance between molecule and tube wall is found to be close to the interlayer spacing in graphene.
Cluster and propensity based approximation of a network
2013-01-01
Background The models in this article generalize current models for both correlation networks and multigraph networks. Correlation networks are widely applied in genomics research. In contrast to general networks, it is straightforward to test the statistical significance of an edge in a correlation network. It is also easy to decompose the underlying correlation matrix and generate informative network statistics such as the module eigenvector. However, correlation networks only capture the connections between numeric variables. An open question is whether one can find suitable decompositions of the similarity measures employed in constructing general networks. Multigraph networks are attractive because they support likelihood based inference. Unfortunately, it is unclear how to adjust current statistical methods to detect the clusters inherent in many data sets. Results Here we present an intuitive and parsimonious parametrization of a general similarity measure such as a network adjacency matrix. The cluster and propensity based approximation (CPBA) of a network not only generalizes correlation network methods but also multigraph methods. In particular, it gives rise to a novel and more realistic multigraph model that accounts for clustering and provides likelihood based tests for assessing the significance of an edge after controlling for clustering. We present a novel Majorization-Minimization (MM) algorithm for estimating the parameters of the CPBA. To illustrate the practical utility of the CPBA of a network, we apply it to gene expression data and to a bi-partite network model for diseases and disease genes from the Online Mendelian Inheritance in Man (OMIM). Conclusions The CPBA of a network is theoretically appealing since a) it generalizes correlation and multigraph network methods, b) it improves likelihood based significance tests for edge counts, c) it directly models higher-order relationships between clusters, and d) it suggests novel clustering
Linear Approximation SAR Azimuth Processing Study
NASA Technical Reports Server (NTRS)
Lindquist, R. B.; Masnaghetti, R. K.; Belland, E.; Hance, H. V.; Weis, W. G.
1979-01-01
A segmented linear approximation of the quadratic phase function that is used to focus the synthetic antenna of a SAR was studied. Ideal focusing, using a quadratic varying phase focusing function during the time radar target histories are gathered, requires a large number of complex multiplications. These can be largely eliminated by using linear approximation techniques. The result is a reduced processor size and chip count relative to ideally focussed processing and a correspondingly increased feasibility for spaceworthy implementation. A preliminary design and sizing for a spaceworthy linear approximation SAR azimuth processor meeting requirements similar to those of the SEASAT-A SAR was developed. The study resulted in a design with approximately 1500 IC's, 1.2 cubic feet of volume, and 350 watts of power for a single look, 4000 range cell azimuth processor with 25 meters resolution.
Niles, Andrea N; Haltom, Kate E Byrne; Mulvenna, Catherine M; Lieberman, Matthew D; Stanton, Annette L
2014-01-01
The current study assessed main effects and moderators (including emotional expressiveness, emotional processing, and ambivalence over emotional expression) of the effects of expressive writing in a sample of healthy adults. Young adult participants (N=116) were randomly assigned to write for 20 minutes on four occasions about deepest thoughts and feelings regarding their most stressful/traumatic event in the past five years (expressive writing) or about a control topic (control). Dependent variables were indicators of anxiety, depression, and physical symptoms. No significant effects of writing condition were evident on anxiety, depressive symptoms, or physical symptoms. Emotional expressiveness emerged as a significant moderator of anxiety outcomes, however. Within the expressive writing group, participants high in expressiveness evidenced a significant reduction in anxiety at three-month follow-up, and participants low in expressiveness showed a significant increase in anxiety. Expressiveness did not predict change in anxiety in the control group. These findings on anxiety are consistent with the matching hypothesis, which suggests that matching a person's naturally elected coping approach with an assigned intervention is beneficial. These findings also suggest that expressive writing about a stressful event may be contraindicated for individuals who do not typically express emotions.
Chemical Laws, Idealization and Approximation
NASA Astrophysics Data System (ADS)
Tobin, Emma
2013-07-01
This paper examines the notion of laws in chemistry. Vihalemm ( Found Chem 5(1):7-22, 2003) argues that the laws of chemistry are fundamentally the same as the laws of physics they are all ceteris paribus laws which are true "in ideal conditions". In contrast, Scerri (2000) contends that the laws of chemistry are fundamentally different to the laws of physics, because they involve approximations. Christie ( Stud Hist Philos Sci 25:613-629, 1994) and Christie and Christie ( Of minds and molecules. Oxford University Press, New York, pp. 34-50, 2000) agree that the laws of chemistry are operationally different to the laws of physics, but claim that the distinction between exact and approximate laws is too simplistic to taxonomise them. Approximations in chemistry involve diverse kinds of activity and often what counts as a scientific law in chemistry is dictated by the context of its use in scientific practice. This paper addresses the question of what makes chemical laws distinctive independently of the separate question as to how they are related to the laws of physics. From an analysis of some candidate ceteris paribus laws in chemistry, this paper argues that there are two distinct kinds of ceteris paribus laws in chemistry; idealized and approximate chemical laws. Thus, while Christie ( Stud Hist Philos Sci 25:613-629, 1994) and Christie and Christie ( Of minds and molecules. Oxford University Press, New York, pp. 34--50, 2000) are correct to point out that the candidate generalisations in chemistry are diverse and heterogeneous, a distinction between idealizations and approximations can nevertheless be used to successfully taxonomise them.
On Nash-Equilibria of Approximation-Stable Games
NASA Astrophysics Data System (ADS)
Awasthi, Pranjal; Balcan, Maria-Florina; Blum, Avrim; Sheffet, Or; Vempala, Santosh
One reason for wanting to compute an (approximate) Nash equilibrium of a game is to predict how players will play. However, if the game has multiple equilibria that are far apart, or ɛ-equilibria that are far in variation distance from the true Nash equilibrium strategies, then this prediction may not be possible even in principle. Motivated by this consideration, in this paper we define the notion of games that are approximation stable, meaning that all ɛ-approximate equilibria are contained inside a small ball of radius Δ around a true equilibrium, and investigate a number of their properties. Many natural small games such as matching pennies and rock-paper-scissors are indeed approximation stable. We show furthermore there exist 2-player n-by-n approximation-stable games in which the Nash equilibrium and all approximate equilibria have support Ω(log n). On the other hand, we show all (ɛ,Δ) approximation-stable games must have an ɛ-equilibrium of support O(Δ^{2-o(1)}/ɛ2{log n}), yielding an immediate n^{O(Δ^{2-o(1)}/ɛ^2log n)}-time algorithm, improving over the bound of [11] for games satisfying this condition. We in addition give a polynomial-time algorithm for the case that Δ and ɛ are sufficiently close together. We also consider an inverse property, namely that all non-approximate equilibria are far from some true equilibrium, and give an efficient algorithm for games satisfying that condition.
Caricaturing facial expressions.
Calder, A J; Rowland, D; Young, A W; Nimmo-Smith, I; Keane, J; Perrett, D I
2000-08-14
The physical differences between facial expressions (e.g. fear) and a reference norm (e.g. a neutral expression) were altered to produce photographic-quality caricatures. In Experiment 1, participants rated caricatures of fear, happiness and sadness for their intensity of these three emotions; a second group of participants rated how 'face-like' the caricatures appeared. With increasing levels of exaggeration the caricatures were rated as more emotionally intense, but less 'face-like'. Experiment 2 demonstrated a similar relationship between emotional intensity and level of caricature for six different facial expressions. Experiments 3 and 4 compared intensity ratings of facial expression caricatures prepared relative to a selection of reference norms - a neutral expression, an average expression, or a different facial expression (e.g. anger caricatured relative to fear). Each norm produced a linear relationship between caricature and rated intensity of emotion; this finding is inconsistent with two-dimensional models of the perceptual representation of facial expression. An exemplar-based multidimensional model is proposed as an alternative account.
NASA Technical Reports Server (NTRS)
Kvaternik, R. G.; Kaza, K. R. V.
1976-01-01
The nonlinear curvature expressions for a twisted rotor blade or a beam undergoing transverse bending in two planes, torsion, and extension were developed. The curvature expressions were obtained using simple geometric considerations. The expressions were first developed in a general manner using the geometrical nonlinear theory of elasticity. These general nonlinear expressions were then systematically reduced to four levels of approximation by imposing various simplifying assumptions, and in each of these levels the second degree nonlinear expressions were given. The assumptions were carefully stated and their implications with respect to the nonlinear theory of elasticity as applied to beams were pointed out. The transformation matrices between the deformed and undeformed blade-fixed coordinates, which were needed in the development of the curvature expressions, were also given for three of the levels of approximation. The present curvature expressions and transformation matrices were compared with corresponding expressions existing in the literature.
Bilello, John A.; Strand, Mette; August, J. T.
1974-01-01
Expression of the major internal protein and the envelope glycoprotein of murine C-type viruses in focus-derived lines of normal rat kidney cells infected with Kirsten murine sarcoma virus was measured by radioimmunoassay. Of the clones selected, which do not produce virus particles or the major viral structural protein, approximately half express the viral envelope glycoprotein at concentrations found in productively infected cells. Expression of the envelope glycoprotein did not appear to alter significantly the properties of the transformed cells in culture. PMID:4370209
NASA Astrophysics Data System (ADS)
Petpairote, Chayanut; Madarasmi, Suthep; Chamnongthai, Kosin
2018-01-01
The practical identification of individuals using facial recognition techniques requires the matching of faces with specific expressions to faces from a neutral face database. A method for facial recognition under varied expressions against neutral face samples of individuals via recognition of expression warping and the use of a virtual expression-face database is proposed. In this method, facial expressions are recognized and the input expression faces are classified into facial expression groups. To aid facial recognition, the virtual expression-face database is sorted into average facial-expression shapes and by coarse- and fine-featured facial textures. Wrinkle information is also employed in classification by using a process of masking to adjust input faces to match the expression-face database. We evaluate the performance of the proposed method using the CMU multi-PIE, Cohn-Kanade, and AR expression-face databases, and we find that it provides significantly improved results in terms of face recognition accuracy compared to conventional methods and is acceptable for facial recognition under expression variation.
Legendre-tau approximations for functional differential equations
NASA Technical Reports Server (NTRS)
Ito, K.; Teglas, R.
1986-01-01
The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.
Legendre-Tau approximations for functional differential equations
NASA Technical Reports Server (NTRS)
Ito, K.; Teglas, R.
1983-01-01
The numerical approximation of solutions to linear functional differential equations are considered using the so called Legendre tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time differentiation. The approximate solution is then represented as a truncated Legendre series with time varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximations is made.
Habata, Shutaro; Iwasaki, Masahiro; Sugio, Asuka; Suzuki, Miwa; Tamate, Masato; Satohisa, Seiro; Tanaka, Ryoichi; Saito, Tsuyoshi
2015-05-01
Approximately 30% of uterine corpus carcinomas are diagnosed at an advanced stage and have a poor prognosis. Our previous study indicated that BCL2-associated athanogene 3 (BAG3) enhances matrix metalloproteinase-2 (MMP2) expression and binds to MMP2 to positively regulate the process of cell invasion in ovarian cancer cells. Recently, altered miRNA expression patterns were observed in several groups of patients with endometrial cancers. One of the altered miRNAs, miR-29b, reportedly reduces tumor invasiveness by suppressing MMP2 expression. Our aim in the present study was to examine the relationships among BAG3, miR-29b and MMP2 in endometrioid adenocarcinoma cells. We found that BAG3 suppresses miR-29b expression and enhances MMP2 expression, which in turn increases cell motility and invasiveness. Moreover, restoration of miR-29b through BAG3 knockdown reduced MMP2 expression, as well as cell motility and invasiveness. Collectively, our findings indicate that BAG3 enhances MMP2 expression by suppressing miR-29b, thereby increasing the metastatic potential of endometrioid adenocarcinomas.
Analytical approximations to the dynamics of an array of coupled DC SQUIDs
NASA Astrophysics Data System (ADS)
Berggren, Susan; Palacios, Antonio
2014-04-01
Coupled dynamical systems that operate near the onset of a bifurcation can lead, under certain conditions, to strong signal amplification effects. Over the past years we have studied this generic feature on a wide range of systems, including: magnetic and electric fields sensors, gyroscopic devices, and arrays of loops of superconducting quantum interference devices, also known as SQUIDs. In this work, we consider an array of SQUID loops connected in series as a case study to derive asymptotic analytical approximations to the exact solutions through perturbation analysis. Two approaches are considered. First, a straightforward expansion in which the non-linear parameter related to the inductance of the DC SQUID is treated as the small perturbation parameter. Second, a more accurate procedure that considers the SQUID phase dynamics as non-uniform motion on a circle. This second procedure is readily extended to the series array and it could serve as a mathematical framework to find approximate solutions to related complex systems with high-dimensionality. To the best of our knowledge, an approximate analytical solutions to an array of SQUIDs has not been reported yet in the literature.
Piecewise linear approximation for hereditary control problems
NASA Technical Reports Server (NTRS)
Propst, Georg
1987-01-01
Finite dimensional approximations are presented for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems when a quadratic cost integral has to be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in case the cost integral ranges over a finite time interval as well as in the case it ranges over an infinite time interval. The arguments in the latter case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense. This feature is established using a vector-component stability criterion in the state space R(n) x L(2) and the favorable eigenvalue behavior of the piecewise linear approximations.
Approximation concepts for efficient structural synthesis
NASA Technical Reports Server (NTRS)
Schmit, L. A., Jr.; Miura, H.
1976-01-01
It is shown that efficient structural synthesis capabilities can be created by using approximation concepts to mesh finite element structural analysis methods with nonlinear mathematical programming techniques. The history of the application of mathematical programming techniques to structural design optimization problems is reviewed. Several rather general approximation concepts are described along with the technical foundations of the ACCESS 1 computer program, which implements several approximation concepts. A substantial collection of structural design problems involving truss and idealized wing structures is presented. It is concluded that since the basic ideas employed in creating the ACCESS 1 program are rather general, its successful development supports the contention that the introduction of approximation concepts will lead to the emergence of a new generation of practical and efficient, large scale, structural synthesis capabilities in which finite element analysis methods and mathematical programming algorithms will play a central role.
Male reproductive development: gene expression profiling of maize anther and pollen ontogeny
Ma, Jiong; Skibbe, David S; Fernandes, John; Walbot, Virginia
2008-01-01
Background During flowering, central anther cells switch from mitosis to meiosis, ultimately forming pollen containing haploid sperm. Four rings of surrounding somatic cells differentiate to support first meiosis and later pollen dispersal. Synchronous development of many anthers per tassel and within each anther facilitates dissection of carefully staged maize anthers for transcriptome profiling. Results Global gene expression profiles of 7 stages representing 29 days of anther development are analyzed using a 44 K oligonucleotide array querying approximately 80% of maize protein-coding genes. Mature haploid pollen containing just two cell types expresses 10,000 transcripts. Anthers contain 5 major cell types and express >24,000 transcript types: each anther stage expresses approximately 10,000 constitutive and approximately 10,000 or more transcripts restricted to one or a few stages. The lowest complexity is present during meiosis. Large suites of stage-specific and co-expressed genes are identified through Gene Ontology and clustering analyses as functional classes for pre-meiotic, meiotic, and post-meiotic anther development. MADS box and zinc finger transcription factors with constitutive and stage-limited expression are identified. Conclusions We propose that the extensive gene expression of anther cells and pollen represents the key test of maize genome fitness, permitting strong selection against deleterious alleles in diploid anthers and haploid pollen. Because flowering plants show a substantial bias for male-sterile compared to female-sterile mutations, we propose that this fitness test is general. Because both somatic and germinal cells are transcriptionally quiescent during meiosis, we hypothesize that successful completion of meiosis is required to trigger maturation of anther somatic cells. PMID:19099579
NASA Astrophysics Data System (ADS)
Aymard, François; Gulminelli, Francesca; Margueron, Jérôme
2016-08-01
We have recently addressed the problem of the determination of the nuclear surface energy for symmetric nuclei in the framework of the extended Thomas-Fermi (ETF) approximation using Skyrme functionals. We presently extend this formalism to the case of asymmetric nuclei and the question of the surface symmetry energy. We propose an approximate expression for the diffuseness and the surface energy. These quantities are analytically related to the parameters of the energy functional. In particular, the influence of the different equation of state parameters can be explicitly quantified. Detailed analyses of the different energy components (local/non-local, isoscalar/isovector, surface/curvature and higher order) are also performed. Our analytical solution of the ETF integral improves previous models and leads to a precision of better than 200 keV per nucleon in the determination of the nuclear binding energy for dripline nuclei.
Approximations of e and ?: An Exploration
ERIC Educational Resources Information Center
Brown, Philip R.
2017-01-01
Fractional approximations of e and p are discovered by searching for repetitions or partial repetitions of digit strings in their expansions in different number bases. The discovery of such fractional approximations is suggested for students and teachers as an entry point into mathematics research.
Topics in Multivariate Approximation Theory.
1982-05-01
once that a continuous function f can be approximated from Sa :o span (N3 )B63 to within *(f, 131 ), with 13 t- sup3 e3 dian PS The simple approximation...N(C) 3- U P s P3AC 0 0 ) . Then, as in Lebesgue’s inequality, we could conclude that f - Qf - f-p - Q(f-p) , for all p e k k therefore I(f-0f) JCI 4 I
Li, Xiao C; Hopfer, Ulrich; Zhuo, Jia L
2009-11-01
Angiotensin II (ANG II) is taken up by proximal tubule (PT) cells via AT1 (AT1a) receptor-mediated endocytosis, but the underlying cellular mechanisms remain poorly understood. The present study tested the hypothesis that the microtubule- rather than the clathrin-dependent endocytic pathway regulates AT1-mediated uptake of ANG II and ANG II-induced sodium and hydrogen exchanger-3 (NHE-3) expression in PT cells. The expression of AT1 receptors, clathrin light (LC) and heavy chain (HC) proteins, and type 1 microtubule-associated proteins (MAPs; MAP-1A and MAP-1B) in PT cells were knocked down by their respective small interfering (si) RNAs before AT1-mediated FITC-ANG II uptake and ANG II-induced NHE-3 expression were studied. AT1 siRNAs inhibited AT1 expression and blocked ANG II-induced NHE-3 expression in PT cells, as expected (P < 0.01). Clathrin LC or HC siRNAs knocked down their respective proteins by approximately 90% with a peak response at 24 h, and blocked the clathrin-dependent uptake of Alexa Fluor 594-transferrin (P < 0.01). However, neither LC nor HC siRNAs inhibited AT1-mediated uptake of FITC-ANG II or affected ANG II-induced NHE-3 expression. MAP-1A or MAP-1B siRNAs markedly knocked down MAP-1A or MAP-1B proteins in a time-dependent manner with peak inhibitions at 48 h (>76.8%, P < 0.01). MAP protein knockdown resulted in approximately 52% decreases in AT1-mediated FITC-ANG II uptake and approximately 66% decreases in ANG II-induced NHE-3 expression (P < 0.01). These effects were associated with threefold decreases in ANG II-induced MAP kinases ERK 1/2 activation (P < 0.01), but not with altered AT1 expression or clathrin-dependent transferrin uptake. Both losartan and AT1a receptor deletion in mouse PT cells completely abolished the effects of MAP-1A knockdown on ANG II-induced NHE-3 expression and activation of MAP kinases ERK1/2. Our findings suggest that the alternative microtubule-dependent endocytic pathway, rather than the canonical clathrin
Altered expression of vesicular glutamate transporters VGLUT1 and VGLUT2 in Parkinson disease.
Kashani, Alireza; Betancur, Catalina; Giros, Bruno; Hirsch, Etienne; El Mestikawy, Salah
2007-04-01
Glutamatergic pathways play a key role in the functional organization of neuronal circuits involved in Parkinson disease (PD). Recently, three vesicular glutamate transporters (VGLUT1-3) were identified. VGLUT1 and VGLUT2 are responsible for the uploading of glutamate into synaptic vesicles and are the first specific markers of glutamatergic neurons available. Here, we analyzed the expression of VGLUT1 and VGLUT2 in autopsy tissues of PD patients and matched controls using Western blot and immunoautoradiography. VGLUT1 and VGLUT2 expression was increased in the Parkinsonian putamen by 24% and 29%, respectively (p<0.01). In contrast, only VGLUT1 was dramatically decreased in the prefrontal and temporal cortex of PD patients (approximately 50%, p<0.01 and p<0.001, respectively). These findings demonstrate the existence of profound alterations of glutamatergic transmission in PD, which are likely to contribute to the motor and cognitive impairments associated with the disease, and should thus be taken into account in the treatment of PD.
Approximation methods for combined thermal/structural design
NASA Technical Reports Server (NTRS)
Haftka, R. T.; Shore, C. P.
1979-01-01
Two approximation concepts for combined thermal/structural design are evaluated. The first concept is an approximate thermal analysis based on the first derivatives of structural temperatures with respect to design variables. Two commonly used first-order Taylor series expansions are examined. The direct and reciprocal expansions are special members of a general family of approximations, and for some conditions other members of that family of approximations are more accurate. Several examples are used to compare the accuracy of the different expansions. The second approximation concept is the use of critical time points for combined thermal and stress analyses of structures with transient loading conditions. Significant time savings are realized by identifying critical time points and performing the stress analysis for those points only. The design of an insulated panel which is exposed to transient heating conditions is discussed.
The Zeldovich & Adhesion approximations and applications to the local universe
NASA Astrophysics Data System (ADS)
Hidding, Johan; van de Weygaert, Rien; Shandarin, Sergei
2016-10-01
The Zeldovich approximation (ZA) predicts the formation of a web of singularities. While these singularities may only exist in the most formal interpretation of the ZA, they provide a powerful tool for the analysis of initial conditions. We present a novel method to find the skeleton of the resulting cosmic web based on singularities in the primordial deformation tensor and its higher order derivatives. We show that the A 3 lines predict the formation of filaments in a two-dimensional model. We continue with applications of the adhesion model to visualise structures in the local (z < 0.03) universe.
Natural selection in avian protein-coding genes expressed in brain.
Axelsson, Erik; Hultin-Rosenberg, Lina; Brandström, Mikael; Zwahlén, Martin; Clayton, David F; Ellegren, Hans
2008-06-01
The evolution of birds from theropod dinosaurs took place approximately 150 million years ago, and was associated with a number of specific adaptations that are still evident among extant birds, including feathers, song and extravagant secondary sexual characteristics. Knowledge about the molecular evolutionary background to such adaptations is lacking. Here, we analyse the evolution of > 5000 protein-coding gene sequences expressed in zebra finch brain by comparison to orthologous sequences in chicken. Mean d(N)/d(S) is 0.085 and genes with their maximal expression in the eye and central nervous system have the lowest mean d(N)/d(S) value, while those expressed in digestive and reproductive tissues exhibit the highest. We find that fast-evolving genes (those which have higher than expected rate of nonsynonymous substitution, indicative of adaptive evolution) are enriched for biological functions such as fertilization, muscle contraction, defence response, response to stress, wounding and endogenous stimulus, and cell death. After alignment to mammalian orthologues, we identify a catalogue of 228 genes that show a significantly higher rate of protein evolution in the two bird lineages than in mammals. These accelerated bird genes, representing candidates for avian-specific adaptations, include genes implicated in vocal learning and other cognitive processes. Moreover, colouration genes evolve faster in birds than in mammals, which may have been driven by sexual selection for extravagant plumage characteristics.
Sodium 4-phenylbutyrate downregulates HSC70 expression by facilitating mRNA degradation.
Rubenstein, R C; Lyons, B M
2001-07-01
Intracellular trafficking of the DeltaF508 cystic fibrosis transmembrane conductance regulator (CFTR) is repaired by sodium 4-phenylbutyrate (4PBA) by an undetermined mechanism. 4PBA downregulates protein and mRNA expression of the heat shock cognate protein HSC70 (the constitutively expressed member of the 70-kDa heat shock protein family) by approximately 40-50% and decreases formation of a HSC70-DeltaF508 CFTR complex that may be important in the intracellular degradation of DeltaF508 CFTR. We examined the potential mechanisms by which 4PBA decreases HSC70 mRNA and protein expression. In IB3-1 cells, 1 mM 4PBA did not alter the activity of the Chinese hamster ovary HSC70 promoter or of a human HSC70 promoter fragment in luciferase reporter assays nor did it alter HSC70 mRNA synthesis in nuclear runoff assays. In contrast, preincubation with 4PBA increased the rate of HSC70 mRNA degradation by approximately 40%. The initial rate of 35S-HSC70 protein synthesis in 4PBA-treated IB3-1 cells was reduced by approximately 40%, consistent with the steady-state mRNA level, whereas its rate of degradation was unaltered by 4PBA. 4PBA also reduced the steady-state accumulation of (35)S-HSC70 by approximately 40%. These data suggest that 4PBA decreases the expression of HSC70 mRNA and protein by inducing cellular adaptations that result in the decreased stability of HSC70 mRNA.
Approximate controllability of a system of parabolic equations with delay
NASA Astrophysics Data System (ADS)
Carrasco, Alexander; Leiva, Hugo
2008-09-01
In this paper we give necessary and sufficient conditions for the approximate controllability of the following system of parabolic equations with delay: where [Omega] is a bounded domain in , D is an n×n nondiagonal matrix whose eigenvalues are semi-simple with nonnegative real part, the control and B[set membership, variant]L(U,Z) with , . The standard notation zt(x) defines a function from [-[tau],0] to (with x fixed) by zt(x)(s)=z(t+s,x), -[tau][less-than-or-equals, slant]s[less-than-or-equals, slant]0. Here [tau][greater-or-equal, slanted]0 is the maximum delay, which is supposed to be finite. We assume that the operator is linear and bounded, and [phi]0[set membership, variant]Z, [phi][set membership, variant]L2([-[tau],0];Z). To this end: First, we reformulate this system into a standard first-order delay equation. Secondly, the semigroup associated with the first-order delay equation on an appropriate product space is expressed as a series of strongly continuous semigroups and orthogonal projections related with the eigenvalues of the Laplacian operator (); this representation allows us to reduce the controllability of this partial differential equation with delay to a family of ordinary delay equations. Finally, we use the well-known result on the rank condition for the approximate controllability of delay system to derive our main result.
Wang, Ya-Xuan; Gao, Ying-Lian; Liu, Jin-Xing; Kong, Xiang-Zhen; Li, Hai-Jun
2017-09-01
Identifying differentially expressed genes from the thousands of genes is a challenging task. Robust principal component analysis (RPCA) is an efficient method in the identification of differentially expressed genes. RPCA method uses nuclear norm to approximate the rank function. However, theoretical studies showed that the nuclear norm minimizes all singular values, so it may not be the best solution to approximate the rank function. The truncated nuclear norm is defined as the sum of some smaller singular values, which may achieve a better approximation of the rank function than nuclear norm. In this paper, a novel method is proposed by replacing nuclear norm of RPCA with the truncated nuclear norm, which is named robust principal component analysis regularized by truncated nuclear norm (TRPCA). The method decomposes the observation matrix of genomic data into a low-rank matrix and a sparse matrix. Because the significant genes can be considered as sparse signals, the differentially expressed genes are viewed as the sparse perturbation signals. Thus, the differentially expressed genes can be identified according to the sparse matrix. The experimental results on The Cancer Genome Atlas data illustrate that the TRPCA method outperforms other state-of-the-art methods in the identification of differentially expressed genes.
DOE Office of Scientific and Technical Information (OSTI.GOV)
Kraisler, Eli; Kronik, Leeor
2014-05-14
The fundamental gap is a central quantity in the electronic structure of matter. Unfortunately, the fundamental gap is not generally equal to the Kohn-Sham gap of density functional theory (DFT), even in principle. The two gaps differ precisely by the derivative discontinuity, namely, an abrupt change in slope of the exchange-correlation energy as a function of electron number, expected across an integer-electron point. Popular approximate functionals are thought to be devoid of a derivative discontinuity, strongly compromising their performance for prediction of spectroscopic properties. Here we show that, in fact, all exchange-correlation functionals possess a derivative discontinuity, which arises naturallymore » from the application of ensemble considerations within DFT, without any empiricism. This derivative discontinuity can be expressed in closed form using only quantities obtained in the course of a standard DFT calculation of the neutral system. For small, finite systems, addition of this derivative discontinuity indeed results in a greatly improved prediction for the fundamental gap, even when based on the most simple approximate exchange-correlation density functional – the local density approximation (LDA). For solids, the same scheme is exact in principle, but when applied to LDA it results in a vanishing derivative discontinuity correction. This failure is shown to be directly related to the failure of LDA in predicting fundamental gaps from total energy differences in extended systems.« less
Assis-Marques, Mariana Aprigio; Oliveira, Aline Ferreira; Ruas, Luciana Pereira; dos Reis, Thaila Fernanda; Roque-Barreira, Maria Cristina; Coelho, Paulo Sergio Rodrigues
2015-01-01
The dimorphic fungus Paracoccidioides brasiliensis is the etiological agent of paracoccidioidomycosis (PCM). It is believed that approximately 10 million people are infected with the fungus and approximately 2% will eventually develop the disease. Unlike viral and bacterial diseases, fungal diseases are the ones against which there is no commercially available vaccine. Saccharomyces cerevisiae may be a suitable vehicle for immunization against fungal infections, as they require the stimulation of different arms of the immune response. Here we evaluated the efficacy of immunizing mice against PCM by using S. cerevisiae yeast expressing gp43. When challenged by inoculation of P. brasiliensis yeasts, immunized animals showed a protective profile in three different assays. Their lung parenchyma was significantly preserved, exhibiting fewer granulomas with fewer fungal cells than found in non-immunized mice. Fungal burden was reduced in the lung and spleen of immunized mice, and both organs contained higher levels of IL-12 and IFN-γ compared to those of non-vaccinated mice, a finding that suggests the occurrence of Th1 immunity. Taken together, our results indicate that the recombinant yeast vaccine represents a new strategy to confer protection against PCM.
Rupert, C.P.; Miller, C.T.
2008-01-01
We examine a variety of polynomial-chaos-motivated approximations to a stochastic form of a steady state groundwater flow model. We consider approaches for truncating the infinite dimensional problem and producing decoupled systems. We discuss conditions under which such decoupling is possible and show that to generalize the known decoupling by numerical cubature, it would be necessary to find new multivariate cubature rules. Finally, we use the acceleration of Monte Carlo to compare the quality of polynomial models obtained for all approaches and find that in general the methods considered are more efficient than Monte Carlo for the relatively small domains considered in this work. A curse of dimensionality in the series expansion of the log-normal stochastic random field used to represent hydraulic conductivity provides a significant impediment to efficient approximations for large domains for all methods considered in this work, other than the Monte Carlo method. PMID:18836519
A result about scale transformation families in approximation
NASA Astrophysics Data System (ADS)
Apprato, Dominique; Gout, Christian
2000-06-01
Scale transformations are common in approximation. In surface approximation from rapidly varying data, one wants to suppress, or at least dampen the oscillations of the approximation near steep gradients implied by the data. In that case, scale transformations can be used to give some control over overshoot when the surface has large variations of its gradient. Conversely, in image analysis, scale transformations are used in preprocessing to enhance some features present on the image or to increase jumps of grey levels before segmentation of the image. In this paper, we establish the convergence of an approximation method which allows some control over the behavior of the approximation. More precisely, we study the convergence of an approximation from a data set of , while using scale transformations on the values before and after classical approximation. In addition, the construction of scale transformations is also given. The algorithm is presented with some numerical examples.
Dadachova, E; Bouzahzah, B; Zuckier, L S; Pestell, R G
2002-01-01
The sodium-iodide symporter (NIS), which transports iodine into the cell, is expressed in thyroid tissue and was recently found to be expressed in approximately 80% of human breast cancers but not in healthy breast tissue. These findings raised the possibility that therapeutics targeting uptake by NIS may be used for breast cancer treatment. To increase the efficacy of such therapy it would be ideal to identify a radioactive therapy with enhanced local emission. The feasibility of using the powerful beta-emitting radiometal (188)Re in the form of (188)Re-perrhenate was therefore compared with 131I for treatment of NIS-expressing mammary tumors. In the current studies, using a xenografted breast cancer model induced by the ErbB2 oncogene in nude mice, (188)Re-perrhenate exhibited NIS-dependent uptake into the mammary tumor. Dosimetry calculations in the mammary tumor demonstrate that (188)Re-perrhenate is able to deliver a dose 4.5 times higher than (131)I suggesting it may provide enhanced therapeutic efficacy.
Approximations to camera sensor noise
NASA Astrophysics Data System (ADS)
Jin, Xiaodan; Hirakawa, Keigo
2013-02-01
Noise is present in all image sensor data. Poisson distribution is said to model the stochastic nature of the photon arrival process, while it is common to approximate readout/thermal noise by additive white Gaussian noise (AWGN). Other sources of signal-dependent noise such as Fano and quantization also contribute to the overall noise profile. Question remains, however, about how best to model the combined sensor noise. Though additive Gaussian noise with signal-dependent noise variance (SD-AWGN) and Poisson corruption are two widely used models to approximate the actual sensor noise distribution, the justification given to these types of models are based on limited evidence. The goal of this paper is to provide a more comprehensive characterization of random noise. We concluded by presenting concrete evidence that Poisson model is a better approximation to real camera model than SD-AWGN. We suggest further modification to Poisson that may improve the noise model.
Approximate techniques of structural reanalysis
NASA Technical Reports Server (NTRS)
Noor, A. K.; Lowder, H. E.
1974-01-01
A study is made of two approximate techniques for structural reanalysis. These include Taylor series expansions for response variables in terms of design variables and the reduced-basis method. In addition, modifications to these techniques are proposed to overcome some of their major drawbacks. The modifications include a rational approach to the selection of the reduced-basis vectors and the use of Taylor series approximation in an iterative process. For the reduced basis a normalized set of vectors is chosen which consists of the original analyzed design and the first-order sensitivity analysis vectors. The use of the Taylor series approximation as a first (initial) estimate in an iterative process, can lead to significant improvements in accuracy, even with one iteration cycle. Therefore, the range of applicability of the reanalysis technique can be extended. Numerical examples are presented which demonstrate the gain in accuracy obtained by using the proposed modification techniques, for a wide range of variations in the design variables.
Accurate expressions for solar cell fill factors including series and shunt resistances
NASA Astrophysics Data System (ADS)
Green, Martin A.
2016-02-01
Together with open-circuit voltage and short-circuit current, fill factor is a key solar cell parameter. In their classic paper on limiting efficiency, Shockley and Queisser first investigated this factor's analytical properties showing, for ideal cells, it could be expressed implicitly in terms of the maximum power point voltage. Subsequently, fill factors usually have been calculated iteratively from such implicit expressions or from analytical approximations. In the absence of detrimental series and shunt resistances, analytical fill factor expressions have recently been published in terms of the Lambert W function available in most mathematical computing software. Using a recently identified perturbative relationship, exact expressions in terms of this function are derived in technically interesting cases when both series and shunt resistances are present but have limited impact, allowing a better understanding of their effect individually and in combination. Approximate expressions for arbitrary shunt and series resistances are then deduced, which are significantly more accurate than any previously published. A method based on the insights developed is also reported for deducing one-diode fits to experimental data.
Broeckhoven, Ken; Desmet, Gert
2007-11-16
Using a combination of both analytical and numerical techniques, approximate analytical expressions have been established for the transient and long time limit band broadening, originating from the presence of a thin disturbed sidewall layer in liquid chromatography columns, including packed, monolithic as well as microfabricated columns. The established expressions can be used to compare the importance of a thin disturbed sidewall layer with that of other radial heterogeneity effects (such as transcolumn packing density variations due to the relief of packing stresses). The expressions are independent of the actual velocity profile inside the layer as long as the disturbed sidewall layer occupies less than 2.5% of the column width.
Halbmayr, Elisabeth; Mathiesen, Geir; Nguyen, Thu-Ha; Maischberger, Thomas; Peterbauer, Clemens K; Eijsink, Vincent G H; Haltrich, Dietmar
2008-06-25
This work presents the cloning and expression of the genes encoding heterodimeric beta-galactosidases from Lactobacillus reuteri L103, Lactobacillus acidophilus R22, Lactobacillus plantarum WCFS1, and Lactobacillus sakei Lb790. These enzymes consist of two subunits of approximately 73 and 35 kDa, which are encoded by two overlapping genes, lacL and lacM, respectively. We have cloned these genes into the lactobacillal expression vectors pSIP403 and pSIP409, which are based on the sakacin P operon of L. sakei ( Sørvig et al. Microbiology 2005, 151, 2439- 2449 ), and expressed them in the host strains L. plantarum WCFS1 and L. sakei Lb790. Results varied considerably, ranging from 2.23 to 61.1 U/mg of beta-galactosidase activity, depending on the origin of the lacLM genes, the host strain, and the expression vector used. Highest expression levels were obtained in a laboratory cultivation of L. plantarum WCFS1 harboring the plasmid pEH3R containing the lacLM gene from L. reuteri L103. These cultivations yielded approximately 23 000 U of beta-galactosidase activity per liter, corresponding to the formation of roughly 100 mg of recombinant protein per liter of fermentation medium, and beta-galactosidase levels amounted to 55% of the total intracellular protein of the host organism. To further verify the suitability of this expression system, recombinant beta-galactosidase from L. reuteri was purified to apparent homogeneity. The properties of the purified enzyme were essentially identical with the properties of purified native beta-galactosidase from L. reuteri L103. The presented results lead the way to efficient overproduction of beta-galactosidase in a food-grade expression system, which is of high interest for applications in food industry.
Kim, H; Putt, D; Reddy, S; Hollenberg, P F; Novak, R F
1993-11-01
Expression of the cytochrome P450 (CYP) 2B subfamily in rat and rabbit hepatic tissues after pyridine (PY) treatment has been examined, and the molecular basis for enhanced 2B1/2B2 expression has been determined. P450 expression was monitored using metabolic activity, sodium dodecyl sulfate-polyacrylamide gel electrophoresis and immunoblot analyses, and the identity of the proteins was confirmed through N-terminus microsequence analysis. PY caused a dose-dependent elevation of hepatic CYP2B1/B2B levels in rats, which ranged from 4- to 22-fold over the dosing regimen of 100 to 400 mg PY/kg/day, for 3 days, respectively. PY at low dose failed to induce CYP2B in rabbit hepatic tissue, suggesting a species-dependent response in 2B expression. Anti-2B1 IgG addition to PY-induced microsomes inhibited benzphetamine N-demethylase activity by only approximately 15%, in sharp contrast to the approximately 73% inhibition observed for phenobarbital-induced microsomes, suggesting the induction of other form(s) of P450 having benzphetamine N-demethylase activity. Northern blot analysis revealed that PY treatment increased 2B1 and 2B2 poly(A)+ RNA levels approximately 69- and approximately 34-fold, respectively, whereas the 2E1 poly(A)+ RNA levels failed to increase. The results of this study show that PY induces CYP2B1/2B2 and that induction is species-dependent and kinetically distinguishable from 2E1 induction. Moreover, 2B1/2B2 induction occurs as a result of elevated mRNA levels associated with either transcriptional activation or mRNA stabilization, and it differs from the mechanism of hepatic 2E1 induction by PY.
NASA Astrophysics Data System (ADS)
Musharbash, Eleonora; Nobile, Fabio
2018-02-01
In this paper we propose a method for the strong imposition of random Dirichlet boundary conditions in the Dynamical Low Rank (DLR) approximation of parabolic PDEs and, in particular, incompressible Navier Stokes equations. We show that the DLR variational principle can be set in the constrained manifold of all S rank random fields with a prescribed value on the boundary, expressed in low rank format, with rank smaller then S. We characterize the tangent space to the constrained manifold by means of a Dual Dynamically Orthogonal (Dual DO) formulation, in which the stochastic modes are kept orthonormal and the deterministic modes satisfy suitable boundary conditions, consistent with the original problem. The Dual DO formulation is also convenient to include the incompressibility constraint, when dealing with incompressible Navier Stokes equations. We show the performance of the proposed Dual DO approximation on two numerical test cases: the classical benchmark of a laminar flow around a cylinder with random inflow velocity, and a biomedical application for simulating blood flow in realistic carotid artery reconstructed from MRI data with random inflow conditions coming from Doppler measurements.
Gene Expression: Sizing it all up
USDA-ARS?s Scientific Manuscript database
Genomic architecture appears to be a largely unexplored component of gene expression. Although surely not the end of the story, we are learning that when it comes to gene expression, size is important. We have been surprised to find that certain patterns of expression, tissue-specific versus constit...
Roles of antinucleon degrees of freedom in the relativistic random phase approximation
NASA Astrophysics Data System (ADS)
Kurasawa, Haruki; Suzuki, Toshio
2015-11-01
The roles of antinucleon degrees of freedom in the relativistic random phase approximation (RPA) are investigated. The energy-weighted sum of the RPA transition strengths is expressed in terms of the double commutator between the excitation operator and the Hamiltonian, as in nonrelativistic models. The commutator, however, should not be calculated in the usual way in the local field theory, because, otherwise, the sum vanishes. The sum value obtained correctly from the commutator is infinite, owing to the Dirac sea. Most of the previous calculations take into account only some of the nucleon-antinucleon states, in order to avoid divergence problems. As a result, RPA states with negative excitation energy appear, which make the sum value vanish. Moreover, disregarding the divergence changes the sign of nuclear interactions in the RPA equation that describes the coupling of the nucleon particle-hole states with the nucleon-antinucleon states. Indeed, the excitation energies of the spurious state and giant monopole states in the no-sea approximation are dominated by these unphysical changes. The baryon current conservation can be described without touching the divergence problems. A schematic model with separable interactions is presented, which makes the structure of the relativistic RPA transparent.
DOE Office of Scientific and Technical Information (OSTI.GOV)
Coombe, D.A.; Snider, R.F.
1980-02-15
ES, CS, and IOS approximations to atom--diatom kinetic cross sections are derived. In doing so, reduced S-matrices in a translational-internal coupling scheme are stressed. This entails the insertion of recently obtained approximate reduced S-matrices in the translational-internal coupling scheme into previously derived general expressions for the kinetic cross sections. Of special interest is the structure (rotational j quantum number dependence) of the kinetic cross sections associated with the Senftleben Beenakker effects and of pure internal state relaxation phenomena. The viscomagnetic effect is used as an illustrative example. It is found in particular that there is a great similarity of structuremore » between the energy sudden (and IOS) approximation and the previously derived distorted wave Born results.« less
Leveraging Terminologies for Retrieval of Radiology Reports with Critical Imaging Findings
Warden, Graham I.; Lacson, Ronilda; Khorasani, Ramin
2011-01-01
Introduction: Communication of critical imaging findings is an important component of medical quality and safety. A fundamental challenge includes retrieval of radiology reports that contain these findings. This study describes the expressiveness and coverage of existing medical terminologies for critical imaging findings and evaluates radiology report retrieval using each terminology. Methods: Four terminologies were evaluated: National Cancer Institute Thesaurus (NCIT), Radiology Lexicon (RadLex), Systemized Nomenclature of Medicine (SNOMED-CT), and International Classification of Diseases (ICD-9-CM). Concepts in each terminology were identified for 10 critical imaging findings. Three findings were subsequently selected to evaluate document retrieval. Results: SNOMED-CT consistently demonstrated the highest number of overall terms (mean=22) for each of ten critical findings. However, retrieval rate and precision varied between terminologies for the three findings evaluated. Conclusion: No single terminology is optimal for retrieving radiology reports with critical findings. The expressiveness of a terminology does not consistently correlate with radiology report retrieval. PMID:22195212
Difference equation state approximations for nonlinear hereditary control problems
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1982-01-01
Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems.
Takahashi, Hiroki; Hotta, Kohji; Takagi, Chiyo; Ueno, Naoto; Satoh, Nori; Shoguchi, Eiichi
2010-02-01
Brachyury, a T-box transcription factor, is expressed in ascidian embryos exclusively in primordial notochord cells and plays a pivotal role in differentiation of notochord cells. Previously, we identified approximately 450 genes downstream of Ciona intestinalis Brachyury (Ci-Bra), and characterized the expression profiles of 45 of these in differentiating notochord cells. In this study, we looked for cisregulatory sequences in minimal enhancers of 20 Ci-Bra downstream genes by electroporating region within approximately 3 kb upstream of each gene fused with lacZ. Eight of the 20 reporters were expressed in notochord cells. The minimal enchancer for each of these eight genes was narrowed to a region approximately 0.5-1.0-kb long. We also explored the genome-wide and coordinate regulation of 43 Ci-Bra-downstream genes. When we determined their chromosomal localization, it became evident that they are not clustered in a given region of the genome, but rather distributed evenly over 13 of the 14 pairs of chromosomes, suggesting that gene clustering does not contribute to coordinate control of the Ci-Bra downstream gene expression. Our results might provide Insights Into the molecular mechanisms underlying notochord formation in chordates.
Assessing Anger Expression: Construct Validity of Three Emotion Expression-Related Measures
Jasinski, Matthew J.; Lumley, Mark A.; Latsch, Deborah V.; Schuster, Erik; Kinner, Ellen; Burns, John W.
2016-01-01
Self-report measures of emotional expression are common, but their validity to predict objective emotional expression, particularly of anger, is unclear. We tested the validity of the Anger Expression Inventory (AEI; Spielberger et al., 1985)), Emotional Approach Coping Scale (EAC; Stanton, Kirk, Cameron & Danoff-Burg, 2000), and Toronto Alexithymia Scale-20 (TAS-20; Bagby, Taylor, & Parker, 1994) to predict objective anger expression in 95 adults with chronic back pain. Participants attempted to solve a difficult computer maze by following the directions of a confederate who treated them rudely and unjustly. Participants then expressed their feelings for 4 minutes. Blinded raters coded the videos for anger expression, and a software program analyzed expression transcripts for anger-related words. Analyses related each questionnaire to anger expression. The AEI anger-out scale predicted greater anger expression, as expected, but AEI anger-in did not. The EAC emotional processing scale predicted less anger expression, but the EAC emotional expression scale was unrelated to anger expression. Finally, the TAS-20 predicted greater anger expression. Findings support the validity of the AEI anger-out scale but raise questions about the other measures. The assessment of emotional expression by self-report is complex and perhaps confounded by general emotional experience, the specificity or generality of the emotion(s) assessed, and self-awareness limitations. Performance-based or clinician-rated measures of emotion expression are needed. PMID:27248355
Leich, Ellen; Salaverria, Itziar; Bea, Silvia; Zettl, Andreas; Wright, George; Moreno, Victor; Gascoyne, Randy D.; Chan, Wing-Chung; Braziel, Rita M.; Rimsza, Lisa M.; Weisenburger, Dennis D.; Delabie, Jan; Jaffe, Elaine S.; Lister, Andrew; Fitzgibbon, Jude; Staudt, Louis M.; Hartmann, Elena M.; Mueller-Hermelink, Hans-Konrad; Campo, Elias; Ott, German
2009-01-01
Follicular lymphoma (FL) is genetically characterized by the presence of the t(14;18)(q32;q21) chromosomal translocation in approximately 90% of cases. In contrast to FL carrying the t(14;18), their t(14;18)-negative counterparts are less well studied about their immunohistochemical, genetic, molecular, and clinical features. Within a previously published series of 184 FLs grades 1 to 3A with available gene expression data, we identified 17 FLs lacking the t(14;18). Comparative genomic hybridization and high-resolution single nucleotide polymorphism (SNP) array profiling showed that gains/amplifications of the BCL2 gene locus in 18q were restricted to the t(14;18)-positive FL subgroup. A comparison of gene expression profiles showed an enrichment of germinal center B cell–associated signatures in t(14;18)-positive FL, whereas activated B cell–like, NFκB, proliferation, and bystander cell signatures were enriched in t(14;18)-negative FL. These findings were confirmed by immunohistochemistry in an independent validation series of 84 FLs, in which 32% of t(14;18)-negative FLs showed weak or absent CD10 expression and 91% an increased Ki67 proliferation rate. Although overall survival did not differ between FL with and without t(14;18), our findings suggest distinct molecular features of t(14;18)-negative FL. PMID:19471018
Approximation algorithms for planning and control
NASA Technical Reports Server (NTRS)
Boddy, Mark; Dean, Thomas
1989-01-01
A control system operating in a complex environment will encounter a variety of different situations, with varying amounts of time available to respond to critical events. Ideally, such a control system will do the best possible with the time available. In other words, its responses should approximate those that would result from having unlimited time for computation, where the degree of the approximation depends on the amount of time it actually has. There exist approximation algorithms for a wide variety of problems. Unfortunately, the solution to any reasonably complex control problem will require solving several computationally intensive problems. Algorithms for successive approximation are a subclass of the class of anytime algorithms, algorithms that return answers for any amount of computation time, where the answers improve as more time is allotted. An architecture is described for allocating computation time to a set of anytime algorithms, based on expectations regarding the value of the answers they return. The architecture described is quite general, producing optimal schedules for a set of algorithms under widely varying conditions.
Geary, David C.; Hoard, Mary K.; Nugent, Lara; Rouder, Jeffrey N.
2015-01-01
The relation between performance on measures of algebraic cognition and acuity of the approximate number system (ANS) and memory for addition facts was assessed for 171 (92 girls) 9th graders, controlling parental education, sex, reading achievement, speed of numeral processing, fluency of symbolic number processing, intelligence, and the central executive component of working memory. The algebraic tasks assessed accuracy in placing x,y pairs in the coordinate plane, speed and accuracy of expression evaluation, and schema memory for algebra equations. ANS acuity was related to accuracy of placements in the coordinate plane and expression evaluation, but not schema memory. Frequency of fact-retrieval errors was related to schema memory but not coordinate plane or expression evaluation accuracy. The results suggest the ANS may contribute to or is influenced by spatial-numerical and numerical only quantity judgments in algebraic contexts, whereas difficulties in committing addition facts to long-term memory may presage slow formation of memories for the basic structure of algebra equations. More generally, the results suggest different brain and cognitive systems are engaged during the learning of different components of algebraic competence, controlling demographic and domain general abilities. PMID:26255604
Gene Expression Noise, Fitness Landscapes, and Evolution
NASA Astrophysics Data System (ADS)
Charlebois, Daniel
The stochastic (or noisy) process of gene expression can have fitness consequences for living organisms. For example, gene expression noise facilitates the development of drug resistance by increasing the time scale at which beneficial phenotypic states can be maintained. The present work investigates the relationship between gene expression noise and the fitness landscape. By incorporating the costs and benefits of gene expression, we track how the fluctuation magnitude and timescale of expression noise evolve in simulations of cell populations under stress. We find that properties of expression noise evolve to maximize fitness on the fitness landscape, and that low levels of expression noise emerge when the fitness benefits of gene expression exceed the fitness costs (and that high levels of noise emerge when the costs of expression exceed the benefits). The findings from our theoretical/computational work offer new hypotheses on the development of drug resistance, some of which are now being investigated in evolution experiments in our laboratory using well-characterized synthetic gene regulatory networks in budding yeast. Nserc Postdoctoral Fellowship (Grant No. PDF-453977-2014).
Approximation methods in gravitational-radiation theory
NASA Technical Reports Server (NTRS)
Will, C. M.
1986-01-01
The observation of gravitational-radiation damping in the binary pulsar PSR 1913 + 16 and the ongoing experimental search for gravitational waves of extraterrestrial origin have made the theory of gravitational radiation an active branch of classical general relativity. In calculations of gravitational radiation, approximation methods play a crucial role. Recent developments are summarized in two areas in which approximations are important: (a) the quadrupole approxiamtion, which determines the energy flux and the radiation reaction forces in weak-field, slow-motion, source-within-the-near-zone systems such as the binary pulsar; and (b) the normal modes of oscillation of black holes, where the Wentzel-Kramers-Brillouin approximation gives accurate estimates of the complex frequencies of the modes.
Preschool acuity of the approximate number system correlates with school math ability.
Libertus, Melissa E; Feigenson, Lisa; Halberda, Justin
2011-11-01
Previous research shows a correlation between individual differences in people's school math abilities and the accuracy with which they rapidly and nonverbally approximate how many items are in a scene. This finding is surprising because the Approximate Number System (ANS) underlying numerical estimation is shared with infants and with non-human animals who never acquire formal mathematics. However, it remains unclear whether the link between individual differences in math ability and the ANS depends on formal mathematics instruction. Earlier studies demonstrating this link tested participants only after they had received many years of mathematics education, or assessed participants' ANS acuity using tasks that required additional symbolic or arithmetic processing similar to that required in standardized math tests. To ask whether the ANS and math ability are linked early in life, we measured the ANS acuity of 200 3- to 5-year-old children using a task that did not also require symbol use or arithmetic calculation. We also measured children's math ability and vocabulary size prior to the onset of formal math instruction. We found that children's ANS acuity correlated with their math ability, even when age and verbal skills were controlled for. These findings provide evidence for a relationship between the primitive sense of number and math ability starting early in life. 2011 Blackwell Publishing Ltd.
Preschool Acuity of the Approximate Number System Correlates with School Math Ability
Libertus, Melissa E.; Feigenson, Lisa; Halberda, Justin
2012-01-01
Previous research shows a correlation between individual differences in people’s school math abilities and the accuracy with which they rapidly and nonverbally approximate how many items are in a scene. This finding is surprising because the Approximate Number System (ANS) underlying numerical estimation is shared with infants and non-human animals who never acquire formal mathematics. However, it remains unclear whether the link between individual differences in math ability and the ANS depends on formal mathematics instruction. Earlier studies demonstrating this link tested participants only after they had received many years of mathematics education, or assessed participants’ ANS acuity using tasks that required additional symbolic or arithmetic processing similar to that required in standardized math tests. To ask whether the ANS and math ability are linked early in life, we measured the ANS acuity of 200 3- to 5-year-old children using a task that did not also require symbol use or arithmetic calculation. We also measured children’s math ability and vocabulary size prior to the onset of formal math instruction. We found that children’s ANS acuity correlated with their math ability, even when age and verbal skills were controlled for. These findings provide evidence for a relationship between the primitive sense of number and math ability starting early in life. PMID:22010889
Stable computations with flat radial basis functions using vector-valued rational approximations
NASA Astrophysics Data System (ADS)
Wright, Grady B.; Fornberg, Bengt
2017-02-01
One commonly finds in applications of smooth radial basis functions (RBFs) that scaling the kernels so they are 'flat' leads to smaller discretization errors. However, the direct numerical approach for computing with flat RBFs (RBF-Direct) is severely ill-conditioned. We present an algorithm for bypassing this ill-conditioning that is based on a new method for rational approximation (RA) of vector-valued analytic functions with the property that all components of the vector share the same singularities. This new algorithm (RBF-RA) is more accurate, robust, and easier to implement than the Contour-Padé method, which is similarly based on vector-valued rational approximation. In contrast to the stable RBF-QR and RBF-GA algorithms, which are based on finding a better conditioned base in the same RBF-space, the new algorithm can be used with any type of smooth radial kernel, and it is also applicable to a wider range of tasks (including calculating Hermite type implicit RBF-FD stencils). We present a series of numerical experiments demonstrating the effectiveness of this new method for computing RBF interpolants in the flat regime. We also demonstrate the flexibility of the method by using it to compute implicit RBF-FD formulas in the flat regime and then using these for solving Poisson's equation in a 3-D spherical shell.
Difference equation state approximations for nonlinear hereditary control problems
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1984-01-01
Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems. Previously announced in STAR as N83-33589
Approximate number word knowledge before the cardinal principle.
Gunderson, Elizabeth A; Spaepen, Elizabet; Levine, Susan C
2015-02-01
Approximate number word knowledge-understanding the relation between the count words and the approximate magnitudes of sets-is a critical piece of knowledge that predicts later math achievement. However, researchers disagree about when children first show evidence of approximate number word knowledge-before, or only after, they have learned the cardinal principle. In two studies, children who had not yet learned the cardinal principle (subset-knowers) produced sets in response to number words (verbal comprehension task) and produced number words in response to set sizes (verbal production task). As evidence of approximate number word knowledge, we examined whether children's numerical responses increased with increasing numerosity of the stimulus. In Study 1, subset-knowers (ages 3.0-4.2 years) showed approximate number word knowledge above their knower-level on both tasks, but this effect did not extend to numbers above 4. In Study 2, we collected data from a broader age range of subset-knowers (ages 3.1-5.6 years). In this sample, children showed approximate number word knowledge on the verbal production task even when only examining set sizes above 4. Across studies, children's age predicted approximate number word knowledge (above 4) on the verbal production task when controlling for their knower-level, study (1 or 2), and parents' education, none of which predicted approximation ability. Thus, children can develop approximate knowledge of number words up to 10 before learning the cardinal principle. Furthermore, approximate number word knowledge increases with age and might not be closely related to the development of exact number word knowledge. Copyright © 2014 Elsevier Inc. All rights reserved.
Computing Functions by Approximating the Input
ERIC Educational Resources Information Center
Goldberg, Mayer
2012-01-01
In computing real-valued functions, it is ordinarily assumed that the input to the function is known, and it is the output that we need to approximate. In this work, we take the opposite approach: we show how to compute the values of some transcendental functions by approximating the input to these functions, and obtaining exact answers for their…
Kaye, Stephen B
2009-04-01
To provide a scalar measure of refractive error, based on geometric lens power through principal, orthogonal and oblique meridians, that is not limited to the paraxial and sag height approximations. A function is derived to model sections through the principal meridian of a lens, followed by rotation of the section through orthogonal and oblique meridians. Average focal length is determined using the definition for the average of a function. Average univariate power in the principal meridian (including spherical aberration), can be computed from the average of a function over the angle of incidence as determined by the parameters of the given lens, or adequately computed from an integrated series function. Average power through orthogonal and oblique meridians, can be similarly determined using the derived formulae. The widely used computation for measuring refractive error, the spherical equivalent, introduces non-constant approximations, leading to a systematic bias. The equations proposed provide a good univariate representation of average lens power and are not subject to a systematic bias. They are particularly useful for the analysis of aggregate data, correlating with biological treatment variables and for developing analyses, which require a scalar equivalent representation of refractive power.
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, PO Box 1207, 3430 BE Nieuwegein
2014-11-15
In this paper, a number of new 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 semi-infinite slab approximations of the heat equation. The main result is the approximation of χ under the influence of V and τ based on the phase of two harmonics making the estimate less sensitive to calibration errors. To understand why the slab approximations can estimate χ well in cylindrical geometry, the relationships betweenmore » heat transport models in slab and cylindrical geometry are studied. In addition, the relationship between amplitude and phase with respect to their derivatives, used to estimate χ, is discussed. The results are presented in terms of the relative error for the different derived approximations for different values of frequency, transport coefficients, and dimensionless radius. The approximations show a significant region in which χ, V, and τ can be estimated well, but also regions in which the error is large. Also, it is shown that some compensation is necessary to estimate V and τ in a cylindrical geometry. On the other hand, errors resulting from the simplified assumptions are also discussed showing that estimating realistic values for V and τ based on infinite domains will be difficult in practice. This paper is the first part (Part I) of a series of three papers. In Part II and Part III, cylindrical approximations based directly on semi-infinite cylindrical domain (outward propagating heat pulses) and inward propagating heat pulses in a cylindrical domain, respectively, will be treated.« less
James, Kevin R; Dowling, David R
2008-09-01
In underwater acoustics, the accuracy of computational field predictions is commonly limited by uncertainty in environmental parameters. An approximate technique for determining the probability density function (PDF) of computed field amplitude, A, from known environmental uncertainties is presented here. The technique can be applied to several, N, uncertain parameters simultaneously, requires N+1 field calculations, and can be used with any acoustic field model. The technique implicitly assumes independent input parameters and is based on finding the optimum spatial shift between field calculations completed at two different values of each uncertain parameter. This shift information is used to convert uncertain-environmental-parameter distributions into PDF(A). The technique's accuracy is good when the shifted fields match well. Its accuracy is evaluated in range-independent underwater sound channels via an L(1) error-norm defined between approximate and numerically converged results for PDF(A). In 50-m- and 100-m-deep sound channels with 0.5% uncertainty in depth (N=1) at frequencies between 100 and 800 Hz, and for ranges from 1 to 8 km, 95% of the approximate field-amplitude distributions generated L(1) values less than 0.52 using only two field calculations. Obtaining comparable accuracy from traditional methods requires of order 10 field calculations and up to 10(N) when N>1.
Pawlak Algebra and Approximate Structure on Fuzzy Lattice
Zhuang, Ying; Liu, Wenqi; Wu, Chin-Chia; Li, Jinhai
2014-01-01
The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to rough set theory. We also investigate molecule Pawlak algebra and obtain some related properties. PMID:25152922
Pawlak algebra and approximate structure on fuzzy lattice.
Zhuang, Ying; Liu, Wenqi; Wu, Chin-Chia; Li, Jinhai
2014-01-01
The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to rough set theory. We also investigate molecule Pawlak algebra and obtain some related properties.
NASA Astrophysics Data System (ADS)
Voloshinov, V. V.
2018-03-01
In computations related to mathematical programming problems, one often has to consider approximate, rather than exact, solutions satisfying the constraints of the problem and the optimality criterion with a certain error. For determining stopping rules for iterative procedures, in the stability analysis of solutions with respect to errors in the initial data, etc., a justified characteristic of such solutions that is independent of the numerical method used to obtain them is needed. A necessary δ-optimality condition in the smooth mathematical programming problem that generalizes the Karush-Kuhn-Tucker theorem for the case of approximate solutions is obtained. The Lagrange multipliers corresponding to the approximate solution are determined by solving an approximating quadratic programming problem.
NASA Astrophysics Data System (ADS)
Kim, SungKun; Lee, Hunpyo
2017-06-01
Via a dynamical cluster approximation with N c = 4 in combination with a semiclassical approximation (DCA+SCA), we study the doped two-dimensional Hubbard model. We obtain a plaquette antiferromagnetic (AF) Mott insulator, a plaquette AF ordered metal, a pseudogap (or d-wave superconductor) and a paramagnetic metal by tuning the doping concentration. These features are similar to the behaviors observed in copper-oxide superconductors and are in qualitative agreement with the results calculated by the cluster dynamical mean field theory with the continuous-time quantum Monte Carlo (CDMFT+CTQMC) approach. The results of our DCA+SCA differ from those of the CDMFT+CTQMC approach in that the d-wave superconducting order parameters are shown even in the high doped region, unlike the results of the CDMFT+CTQMC approach. We think that the strong plaquette AF orderings in the dynamical cluster approximation (DCA) with N c = 4 suppress superconducting states with increasing doping up to strongly doped region, because frozen dynamical fluctuations in a semiclassical approximation (SCA) approach are unable to destroy those orderings. Our calculation with short-range spatial fluctuations is initial research, because the SCA can manage long-range spatial fluctuations in feasible computational times beyond the CDMFT+CTQMC tool. We believe that our future DCA+SCA calculations should supply information on the fully momentum-resolved physical properties, which could be compared with the results measured by angle-resolved photoemission spectroscopy experiments.
Approximate analytic solutions to coupled nonlinear Dirac equations
Khare, Avinash; Cooper, Fred; Saxena, Avadh
2017-01-30
Here, we consider the coupled nonlinear Dirac equations (NLDEs) in 1+11+1 dimensions with scalar–scalar self-interactions g 1 2/2(more » $$\\bar{ψ}$$ψ) 2 + g 2 2/2($$\\bar{Φ}$$Φ) 2 + g 2 3($$\\bar{ψ}$$ψ)($$\\bar{Φ}$$Φ) as well as vector–vector interactions g 1 2/2($$\\bar{ψ}$$γμψ)($$\\bar{ψ}$$γμψ) + g 2 2/2($$\\bar{Φ}$$γμΦ)($$\\bar{Φ}$$γμΦ) + g 2 3($$\\bar{ψ}$$γμψ)($$\\bar{Φ}$$γμΦ). Writing the two components of the assumed rest frame solution of the coupled NLDE equations in the form ψ=e –iω1tR 1cosθ,R 1sinθΦ=e –iω2tR 2cosη,R 2sinη, and assuming that θ(x),η(x) have the same functional form they had when g3 = 0, which is an approximation consistent with the conservation laws, we then find approximate analytic solutions for Ri(x) which are valid for small values of g 3 2/g 2 2 and g 3 2/g 1 2. In the nonrelativistic limit we show that both of these coupled models go over to the same coupled nonlinear Schrödinger equation for which we obtain two exact pulse solutions vanishing at x → ±∞.« less
Approximate analytic solutions to coupled nonlinear Dirac equations
DOE Office of Scientific and Technical Information (OSTI.GOV)
Khare, Avinash; Cooper, Fred; Saxena, Avadh
Here, we consider the coupled nonlinear Dirac equations (NLDEs) in 1+11+1 dimensions with scalar–scalar self-interactions g 1 2/2(more » $$\\bar{ψ}$$ψ) 2 + g 2 2/2($$\\bar{Φ}$$Φ) 2 + g 2 3($$\\bar{ψ}$$ψ)($$\\bar{Φ}$$Φ) as well as vector–vector interactions g 1 2/2($$\\bar{ψ}$$γμψ)($$\\bar{ψ}$$γμψ) + g 2 2/2($$\\bar{Φ}$$γμΦ)($$\\bar{Φ}$$γμΦ) + g 2 3($$\\bar{ψ}$$γμψ)($$\\bar{Φ}$$γμΦ). Writing the two components of the assumed rest frame solution of the coupled NLDE equations in the form ψ=e –iω1tR 1cosθ,R 1sinθΦ=e –iω2tR 2cosη,R 2sinη, and assuming that θ(x),η(x) have the same functional form they had when g3 = 0, which is an approximation consistent with the conservation laws, we then find approximate analytic solutions for Ri(x) which are valid for small values of g 3 2/g 2 2 and g 3 2/g 1 2. In the nonrelativistic limit we show that both of these coupled models go over to the same coupled nonlinear Schrödinger equation for which we obtain two exact pulse solutions vanishing at x → ±∞.« less
Approximate Bayesian computation for forward modeling in cosmology
DOE Office of Scientific and Technical Information (OSTI.GOV)
Akeret, Joël; Refregier, Alexandre; Amara, Adam
Bayesian inference is often used in cosmology and astrophysics to derive constraints on model parameters from observations. This approach relies on the ability to compute the likelihood of the data given a choice of model parameters. In many practical situations, the likelihood function may however be unavailable or intractable due to non-gaussian errors, non-linear measurements processes, or complex data formats such as catalogs and maps. In these cases, the simulation of mock data sets can often be made through forward modeling. We discuss how Approximate Bayesian Computation (ABC) can be used in these cases to derive an approximation to themore » posterior constraints using simulated data sets. This technique relies on the sampling of the parameter set, a distance metric to quantify the difference between the observation and the simulations and summary statistics to compress the information in the data. We first review the principles of ABC and discuss its implementation using a Population Monte-Carlo (PMC) algorithm and the Mahalanobis distance metric. We test the performance of the implementation using a Gaussian toy model. We then apply the ABC technique to the practical case of the calibration of image simulations for wide field cosmological surveys. We find that the ABC analysis is able to provide reliable parameter constraints for this problem and is therefore a promising technique for other applications in cosmology and astrophysics. Our implementation of the ABC PMC method is made available via a public code release.« less
Approximate analytic solutions to 3D unconfined groundwater flow within regional 2D models
NASA Astrophysics Data System (ADS)
Luther, K.; Haitjema, H. M.
2000-04-01
We present methods for finding approximate analytic solutions to three-dimensional (3D) unconfined steady state groundwater flow near partially penetrating and horizontal wells, and for combining those solutions with regional two-dimensional (2D) models. The 3D solutions use distributed singularities (analytic elements) to enforce boundary conditions on the phreatic surface and seepage faces at vertical wells, and to maintain fixed-head boundary conditions, obtained from the 2D model, at the perimeter of the 3D model. The approximate 3D solutions are analytic (continuous and differentiable) everywhere, including on the phreatic surface itself. While continuity of flow is satisfied exactly in the infinite 3D flow domain, water balance errors can occur across the phreatic surface.
Local Approximation and Hierarchical Methods for Stochastic Optimization
NASA Astrophysics Data System (ADS)
Cheng, Bolong
In this thesis, we present local and hierarchical approximation methods for two classes of stochastic optimization problems: optimal learning and Markov decision processes. For the optimal learning problem class, we introduce a locally linear model with radial basis function for estimating the posterior mean of the unknown objective function. The method uses a compact representation of the function which avoids storing the entire history, as is typically required by nonparametric methods. We derive a knowledge gradient policy with the locally parametric model, which maximizes the expected value of information. We show the policy is asymptotically optimal in theory, and experimental works suggests that the method can reliably find the optimal solution on a range of test functions. For the Markov decision processes problem class, we are motivated by an application where we want to co-optimize a battery for multiple revenue, in particular energy arbitrage and frequency regulation. The nature of this problem requires the battery to make charging and discharging decisions at different time scales while accounting for the stochastic information such as load demand, electricity prices, and regulation signals. Computing the exact optimal policy becomes intractable due to the large state space and the number of time steps. We propose two methods to circumvent the computation bottleneck. First, we propose a nested MDP model that structure the co-optimization problem into smaller sub-problems with reduced state space. This new model allows us to understand how the battery behaves down to the two-second dynamics (that of the frequency regulation market). Second, we introduce a low-rank value function approximation for backward dynamic programming. This new method only requires computing the exact value function for a small subset of the state space and approximate the entire value function via low-rank matrix completion. We test these methods on historical price data from the
Differential equation based method for accurate approximations in optimization
NASA Technical Reports Server (NTRS)
Pritchard, Jocelyn I.; Adelman, Howard M.
1990-01-01
This paper describes a method to efficiently and accurately approximate the effect of design changes on structural response. The key to this new method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in msot cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacement are used to approximate bending stresses.
Differential equation based method for accurate approximations in optimization
NASA Technical Reports Server (NTRS)
Pritchard, Jocelyn I.; Adelman, Howard M.
1990-01-01
A method to efficiently and accurately approximate the effect of design changes on structural response is described. The key to this method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in most cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacements are used to approximate bending stresses.
Variationally consistent approximation scheme for charge transfer
NASA Technical Reports Server (NTRS)
Halpern, A. M.
1978-01-01
The author has developed a technique for testing various charge-transfer approximation schemes for consistency with the requirements of the Kohn variational principle for the amplitude to guarantee that the amplitude is correct to second order in the scattering wave functions. Applied to Born-type approximations for charge transfer it allows the selection of particular groups of first-, second-, and higher-Born-type terms that obey the consistency requirement, and hence yield more reliable approximation to the amplitude.
Inversion and approximation of Laplace transforms
NASA Technical Reports Server (NTRS)
Lear, W. M.
1980-01-01
A method of inverting Laplace transforms by using a set of orthonormal functions is reported. As a byproduct of the inversion, approximation of complicated Laplace transforms by a transform with a series of simple poles along the left half plane real axis is shown. The inversion and approximation process is simple enough to be put on a programmable hand calculator.
Minimal entropy approximation for cellular automata
NASA Astrophysics Data System (ADS)
Fukś, Henryk
2014-02-01
We present a method for the construction of approximate orbits of measures under the action of cellular automata which is complementary to the local structure theory. The local structure theory is based on the idea of Bayesian extension, that is, construction of a probability measure consistent with given block probabilities and maximizing entropy. If instead of maximizing entropy one minimizes it, one can develop another method for the construction of approximate orbits, at the heart of which is the iteration of finite-dimensional maps, called minimal entropy maps. We present numerical evidence that the minimal entropy approximation sometimes outperforms the local structure theory in characterizing the properties of cellular automata. The density response curve for elementary CA rule 26 is used to illustrate this claim.
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.
Approximation Set of the Interval Set in Pawlak's Space
Wang, Jin; Wang, Guoyin
2014-01-01
The interval set is a special set, which describes uncertainty of an uncertain concept or set Z with its two crisp boundaries named upper-bound set and lower-bound set. In this paper, the concept of similarity degree between two interval sets is defined at first, and then the similarity degrees between an interval set and its two approximations (i.e., upper approximation set R¯(Z) and lower approximation set R_(Z)) are presented, respectively. The disadvantages of using upper-approximation set R¯(Z) or lower-approximation set R_(Z) as approximation sets of the uncertain set (uncertain concept) Z are analyzed, and a new method for looking for a better approximation set of the interval set Z is proposed. The conclusion that the approximation set R 0.5(Z) is an optimal approximation set of interval set Z is drawn and proved successfully. The change rules of R 0.5(Z) with different binary relations are analyzed in detail. Finally, a kind of crisp approximation set of the interval set Z is constructed. We hope this research work will promote the development of both the interval set model and granular computing theory. PMID:25177721
Function approximation using combined unsupervised and supervised learning.
Andras, Peter
2014-03-01
Function approximation is one of the core tasks that are solved using neural networks in the context of many engineering problems. However, good approximation results need good sampling of the data space, which usually requires exponentially increasing volume of data as the dimensionality of the data increases. At the same time, often the high-dimensional data is arranged around a much lower dimensional manifold. Here we propose the breaking of the function approximation task for high-dimensional data into two steps: (1) the mapping of the high-dimensional data onto a lower dimensional space corresponding to the manifold on which the data resides and (2) the approximation of the function using the mapped lower dimensional data. We use over-complete self-organizing maps (SOMs) for the mapping through unsupervised learning, and single hidden layer neural networks for the function approximation through supervised learning. We also extend the two-step procedure by considering support vector machines and Bayesian SOMs for the determination of the best parameters for the nonlinear neurons in the hidden layer of the neural networks used for the function approximation. We compare the approximation performance of the proposed neural networks using a set of functions and show that indeed the neural networks using combined unsupervised and supervised learning outperform in most cases the neural networks that learn the function approximation using the original high-dimensional data.
Hayward, David C.; Hetherington, Suzannah; Behm, Carolyn A.; Grasso, Lauretta C.; Forêt, Sylvain; Miller, David J.; Ball, Eldon E.
2011-01-01
Background A successful metamorphosis from a planktonic larva to a settled polyp, which under favorable conditions will establish a future colony, is critical for the survival of corals. However, in contrast to the situation in other animals, e.g., frogs and insects, little is known about the molecular basis of coral metamorphosis. We have begun to redress this situation with previous microarray studies, but there is still a great deal to learn. In the present paper we have utilized a different technology, subtractive hybridization, to characterize genes differentially expressed across this developmental transition and to compare the success of this method to microarray. Methodology/Principal Findings Suppressive subtractive hybridization (SSH) was used to identify two pools of transcripts from the coral, Acropora millepora. One is enriched for transcripts expressed at higher levels at the pre-settlement stage, and the other for transcripts expressed at higher levels at the post-settlement stage. Virtual northern blots were used to demonstrate the efficacy of the subtractive hybridization technique. Both pools contain transcripts coding for proteins in various functional classes but transcriptional regulatory proteins were represented more frequently in the post-settlement pool. Approximately 18% of the transcripts showed no significant similarity to any other sequence on the public databases. Transcripts of particular interest were further characterized by in situ hybridization, which showed that many are regulated spatially as well as temporally. Notably, many transcripts exhibit axially restricted expression patterns that correlate with the pool from which they were isolated. Several transcripts are expressed in patterns consistent with a role in calcification. Conclusions We have characterized over 200 transcripts that are differentially expressed between the planula larva and post-settlement polyp of the coral, Acropora millepora. Sequence, putative function
Harris, W F
1989-03-01
The exact equation for sagitta of spherical surfaces is generalized to toric surfaces which include spherical and cylindrical surfaces as special cases. Lens thickness, therefore, can be calculated accurately anywhere on a lens even in cases of extreme spherical and cylindrical powers and large diameters. The sagittae of tire- and barrel-form toric surfaces differ off the principal meridians, as is shown by a numerical example. The same holds for pulley- and capstan-form toric surfaces. A general expression is given for thickness at an arbitrary point on a toric lens. Approximate expressions are derived and re-expressed in terms of matrices. The matrix provides an elegant means of generalizing equations for spherical surfaces and lenses to toric surfaces and lenses.
Borges, Beatriz C; Garcia-Galiano, David; da Silveira Cruz-Machado, Sanseray; Han, Xingfa; Gavrilina, Galina B; Saunders, Thomas L; Auchus, Richard J; Hammoud, Saher S; Smith, Gary D; Elias, Carol F
2017-09-01
Approximately 15% of human couples of reproductive age have impaired fertility, and the male component accounts for about half of these cases. The etiology is usually unknown, but high correlation with the increase in obesity rates is documented. In this study, we show that diet-induced and genetically obese mice display copulatory behavior comparable to controls, but the number of females impregnated by obese males is remarkably low. Screening for changes in gene expression in the male reproductive tract showed decreased Crisp4 expression in testis and epididymis of obese mice. Lack of CRISP4 in the luminal membrane of epididymal cells indicated inadequate secretion. Consistent with CRISP4 action in acrosome reaction, sperm from mice fed a high-fat diet (HFD) had decreased fertilization capacity. CRISP4 treatment of sperm from HFD mice prior to in vitro fertilization improved fertilization rate. In leptin-deficient obese and infertile mice, leptin's effect to restore CRISP4 expression and function required gonadal hormones. Our findings indicate that the obesity-induced decline in sperm motility and fertilization capacity results in part from the disruption of epididymal CRISP4 expression and secretion. Copyright © 2017 Endocrine Society.
Weierstrass method for quaternionic polynomial root-finding
NASA Astrophysics Data System (ADS)
Falcão, M. Irene; Miranda, Fernando; Severino, Ricardo; Soares, M. Joana
2018-01-01
Quaternions, introduced by Hamilton in 1843 as a generalization of complex numbers, have found, in more recent years, a wealth of applications in a number of different areas which motivated the design of efficient methods for numerically approximating the zeros of quaternionic polynomials. In fact, one can find in the literature recent contributions to this subject based on the use of complex techniques, but numerical methods relying on quaternion arithmetic remain scarce. In this paper we propose a Weierstrass-like method for finding simultaneously {\\sl all} the zeros of unilateral quaternionic polynomials. The convergence analysis and several numerical examples illustrating the performance of the method are also presented.
Application of geometric approximation to the CPMG experiment: Two- and three-site exchange.
Chao, Fa-An; Byrd, R Andrew
2017-04-01
The Carr-Purcell-Meiboom-Gill (CPMG) experiment is one of the most classical and well-known relaxation dispersion experiments in NMR spectroscopy, and it has been successfully applied to characterize biologically relevant conformational dynamics in many cases. Although the data analysis of the CPMG experiment for the 2-site exchange model can be facilitated by analytical solutions, the data analysis in a more complex exchange model generally requires computationally-intensive numerical analysis. Recently, a powerful computational strategy, geometric approximation, has been proposed to provide approximate numerical solutions for the adiabatic relaxation dispersion experiments where analytical solutions are neither available nor feasible. Here, we demonstrate the general potential of geometric approximation by providing a data analysis solution of the CPMG experiment for both the traditional 2-site model and a linear 3-site exchange model. The approximate numerical solution deviates less than 0.5% from the numerical solution on average, and the new approach is computationally 60,000-fold more efficient than the numerical approach. Moreover, we find that accurate dynamic parameters can be determined in most cases, and, for a range of experimental conditions, the relaxation can be assumed to follow mono-exponential decay. The method is general and applicable to any CPMG RD experiment (e.g. N, C', C α , H α , etc.) The approach forms a foundation of building solution surfaces to analyze the CPMG experiment for different models of 3-site exchange. Thus, the geometric approximation is a general strategy to analyze relaxation dispersion data in any system (biological or chemical) if the appropriate library can be built in a physically meaningful domain. Published by Elsevier Inc.
NASA Technical Reports Server (NTRS)
Zoby, E. V.
1981-01-01
An engineering method has been developed for computing the windward-symmetry plane convective heat-transfer rates on Shuttle-like vehicles at large angles of attack. The engineering code includes an approximate inviscid flowfield technique, laminar and turbulent heating-rate expressions, an approximation to account for the variable-entropy effects on the surface heating and the concept of an equivalent axisymmetric body to model the windward-ray flowfields of Shuttle-like vehicles at angles of attack from 25 to 45 degrees. The engineering method is validated by comparing computed heating results with corresponding experimental data measured on Shuttle and advanced transportation models over a wide range of flow conditions and angles of attack from 25 to 40 degrees and also with results of existing prediction techniques. The comparisons are in good agreement.
NASA Astrophysics Data System (ADS)
Filatov, Michael; Cremer, Dieter
2005-02-01
The regular approximation to the normalized elimination of the small component (NESC) in the modified Dirac equation has been developed and presented in matrix form. The matrix form of the infinite-order regular approximation (IORA) expressions, obtained in [Filatov and Cremer, J. Chem. Phys. 118, 6741 (2003)] using the resolution of the identity, is the exact matrix representation and corresponds to the zeroth-order regular approximation to NESC (NESC-ZORA). Because IORA (=NESC-ZORA) is a variationally stable method, it was used as a suitable starting point for the development of the second-order regular approximation to NESC (NESC-SORA). As shown for hydrogenlike ions, NESC-SORA energies are closer to the exact Dirac energies than the energies from the fifth-order Douglas-Kroll approximation, which is much more computationally demanding than NESC-SORA. For the application of IORA (=NESC-ZORA) and NESC-SORA to many-electron systems, the number of the two-electron integrals that need to be evaluated (identical to the number of the two-electron integrals of a full Dirac-Hartree-Fock calculation) was drastically reduced by using the resolution of the identity technique. An approximation was derived, which requires only the two-electron integrals of a nonrelativistic calculation. The accuracy of this approach was demonstrated for heliumlike ions. The total energy based on the approximate integrals deviates from the energy calculated with the exact integrals by less than 5×10-9hartree units. NESC-ZORA and NESC-SORA can easily be implemented in any nonrelativistic quantum chemical program. Their application is comparable in cost with that of nonrelativistic methods. The methods can be run with density functional theory and any wave function method. NESC-SORA has the advantage that it does not imply a picture change.
Oncologists' negative attitudes towards expressing emotion over patient death and burnout.
Granek, Leeat; Ben-David, Merav; Nakash, Ora; Cohen, Michal; Barbera, Lisa; Ariad, Samuel; Krzyzanowska, Monika K
2017-05-01
The aims of this study were to examine the relationship between negative attitudes towards expressing emotion following patient death and burnout in oncologists and to explore oncologists' preferences for institutional interventions to deal with patient death. The participants included a convenience sample of 177 oncologists from Israel and Canada. Oncologists completed a questionnaire package that included a sociodemographic survey, a burnout measure, a survey assessing negative attitudes towards expressing emotion, and a survey assessing desired interventions to cope with patient death. To examine the association between burnout and negative attitudes while controlling for the effect of sociodemographic variables, a hierarchical linear regression was computed. Higher burnout scores were related to higher negative attitudes towards perceived expressed emotion (partial r = .25, p < .01) of those who viewed this affect as a weakness and as a sign of unprofessionalism. Approximately half of the oncologists found each of the five categories of institutional interventions (pedagogical strategies, emotional support, group/peer support, taking time off, and research and training) helpful in coping with patient death. Our findings suggest that high burnout scores are associated with negative attitudes towards expressing emotion and that there is a wide variation in oncologist preferences in coping with patient death. Institutions should promote interventions that are varied and that focus on the needs of oncologists in order to reduce burnout. Interventions that legitimize expression of emotion about patient death may be useful. Another way to reduce stigma would be to require oncologists to "opt out" rather than "opt in" to accessing a selection of social and/or individual interventions.
On the derivation of the semiclassical approximation to the quantum propagator
DOE Office of Scientific and Technical Information (OSTI.GOV)
Fischer, Stefan G., E-mail: stefan.fischer@physik.uni-freiburg.de; Buchleitner, Andreas
2015-07-15
In order to rigorously derive the amplitude factor of the semiclassical approximation to the quantum propagator, we extend an existing method originally devised to evaluate Gaussian path-integral expressions. Using a result which relates the determinant of symmetric block-tridiagonal matrices to the determinants of their blocks, two difference equations are obtained. The first one allows to establish the connection of the amplitude factor to Jacobi’s accessory equations in the continuous-time limit, while the second one leads to an additional factor which, however, contributes to the final result only in exceptional cases. In order to demonstrate the wide applicability of these differencemore » equations, we treat explicitly the case where the time-sliced Lagrangian is written in generalized coordinates, for which a general derivation has so far been unavailable.« less
Meta-Regression Approximations to Reduce Publication Selection Bias
ERIC Educational Resources Information Center
Stanley, T. D.; Doucouliagos, Hristos
2014-01-01
Publication selection bias is a serious challenge to the integrity of all empirical sciences. We derive meta-regression approximations to reduce this bias. Our approach employs Taylor polynomial approximations to the conditional mean of a truncated distribution. A quadratic approximation without a linear term, precision-effect estimate with…
Thin-wall approximation in vacuum decay: A lemma
NASA Astrophysics Data System (ADS)
Brown, Adam R.
2018-05-01
The "thin-wall approximation" gives a simple estimate of the decay rate of an unstable quantum field. Unfortunately, the approximation is uncontrolled. In this paper I show that there are actually two different thin-wall approximations and that they bracket the true decay rate: I prove that one is an upper bound and the other a lower bound. In the thin-wall limit, the two approximations converge. In the presence of gravity, a generalization of this lemma provides a simple sufficient condition for nonperturbative vacuum instability.
Tissue-specific expression of human CD4 in transgenic mice.
Gillespie, F P; Doros, L; Vitale, J; Blackwell, C; Gosselin, J; Snyder, B W; Wadsworth, S C
1993-01-01
The gene for the human CD4 glycoprotein, which serves as the receptor for human immunodeficiency virus type 1, along with approximately 23 kb of sequence upstream of the translational start site, was cloned. The ability of 5' flanking sequences to direct tissue-specific expression was tested in cell culture and in transgenic mice. A 5' flanking region of 6 kb was able to direct transcription of the CD4 gene in NIH 3T3 cells but did not result in detectable expression in the murine T-cell line EL4 or in four lines of transgenic mice. A larger 5' flanking region of approximately 23 kb directed high-level CD4 transcription in the murine T-cell line EL4 and in three independent lines of transgenic mice. Human CD4 expression in all tissues analyzed was tightly correlated with murine CD4 expression; the highest levels of human CD4 RNA expression were found in the thymus and spleen, with relatively low levels detected in other tissues. Expression of human CD4 protein in peripheral blood mononuclear cells was examined by flow cytometry in these transgenic animals and found to be restricted to the murine CD4+ subset of lymphocytes. Human CD4 protein, detected with an anti-human CD4 monoclonal antibody, was present on the surface of 45 to 50% of the peripheral blood mononuclear cells from all transgenic lines. Images PMID:8474453
Smooth function approximation using neural networks.
Ferrari, Silvia; Stengel, Robert F
2005-01-01
An algebraic approach for representing multidimensional nonlinear functions by feedforward neural networks is presented. In this paper, the approach is implemented for the approximation of smooth batch data containing the function's input, output, and possibly, gradient information. The training set is associated to the network adjustable parameters by nonlinear weight equations. The cascade structure of these equations reveals that they can be treated as sets of linear systems. Hence, the training process and the network approximation properties can be investigated via linear algebra. Four algorithms are developed to achieve exact or approximate matching of input-output and/or gradient-based training sets. Their application to the design of forward and feedback neurocontrollers shows that algebraic training is characterized by faster execution speeds and better generalization properties than contemporary optimization techniques.
Random-Phase Approximation Methods
NASA Astrophysics Data System (ADS)
Chen, Guo P.; Voora, Vamsee K.; Agee, Matthew M.; Balasubramani, Sree Ganesh; Furche, Filipp
2017-05-01
Random-phase approximation (RPA) methods are rapidly emerging as cost-effective validation tools for semilocal density functional computations. We present the theoretical background of RPA in an intuitive rather than formal fashion, focusing on the physical picture of screening and simple diagrammatic analysis. A new decomposition of the RPA correlation energy into plasmonic modes leads to an appealing visualization of electron correlation in terms of charge density fluctuations. Recent developments in the areas of beyond-RPA methods, RPA correlation potentials, and efficient algorithms for RPA energy and property calculations are reviewed. The ability of RPA to approximately capture static correlation in molecules is quantified by an analysis of RPA natural occupation numbers. We illustrate the use of RPA methods in applications to small-gap systems such as open-shell d- and f-element compounds, radicals, and weakly bound complexes, where semilocal density functional results exhibit strong functional dependence.
NASA Astrophysics Data System (ADS)
Zounia, M.; Shamirzaie, M.; Ashouri, A.
2017-09-01
In this paper quantum teleportation of an unknown quantum state via noisy maximally bipartite (Bell) and maximally tripartite (Greenberger-Horne-Zeilinger (GHZ)) entangled states are investigated. We suppose that one of the observers who would receive the sent state accelerates uniformly with respect to the sender. The interactions of the quantum system with its environment during the teleportation process impose noises. These (unital and nonunital) noises are: phase damping, phase flip, amplitude damping and bit flip. In expressing the modes of the Dirac field used as qubits, in the accelerating frame, the so-called single mode approximation is not imposed. We calculate the fidelities of teleportation, and discuss their behaviors using suitable plots. The effects of noise, acceleration and going beyond the single mode approximation are discussed. Although the Bell states bring higher fidelities than GHZ states, the global behaviors of the two quantum systems with respect to some noise types, and therefore their fidelities, are different.
Lamitina, Todd; Huang, Chunyi George; Strange, Kevin
2006-08-08
The detection, stabilization, and repair of stress-induced damage are essential requirements for cellular life. All cells respond to osmotic stress-induced water loss with increased expression of genes that mediate accumulation of organic osmolytes, solutes that function as chemical chaperones and restore osmotic homeostasis. The signals and signaling mechanisms that regulate osmoprotective gene expression in animal cells are poorly understood. Here, we show that gpdh-1 and gpdh-2, genes that mediate the accumulation of the organic osmolyte glycerol, are essential for survival of the nematode Caenorhabditis elegans during osmotic stress. Expression of GFP driven by the gpdh-1 promoter (P(gpdh-1)::GFP) is detected only during hypertonic stress but is not induced by other stressors. Using P(gpdh-1)::GFP expression as a phenotype, we screened approximately 16,000 genes by RNAi feeding and identified 122 that cause constitutive activation of gpdh-1 expression and glycerol accumulation. Many of these genes function to regulate protein translation and cotranslational protein folding and to target and degrade denatured proteins, suggesting that the accumulation of misfolded proteins functions as a signal to activate osmoprotective gene expression and organic osmolyte accumulation in animal cells. Consistent with this hypothesis, 73% of these protein-homeostasis genes have been shown to slow age-dependent protein aggregation in C. elegans. Because diverse environmental stressors and numerous disease states result in protein misfolding, mechanisms must exist that discriminate between osmotically induced and other forms of stress-induced protein damage. Our findings provide a foundation for understanding how these damage-selectivity mechanisms function.
Monotonically improving approximate answers to relational algebra queries
NASA Technical Reports Server (NTRS)
Smith, Kenneth P.; Liu, J. W. S.
1989-01-01
We present here a query processing method that produces approximate answers to queries posed in standard relational algebra. This method is monotone in the sense that the accuracy of the approximate result improves with the amount of time spent producing the result. This strategy enables us to trade the time to produce the result for the accuracy of the result. An approximate relational model that characterizes appromimate relations and a partial order for comparing them is developed. Relational operators which operate on and return approximate relations are defined.
Approximate isotropic cloak for the Maxwell equations
NASA Astrophysics Data System (ADS)
Ghosh, Tuhin; Tarikere, Ashwin
2018-05-01
We construct a regular isotropic approximate cloak for the Maxwell system of equations. The method of transformation optics has enabled the design of electromagnetic parameters that cloak a region from external observation. However, these constructions are singular and anisotropic, making practical implementation difficult. Thus, regular approximations to these cloaks have been constructed that cloak a given region to any desired degree of accuracy. In this paper, we show how to construct isotropic approximations to these regularized cloaks using homogenization techniques so that one obtains cloaking of arbitrary accuracy with regular and isotropic parameters.
Uhm, Jesik; Lee, Jinuk; Eun, Changsun; Lee, Sangyoub
2006-08-07
We generalize the Wilemski-Fixman-Weiss decoupling approximation to calculate the transient rate of absorption of point particles into multiple sinks of different sizes, shapes, and reactivities. As an application we consider the case involving two spherical sinks. We obtain a Laplace-transform expression for the transient rate that is in excellent agreement with computer simulations. The long-time steady-state rate has a relatively simple expression, which clearly shows the dependence on the diffusion constant of the particles and on the sizes and reactivities of sinks, and its numerical result is in good agreement with the known exact result that is given in terms of recursion relations.
Hamiltonian term for a uniform dc electric field under the adiabatic approximation
NASA Astrophysics Data System (ADS)
Siu, Zhuo Bin; Jalil, Mansoor B. A.; Tan, Seng Ghee
2018-02-01
In this work, we show that the disorder-free Kubo formula for the nonequilibrium value of an observable due to a dc electric field, represented by Exx ̂ in the Hamiltonian, can be interpreted as the standard time-independent theory response of the observable due to a time- and position-independent perturbation HMF. We derive the explicit expression for HMF and show that it originates from the adiabatic approximation to
Expression and purification of recombinant nattokinase in Spodoptera frugiperda cells.
Li, Xiaoxiang; Wang, Xiaoli; Xiong, Shaoling; Zhang, Jing; Cai, Litao; Yang, Yanyan
2007-10-01
A recombinant baculovirus, rv-egfp-NK, containing a reporter gene encoding the enhanced green fluorescent protein (EGFP), was used to express nattokinase (NK), a fibrinolytic enzyme, in Spodoptera frugiperda (SF-9) cells. The recombinant protein also included a histidine tag for purification using Ni(2+) resins. The recombinant NK, approximately 30 kDa, retained fibrinolytic activity (60 U/ml). The integration of the EGFP expression cassette in the Bac-to-Bac system is thus an effective method for the expression and purification of recombinant NK protein in Spodoptera frugiperda insect cells.
Bonny, Justin W.; Lourenco, Stella F.
2012-01-01
Humans rely on two main systems of quantification - one is non-symbolic and involves approximate number representations (known as the approximate number system or ANS), the other is symbolic and allows for exact calculations of number. Despite the pervasiveness of the ANS across development, recent studies with adolescents and school-aged children point to individual differences in the precision of these representations, which, importantly, have been shown to relate to symbolic math competence, even after controlling for general aspects of intelligence. Such findings suggest that the ANS, which humans share with nonhuman animals, interfaces specifically with a uniquely human system of formal mathematics. Other findings, however, point to a less straightforward picture, leaving open questions about the nature and ontogenetic origins of the relation between these two systems. Testing children across the preschool period, we found that ANS precision correlated with early math achievement, but, critically, that this relation was non-linear. More specifically, the correlation between ANS precision and math competence was stronger for children with lower math scores than for children with higher math scores. Taken together, our findings suggest that early-developing connections between the ANS and mathematics may be fundamentally discontinuous. Possible mechanisms underlying such non-linearity are discussed. PMID:23201156
Bonny, Justin W; Lourenco, Stella F
2013-03-01
Humans rely on two main systems of quantification; one is nonsymbolic and involves approximate number representations (known as the approximate number system or ANS), and the other is symbolic and allows for exact calculations of number. Despite the pervasiveness of the ANS across development, recent studies with adolescents and school-aged children point to individual differences in the precision of these representations that, importantly, have been shown to relate to symbolic math competence even after controlling for general aspects of intelligence. Such findings suggest that the ANS, which humans share with nonhuman animals, interfaces specifically with a uniquely human system of formal mathematics. Other findings, however, point to a less straightforward picture, leaving open questions about the nature and ontogenetic origins of the relation between these two systems. Testing children across the preschool period, we found that ANS precision correlated with early math achievement but, critically, that this relation was nonlinear. More specifically, the correlation between ANS precision and math competence was stronger for children with lower math scores than for children with higher math scores. Taken together, our findings suggest that early-developing connections between the ANS and mathematics may be fundamentally discontinuous. Possible mechanisms underlying such nonlinearity are discussed. Copyright © 2012 Elsevier Inc. All rights reserved.
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
Art Works ... when Students Find Inspiration
ERIC Educational Resources Information Center
Herberholz, Barbara
2011-01-01
Artworks are not produced in a vacuum, but by the interaction of experiences, and interrelationships of ideas, perceptions and feelings acknowledged and expressed in some form. Students, like mature artists, may be inspired and motivated by their memories and observations of their surroundings. Like adult artists, students may find that their own…
Urry, Dan W.
1969-01-01
Starting with the expression for optical rotatory dispersion in the absorption region that was arrived at by Condon, two series were considered for the purpose of achieving the experimentally observed, steeper wavelength dependence in the absorption region while retaining the established 1/λ2 law in regions removed from absorption. The first two terms of one series in which the second term exhibits a 1/λ6 wavelength dependence were found to calculate satisfactorily the optical rotatory dispersion curve of d-camphor-10-sulfonate from 400 mμ to 190 mμ when only three bands were considered. Evaluated at the extrema, the two-term expression can be approximated by a simple equation which allows calculation of the rotational strength of a nonoverlapping band by using only the wavelength and molar rotation of the extrema and the index of refraction of the solution. The rotational strengths calculated from optical rotatory dispersion data in this manner closely agree with those calculated from corresponding circular dichroism data. Thus when position and magnitude of rotatory dispersion extrema alone are reported for carbonyls, it is suggested that such published data may be converted to approximate rotational strengths. PMID:5257123
Approximate Computing Techniques for Iterative Graph Algorithms
DOE Office of Scientific and Technical Information (OSTI.GOV)
Panyala, Ajay R.; Subasi, Omer; Halappanavar, Mahantesh
Approximate computing enables processing of large-scale graphs by trading off quality for performance. Approximate computing techniques have become critical not only due to the emergence of parallel architectures but also the availability of large scale datasets enabling data-driven discovery. Using two prototypical graph algorithms, PageRank and community detection, we present several approximate computing heuristics to scale the performance with minimal loss of accuracy. We present several heuristics including loop perforation, data caching, incomplete graph coloring and synchronization, and evaluate their efficiency. We demonstrate performance improvements of up to 83% for PageRank and up to 450x for community detection, with lowmore » impact of accuracy for both the algorithms. We expect the proposed approximate techniques will enable scalable graph analytics on data of importance to several applications in science and their subsequent adoption to scale similar graph algorithms.« less
Relationship of expressed emotion with relapse of schizophrenia patients in Kelantan.
Azhar, M Z; Varma, S L
1996-02-01
The families of 83 schizophrenic patients were studied to find out the level of expressed emotion in them leading to the relapse of these patients. The patients were having more than two episodes of schizophrenia (DSM-III-R). The most salient finding was the virtual absence of high level of expressed emotion as the cause of relapse. It was found that the majority of the families (72.3%) had low expressed emotion while only 25.3% had high expressed emotion and only 2.4% families were equivocal in this respect. This finding is in contrast with various other findings in this area. The most likely explanation for this disagreement is the cultural differences between Malaysian patients and Western patients.
Bull, Rebecca; Marschark, Marc; Nordmann, Emily; Sapere, Patricia; Skene, Wendy A
2018-06-01
Many children with hearing loss (CHL) show a delay in mathematical achievement compared to children with normal hearing (CNH). This study examined whether there are differences in acuity of the approximate number system (ANS) between CHL and CNH, and whether ANS acuity is related to math achievement. Working memory (WM), short-term memory (STM), and inhibition were considered as mediators of any relationship between ANS acuity and math achievement. Seventy-five CHL were compared with 75 age- and gender-matched CNH. ANS acuity, mathematical reasoning, WM, and STM of CHL were significantly poorer compared to CNH. Group differences in math ability were no longer significant when ANS acuity, WM, or STM was controlled. For CNH, WM and STM fully mediated the relationship of ANS acuity to math ability; for CHL, WM and STM only partially mediated this relationship. ANS acuity, WM, and STM are significant contributors to hearing status differences in math achievement, and to individual differences within the group of CHL. Statement of contribution What is already known on this subject? Children with hearing loss often perform poorly on measures of math achievement, although there have been few studies focusing on basic numerical cognition in these children. In typically developing children, the approximate number system predicts math skills concurrently and longitudinally, although there have been some contradictory findings. Recent studies suggest that domain-general skills, such as inhibition, may account for the relationship found between the approximate number system and math achievement. What does this study adds? This is the first robust examination of the approximate number system in children with hearing loss, and the findings suggest poorer acuity of the approximate number system in these children compared to hearing children. The study addresses recent issues regarding the contradictory findings of the relationship of the approximate number system to math ability
Pumping approximately integrable systems
Lange, Florian; Lenarčič, Zala; Rosch, Achim
2017-01-01
Weak perturbations can drive an interacting many-particle system far from its initial equilibrium state if one is able to pump into degrees of freedom approximately protected by conservation laws. This concept has for example been used to realize Bose–Einstein condensates of photons, magnons and excitons. Integrable quantum systems, like the one-dimensional Heisenberg model, are characterized by an infinite set of conservation laws. Here, we develop a theory of weakly driven integrable systems and show that pumping can induce large spin or heat currents even in the presence of integrability breaking perturbations, since it activates local and quasi-local approximate conserved quantities. The resulting steady state is qualitatively captured by a truncated generalized Gibbs ensemble with Lagrange parameters that depend on the structure but not on the overall amplitude of perturbations nor the initial state. We suggest to use spin-chain materials driven by terahertz radiation to realize integrability-based spin and heat pumps. PMID:28598444
NASA Technical Reports Server (NTRS)
Banks, H. T.; Rosen, I. G.
1984-01-01
Approximation ideas are discussed that can be used in parameter estimation and feedback control for Euler-Bernoulli models of elastic systems. Focusing on parameter estimation problems, ways by which one can obtain convergence results for cubic spline based schemes for hybrid models involving an elastic cantilevered beam with tip mass and base acceleration are outlined. Sample numerical findings are also presented.
New Tests of the Fixed Hotspot Approximation
NASA Astrophysics Data System (ADS)
Gordon, R. G.; Andrews, D. L.; Horner-Johnson, B. C.; Kumar, R. R.
2005-05-01
We present new methods for estimating uncertainties in plate reconstructions relative to the hotspots and new tests of the fixed hotspot approximation. We find no significant motion between Pacific hotspots, on the one hand, and Indo-Atlantic hotspots, on the other, for the past ~ 50 Myr, but large and significant apparent motion before 50 Ma. Whether this motion is truly due to motion between hotspots or alternatively due to flaws in the global plate motion circuit can be tested with paleomagnetic data. These tests give results consistent with the fixed hotspot approximation and indicate significant misfits when a relative plate motion circuit through Antarctica is employed for times before 50 Ma. If all of the misfit to the global plate motion circuit is due to motion between East and West Antarctica, then that motion is 800 ± 500 km near the Ross Sea Embayment and progressively less along the Trans-Antarctic Mountains toward the Weddell Sea. Further paleomagnetic tests of the fixed hotspot approximation can be made. Cenozoic and Cretaceous paleomagnetic data from the Pacific plate, along with reconstructions of the Pacific plate relative to the hotspots, can be used to estimate an apparent polar wander (APW) path of Pacific hotspots. An APW path of Indo-Atlantic hotspots can be similarly estimated (e.g. Besse & Courtillot 2002). If both paths diverge in similar ways from the north pole of the hotspot reference frame, it would indicate that the hotspots have moved in unison relative to the spin axis, which may be attributed to true polar wander. If the two paths diverge from one another, motion between Pacific hotspots and Indo-Atlantic hotspots would be indicated. The general agreement of the two paths shows that the former is more important than the latter. The data require little or no motion between groups of hotspots, but up to ~10 mm/yr of motion is allowed within uncertainties. The results disagree, in particular, with the recent extreme interpretation of
Non-Gaussian distributions of melodic intervals in music: The Lévy-stable approximation
NASA Astrophysics Data System (ADS)
Niklasson, Gunnar A.; Niklasson, Maria H.
2015-11-01
The analysis of structural patterns in music is of interest in order to increase our fundamental understanding of music, as well as for devising algorithms for computer-generated music, so called algorithmic composition. Musical melodies can be analyzed in terms of a “music walk” between the pitches of successive tones in a notescript, in analogy with the “random walk” model commonly used in physics. We find that the distribution of melodic intervals between tones can be approximated with a Lévy-stable distribution. Since music also exibits self-affine scaling, we propose that the “music walk” should be modelled as a Lévy motion. We find that the Lévy motion model captures basic structural patterns in classical as well as in folk music.
Sensitivity analysis and approximation methods for general eigenvalue problems
NASA Technical Reports Server (NTRS)
Murthy, D. V.; Haftka, R. T.
1986-01-01
Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.
Validity of the local approximation in iron pnictides and chalcogenides
Sémon, Patrick; Haule, Kristjan; Kotliar, Gabriel
2017-05-08
We introduce a methodology to treat different degrees of freedom at different levels of approximation. We use cluster DMFT (dynamical mean field theory) for the t 2g electrons and single site DMFT for the e g electrons to study the normal state of the iron pnictides and chalcogenides. Furthermore, in the regime of moderate mass renormalizations, the self-energy is very local, justifying the success of single site DMFT for these materials and for other Hunds metals. Here we solve the corresponding impurity model with CTQMC (continuous time quantum Monte Carlo) and find that the minus sign problem is not severemore » in regimes of moderate mass renormalization.« less
Geary, David C; Hoard, Mary K; Nugent, Lara; Rouder, Jeffrey N
2015-12-01
The relation between performance on measures of algebraic cognition and acuity of the approximate number system (ANS) and memory for addition facts was assessed for 171 ninth graders (92 girls) while controlling for parental education, sex, reading achievement, speed of numeral processing, fluency of symbolic number processing, intelligence, and the central executive component of working memory. The algebraic tasks assessed accuracy in placing x,y pairs in the coordinate plane, speed and accuracy of expression evaluation, and schema memory for algebra equations. ANS acuity was related to accuracy of placements in the coordinate plane and expression evaluation but not to schema memory. Frequency of fact retrieval errors was related to schema memory but not to coordinate plane or expression evaluation accuracy. The results suggest that the ANS may contribute to or be influenced by spatial-numerical and numerical-only quantity judgments in algebraic contexts, whereas difficulties in committing addition facts to long-term memory may presage slow formation of memories for the basic structure of algebra equations. More generally, the results suggest that different brain and cognitive systems are engaged during the learning of different components of algebraic competence while controlling for demographic and domain general abilities. Copyright © 2015 Elsevier Inc. All rights reserved.
Models of stochastic gene expression
NASA Astrophysics Data System (ADS)
Paulsson, Johan
2005-06-01
Gene expression is an inherently stochastic process: Genes are activated and inactivated by random association and dissociation events, transcription is typically rare, and many proteins are present in low numbers per cell. The last few years have seen an explosion in the stochastic modeling of these processes, predicting protein fluctuations in terms of the frequencies of the probabilistic events. Here I discuss commonalities between theoretical descriptions, focusing on a gene-mRNA-protein model that includes most published studies as special cases. I also show how expression bursts can be explained as simplistic time-averaging, and how generic approximations can allow for concrete interpretations without requiring concrete assumptions. Measures and nomenclature are discussed to some extent and the modeling literature is briefly reviewed.
Approximate correlations for chevron-type plate heat exchangers
DOE Office of Scientific and Technical Information (OSTI.GOV)
Wanniarachchi, A.S.; Ratnam, U.; Tilton, B.E.
1995-12-31
There exists very little useful data representing the performance of industrial plate heat exchangers (PHEs) in the open literature. As a result, it has been difficult to arrive at any generalized correlations. While every PHE manufacturer is believed to have a comprehensive set of performance curves for their own designs, there exists the need to generate an approximate set of generalized correlations for the heat-transfer community. Such correlations can be used for preliminary designs and analytical studies. This paper attempts to develop such a set of generalized correlations to quantify the heat-transfer and pressure-drop performance of chevron-type PHEs. For thismore » purpose, the experimental data reported by Heavner et al. were used for the turbulent region. For the laminar region, a semi-theoretical approach was used to express, for example, the friction factor as a function of the Reynolds number and the chevron angle. Asymptotic curves were used for the transitional region. Physical explanations are provided for the trends shown by the generalized correlations. The correlations are compared against the open-literature data, where appropriate. These correlations are expected to be improved in the future when more data become available.« less
Convergence Rates of Finite Difference Stochastic Approximation Algorithms
2016-06-01
dfferences as gradient approximations. It is shown that the convergence of these algorithms can be accelerated by controlling the implementation of the...descent algorithm, under various updating schemes using finite dfferences as gradient approximations. It is shown that the convergence of these...the Kiefer-Wolfowitz algorithm and the mirror descent algorithm, under various updating schemes using finite differences as gradient approximations. It
Kiliç, Türker; Bayri, Yaşar; Ozduman, Koray; Acar, Melih; Diren, Semin; Kurtkaya, Ozlem; Ekinci, Gazanfer; Buğra, Kuyaş; Sav, Aydin; Ozek, M Memet; Pamir, M Necmettin
2002-07-01
Tenascin is an extracellular matrix glycoprotein that is expressed during embryogenesis, inflammation, angiogenesis, and carcinogenesis. The aim of this study was to investigate how tenascin expression relates to histological grade, angiogenesis, and radiological findings in meningiomas. Twenty typical, 20 atypical, and 5 malignant meningiomas were studied retrospectively. Tenascin expression and vascular endothelial growth factor (VEGF) expression in the tumor tissue were investigated by immunohistochemistry. Tenascin messenger ribonucleic acid expression was also studied by comparative reverse transcriptase-polymerase chain reaction. Magnetic resonance images from each case were assessed for peritumoral edema and tumor border shape. The atypical and malignant meningiomas showed higher levels of tenascin expression than the typical meningiomas. The more sensitive messenger ribonucleic acid-based methods confirmed this finding. Tenascin expression was correlated with peritumoral edema and VEGF expression but not with tumor border shape. In the 13 tumors with marked tenascin expression, peritumoral edema was Grade 0 in one, Grade 1 in three, and Grade 2 in nine specimens. In the same 13 tumors, VEGF expression was Grade 1 in five and Grade 2 in eight specimens, and the findings for tumor border shape were Grade 0 in seven, Grade 1 in four, and Grade 2 in two specimens. In meningiomas, tenascin expression is correlated with anaplasia, tumor-associated edema, and VEGF expression but not with tumor border shape. This protein may play a role in the neoplastic and/or angiogenic processes in atypical and malignant meningiomas and may thus be a potential target for meningioma therapy.
Modeling gene expression measurement error: a quasi-likelihood approach
Strimmer, Korbinian
2003-01-01
Background Using suitable error models for gene expression measurements is essential in the statistical analysis of microarray data. However, the true probabilistic model underlying gene expression intensity readings is generally not known. Instead, in currently used approaches some simple parametric model is assumed (usually a transformed normal distribution) or the empirical distribution is estimated. However, both these strategies may not be optimal for gene expression data, as the non-parametric approach ignores known structural information whereas the fully parametric models run the risk of misspecification. A further related problem is the choice of a suitable scale for the model (e.g. observed vs. log-scale). Results Here a simple semi-parametric model for gene expression measurement error is presented. In this approach inference is based an approximate likelihood function (the extended quasi-likelihood). Only partial knowledge about the unknown true distribution is required to construct this function. In case of gene expression this information is available in the form of the postulated (e.g. quadratic) variance structure of the data. As the quasi-likelihood behaves (almost) like a proper likelihood, it allows for the estimation of calibration and variance parameters, and it is also straightforward to obtain corresponding approximate confidence intervals. Unlike most other frameworks, it also allows analysis on any preferred scale, i.e. both on the original linear scale as well as on a transformed scale. It can also be employed in regression approaches to model systematic (e.g. array or dye) effects. Conclusions The quasi-likelihood framework provides a simple and versatile approach to analyze gene expression data that does not make any strong distributional assumptions about the underlying error model. For several simulated as well as real data sets it provides a better fit to the data than competing models. In an example it also improved the power of
Rational Approximations with Hankel-Norm Criterion
1980-01-01
REPORT TYPE ANDu DATES COVERED It) L. TITLE AND SLWUIlL Fi901 ia FUNDING NUMOIRS, RATIONAL APPROXIMATIONS WITH HANKEL-NORM CRITERION PE61102F i...problem is proved to be reducible to obtain a two-variable all- pass ration 1 function, interpolating a set of parametric values at specified points inside...PAGES WHICH DO NOT REPRODUCE LEGIBLY. V" C - w RATIONAL APPROXIMATIONS WITH HANKEL-NORM CRITERION* Y. Genin* Philips Research Lab. 2, avenue van
NASA Astrophysics Data System (ADS)
Bania, Piotr; Baranowski, Jerzy
2018-02-01
Quantisation of signals is a ubiquitous property of digital processing. In many cases, it introduces significant difficulties in state estimation and in consequence control. Popular approaches either do not address properly the problem of system disturbances or lead to biased estimates. Our intention was to find a method for state estimation for stochastic systems with quantised and discrete observation, that is free of the mentioned drawbacks. We have formulated a general form of the optimal filter derived by a solution of Fokker-Planck equation. We then propose the approximation method based on Galerkin projections. We illustrate the approach for the Ornstein-Uhlenbeck process, and derive analytic formulae for the approximated optimal filter, also extending the results for the variant with control. Operation is illustrated with numerical experiments and compared with classical discrete-continuous Kalman filter. Results of comparison are substantially in favour of our approach, with over 20 times lower mean squared error. The proposed filter is especially effective for signal amplitudes comparable to the quantisation thresholds. Additionally, it was observed that for high order of approximation, state estimate is very close to the true process value. The results open the possibilities of further analysis, especially for more complex processes.
Comparison of dynamical approximation schemes for nonlinear gravitaional clustering
NASA Technical Reports Server (NTRS)
Melott, Adrian L.
1994-01-01
We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the lognormal approximation, the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of the approximation by truncation, i.e., by smoothing the initial conditions with various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was cross-correlation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(sub G(exp 2)), where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present. This in turn provides a natural explanation for the presence of sheets and filaments in the observed galaxy distribution. Use of the approximation scheme can permit extremely rapid generation of large numbers of realizations of model universes with good accuracy down to galaxy group mass scales.
Embedding impedance approximations in the analysis of SIS mixers
NASA Technical Reports Server (NTRS)
Kerr, A. R.; Pan, S.-K.; Withington, S.
1992-01-01
Future millimeter-wave radio astronomy instruments will use arrays of many SIS receivers, either as focal plane arrays on individual radio telescopes, or as individual receivers on the many antennas of radio interferometers. Such applications will require broadband integrated mixers without mechanical tuners. To produce such mixers, it will be necessary to improve present mixer design techniques, most of which use the three-frequency approximation to Tucker's quantum mixer theory. This paper examines the adequacy of three approximations to Tucker's theory: (1) the usual three-frequency approximation which assumes a sinusoidal LO voltage at the junction, and a short-circuit at all frequencies above the upper sideband; (2) a five-frequency approximation which allows two LO voltage harmonics and five small-signal sidebands; and (3) a quasi five-frequency approximation in which five small-signal sidebands are allowed, but the LO voltage is assumed sinusoidal. These are compared with a full harmonic-Newton solution of Tucker's equations, including eight LO harmonics and their corresponding sidebands, for realistic SIS mixer circuits. It is shown that the accuracy of the three approximations depends strongly on the value of omega R(sub N)C for the SIS junctions used. For large omega R(sub N)C, all three approximations approach the eight-harmonic solution. For omega R(sub N)C values in the range 0.5 to 10, the range of most practical interest, the quasi five-frequency approximation is a considerable improvement over the three-frequency approximation, and should be suitable for much design work. For the realistic SIS mixers considered here, the five-frequency approximation gives results very close to those of the eight-harmonic solution. Use of these approximations, where appropriate, considerably reduces the computational effort needed to analyze an SIS mixer, and allows the design and optimization of mixers using a personal computer.
Computerised analysis of facial emotion expression in eating disorders
2017-01-01
Background Problems with social-emotional processing are known to be an important contributor to the development and maintenance of eating disorders (EDs). Diminished facial communication of emotion has been frequently reported in individuals with anorexia nervosa (AN). Less is known about facial expressivity in bulimia nervosa (BN) and in people who have recovered from AN (RecAN). This study aimed to pilot the use of computerised facial expression analysis software to investigate emotion expression across the ED spectrum and recovery in a large sample of participants. Method 297 participants with AN, BN, RecAN, and healthy controls were recruited. Participants watched film clips designed to elicit happy or sad emotions, and facial expressions were then analysed using FaceReader. Results The finding mirrored those from previous work showing that healthy control and RecAN participants expressed significantly more positive emotions during the positive clip compared to the AN group. There were no differences in emotion expression during the sad film clip. Discussion These findings support the use of computerised methods to analyse emotion expression in EDs. The findings also demonstrate that reduced positive emotion expression is likely to be associated with the acute stage of AN illness, with individuals with BN showing an intermediate profile. PMID:28575109
Computerised analysis of facial emotion expression in eating disorders.
Leppanen, Jenni; Dapelo, Marcela Marin; Davies, Helen; Lang, Katie; Treasure, Janet; Tchanturia, Kate
2017-01-01
Problems with social-emotional processing are known to be an important contributor to the development and maintenance of eating disorders (EDs). Diminished facial communication of emotion has been frequently reported in individuals with anorexia nervosa (AN). Less is known about facial expressivity in bulimia nervosa (BN) and in people who have recovered from AN (RecAN). This study aimed to pilot the use of computerised facial expression analysis software to investigate emotion expression across the ED spectrum and recovery in a large sample of participants. 297 participants with AN, BN, RecAN, and healthy controls were recruited. Participants watched film clips designed to elicit happy or sad emotions, and facial expressions were then analysed using FaceReader. The finding mirrored those from previous work showing that healthy control and RecAN participants expressed significantly more positive emotions during the positive clip compared to the AN group. There were no differences in emotion expression during the sad film clip. These findings support the use of computerised methods to analyse emotion expression in EDs. The findings also demonstrate that reduced positive emotion expression is likely to be associated with the acute stage of AN illness, with individuals with BN showing an intermediate profile.
A case of alkaptonuria - ultrasonographic findings.
Damian, Laura Otilia; Felea, Ioana; Boloşiu, Călin; Botar-Jid, Carolina; Fodor, Daniela; Rednic, Simona
2013-12-01
Alkaptonuria is a rare disease with autosomal recessive inheritance and variable expression. The weight-bearing joint involvement and spondylitis-like vertebral changes occur only after the 3rd decade. Musculoskeletal ultrasonographic findings in alkaptonuria were only rarely described, consisting mainly into enthesopathy and non-synovial tendon degeneration. We present the case of a 50 years old man with alkaptonuria and discuss the ultrasonographic findings and the relationship of the disease with chondrocalcinosis. The tendinous and synovial aspect may be peculiar and it could therefore allow recognition and screening for alkaptonuria, along with clinical and radiologic data.
NASA Technical Reports Server (NTRS)
Manning, Robert M.
2011-01-01
An expression for the mutual coherence function (MCF) of an electromagnetic beam wave propagating through atmospheric turbulence is derived within the confines of the Rytov approximation. It is shown that both the first and second Rytov approximations are required. The Rytov MCF is then compared to that which issues from the parabolic equation method of strong fluctuation theory. The agreement is found to be quite good in the weak fluctuation case. However, an instability is observed for the special case of beam wave intensities. The source of the instabilities is identified to be the characteristic way beam wave amplitudes are treated within the Rytov method.
When can time-dependent currents be reproduced by the Landauer steady-state approximation?
NASA Astrophysics Data System (ADS)
Carey, Rachel; Chen, Liping; Gu, Bing; Franco, Ignacio
2017-05-01
We establish well-defined limits in which the time-dependent electronic currents across a molecular junction subject to a fluctuating environment can be quantitatively captured via the Landauer steady-state approximation. For this, we calculate the exact time-dependent non-equilibrium Green's function (TD-NEGF) current along a model two-site molecular junction, in which the site energies are subject to correlated noise, and contrast it with that obtained from the Landauer approach. The ability of the steady-state approximation to capture the TD-NEGF behavior at each instant of time is quantified via the same-time correlation function of the currents obtained from the two methods, while their global agreement is quantified by examining differences in the average currents. The Landauer steady-state approach is found to be a useful approximation when (i) the fluctuations do not disrupt the degree of delocalization of the molecular eigenstates responsible for transport and (ii) the characteristic time for charge exchange between the molecule and leads is fast with respect to the molecular correlation time. For resonant transport, when these conditions are satisfied, the Landauer approach is found to accurately describe the current, both on average and at each instant of time. For non-resonant transport, we find that while the steady-state approach fails to capture the time-dependent transport at each instant of time, it still provides a good approximation to the average currents. These criteria can be employed to adopt effective modeling strategies for transport through molecular junctions in interaction with a fluctuating environment, as is necessary to describe experiments.
A Gaussian-based rank approximation for subspace clustering
NASA Astrophysics Data System (ADS)
Xu, Fei; Peng, Chong; Hu, Yunhong; He, Guoping
2018-04-01
Low-rank representation (LRR) has been shown successful in seeking low-rank structures of data relationships in a union of subspaces. Generally, LRR and LRR-based variants need to solve the nuclear norm-based minimization problems. Beyond the success of such methods, it has been widely noted that the nuclear norm may not be a good rank approximation because it simply adds all singular values of a matrix together and thus large singular values may dominant the weight. This results in far from satisfactory rank approximation and may degrade the performance of lowrank models based on the nuclear norm. In this paper, we propose a novel nonconvex rank approximation based on the Gaussian distribution function, which has demanding properties to be a better rank approximation than the nuclear norm. Then a low-rank model is proposed based on the new rank approximation with application to motion segmentation. Experimental results have shown significant improvements and verified the effectiveness of our method.
NASA Astrophysics Data System (ADS)
Lisenko, S. A.; Kugeiko, M. M.
2014-03-01
Approximating expressions are derived to calculate spectral and spatial characteristics of diffuse reflection of light from a two-layer medium mimicking human skin. The effectiveness of the use of these expressions in the optical diagnosis of skin biophysical parameters (tissue scattering parameters, concentration of melanin in the epidermis, concentration of total haemoglobin and bilirubin in the tissues of the dermis) and content of haemoglobin derivatives in blood (oxy-, deoxy-, met-, carboxy- and sulfhaemoglobin) is analysed numerically. The methods are proposed to determine in realtime these parameters without contact of the measuring instrument with the patient's body.
NASA Technical Reports Server (NTRS)
Phillips, D. H.; Schug, J. C.
1974-01-01
The approximate spin projection method of Amos et al. is extended to handle UHF wave functions having three significant components of differing multiplicity. An expression is given for the energy after single annihilation which differs from that of Amos and Hall. The new expression reproduces the results obtained from a previous exact calculation for which the weights and energies of the components are known. The extended approximate projection method is applied to the pi-electron UHF wave functions for the ground states of the pentachlorocyclopentadienyl cation and the croconate dianion, C5O5(2-). The results indicate a triplet ground state for the former and a singlet ground state for the latter, in agreement with experimental ESR susceptibility measurements for these molecular ions. C5C15(-) cannont be treated by restricted Hartree-Fock theory, due to its open-shell ground state. Incorrect results are obtained for the croconate dianion, if restricted Hartree-Fock theory and singly excited configuration interactions are utilized.
Nozadi, Sara S; Spinrad, Tracy L; Eisenberg, Nancy; Bolnick, Rebecca; Eggum-Wilkens, Natalie. D; Smith, Cynthia L; Gaertner, Bridget; Kupfer, Anne; Sallquist, Julie
2013-01-01
Despite evidence for the importance of individual differences in expressive language during toddlerhood in predicting later literacy skills, few researchers have examined individual and contextual factors related to language abilities across the toddler years. Furthermore, a gap remains in the literature about the extent to which the relations of negative emotions and parenting to language skills may differ for girls and boys. The purpose of this longitudinal study was to investigate the associations among maternal sensitivity, children’s observed anger reactivity, and expressive language when children were 18 (T1; n = 247) and 30 (T2; n = 216) months. At each age, mothers reported on their toddlers’ expressive language, and mothers’ sensitive parenting behavior was observed during an unstructured free-play task. Toddlers’ anger expressions were observed during an emotion-eliciting task. Using path modeling, results showed few relations at T1. At T2, maternal sensitivity was negatively related to anger, and in turn, anger was associated with lower language skills. However, moderation analyses showed that these findings were significant for boys but not for girls. In addition, T1 maternal sensitivity and anger positively predicted expressive language longitudinally for both sexes. Findings suggest that the relations between maternal sensitivity, anger reactivity and expressive language may vary depending on the child’s developmental stage and sex. PMID:23911594
McKinley, Brian; Rooney, William; Wilkerson, Curtis; Mullet, John
2016-11-01
Biomass accumulated preferentially in leaves of the sweet sorghum Della until floral initiation, then stems until anthesis, followed by panicles until grain maturity, and apical tillers. Sorghum stem RNA-seq transcriptome profiles and composition data were collected for approximately 100 days of development beginning at floral initiation. The analysis identified >200 differentially expressed genes involved in stem growth, cell wall biology, and sucrose accumulation. Genes encoding expansins and xyloglucan endotransglucosylase/hydrolases were differentially expressed in growing stem internodes. Genes encoding enzymes involved in the synthesis of cellulose, lignin, and glucuronoarabinoxylan were expressed at elevated levels in stems until approximately 7 days before anthesis and then down-regulated. CESA genes involved in primary and secondary cell wall synthesis showed different temporal patterns of expression. Following floral initiation, the level of sucrose and other non-structural carbohydrates increased to approximately 50% of the stem's dry weight. Stem sucrose accumulation was inversely correlated with >100-fold down-regulation of SbVIN1, a gene encoding a vacuolar invertase. Accumulation of stem sucrose was also correlated with cessation of leaf and stem growth at anthesis, decreased expression of genes involved in stem cell wall synthesis, and approximately 10-fold lower expression of SbSUS4, a gene encoding sucrose synthase that generates UDP-glucose from sucrose for cell wall biosynthesis. Genes for mixed linkage glucan synthesis (CSLF) and turnover were expressed at high levels in stems throughout development. Overall, the stem transcription profile resource and the genes and regulatory dynamics identified in this study will be useful for engineering sorghum stem composition for improved conversion to biofuels and bio-products. © 2016 The Authors The Plant Journal © 2016 John Wiley & Sons Ltd.
Fundamentals and Recent Developments in Approximate Bayesian Computation
Lintusaari, Jarno; Gutmann, Michael U.; Dutta, Ritabrata; Kaski, Samuel; Corander, Jukka
2017-01-01
Abstract Bayesian inference plays an important role in phylogenetics, evolutionary biology, and in many other branches of science. It provides a principled framework for dealing with uncertainty and quantifying how it changes in the light of new evidence. For many complex models and inference problems, however, only approximate quantitative answers are obtainable. Approximate Bayesian computation (ABC) refers to a family of algorithms for approximate inference that makes a minimal set of assumptions by only requiring that sampling from a model is possible. We explain here the fundamentals of ABC, review the classical algorithms, and highlight recent developments. [ABC; approximate Bayesian computation; Bayesian inference; likelihood-free inference; phylogenetics; simulator-based models; stochastic simulation models; tree-based models.] PMID:28175922
Spontaneous Regulation of Emotions in Preschool Children Who Stutter: Preliminary Findings
Johnson, Kia N.; Walden, Tedra A.; Conture, Edward G.; Karrass, Jan
2013-01-01
Purpose Emotional regulation of preschool children who do (CWS) and do not stutter (CWNS) was assessed using a disappointing gift (DG) procedure (Cole, 1986; Saarni, 1984, 1992). Method Participants consisted of 16 3- to 5-year-old CWS and CWNS (11 boys and 5 girls in each talker group). After assessing each child’s knowledge of display rules about socially-appropriate expression of emotions, children participated in a DG procedure and received a desirable gift preceding a free-play task and a disappointing gift preceding a second free-play task. Dependent variables consisted of participants’ positive and negative expressive nonverbal behaviors exhibited during receipt of a desirable gift and disappointing gift, as well as conversational speech disfluencies exhibited following receipt of each gift. Results Findings indicated that CWS and CWNS exhibited no significant differences in amount of positive emotional expressions after receiving the desired gift; however, CWS, when compared to CWNS, exhibited more negative emotional expressions after receiving the undesirable gift. Furthermore, CWS were more disfluent after receiving the desired gift when compared to receiving the disappointing gift. Ancillary findings also indicated that CWS and CWNS had equivalent knowledge of display rules. Conclusion Findings suggest that efforts to concurrently regulate emotional behaviors and (non)stutterings may be problematic for preschool-age CWS. PMID:20643793
Expanding the histological findings in postvaccinial non-viral folliculitis
Bunick, Christopher G.; Mariwalla, Kavita; Ibrahim, Omer; Modi, Badri; Imaeda, Suguru; McNiff, Jennifer
2014-01-01
Postvaccinial non-viral folliculitis has been recognized in the past decade as a new adverse cutaneous reaction to the smallpox vaccination. Contrary to more serious smallpox vaccine reactions, postvaccinial non-viral folliculitis has a benign course resolving spontaneously within approximately seven days. We describe additional histopathological findings associated with postvaccinial non-viral folliculitis, which has only been described once previously. New findings include the presence of neutrophilic or lymphohistiocytic infiltrates that concentrate around the hair follicles. We compare our findings to the follicular nature of varicella and herpes zoster infections, generating the hypothesis of deposition of vaccinia protein within folliculosebaceous units as a potential pathophysiologic mechanism behind postvaccinial non-viral folliculitis. PMID:23278890
Kim, Eunwoo; Lee, Minsik; Choi, Chong-Ho; Kwak, Nojun; Oh, Songhwai
2015-02-01
Low-rank matrix approximation plays an important role in the area of computer vision and image processing. Most of the conventional low-rank matrix approximation methods are based on the l2 -norm (Frobenius norm) with principal component analysis (PCA) being the most popular among them. However, this can give a poor approximation for data contaminated by outliers (including missing data), because the l2 -norm exaggerates the negative effect of outliers. Recently, to overcome this problem, various methods based on the l1 -norm, such as robust PCA methods, have been proposed for low-rank matrix approximation. Despite the robustness of the methods, they require heavy computational effort and substantial memory for high-dimensional data, which is impractical for real-world problems. In this paper, we propose two efficient low-rank factorization methods based on the l1 -norm that find proper projection and coefficient matrices using the alternating rectified gradient method. The proposed methods are applied to a number of low-rank matrix approximation problems to demonstrate their efficiency and robustness. The experimental results show that our proposals are efficient in both execution time and reconstruction performance unlike other state-of-the-art methods.
On the origins of approximations for stochastic chemical kinetics.
Haseltine, Eric L; Rawlings, James B
2005-10-22
This paper considers the derivation of approximations for stochastic chemical kinetics governed by the discrete master equation. Here, the concepts of (1) partitioning on the basis of fast and slow reactions as opposed to fast and slow species and (2) conditional probability densities are used to derive approximate, partitioned master equations, which are Markovian in nature, from the original master equation. Under different conditions dictated by relaxation time arguments, such approximations give rise to both the equilibrium and hybrid (deterministic or Langevin equations coupled with discrete stochastic simulation) approximations previously reported. In addition, the derivation points out several weaknesses in previous justifications of both the hybrid and equilibrium systems and demonstrates the connection between the original and approximate master equations. Two simple examples illustrate situations in which these two approximate methods are applicable and demonstrate the two methods' efficiencies.
Ghorai, Santanu; Mukherjee, Anirban; Dutta, Pranab K
2010-06-01
In this brief we have proposed the multiclass data classification by computationally inexpensive discriminant analysis through vector-valued regularized kernel function approximation (VVRKFA). VVRKFA being an extension of fast regularized kernel function approximation (FRKFA), provides the vector-valued response at single step. The VVRKFA finds a linear operator and a bias vector by using a reduced kernel that maps a pattern from feature space into the low dimensional label space. The classification of patterns is carried out in this low dimensional label subspace. A test pattern is classified depending on its proximity to class centroids. The effectiveness of the proposed method is experimentally verified and compared with multiclass support vector machine (SVM) on several benchmark data sets as well as on gene microarray data for multi-category cancer classification. The results indicate the significant improvement in both training and testing time compared to that of multiclass SVM with comparable testing accuracy principally in large data sets. Experiments in this brief also serve as comparison of performance of VVRKFA with stratified random sampling and sub-sampling.
The Communicative Function of Sad Facial Expressions.
Reed, Lawrence Ian; DeScioli, Peter
2017-01-01
What are the communicative functions of sad facial expressions? Research shows that people feel sadness in response to losses but it's unclear whether sad expressions function to communicate losses to others and if so, what makes these signals credible. Here we use economic games to test the hypothesis that sad expressions lend credibility to claims of loss. Participants play the role of either a proposer or recipient in a game with a fictional backstory and real monetary payoffs. The proposers view a (fictional) video of the recipient's character displaying either a neutral or sad expression paired with a claim of loss. The proposer then decided how much money to give to the recipient. In three experiments, we test alternative theories by using situations in which the recipient's losses were uncertain (Experiment 1), the recipient's losses were certain (Experiment 2), or the recipient claims failed gains rather than losses (Experiment 3). Overall, we find that participants gave more money to recipients who displayed sad expressions compared to neutral expressions, but only under conditions of uncertain loss. This finding supports the hypothesis that sad expressions function to increase the credibility of claims of loss.
Stopping power beyond the adiabatic approximation
DOE Office of Scientific and Technical Information (OSTI.GOV)
Caro, M.; Correa, A. A.; Artacho, E.
2017-06-01
Energetic ions traveling in solids deposit energy in a variety of ways, being nuclear and electronic stopping the two avenues in which dissipation is usually treated. This separation between electrons and ions relies on the adiabatic approximation in which ions interact via forces derived from the instantaneous electronic ground state. In a more detailed view, in which non-adiabatic effects are explicitly considered, electronic excitations alter the atomic bonding, which translates into changes in the interatomic forces. In this work, we use time dependent density functional theory and forces derived from the equations of Ehrenfest dynamics that depend instantaneously on themore » time-dependent electronic density. With them we analyze how the inter-ionic forces are affected by electronic excitations in a model of a Ni projectile interacting with a Ni target, a metallic system with strong electronic stopping and shallow core level states. We find that the electronic excitations induce substantial modifications to the inter-ionic forces, which translate into nuclear stopping power well above the adiabatic prediction. Particularly, we observe that most of the alteration of the adiabatic potential in early times comes from the ionization of the core levels of the target ions, not readily screened by the valence electrons.« less
NASA Astrophysics Data System (ADS)
Yamasaki, Hayata; Soeda, Akihito; Murao, Mio
2017-09-01
We introduce and analyze graph-associated entanglement cost, a generalization of the entanglement cost of quantum states to multipartite settings. We identify a necessary and sufficient condition for any multipartite entangled state to be constructible when quantum communication between the multiple parties is restricted to a quantum network represented by a tree. The condition for exact state construction is expressed in terms of the Schmidt ranks of the state defined with respect to edges of the tree. We also study approximate state construction and provide a second-order asymptotic analysis.
Approximate Model for Turbulent Stagnation Point Flow.
DOE Office of Scientific and Technical Information (OSTI.GOV)
Dechant, Lawrence
2016-01-01
Here we derive an approximate turbulent self-similar model for a class of favorable pressure gradient wedge-like flows, focusing on the stagnation point limit. While the self-similar model provides a useful gross flow field estimate this approach must be combined with a near wall model is to determine skin friction and by Reynolds analogy the heat transfer coefficient. The combined approach is developed in detail for the stagnation point flow problem where turbulent skin friction and Nusselt number results are obtained. Comparison to the classical Van Driest (1958) result suggests overall reasonable agreement. Though the model is only valid near themore » stagnation region of cylinders and spheres it nonetheless provides a reasonable model for overall cylinder and sphere heat transfer. The enhancement effect of free stream turbulence upon the laminar flow is used to derive a similar expression which is valid for turbulent flow. Examination of free stream enhanced laminar flow suggests that the rather than enhancement of a laminar flow behavior free stream disturbance results in early transition to turbulent stagnation point behavior. Excellent agreement is shown between enhanced laminar flow and turbulent flow behavior for high levels, e.g. 5% of free stream turbulence. Finally the blunt body turbulent stagnation results are shown to provide realistic heat transfer results for turbulent jet impingement problems.« less
Alternative approximation concepts for space frame synthesis
NASA Technical Reports Server (NTRS)
Lust, R. V.; Schmit, L. A.
1985-01-01
A structural synthesis methodology for the minimum mass design of 3-dimensionall frame-truss structures under multiple static loading conditions and subject to limits on displacements, rotations, stresses, local buckling, and element cross-sectional dimensions is presented. A variety of approximation concept options are employed to yield near optimum designs after no more than 10 structural analyses. Available options include: (A) formulation of the nonlinear mathematcal programming problem in either reciprocal section property (RSP) or cross-sectional dimension (CSD) space; (B) two alternative approximate problem structures in each design space; and (C) three distinct assumptions about element end-force variations. Fixed element, design element linking, and temporary constraint deletion features are also included. The solution of each approximate problem, in either its primal or dual form, is obtained using CONMIN, a feasible directions program. The frame-truss synthesis methodology is implemented in the COMPASS computer program and is used to solve a variety of problems. These problems were chosen so that, in addition to exercising the various approximation concepts options, the results could be compared with previously published work.
Approximating Integrals Using Probability
ERIC Educational Resources Information Center
Maruszewski, Richard F., Jr.; Caudle, Kyle A.
2005-01-01
As part of a discussion on Monte Carlo methods, which outlines how to use probability expectations to approximate the value of a definite integral. The purpose of this paper is to elaborate on this technique and then to show several examples using visual basic as a programming tool. It is an interesting method because it combines two branches of…
Light scattering by a nematic liquid crystal droplet: Wentzel–Kramers–Brillouin approximation
DOE Office of Scientific and Technical Information (OSTI.GOV)
Loiko, V. A., E-mail: loiko@dragon.bas-net.by; Konkolovich, A. V.; Miskevich, A. A.
2016-01-15
Light scattering by an optically anisotropic liquid crystal (LC) droplet of a nematic in an isotropic polymer matrix is considered in the Wentzel–Kramers–Brillouin (WKB) approximation. General relations are obtained for elements of the amplitude matrix of light scattering by a droplet of arbitrary shape and for the structure of the director field. Analytic expressions for the amplitude matrices are derived for spherical LC droplets with a uniformly oriented structure of local optical axes for strictly forward and strictly backward scattering. The efficiency factors of extinction and backward scattering for a spherical nonabsorbing LC droplet depending on the LC optical anisotropy,more » refractive index of the polymer, illumination conditions, and orientation of the optical axis of the droplet are analyzed. Verification of the obtained solutions has been performed.« less
N-point statistics of large-scale structure in the Zel'dovich approximation
DOE Office of Scientific and Technical Information (OSTI.GOV)
Tassev, Svetlin, E-mail: tassev@astro.princeton.edu
2014-06-01
Motivated by the results presented in a companion paper, here we give a simple analytical expression for the matter n-point functions in the Zel'dovich approximation (ZA) both in real and in redshift space (including the angular case). We present numerical results for the 2-dimensional redshift-space correlation function, as well as for the equilateral configuration for the real-space 3-point function. We compare those to the tree-level results. Our analysis is easily extendable to include Lagrangian bias, as well as higher-order perturbative corrections to the ZA. The results should be especially useful for modelling probes of large-scale structure in the linear regime,more » such as the Baryon Acoustic Oscillations. We make the numerical code used in this paper freely available.« less
Approximate supernova remnant dynamics with cosmic ray production
NASA Technical Reports Server (NTRS)
Voelk, H. J.; Drury, L. O.; Dorfi, E. A.
1985-01-01
Supernova explosions are the most violent and energetic events in the galaxy and have long been considered probably sources of Cosmic Rays. Recent shock acceleration models treating the Cosmic Rays (CR's) as test particles nb a prescribed Supernova Remnant (SNR) evolution, indeed indicate an approximate power law momentum distribution f sub source (p) approximation p(-a) for the particles ultimately injected into the Interstellar Medium (ISM). This spectrum extends almost to the momentum p = 1 million GeV/c, where the break in the observed spectrum occurs. The calculated power law index approximately less than 4.2 agrees with that inferred for the galactic CR sources. The absolute CR intensity can however not be well determined in such a test particle approximation.
Aberrant Gene Expression in Humans
Yang, Ence; Ji, Guoli; Brinkmeyer-Langford, Candice L.; Cai, James J.
2015-01-01
Gene expression as an intermediate molecular phenotype has been a focus of research interest. In particular, studies of expression quantitative trait loci (eQTL) have offered promise for understanding gene regulation through the discovery of genetic variants that explain variation in gene expression levels. Existing eQTL methods are designed for assessing the effects of common variants, but not rare variants. Here, we address the problem by establishing a novel analytical framework for evaluating the effects of rare or private variants on gene expression. Our method starts from the identification of outlier individuals that show markedly different gene expression from the majority of a population, and then reveals the contributions of private SNPs to the aberrant gene expression in these outliers. Using population-scale mRNA sequencing data, we identify outlier individuals using a multivariate approach. We find that outlier individuals are more readily detected with respect to gene sets that include genes involved in cellular regulation and signal transduction, and less likely to be detected with respect to the gene sets with genes involved in metabolic pathways and other fundamental molecular functions. Analysis of polymorphic data suggests that private SNPs of outlier individuals are enriched in the enhancer and promoter regions of corresponding aberrantly-expressed genes, suggesting a specific regulatory role of private SNPs, while the commonly-occurring regulatory genetic variants (i.e., eQTL SNPs) show little evidence of involvement. Additional data suggest that non-genetic factors may also underlie aberrant gene expression. Taken together, our findings advance a novel viewpoint relevant to situations wherein common eQTLs fail to predict gene expression when heritable, rare inter-individual variation exists. The analytical framework we describe, taking into consideration the reality of differential phenotypic robustness, may be valuable for investigating
NASA Astrophysics Data System (ADS)
Rao, T. R. Ramesh
2018-04-01
In this paper, we study the analytical method based on reduced differential transform method coupled with sumudu transform through Pades approximants. The proposed method may be considered as alternative approach for finding exact solution of Gas dynamics equation in an effective manner. This method does not require any discretization, linearization and perturbation.
Properties of the Boltzmann equation in the classical approximation
Epelbaum, Thomas; Gelis, François; Tanji, Naoto; ...
2014-12-30
We examine the Boltzmann equation with elastic point-like scalar interactions in two different versions of the the classical approximation. Although solving numerically the Boltzmann equation with the unapproximated collision term poses no problem, this allows one to study the effect of the ultraviolet cutoff in these approximations. This cutoff dependence in the classical approximations of the Boltzmann equation is closely related to the non-renormalizability of the classical statistical approximation of the underlying quantum field theory. The kinetic theory setup that we consider here allows one to study in a much simpler way the dependence on the ultraviolet cutoff, since onemore » has also access to the non-approximated result for comparison.« less
Recent advances in approximation concepts for optimum structural design
NASA Technical Reports Server (NTRS)
Barthelemy, Jean-Francois M.; Haftka, Raphael T.
1991-01-01
The basic approximation concepts used in structural optimization are reviewed. Some of the most recent developments in that area since the introduction of the concept in the mid-seventies are discussed. The paper distinguishes between local, medium-range, and global approximations; it covers functions approximations and problem approximations. It shows that, although the lack of comparative data established on reference test cases prevents an accurate assessment, there have been significant improvements. The largest number of developments have been in the areas of local function approximations and use of intermediate variable and response quantities. It also appears that some new methodologies are emerging which could greatly benefit from the introduction of new computer architecture.
Attema, Joanne L.; Bert, Andrew G.; Lim, Yat-Yuen; Kolesnikoff, Natasha; Lawrence, David M.; Pillman, Katherine A.; Smith, Eric; Drew, Paul A.; Khew-Goodall, Yeesim; Shannon, Frances; Goodall, Gregory J.
2013-01-01
The miR-200b~200a~429 gene cluster is a key regulator of EMT and cancer metastasis, however the transcription-based mechanisms controlling its expression during this process are not well understood. We have analyzed the miR-200b~200a~429 locus for epigenetic modifications in breast epithelial and mesenchymal cell lines using chromatin immunoprecipitation assays and DNA methylation analysis. We discovered a novel enhancer located approximately 5.1kb upstream of the miR-200b~200a~429 transcriptional start site. This region was associated with the active enhancer chromatin signature comprising H3K4me1, H3K27ac, RNA polymerase II and CpG dinucleotide hypomethylation. Luciferase reporter assays revealed the upstream enhancer stimulated the transcription of the miR-200b~200a~429 minimal promoter region approximately 27-fold in breast epithelial cells. Furthermore, we found that a region of the enhancer was transcribed, producing a short, GC-rich, mainly nuclear, non-polyadenylated RNA transcript designated miR-200b eRNA. Over-expression of miR-200b eRNA had little effect on miR-200b~200a~429 promoter activity and its production did not correlate with miR-200b~200a~429 gene expression. While additional investigations of miR-200b eRNA function will be necessary, it is possible that miR-200b eRNA may be involved in the regulation of miR-200b~200a~429 gene expression and silencing. Taken together, these findings reveal the presence of a novel enhancer, which contributes to miR-200b~200a~429 transcriptional regulation in epithelial cells. PMID:24086551
Al-Quraishy, Saleh; Dkhil, Mohamed A; Alomar, Suliman; Abdel-Baki, Abdel Azeem S; Delic, Denis; Wunderlich, Frank; Araúzo-Bravo, Marcos J
2016-05-01
Protective vaccination induces self-healing of otherwise lethal blood-stage infections of Plasmodium chabaudi malaria. Here, we investigate mRNA expression patterns of all 12 members of the Toll-like receptor (Tlr) gene family in the liver, a major effector organ against blood-stage malaria, during lethal and vaccination-induced self-healing infections of P. chabaudi in female Balb/c mice. Gene expression microarrays reveal that all 12 Tlr genes are constitutively expressed, though at varying levels, and specifically respond to infection. Protective vaccination does not affect constitutive expression of any of the 12 Tlr genes but leads to differential expression (p < 0.05) of seven Tlrs (1, 2, 4, 7, 8, 12, and 13) in response to malaria. Quantitative PCR substantiates differential expression at p < 0.01. There is an increased expression of Tlr2 by approximately five-fold on day 1 post-infection (p.i.) and Tlr1 by approximately threefold on day 4 p.i.. At peak parasitemia on day 8 p.i., none of the 12 Tlrs display any differential expression. After peak parasitemia, towards the end of the crisis phase on day 11 p.i., expression of Tlrs 1, 4, and 12 is increased by approximately four-, two-, and three-fold, respectively, and that of Tlr7 is decreased by approximately two-fold. Collectively, our data suggest that though all 12 members of the Tlr gene family are specifically responsive to malaria in the liver, not only Tlr2 at the early stage of infection but also the Tlrs 1, 4, 7, and 12 towards the end of crisis phase are critical for vaccination-induced resolution and survival of otherwise lethal blood-stage malaria.
Changes in ABA and gene expression in cold-acclimated sugar maple.
Bertrand, A; Robitaille, G; Castonguay, Y; Nadeau, P; Boutin, R
1997-01-01
To determine if cold acclimation of sugar maple (Acer saccharum Marsh.) is associated with specific changes in gene expression under natural hardening conditions, we compared bud and root translatable mRNAs of potted maple seedlings after cold acclimation under natural conditions and following spring dehardening. Cold-hardened roots and buds were sampled in January when tissues reached their maximum hardiness. Freezing tolerance, expressed as the lethal temperature for 50% of the tissues (LT(50)), was estimated at -17 degrees C for roots, and at lower than -36 degrees C for buds. Approximately ten transcripts were specifically synthesized in cold-acclimated buds, or were more abundant in cold-acclimated buds than in unhardened buds. Cold hardening was also associated with changes in translation. At least five translation products were more abundant in cold-acclimated buds and roots compared with unhardened tissues. Abscisic acid (ABA) concentration increased approximately tenfold in the xylem sap following winter acclimation, and the maximum concentration was reached just before maximal acclimation. We discuss the potential involvement of ABA in the observed modification of gene expression during cold hardening.
Valiente, Carlos; Eisenberg, Nancy; Shepard, Stephanie A; Fabes, Richard A; Cumberland, Amanda J; Losoya, Sandra H; Spinrad, Tracy L
2004-03-01
Guided by the heuristic model proposed by Eisenberg et al. [Psychol. Inq. 9 (1998) 241], we examined the relations of mothers' reported and observed negative expressivity to children's (N = 159; 74 girls; M age = 7.67 years) experience and expression of emotion. Children's experience and/or expression of emotion in response to a distressing film were measured with facial, heart rate, and self-report measures. Children's heart rate and facial distress were modestly positively related. Children's facial distress was significantly positively related to mothers' reports of negative (dominant and submissive) expressivity; the positive relation between children's facial distress and mothers' observed negative expressivity approached the conventional level of significance. Moreover, mothers' observed negative expressivity was significantly negatively related to children's heart rate reactivity during the conflict film. The positive relation between children's reported distress and mothers' observed negative expressivity approached the conventional level of significance. Several possible explanations for the pattern of findings are discussed.
Is approximated de-epithelized glanuloplasty beneficial for hypospadiologist?
ZakiEldahshoury, M; Gamal, W; Salem, E; Rashed, E; Mamdouh, A
2016-05-01
Further evaluation of the cosmetic and functional results of approximated de-epithelized glanuloplasty in different degree of hypospadias. This study included 96 male patients (DPH=68 & MPH=28). Patients selected for repair with glans approximation should have wide urethral plate & grooved glans. All cases were repaired with the classic TIP and glans approximation technique. Follow up was for one year by clinical examination of the meatal shape, size & site, glans shape, skin covering, suture line, urethral catheter, edema & fistula in addition to parent satisfaction. Mean operative time was 49±9minutes. As regards the functional and cosmetic outcomes, success was reported in 95.8%, while failure was in 4.16% in the form of glanular disruption in two patients and subcoronal urethrocutaneous fistula in another two patients. Glans approximation has many advantages, good cosmetic and functional results, short operative time, less blood loss, no need for tourniquet. Study of a large number of cases and comparing glans approximation with the classic TIP technique. Copyright © 2015 AEU. Publicado por Elsevier España, S.L.U. All rights reserved.
Adaptive control using neural networks and approximate models.
Narendra, K S; Mukhopadhyay, S
1997-01-01
The NARMA model is an exact representation of the input-output behavior of finite-dimensional nonlinear discrete-time dynamical systems in a neighborhood of the equilibrium state. However, it is not convenient for purposes of adaptive control using neural networks due to its nonlinear dependence on the control input. Hence, quite often, approximate methods are used for realizing the neural controllers to overcome computational complexity. In this paper, we introduce two classes of models which are approximations to the NARMA model, and which are linear in the control input. The latter fact substantially simplifies both the theoretical analysis as well as the practical implementation of the controller. Extensive simulation studies have shown that the neural controllers designed using the proposed approximate models perform very well, and in many cases even better than an approximate controller designed using the exact NARMA model. In view of their mathematical tractability as well as their success in simulation studies, a case is made in this paper that such approximate input-output models warrant a detailed study in their own right.
Autopsy findings in botulinum toxin poisoning.
Devers, Kelly G; Nine, Jeffrey S
2010-11-01
In the United States, foodborne botulism is most commonly associated with home-canned food products. Between 1950 and 2005, 405 separate outbreaks of botulism were reported to the Centers for Disease Control and Prevention (CDC). Approximately 8% of these outbreaks were attributed to commercially produced canned food products. Overall, 5-10% of persons ingesting botulinum toxin die. Few reports exist pertaining to autopsy findings in cases of foodborne botulism. Here, we report the autopsy findings of a man who died after a prolonged illness caused by botulinum toxin exposure likely attributable to a commercially prepared food source. Despite extensive testing, our histopathologic findings were nonspecific. We therefore conclude that the forensic pathologist must become familiar with the neurotoxicity syndrome associated with this illness. Maintaining vigilance for botulism by carefully reviewing the decedent's clinical history will aid in the early identification and control of outbreaks, either foodborne or terrorism-related. 2010 American Academy of Forensic Sciences. Published 2010. This article is a U.S. Government work and is in the public domain in the U.S.A.
Hudson, Sandra; Wang, Dongliang; Middleton, Frank; Nevaldine, Barbara H; Naous, Rana; Hutchison, Robert E
2018-04-26
Anaplastic lymphoma kinase (ALK)-positive anaplastic large cell lymphoma (ALCL) shows 60-70% event free survival with standard treatments. Targeted therapies are being tested for increased benefit and/or reduced toxicity, but interactions with standard agents are not well known. We exposed four ALCL cell lines to two targeted agents, crizotinib and brentuximab vedotin, and to two standard agents, doxorubicin and vinblastine. For each agent and combination, we measured apoptosis and expression of approximately 300 previously annotated genes of interest using targeted RNA-sequencing. An aurora kinase inhibitor, alisertib, was similarly tested for gene expression effects. Only crizotinib, alone or in combination, showed significant effects (adjusted P < 0.05) on expression and apoptosis. One hundred and nine of 277 gene expressions showed crizotinib-associated differential expression, mostly downregulation, 62 associated with apoptosis, and 28 associated with both crizotinib and apoptosis. Doxorubicin was antagonistic with crizotinib on gene expression and apoptosis. Brentuximab was synergistic with crizotinib in apoptosis, and not antagonistic in gene expression. Vinblastine also appeared synergistic with crizotinib but did not achieve statistical significance. Alisertib did not show significant expression changes. Our data suggest that crizotinib induces apoptosis through orderly changes in cell signaling associated with ALK inhibition. Expression effects of crizotinib and associated apoptosis are antagonized by doxorubicin, but apoptosis is synergized by brentuximab vedotin and possibly vinblastine. These findings suggest that concurrent use of crizotinib and doxorubicin may be counterproductive, while the pairing of crizotinib with brentuximab (or vinblastine) may increase efficacy. Alisertib did not induce expression changes at cytotoxic dosage. © 2018 Wiley Periodicals, Inc.
Wang, Huanbin; Yao, Han; Li, Chushu; Liang, Lunxi; Zhang, Yao; Shi, Hubing; Zhou, Chongzhi; Chen, Yingxuan; Fang, Jing-Yuan; Xu, Jie
2017-01-01
Colorectal cancer (CRC) is the second leading cause of cancer death worldwide, and immune checkpoint blockade therapy provides an opportunity for improving the outcome of CRC patients. Recent studies suggest that programmed death ligand-1 (PD-L1) is only expressed in 12% of CRCs. Here, we demonstrate that PD-L2 is expressed in approximately 40% CRCs, and its expression independently associates with poor survival of CRC patients. By detection of PD-L2 expression by immunofluorescence in 124 CRC cases with 10-y survival data, we found significant association between PD-L2 overexpression in cancer cells and worse overall survival (46.3 vs 69.1 mo; p = 0.0004). The association remained significant in multivariate COX regression analysis (hazard ratio = 2.778, 95% confidence interval [CI] = 1.668-4.627; p < 0.0001). In the validation CRC data set, significant association between PD-L2 overexpression and poor survival was supported by the univariate analysis (27.1 vs. 88.9 mo; p = 0.0002) and multivariate model (hazard ratio = 7.09, 95%CI 1.78-28.16; p = 0.005). Western Blot revealed strong induction of PD-L2 expression by interferon-γ (IFNγ) in CRC cells, and the mRNA levels of both genes were significantly correlated in CRC tissue samples. Suppression of glycosylation with tunicamycin caused a shift in molecular weight and significant decrease in the expression of PD-L2 protein. In conclusion, PD-L2 overexpression in CRC cells, under the regulation by IFNγ and glycosylation, associates with poor survival of patients with colorectal cancer. These findings highlight PD-L2 as a promising therapeutic target in CRC and suggest potential routes to control PD-L2 expression in CRC cells.
Wang, Huanbin; Yao, Han; Li, Chushu; Liang, Lunxi; Zhang, Yao; Shi, Hubing; Zhou, Chongzhi; Chen, Yingxuan; Fang, Jing-Yuan
2017-01-01
ABSTRACT Colorectal cancer (CRC) is the second leading cause of cancer death worldwide, and immune checkpoint blockade therapy provides an opportunity for improving the outcome of CRC patients. Recent studies suggest that programmed death ligand-1 (PD-L1) is only expressed in 12% of CRCs. Here, we demonstrate that PD-L2 is expressed in approximately 40% CRCs, and its expression independently associates with poor survival of CRC patients. By detection of PD-L2 expression by immunofluorescence in 124 CRC cases with 10-y survival data, we found significant association between PD-L2 overexpression in cancer cells and worse overall survival (46.3 vs 69.1 mo; p = 0.0004). The association remained significant in multivariate COX regression analysis (hazard ratio = 2.778, 95% confidence interval [CI] = 1.668–4.627; p < 0.0001). In the validation CRC data set, significant association between PD-L2 overexpression and poor survival was supported by the univariate analysis (27.1 vs. 88.9 mo; p = 0.0002) and multivariate model (hazard ratio = 7.09, 95%CI 1.78–28.16; p = 0.005). Western Blot revealed strong induction of PD-L2 expression by interferon-γ (IFNγ) in CRC cells, and the mRNA levels of both genes were significantly correlated in CRC tissue samples. Suppression of glycosylation with tunicamycin caused a shift in molecular weight and significant decrease in the expression of PD-L2 protein. In conclusion, PD-L2 overexpression in CRC cells, under the regulation by IFNγ and glycosylation, associates with poor survival of patients with colorectal cancer. These findings highlight PD-L2 as a promising therapeutic target in CRC and suggest potential routes to control PD-L2 expression in CRC cells. PMID:28811964
Freedom of Choice About Incidental Findings Can Frustrate Participants' True Preferences.
Viberg, Jennifer; Segerdahl, Pär; Langenskiöld, Sophie; Hansson, Mats G
2016-03-01
Ethicists, regulators and researchers have struggled with the question of whether incidental findings in genomics studies should be disclosed to participants. In the ethical debate, a general consensus is that disclosed information should benefit participants. However, there is no agreement that genetic information will benefit participants, rather it may cause problems such as anxiety. One could get past this disagreement about disclosure of incidental findings by letting participants express their preferences in the consent form. We argue that this freedom of choice is problematic. In transferring the decision to participants, it is assumed that participants will understand what they decide about and that they will express what they truly want. However, psychological findings about people's reaction to probabilities and risk have been shown to involve both cognitive and emotional challenges. People change their attitude to risk depending on what is at stake. Their mood affects judgments and choices, and they over- and underestimate probabilities depending on whether they are low or high. Moreover, different framing of the options can steer people to a specific choice. Although it seems attractive to let participants express their preferences to incidental findings in the consent form, it is uncertain if this choice enables people to express what they truly prefer. In order to better understand the participants' preferences, we argue that future empirical work needs to confront the participant with the complexity of the uncertainty and the trade-offs that are connected with the uncertain predictive value of genetic risk information. © 2015 John Wiley & Sons Ltd.
Self-consistent approximation beyond the CPA: Part II
DOE Office of Scientific and Technical Information (OSTI.GOV)
Kaplan, T.; Gray, L.J.
1981-08-01
In Part I, Professor Leath has described the substantial efforts to generalize the CPA. In this second part, a particular self-consistent approximation for random alloys developed by Kaplan, Leath, Gray, and Diehl is described. This approximation is applicable to diagonal, off-diagonal and environmental disorder, includes cluster scattering, and yields a translationally invariant and analytic (Herglotz) average Green's function. Furthermore Gray and Kaplan have shown that an approximation for alloys with short-range order can be constructed from this theory.
de la Rosa, Stephan; Fademrecht, Laura; Bülthoff, Heinrich H; Giese, Martin A; Curio, Cristóbal
2018-06-01
Motor-based theories of facial expression recognition propose that the visual perception of facial expression is aided by sensorimotor processes that are also used for the production of the same expression. Accordingly, sensorimotor and visual processes should provide congruent emotional information about a facial expression. Here, we report evidence that challenges this view. Specifically, the repeated execution of facial expressions has the opposite effect on the recognition of a subsequent facial expression than the repeated viewing of facial expressions. Moreover, the findings of the motor condition, but not of the visual condition, were correlated with a nonsensory condition in which participants imagined an emotional situation. These results can be well accounted for by the idea that facial expression recognition is not always mediated by motor processes but can also be recognized on visual information alone.
Identification and validation of Asteraceae miRNAs by the expressed sequence tag analysis.
Monavar Feshani, Aboozar; Mohammadi, Saeed; Frazier, Taylor P; Abbasi, Abbas; Abedini, Raha; Karimi Farsad, Laleh; Ehya, Farveh; Salekdeh, Ghasem Hosseini; Mardi, Mohsen
2012-02-10
MicroRNAs (miRNAs) are small non-coding RNA molecules that play a vital role in the regulation of gene expression. Despite their identification in hundreds of plant species, few miRNAs have been identified in the Asteraceae, a large family that comprises approximately one tenth of all flowering plants. In this study, we used the expressed sequence tag (EST) analysis to identify potential conserved miRNAs and their putative target genes in the Asteraceae. We applied quantitative Real-Time PCR (qRT-PCR) to confirm the expression of eight potential miRNAs in Carthamus tinctorius and Helianthus annuus. We also performed qRT-PCR analysis to investigate the differential expression pattern of five newly identified miRNAs during five different cotyledon growth stages in safflower. Using these methods, we successfully identified and characterized 151 potentially conserved miRNAs, belonging to 26 miRNA families, in 11 genus of Asteraceae. EST analysis predicted that the newly identified conserved Asteraceae miRNAs target 130 total protein-coding ESTs in sunflower and safflower, as well as 433 additional target genes in other plant species. We experimentally confirmed the existence of seven predicted miRNAs, (miR156, miR159, miR160, miR162, miR166, miR396, and miR398) in safflower and sunflower seedlings. We also observed that five out of eight miRNAs are differentially expressed during cotyledon development. Our results indicate that miRNAs may be involved in the regulation of gene expression during seed germination and the formation of the cotyledons in the Asteraceae. The findings of this study might ultimately help in the understanding of miRNA-mediated gene regulation in important crop species. Copyright © 2011 Elsevier B.V. All rights reserved.
Finding gene clusters for a replicated time course study
2014-01-01
Background Finding genes that share similar expression patterns across samples is an important question that is frequently asked in high-throughput microarray studies. Traditional clustering algorithms such as K-means clustering and hierarchical clustering base gene clustering directly on the observed measurements and do not take into account the specific experimental design under which the microarray data were collected. A new model-based clustering method, the clustering of regression models method, takes into account the specific design of the microarray study and bases the clustering on how genes are related to sample covariates. It can find useful gene clusters for studies from complicated study designs such as replicated time course studies. Findings In this paper, we applied the clustering of regression models method to data from a time course study of yeast on two genotypes, wild type and YOX1 mutant, each with two technical replicates, and compared the clustering results with K-means clustering. We identified gene clusters that have similar expression patterns in wild type yeast, two of which were missed by K-means clustering. We further identified gene clusters whose expression patterns were changed in YOX1 mutant yeast compared to wild type yeast. Conclusions The clustering of regression models method can be a valuable tool for identifying genes that are coordinately transcribed by a common mechanism. PMID:24460656
A Gaussian Approximation Potential for Silicon
NASA Astrophysics Data System (ADS)
Bernstein, Noam; Bartók, Albert; Kermode, James; Csányi, Gábor
We present an interatomic potential for silicon using the Gaussian Approximation Potential (GAP) approach, which uses the Gaussian process regression method to approximate the reference potential energy surface as a sum of atomic energies. Each atomic energy is approximated as a function of the local environment around the atom, which is described with the smooth overlap of atomic environments (SOAP) descriptor. The potential is fit to a database of energies, forces, and stresses calculated using density functional theory (DFT) on a wide range of configurations from zero and finite temperature simulations. These include crystalline phases, liquid, amorphous, and low coordination structures, and diamond-structure point defects, dislocations, surfaces, and cracks. We compare the results of the potential to DFT calculations, as well as to previously published models including Stillinger-Weber, Tersoff, modified embedded atom method (MEAM), and ReaxFF. We show that it is very accurate as compared to the DFT reference results for a wide range of properties, including low energy bulk phases, liquid structure, as well as point, line, and plane defects in the diamond structure.
Bovine mammary gene expression profiling during the onset of lactation.
Gao, Yuanyuan; Lin, Xueyan; Shi, Kerong; Yan, Zhengui; Wang, Zhonghua
2013-01-01
Lactogenesis includes two stages. Stage I begins a few weeks before parturition. Stage II is initiated around the time of parturition and extends for several days afterwards. To better understand the molecular events underlying these changes, genome-wide gene expression profiling was conducted using digital gene expression (DGE) on bovine mammary tissue at three time points (on approximately day 35 before parturition (-35 d), day 7 before parturition (-7 d) and day 3 after parturition (+3 d)). Approximately 6.2 million (M), 5.8 million (M) and 6.1 million (M) 21-nt cDNA tags were sequenced in the three cDNA libraries (-35 d, -7 d and +3 d), respectively. After aligning to the reference sequences, the three cDNA libraries included 8,662, 8,363 and 8,359 genes, respectively. With a fold change cutoff criteria of ≥ 2 or ≤-2 and a false discovery rate (FDR) of ≤ 0.001, a total of 812 genes were significantly differentially expressed at -7 d compared with -35 d (stage I). Gene ontology analysis showed that those significantly differentially expressed genes were mainly associated with cell cycle, lipid metabolism, immune response and biological adhesion. A total of 1,189 genes were significantly differentially expressed at +3 d compared with -7 d (stage II), and these genes were mainly associated with the immune response and cell cycle. Moreover, there were 1,672 genes significantly differentially expressed at +3 d compared with -35 d. Gene ontology analysis showed that the main differentially expressed genes were those associated with metabolic processes. The results suggest that the mammary gland begins to lactate not only by a gain of function but also by a broad suppression of function to effectively push most of the cell's resources towards lactation.
Sample entropy analysis of cervical neoplasia gene-expression signatures
Botting, Shaleen K; Trzeciakowski, Jerome P; Benoit, Michelle F; Salama, Salama A; Diaz-Arrastia, Concepcion R
2009-01-01
Background We introduce Approximate Entropy as a mathematical method of analysis for microarray data. Approximate entropy is applied here as a method to classify the complex gene expression patterns resultant of a clinical sample set. Since Entropy is a measure of disorder in a system, we believe that by choosing genes which display minimum entropy in normal controls and maximum entropy in the cancerous sample set we will be able to distinguish those genes which display the greatest variability in the cancerous set. Here we describe a method of utilizing Approximate Sample Entropy (ApSE) analysis to identify genes of interest with the highest probability of producing an accurate, predictive, classification model from our data set. Results In the development of a diagnostic gene-expression profile for cervical intraepithelial neoplasia (CIN) and squamous cell carcinoma of the cervix, we identified 208 genes which are unchanging in all normal tissue samples, yet exhibit a random pattern indicative of the genetic instability and heterogeneity of malignant cells. This may be measured in terms of the ApSE when compared to normal tissue. We have validated 10 of these genes on 10 Normal and 20 cancer and CIN3 samples. We report that the predictive value of the sample entropy calculation for these 10 genes of interest is promising (75% sensitivity, 80% specificity for prediction of cervical cancer over CIN3). Conclusion The success of the Approximate Sample Entropy approach in discerning alterations in complexity from biological system with such relatively small sample set, and extracting biologically relevant genes of interest hold great promise. PMID:19232110
Heskes, Tom; Eisinga, Rob; Breitling, Rainer
2014-11-21
The rank product method is a powerful statistical technique for identifying differentially expressed molecules in replicated experiments. A critical issue in molecule selection is accurate calculation of the p-value of the rank product statistic to adequately address multiple testing. Both exact calculation and permutation and gamma approximations have been proposed to determine molecule-level significance. These current approaches have serious drawbacks as they are either computationally burdensome or provide inaccurate estimates in the tail of the p-value distribution. We derive strict lower and upper bounds to the exact p-value along with an accurate approximation that can be used to assess the significance of the rank product statistic in a computationally fast manner. The bounds and the proposed approximation are shown to provide far better accuracy over existing approximate methods in determining tail probabilities, with the slightly conservative upper bound protecting against false positives. We illustrate the proposed method in the context of a recently published analysis on transcriptomic profiling performed in blood. We provide a method to determine upper bounds and accurate approximate p-values of the rank product statistic. The proposed algorithm provides an order of magnitude increase in throughput as compared with current approaches and offers the opportunity to explore new application domains with even larger multiple testing issue. The R code is published in one of the Additional files and is available at http://www.ru.nl/publish/pages/726696/rankprodbounds.zip .
Fermat's Technique of Finding Areas under Curves
ERIC Educational Resources Information Center
Staples, Ed
2004-01-01
Perhaps next time teachers head towards the fundamental theorem of calculus in their classroom, they may wish to consider Fermat's technique of finding expressions for areas under curves, beautifully outlined in Boyer's History of Mathematics. Pierre de Fermat (1601-1665) developed some important results in the journey toward the discovery of the…
Stimulation of GLUT-1 glucose transporter expression in response to hyperosmolarity.
Hwang, D Y; Ismail-Beigi, F
2001-10-01
Glucose transporter isoform-1 (GLUT-1) expression is stimulated in response to stressful conditions. Here we examined the mechanisms mediating the enhanced expression of GLUT-1 by hyperosmolarity. GLUT-1 mRNA, GLUT-1 protein, and glucose transport increased after exposure of Clone 9 cells to 600 mosmol/l (produced by addition of mannitol). The stimulation of glucose transport was biphasic: in the early phase (0-6 h) a approximately 2.5-fold stimulation of glucose uptake was associated with no change in the content of GLUT-1 mRNA, GLUT-1 protein, or GLUT-1 in the plasma membrane, whereas the approximately 17-fold stimulation of glucose transport during the late phase (12-24 h) was associated with increases in both GLUT-1 mRNA (approximately 7.5-fold) and GLUT-1 protein content. Cell sorbitol increased after 3 h of exposure to hyperosmolarity. The increase in GLUT-1 mRNA content was associated with an increase in the half-life of the mRNA from 2 to 8 h. A 44-bp region in the proximal GLUT-1 promoter was necessary for basal activity and for the two- to threefold increases in expression by hyperosmolarity. It is concluded that the increase in GLUT-1 mRNA content is mediated by both enhanced transcription and stabilization of GLUT-1 mRNA and is associated with increases in GLUT-1 content and glucose transport activity.
Statistical evaluation of the influence of the uncertainty budget on B-spline curve approximation
NASA Astrophysics Data System (ADS)
Zhao, Xin; Alkhatib, Hamza; Kargoll, Boris; Neumann, Ingo
2017-12-01
In the field of engineering geodesy, terrestrial laser scanning (TLS) has become a popular method for detecting deformations. This paper analyzes the influence of the uncertainty budget on free-form curves modeled by B-splines. Usually, free-form estimation is based on scanning points assumed to have equal accuracies, which is not realistic. Previous findings demonstrate that the residuals still contain random and systematic uncertainties caused by instrumental, object-related and atmospheric influences. In order to guarantee the quality of derived estimates, it is essential to be aware of all uncertainties and their impact on the estimation. In this paper, a more detailed uncertainty budget is considered, in the context of the "Guide to the Expression of Uncertainty in Measurement" (GUM), which leads to a refined, heteroskedastic variance covariance matrix (VCM) of TLS measurements. Furthermore, the control points of B-spline curves approximating a measured bridge are estimated. Comparisons are made between the estimated B-spline curves using on the one hand a homoskedastic VCM and on the other hand the refined VCM. To assess the statistical significance of the differences displayed by the estimates for the two stochastic models, a nested model misspecification test and a non-nested model selection test are described and applied. The test decisions indicate that the homoskedastic VCM should be replaced by a heteroskedastic VCM in the direction of the suggested VCM. However, the tests also indicate that the considered VCM is still inadequate in light of the given data set and should therefore be improved.
A Discrete Approximation Framework for Hereditary Systems.
1980-05-01
schemes which are included in the general framework and which may be implemented directly on high-speed computing machines are developed. A numerical...an appropriately chosen Hilbert space. We then proceed to develop general approximation schemes for the solutions to the homogeneous AEE which in turn...rich classes of these schemes . In addition, two particular families of approximation schemes included in the general framework are developed and
Spontaneous regulation of emotions in preschool children who stutter: preliminary findings.
Johnson, Kia N; Walden, Tedra A; Conture, Edward G; Karrass, Jan
2010-12-01
Emotional regulation of preschool children who stutter (CWS) and children who do not stutter (CWNS) was assessed through use of a disappointing gift (DG) procedure (P. M. Cole, 1986; C. Saarni, 1984, 1992). Participants consisted of 16 CWS and CWNS (11 boys and 5 girls in each talker group) who were 3 to 5 years of age. After assessing each child's knowledge of display rules about socially appropriate expression of emotions, the authors asked the children to participate in a DG procedure. The children received a desirable gift preceding the first free-play task and a disappointing gift preceding a second free-play task. Dependent variables consisted of participants' positive and negative expressive nonverbal behaviors exhibited during receipt of a desirable gift and disappointing gift as well as conversational speech disfluencies exhibited following receipt of each gift. Findings indicated that CWS and CWNS exhibited no significant differences in amount of positive emotional expressions after receiving the desired gift; however, CWS--when compared with CWNS--exhibited more negative emotional expressions after receiving the undesirable gift. Furthermore, CWS were more disfluent after receiving the desired gift than after receiving the disappointing gift. Ancillary findings also indicated that CWS and CWNS had equivalent knowledge of display rules. Findings suggest that efforts to concurrently regulate emotional behaviors and that speech disfluencies may be problematic for preschool-age CWS.
Positive facial expressions during retrieval of self-defining memories.
Gandolphe, Marie Charlotte; Nandrino, Jean Louis; Delelis, Gérald; Ducro, Claire; Lavallee, Audrey; Saloppe, Xavier; Moustafa, Ahmed A; El Haj, Mohamad
2017-11-14
In this study, we investigated, for the first time, facial expressions during the retrieval of Self-defining memories (i.e., those vivid and emotionally intense memories of enduring concerns or unresolved conflicts). Participants self-rated the emotional valence of their Self-defining memories and autobiographical retrieval was analyzed with a facial analysis software. This software (Facereader) synthesizes the facial expression information (i.e., cheek, lips, muscles, eyebrow muscles) to describe and categorize facial expressions (i.e., neutral, happy, sad, surprised, angry, scared, and disgusted facial expressions). We found that participants showed more emotional than neutral facial expressions during the retrieval of Self-defining memories. We also found that participants showed more positive than negative facial expressions during the retrieval of Self-defining memories. Interestingly, participants attributed positive valence to the retrieved memories. These findings are the first to demonstrate the consistency between facial expressions and the emotional subjective experience of Self-defining memories. These findings provide valuable physiological information about the emotional experience of the past.
Smith, J. C.; Pribram-Jones, A.; Burke, K.
2016-06-14
Thermal density functional theory calculations often use the Mermin-Kohn-Sham scheme, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable nontrivial model, an asymmetric Hubbard dimer, we calculate the exact many-body energies and the exact Mermin-Kohn-Sham functionals for this system and extract the exact XC free energy. For moderate temperatures and weak correlation, we find this approximation to be excellent. Here we extract various exact free-energy correlation components and the exact adiabatic connection formula.
DOE Office of Scientific and Technical Information (OSTI.GOV)
Smith, J. C.; Pribram-Jones, A.; Burke, K.
Thermal density functional theory calculations often use the Mermin-Kohn-Sham scheme, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable nontrivial model, an asymmetric Hubbard dimer, we calculate the exact many-body energies and the exact Mermin-Kohn-Sham functionals for this system and extract the exact XC free energy. For moderate temperatures and weak correlation, we find this approximation to be excellent. Here we extract various exact free-energy correlation components and the exact adiabatic connection formula.
Jiang, Jinjin; Wang, Yue; Zhu, Bao; Fang, Tingting; Fang, Yujie; Wang, Youping
2015-01-27
Brassica includes many successfully cultivated crop species of polyploid origin, either by ancestral genome triplication or by hybridization between two diploid progenitors, displaying complex repetitive sequences and transposons. The U's triangle, which consists of three diploids and three amphidiploids, is optimal for the analysis of complicated genomes after polyploidization. Next-generation sequencing enables the transcriptome profiling of polyploids on a global scale. We examined the gene expression patterns of three diploids (Brassica rapa, B. nigra, and B. oleracea) and three amphidiploids (B. napus, B. juncea, and B. carinata) via digital gene expression analysis. In total, the libraries generated between 5.7 and 6.1 million raw reads, and the clean tags of each library were mapped to 18547-21995 genes of B. rapa genome. The unambiguous tag-mapped genes in the libraries were compared. Moreover, the majority of differentially expressed genes (DEGs) were explored among diploids as well as between diploids and amphidiploids. Gene ontological analysis was performed to functionally categorize these DEGs into different classes. The Kyoto Encyclopedia of Genes and Genomes analysis was performed to assign these DEGs into approximately 120 pathways, among which the metabolic pathway, biosynthesis of secondary metabolites, and peroxisomal pathway were enriched. The non-additive genes in Brassica amphidiploids were analyzed, and the results indicated that orthologous genes in polyploids are frequently expressed in a non-additive pattern. Methyltransferase genes showed differential expression pattern in Brassica species. Our results provided an understanding of the transcriptome complexity of natural Brassica species. The gene expression changes in diploids and allopolyploids may help elucidate the morphological and physiological differences among Brassica species.
Approximating the Helium Wavefunction in Positronium-Helium Scattering
NASA Technical Reports Server (NTRS)
DiRienzi, Joseph; Drachman, Richard J.
2003-01-01
In the Kohn variational treatment of the positronium- hydrogen scattering problem the scattering wave function is approximated by an expansion in some appropriate basis set, but the target and projectile wave functions are known exactly. In the positronium-helium case, however, a difficulty immediately arises in that the wave function of the helium target atom is not known exactly, and there are several ways to deal with the associated eigenvalue in formulating the variational scattering equations to be solved. In this work we will use the Kohn variational principle in the static exchange approximation to d e t e e the zero-energy scattering length for the Ps-He system, using a suite of approximate target functions. The results we obtain will be compared with each other and with corresponding values found by other approximation techniques.
Minimax rational approximation of the Fermi-Dirac distribution.
Moussa, Jonathan E
2016-10-28
Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(ϵ -1 )) poles to achieve an error tolerance ϵ at temperature β -1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δ occ , the occupied energy interval. This is particularly beneficial when Δ ≫ Δ occ , such as in electronic structure calculations that use a large basis set.
Minimax rational approximation of the Fermi-Dirac distribution
NASA Astrophysics Data System (ADS)
Moussa, Jonathan E.
2016-10-01
Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(ɛ-1)) poles to achieve an error tolerance ɛ at temperature β-1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δocc, the occupied energy interval. This is particularly beneficial when Δ ≫ Δocc, such as in electronic structure calculations that use a large basis set.
Analytical approximations for effective relative permeability in the capillary limit
NASA Astrophysics Data System (ADS)
Rabinovich, Avinoam; Li, Boxiao; Durlofsky, Louis J.
2016-10-01
We present an analytical method for calculating two-phase effective relative permeability, krjeff, where j designates phase (here CO2 and water), under steady state and capillary-limit assumptions. These effective relative permeabilities may be applied in experimental settings and for upscaling in the context of numerical flow simulations, e.g., for CO2 storage. An exact solution for effective absolute permeability, keff, in two-dimensional log-normally distributed isotropic permeability (k) fields is the geometric mean. We show that this does not hold for krjeff since log normality is not maintained in the capillary-limit phase permeability field (Kj=k·krj) when capillary pressure, and thus the saturation field, is varied. Nevertheless, the geometric mean is still shown to be suitable for approximating krjeff when the variance of lnk is low. For high-variance cases, we apply a correction to the geometric average gas effective relative permeability using a Winsorized mean, which neglects large and small Kj values symmetrically. The analytical method is extended to anisotropically correlated log-normal permeability fields using power law averaging. In these cases, the Winsorized mean treatment is applied to the gas curves for cases described by negative power law exponents (flow across incomplete layers). The accuracy of our analytical expressions for krjeff is demonstrated through extensive numerical tests, using low-variance and high-variance permeability realizations with a range of correlation structures. We also present integral expressions for geometric-mean and power law average krjeff for the systems considered, which enable derivation of closed-form series solutions for krjeff without generating permeability realizations.
Women process multisensory emotion expressions more efficiently than men.
Collignon, O; Girard, S; Gosselin, F; Saint-Amour, D; Lepore, F; Lassonde, M
2010-01-01
Despite claims in the popular press, experiments investigating whether female are more efficient than male observers at processing expression of emotions produced inconsistent findings. In the present study, participants were asked to categorize fear and disgust expressions displayed auditorily, visually, or audio-visually. Results revealed an advantage of women in all the conditions of stimulus presentation. We also observed more nonlinear probabilistic summation in the bimodal conditions in female than male observers, indicating greater neural integration of different sensory-emotional informations. These findings indicate robust differences between genders in the multisensory perception of emotion expression.
Mustroph, Heinz
2016-09-05
The concept of a potential-energy surface (PES) is central to our understanding of spectroscopy, photochemistry, and chemical kinetics. However, the terminology used in connection with the basic approximations is variously, and somewhat confusingly, represented with such phrases as "adiabatic", "Born-Oppenheimer", or "Born-Oppenheimer adiabatic" approximation. Concerning the closely relevant and important Franck-Condon principle (FCP), the IUPAC definition differentiates between a classical and quantum mechanical formulation. Consequently, in many publications we find terms such as "Franck-Condon (excited) state", or a vertical transition to the "Franck-Condon point" with the "Franck-Condon geometry" that relaxes to the excited-state equilibrium geometry. The Born-Oppenheimer approximation and the "classical" model of the Franck-Condon principle are typical examples of misused terms and lax interpretations of the original theories. In this essay, we revisit the original publications of pioneers of the PES concept and the FCP to help stimulate a lively discussion and clearer thinking around these important concepts. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Fisher, Charles K; Mehta, Pankaj
2015-06-01
Feature selection, identifying a subset of variables that are relevant for predicting a response, is an important and challenging component of many methods in statistics and machine learning. Feature selection is especially difficult and computationally intensive when the number of variables approaches or exceeds the number of samples, as is often the case for many genomic datasets. Here, we introduce a new approach--the Bayesian Ising Approximation (BIA)-to rapidly calculate posterior probabilities for feature relevance in L2 penalized linear regression. In the regime where the regression problem is strongly regularized by the prior, we show that computing the marginal posterior probabilities for features is equivalent to computing the magnetizations of an Ising model with weak couplings. Using a mean field approximation, we show it is possible to rapidly compute the feature selection path described by the posterior probabilities as a function of the L2 penalty. We present simulations and analytical results illustrating the accuracy of the BIA on some simple regression problems. Finally, we demonstrate the applicability of the BIA to high-dimensional regression by analyzing a gene expression dataset with nearly 30 000 features. These results also highlight the impact of correlations between features on Bayesian feature selection. An implementation of the BIA in C++, along with data for reproducing our gene expression analyses, are freely available at http://physics.bu.edu/∼pankajm/BIACode. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.
Multilayer neural networks for reduced-rank approximation.
Diamantaras, K I; Kung, S Y
1994-01-01
This paper is developed in two parts. First, the authors formulate the solution to the general reduced-rank linear approximation problem relaxing the invertibility assumption of the input autocorrelation matrix used by previous authors. The authors' treatment unifies linear regression, Wiener filtering, full rank approximation, auto-association networks, SVD and principal component analysis (PCA) as special cases. The authors' analysis also shows that two-layer linear neural networks with reduced number of hidden units, trained with the least-squares error criterion, produce weights that correspond to the generalized singular value decomposition of the input-teacher cross-correlation matrix and the input data matrix. As a corollary the linear two-layer backpropagation model with reduced hidden layer extracts an arbitrary linear combination of the generalized singular vector components. Second, the authors investigate artificial neural network models for the solution of the related generalized eigenvalue problem. By introducing and utilizing the extended concept of deflation (originally proposed for the standard eigenvalue problem) the authors are able to find that a sequential version of linear BP can extract the exact generalized eigenvector components. The advantage of this approach is that it's easier to update the model structure by adding one more unit or pruning one or more units when the application requires it. An alternative approach for extracting the exact components is to use a set of lateral connections among the hidden units trained in such a way as to enforce orthogonality among the upper- and lower-layer weights. The authors call this the lateral orthogonalization network (LON) and show via theoretical analysis-and verify via simulation-that the network extracts the desired components. The advantage of the LON-based model is that it can be applied in a parallel fashion so that the components are extracted concurrently. Finally, the authors show the
On direct theorems for best polynomial approximation
NASA Astrophysics Data System (ADS)
Auad, A. A.; AbdulJabbar, R. S.
2018-05-01
This paper is to obtain similarity for the best approximation degree of functions, which are unbounded in L p,α (A = [0,1]), which called weighted space by algebraic polynomials. {E}nH{(f)}p,α and the best approximation degree in the same space on the interval [0,2π] by trigonometric polynomials {E}nT{(f)}p,α of direct wellknown theorems in forms the average modules.
Background magnetic spectra - Approximately 10 to the -5th to approximately 10 to the 5th Hz
NASA Astrophysics Data System (ADS)
Lanzerotti, L. J.; Maclennan, C. G.; Fraser-Smith, A. C.
1990-09-01
The determination of the amplitude and functional form of the geomagnetic fluctuations measured at the Arrival Heights area of the Hut Point Peninsula on Ross Island in June 1986 is presented. The frequency range covered is from approximately 10 to the -5th to approximately 10 to the 5th Hz, with a gap between 0.1 and 10 Hz due to instrumentation limitations. In spite of this gap, it is thought that these magnetic fluctuation spectra, obtained from data acquired simultaneously with two instruments, cover the broadest frequency range to date. Schematic spectra derived from the data obtained are provided.
Lambert, Nathaniel M; Clark, Margaret S; Durtschi, Jared; Fincham, Frank D; Graham, Steven M
2010-04-01
This research was conducted to examine the hypothesis that expressing gratitude to a relationship partner enhances one's perception of the relationship's communal strength. In Study 1 (N = 137), a cross-sectional survey, expressing gratitude to a relationship partner was positively associated with the expresser's perception of the communal strength of the relationship. In Study 2 (N = 218), expressing gratitude predicted increases in the expresser's perceptions of the communal strength of the relationship across time. In Study 3 (N = 75), participants were randomly assigned to an experimental condition, in which they expressed gratitude to a friend, or to one of three control conditions, in which they thought grateful thoughts about a friend, thought about daily activities, or had positive interactions with a friend. At the end of the study, perceived communal strength was higher among participants in the expression-of-gratitude condition than among those in all three control conditions. We discuss the theoretical and applied implications of these findings and suggest directions for future research.
Valiente, Carlos; Eisenberg, Nancy; Shepard, Stephanie A.; Fabes, Richard A.; Cumberland, Amanda J.; Losoya, Sandra H.; Spinrad, Tracy L.
2010-01-01
Guided by the heuristic model proposed by Eisenberg et al. [Psychol. Inq. 9 (1998) 241], we examined the relations of mothers’ reported and observed negative expressivity to children’s (N = 159; 74 girls; M age = 7.67 years) experience and expression of emotion. Children’s experience and/or expression of emotion in response to a distressing film were measured with facial, heart rate, and self-report measures. Children’s heart rate and facial distress were modestly positively related. Children’s facial distress was significantly positively related to mothers’ reports of negative (dominant and submissive) expressivity; the positive relation between children’s facial distress and mothers’ observed negative expressivity approached the conventional level of significance. Moreover, mothers’ observed negative expressivity was significantly negatively related to children’s heart rate reactivity during the conflict film. The positive relation between children’s reported distress and mothers’ observed negative expressivity approached the conventional level of significance. Several possible explanations for the pattern of findings are discussed. PMID:20617103