α-cluster asymptotic normalization coefficients for nuclear astrophysics
Avila, M. L.; Rogachev, G. V.; Koshchiy, E.; Baby, L. T.; Belarge, J.; Kemper, K. W.; Kuchera, A. N.; Santiago-Gonzalez, D.
2014-10-01
Background: Many important α-particle induced reactions for nuclear astrophysics may only be measured using indirect techniques due to the small cross sections at the energy of interest. One such indirect technique is to determine the asymptotic normalization coefficients (ANCs) for near-threshold resonances extracted from sub-Coulomb α-transfer reactions. This approach provides a very valuable tool for studies of astrophysically important reaction rates since the results are practically model independent. However, the validity of the method has not been directly verified. Purpose: The aim of this Rapid Communication is to verify the technique using the O16(Li6,d)Ne20 reaction as a benchmark. The Ne20 nucleus has a well-known 1- state at an excitation energy of 5.79 MeV with a width of 28 eV. Reproducing the known value with this technique is an ideal opportunity to verify the method. Method: The 1- state at 5.79 MeV is studied using the α-transfer reaction O16(Li6,d)Ne20 at sub-Coulomb energies. Results: The partial α width for the 1- state at excitation energy of 5.79 MeV is extracted and compared with the known value, allowing the accuracy of the method to be evaluated. Conclusions: This study demonstrates that extracting the ANCs using sub-Coulomb α-transfer reactions is a powerful tool that can be used to determine the partial α width of near-threshold states that may dominate astrophysically important nuclear reaction rates.
Yarmukhamedov, R. [Institute of Nuclear Physics, Academy of Sciences of Uzbekistan, 100214 Tashkent (Uzbekistan)
2014-05-09
The basic methods of the determination of asymptotic normalization coefficient for A+a→B of astrophysical interest are briefly presented. The results of the application of the specific asymptotic normalization coefficients derived within these methods for the extrapolation of the astrophysical S factors to experimentally inaccessible energy regions (E ≤ 25 keV) for the some specific radiative capture A(a,γ)B reactions of the pp-chain and the CNO cycle are presented.
Indirect Techniques in Nuclear Astrophysics. Asymptotic Normalization Coefficient and Trojan Horse
Mukhamedzhanov, A.M. [Cyclotron Institute, Texas A and M University, College Station, TX, 77843 (United States); Blokhintsev, L.D. [Institute of Nuclear Physics, Moscow State University, Moscow (Russian Federation); Brown, S. [Florida State University, Tallahassee, FL (United States)] (and others)
2007-05-01
We address two important indirect techniques, the asymptotic normalization coefficient (ANC) and the Trojan Horse (TH) methods. We discuss the application of the ANC technique to determine the astrophysical factor for the {sup 13}C({alpha}, n){sup 16}O reaction which is one of the neutron generators for the s processes in AGB stars. The TH method is a unique indirect technique allowing one to measure astrophysical S factors for rearrangement reactions down to astrophysically relevant energies. We derive equations connecting the cross sections for the binary direct and resonant reactions determined from the indirect TH reactions to direct cross sections measurements.
Indirect techniques in nuclear astrophysics. Asymptotic Normalization Coefficient and Trojan Horse
Mukhamedzhanov, A M; Brown, B A; Burjan, V; Cherubini, S; Gagliardi, C A; Irgaziev, B F; Kroha, V; Nunes, F M; Pirlepesov, F; Pizzone, R G; Romano, S; Spitaleri, C; Tang, X D; Trache, L; Tribble, R E; Tumino, A
2005-01-01
Owing to the presence of the Coulomb barrier at astrophysically relevant kinetic energies it is very difficult, or sometimes impossible, to measure astrophysical reaction rates in the laboratory. That is why different indirect techniques are being used along with direct measurements. Here we address two important indirect techniques, the asymptotic normalization coefficient (ANC) and the Trojan Horse (TH) methods. We discuss the application of the ANC technique for calculation of the astrophysical processes in the presence of subthreshold bound states, in particular, two different mechanisms are discussed: direct capture to the subthreshold state and capture to the low-lying bound states through the subthreshold state, which plays the role of the subthreshold resonance. The ANC technique can also be used to determine the interference sign of the resonant and nonresonant (direct) terms of the reaction amplitude. The TH method is unique indirect technique allowing one to measure astrophysical rearrangement reac...
Full text: A reliable estimation of rates of nuclear astrophysical radiative cupture reaction A(a,γ)B responsible for the abundance of the light elements B in the Universe is one of the most important problems of the modern astrophysics (1). Solution of this problem in its turn is impossible without obtaining the cross sections (or their equivalent the astrophysical S(E) factors for the reactions under consideration. In this report the review of the results of calculations of the astrophysical S- factors S(E) for the t(α,γ )7Li, 3He( α,γ )7Be, 7Be(p,γ )8B, 12C(p, γ )13N and 13C(p, γ )14N reactions at extremely low energies E, including value E=0, performed within the framework of the new two -body approach and the R-matrix method are presented. The calculation is carried out taking into account the information about the asymptotic normalization coefficient (or the respective nuclear vertex constant of virtual decay of the residual nuclei into two fragments of the initial states of the aforesaid reactions , which belong to the fundamental nuclear constants). The required values of the asymptotic normalization coefficients can be obtained from an analysis of both the same direct cupture reactions performed within the modified two-body approach and the peripheral proton transfer reactions performed within the framework DWBA approach. A comparative analysis between the experimental and theoretical results obtained by different authors is also done. (author)
Nuclear asymptotic normalization coefficients and neutron halo of the excited states
The authors have extracted the nuclear asymptotic normalization coefficients for the virtual transitions 12B ↔ 11B + n and 13C ↔12C + n via two transfer reactions 11B(d, p)12B and 12C(d, p)13C. With these coefficients, root-mean-square radii for the valence neutron in 12B and 13C have been calculated. Authors' results show that the second (Jπ = 2-), third (Jπ = 1-) excited states in 12B, and the first (Jπ = 1/2+) excited state in 13C are neutron halo states, whereas the third (Jπ = 5/2+) excited state in 13C is a neutron skin state. The retard effects of the Coulomb potential and the orbital angular momentum on halo formation have been quantitatively examined. A unified scaling law for the mean-square radius versus the effective nucleon separation energy is established for the systems with a neutron or proton in a weekly bound state
Extraction of the rms Radii of 13C from Asymptotic Normalization Coefficients
林承键; 刘祖华; 张焕乔; 吴岳伟; 杨峰; 阮明
2001-01-01
The asymptotic normalization coefficients (ANCs) for three bound states of 13C (12 C+n) are extracted from the angular distributions of 12C(d,p) reactions at E1ab = 11.8MeV. With these ANCs, the calculated root-meansquare (rms) radii of these three states agree with our previous results. The ANCs are 1.93±0.17, 1.84±0.16and 0.149±0.012fm-1/2, and the rms radii 〈r2〉1/2 are 3.39±0.31, 5.04±0.75 and 3.68±0.40fm for the ground state, the first and third excitation states, respectively. Further analyses show that the first excitation state with D1=50.3% is a true neutron halo state, while the third excitation state with D1=25.2% is a neutron skin state.
Indirect techniques in nuclear astrophysics. Asymptotic normalization coefficient and trojan horse
Mukhamedzhanov, A.M.; Gagliardi, C.A.; Pirlepesov, F.; Trache, L.; Tribble, R.E. [Texas A and M University, Cyclotron Institute, College Station, TX (United States); Blokhintsev, L.D. [Moscow State University, Institute of Nuclear Physics, Moscow (Russian Federation); Brown, B.A.; Nunes, F.M. [Michigan State University, N.S.C.L. and Department of Physics and Astronomy, East Lansing, MI (United States); Burjan, V.; Kroha, V. [Nuclear Physics Institute of Czech Academy of Sciences, Prague-Rez (Czech Republic); Cherubini, S.; Pizzone, R.G.; Romano, S.; Spitaleri, C.; Tumino, A. [DMFCI, Universita di Catania, Catania, Italy and INFN, Laboratori Nazionali del Sud, Catania (Italy); Irgaziev, B.F. [National University, Physics Department, Tashkent (Uzbekistan); Tang, X.D. [Argonne National Laboratory, Physics Division, Argonne, IL (United States)
2006-03-15
Owing to the presence of the Coulomb barrier at astrophysically relevant kinetic energies it is very difficult, or sometimes impossible, to measure astrophysical reaction rates in the laboratory. That is why different indirect techniques are being used along with direct measurements. Here we address two important indirect techniques, the asymptotic normalization coefficient (ANC) and the Trojan Horse (TH) methods. We discuss the application of the ANC technique for calculation of the astrophysical processes in the presence of subthreshold bound states, in particular, two different mechanisms are discussed: direct capture to the subthreshold state and capture to the low-lying bound states through the subthreshold state, which plays the role of the subthreshold resonance. The ANC technique can also be used to determine the interference sign of the resonant and nonresonant (direct) terms of the reaction amplitude. The TH method is unique indirect technique allowing one to measure astrophysical rearrangement reactions down to astrophysically relevant energies. We explain why there is no Coulomb barrier in the sub-process amplitudes extracted from the TH reaction. The expressions for the TH amplitude for direct and resonant cases are presented. (orig.)
Asymptotic properties of order statistics correlation coefficient in the normal cases
Xu, W; Chang, C.; Hung, YS; Fung, PCW
2008-01-01
We have previously proposed a novel order statistics correlation coefficient (OSCC), which possesses some desirable advantages when measuring linear and monotone nonlinear associations between two signals. However, the understanding of this new coefficient is far from complete. A lot of theoretical questions, such as the expressions of its distribution and moments, remain to be addressed. Motivated by this unsatisfactory situation, in this paper we prove that for samples drawn from bivariate ...
Full text: It is interesting to obtain values of asymptotical normalization coefficients (ANC) of overlapping functions for a few first levels of bound state of nuclei 14N and 20Ne for calculation of astrophysical S-factors of radiative proton capture 13C(p,γ )14N and 19F(p,γ )20Ne. For this purpose the differential cross sections of the reaction 19F(3He,d20Ne at projectile beam of 3He with energy of 22.3 MeV measured at angels of forward hemisphere and cross sections of reaction 13C(3He,d)14N at region of main stripping peak have been analyzed. The experimental values are taken from our earlier work [1]. At that work the role of coupling channels and contribution of peripheral processes into the amplitude of the reaction were analyzed. In present work in frame of modified DWBA [2, 3] empirical values of ANC of proton binding have been obtained. In frame of EPN [4, 5] method the values of asymptotical coefficients b of bound state function for bindings 14N->13C+p and 20Ne->19F+ p for a few first levels have been calculated. With the values of ANC and b the empirical values of spectroscopic factors have been calculated. The theoretical values of ANC corresponding shell model were calculated with the theoretical values of spectroscopic factors known from literature. Some comparative analysis is made. An opportunity of using the data for estimation of contribution of direct processes into cross section of radiative proton capture is discussed. The work is supported by grant Uzbek Acad. Sci. No 5-04
WU Kai-Su; CHEN Yong-Shou; LIU Zu-Hua; LIN Cheng-Jian; ZHANG Huan-Qiao
2003-01-01
The cross section of the direct neutron capture reaction 12C(n,7)13C(l/2+) is calculated with the asymptotic normalization coefficient method. The result is in good agreement with a recent experiment at low energy. An enormous enhancement of cross section is found for this direct neutron capture in which a p-wave neutron is captured into an 2?i/2 orbit with neutron halo. The possible effect of the neutron halo structure presented in this reaction on the s-process in astrophysics is discussed in general.
McCleskey, M.; Mukhamedzhanov, A. M.; Trache, L.; Tribble, R. E.; Banu, A.; Eremenko, V.; Goldberg, V. Z.; Lui, Y. W.; McCleskey, E.; Roeder, B. T.; Spiridon, A.; Carstoiu, F.; Burjan, Václav; Hons, Zdeněk; Thompson, I. J.
2014-01-01
Roč. 89, č. 4 (2014), 044605. ISSN 0556-2813 R&D Projects: GA MŠk(CZ) LH11001 Institutional support: RVO:61389005 Keywords : capture reactions * cross-section * asymptotic normalization coefficient Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 3.733, year: 2014
Asymptotic mean and variance of gini correlation for bivariate normal samples
Xu, W.; Hung, YS; Niranjan, M.; Shen, M
2010-01-01
This paper derives the asymptotic analytical forms of the mean and variance of the Gini correlation (GC) with respect to samples drawn from bivariate normal populations. The asymptotic relative efficiency (ARE) of the Gini correlation to Pearson's product moment correlation coefficient (PPMCC) is investigated under the normal assumptions. To gain further insight into GC, we also compare the Gini correlation to other two closely related correlation coefficients, namely, the order statistics co...
Generalized heat kernel coefficients for a new asymptotic expansion
The method which allows for asymptotic expansion of the one-loop effective action W = lndetA is formulated. The positively defined elliptic operator A = U + M2 depends on the external classical fields taking values in the Lie algebra of the internal symmetry group G. Unlike the standard method of Schwinger - DeWitt, the more general case with the nongenerate mass matrix M = diag(m1, m2, ...) is considered. The first coefficients of the new asymptotic series are calculated and their relationship with the Seeley - DeWitt coefficients is clarified
Uniform asymptotics of the coefficients of unitary moment polynomials
Hiary, Ghaith A
2010-01-01
Keating and Snaith showed that the $2k^{th}$ absolute moment of the characteristic polynomial of a random unitary matrix evaluated on the unit circle is given by a polynomial of degree $k^2$. In this article, uniform asymptotics for the coefficients of that polynomial are derived, and a maximal coefficient is located. Some of the asymptotics are given in explicit form. Numerical data to support these calculations are presented. Some apparent connections between random matrix theory and the Riemann zeta function are discussed.
Avila, M L; Koshchiy, E; Baby, L T; Belarge, J; Kemper, K W; Kuchera, A N; Mukhamedzhanov, A M; Santiago-Gonzalez, D; Uberseder, E
2014-01-01
Background. The $^{12}$C($\\alpha,\\gamma$)$^{16}$O reaction plays a fundamental role in astrophysics because its cross section near 300 keV in c.m. determines the $^{12}$C/$^{16}$O ratio at the end of the helium burning stage of stellar evolution. The astrophysically desired accuracy of better than 10\\% has not been achieved. Cascade $\\gamma$ transitions through the excited states of $^{16}$O are contributing to the uncertainty. Purpose. To measure the Asymptotic Normalization Coefficients (ANCs) for the 0$^+$ (6.05 MeV) and 3$^-$ (6.13 MeV) excited states in $^{16}$O and provide constraints on the cross section for the corresponding cascade transitions. Method. The ANCs were measured using the $\\alpha$-transfer reaction $^{12}$C($^6$Li,$d$)$^{16}$O performed at sub-Coulomb energies for both the entrance and exit channels. Results. The ANCs for the 0$^+$(6.05 MeV), 3$^-$(6.13 MeV), 2$^+$(6.92 MeV) and 1$^-$(7.12 MeV) states in $^{16}$O have been measured. The contribution of the 0$^+$ and 3$^-$ cascade transit...
Asymptotic results for bifurcating random coefficient autoregressive processes
Blandin, Vassili
2012-01-01
The purpose of this paper is to study the asymptotic behavior of the weighted least square estimators of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on the immigration and the inheritance, we establish the almost sure convergence of our estimators, as well as a quadratic strong law and central limit theorems. Our study mostly relies on limit theorems for vector-valued martingales.
Asymptotic normality through factorial cumulants and partitions identities
Bobecka, Konstancja; Lopez-Blazquez, Fernando; Rempala, Grzegorz; Wesolowski, Jacek
2011-01-01
In the paper we develop an approach to asymptotic normality through factorial cumulants. Factorial cumulants arise in the same manner from factorial moments, as (ordinary) cumulants from (ordinary) moments. Another tool we exploit is a new identity for "moments" of partitions of numbers. The general limiting result is then used to (re)derive asymptotic normality for several models including classical discrete distributions, occupancy problems in some generalized allocation schemes and two models related to negative multinomial distribution.
Molzon, Raymond; Pinelis, Iosif
2009-01-01
Pearson's is the most common correlation statistic, used mainly in parametric settings. Most common among nonparametric correlation statistics are Spearman's and Kendall's. We show that for bivariate normal i.i.d. samples the pairwise asymptotic relative efficiency between these three statistics depends monotonically on the population correlation coefficient. This monotonicity is a corollary to a stronger result. The proofs rely on the use of l'Hospital-type rules for monotonicity patterns.
Li-qun Cao; De-chao Zhu; Jian-Lan Luo
2002-01-01
In this paper, we will discuss the asymptotic behaviour for a class of hyper bolic -parabolic type equation with highly oscillatory coefficients arising from the strong-transient heat and mass transfer problems of composite media. A complete multiscale asymptotic expansion and its rigorous verification will be reported.
McCleskey, M; Mukhamedzhanov, A M; Trache, L; Tribble, R E; Banu, A; Eremenko, V; Goldberg, V Z; Lui, Y W; McCleskey, E; Roeder, B T; Spiridon, A; Carstoiu, F; Burjan, V; Hons, Z; Thompson, I J
2014-04-17
The ^{14}C + n <--> ^{15}C system has been used as a test case in the evaluation of a new method to determine spectroscopic factors that uses the asymptotic normalization coefficient (ANC). The method proved to be unsuccessful for this case. As part of this experimental program, the ANCs for the ^{15}C ground state and first excited state were determined using a heavy-ion neutron transfer reaction as well as the inverse kinematics (d,p) reaction, measured at the Texas A&M Cyclotron Institute. The ANCs were used to evaluate the astrophysical direct neutron capture rate on ^{14}C, which was then compared with the most recent direct measurement and found to be in good agreement. A study of the ^{15}C SF via its mirror nucleus ^{15}F and a new insight into deuteron stripping theory are also presented.
Asymptotic Behavior of a Competition-Diffusion System with Variable Coefficients and Time Delays
Miguel Uh Zapata; Eric Avila Vales; Angel G. Estrella
2008-01-01
A class of time-delay reaction-diffusion systems with variable coefficients which arise from the model of two competing ecological species is discussed. An asymptotic global attractor is established in terms of the variable coefficients, independent of the time delays and the effect of diffusion by the upper-lower solutions and iteration method.
Asymptotic behavior for a dissipative plate equation in $R^N$ with periodic coefficients
Eleni Bisognin
2008-03-01
Full Text Available In this work we study the asymptotic behavior of solutions of a dissipative plate equation in $mathbb{R}^N$ with periodic coefficients. We use the Bloch waves decomposition and a convenient Lyapunov function to derive a complete asymptotic expansion of solutions as $to infty$. In a first approximation, we prove that the solutions for the linear model behave as the homogenized heat kernel.
Asymptotically Median Unbiased Estimation of Coefficient Variance in a Time Varying Parameter Model
Stock, James H.; Mark W. Watson
1996-01-01
This paper considers the estimation of the variance of coefficients in time varying parameter models with stationary regressors. The maximum likelihood estimator has large point mass at zero. We therefore develop asymptotically median unbiased estimators and confidence intervals by inverting median functions of regression-based parameter stability test statistics, computed under the constant-parameter null. These estimators have good asymptotic relative efficiencies for small to moderate amou...
Asymptotic Normality of LS Estimate in Simple Linear EV Regression Model
Jixue LIU
2006-01-01
Though EV model is theoretically more appropriate for applications in which measurement errors exist, people are still more inclined to use the ordinary regression models and the traditional LS method owing to the difficulties of statistical inference and computation. So it is meaningful to study the performance of LS estimate in EV model.In this article we obtain general conditions guaranteeing the asymptotic normality of the estimates of regression coefficients in the linear EV model. It is noticeable that the result is in some way different from the corresponding result in the ordinary regression model.
Zhang, Zhengjun; Qi, Yongcheng; Ma, Xiwen
2011-01-01
This paper first proves that the sample based Pearson’s product-moment correlation coefficient and the quotient correlation coefficient are asymptotically independent, which is a very important property as it shows that these two correlation coefficients measure completely different dependencies between two random variables, and they can be very useful if they are simultaneously applied to data analysis. Motivated from this fact, the paper introduces a new way of combining these two sample ba...
A simple approximation to the bivariate normal distribution with large correlation coefficient
Albers, Willem; Kallenberg, Wilbert C.M.
1994-01-01
The bivariate normal distribution function is approximated with emphasis on situations where the correlation coefficient is large. The high accuracy of the approximation is illustrated by numerical examples. Moreover, exact upper and lower bounds are presented as well as asymptotic results on the error terms.
Tian, Jianxiang; Mulero, A
2016-01-01
Despite the fact that more that more than 30 analytical expressions for the equation of state of hard-disk fluids have been proposed in the literature, none of them is capable of reproducing the currently accepted numeric or estimated values for the first eighteen virial coefficients. Using the asymptotic expansion method, extended to the first ten virial coefficients for hard-disk fluids, fifty-seven new expressions for the equation of state have been studied. Of these, a new equation of state is selected which reproduces accurately all the first eighteen virial coefficients. Comparisons for the compressibility factor with computer simulations show that this new equation is as accurate as other similar expressions with the same number of parameters. Finally, the location of the poles of the 57 new equations shows that there are some particular configurations which could give both the accurate virial coefficients and the correct closest packing fraction in the future when higher virial coefficients than the t...
Rubao Ma; Weichao Xu; Yun Zhang; Zhongfu Ye
2014-01-01
This paper investigates the robustness properties of Pearson's rank-variate correlation coefficient (PRVCC) in scenarios where one channel is corrupted by impulsive noise and the other is impulsive noise-free. As shown in our previous work, these scenarios that frequently encountered in radar and/or sonar, can be well emulated by a particular bivariate contaminated Gaussian model (CGM). Under this CGM, we establish the asymptotic closed forms of the expectation and variance of PRVCC by means ...
Neerven, W L; Matiounine, Y; Smith, J; Migneron, R
1996-01-01
Using renormalization group techniques we have derived analytic formulae for the next-to-leading order heavy-quark coefficient functions in deep inelastic lepton hadron scattering. These formulae are only valid in the kinematic regime Q^2 >> m^2, where Q^2 and m^2 stand for the masses squared of the virtual photon and heavy quark respectively. Some of the applications of these asymptotic formulae will be discussed.
Heavy quark coefficient functions at asymptotic values Q$^{2}$ $>$ m$^{2}$
Buza, M; Smith, J; Migneron, R; van Neerven, W L
1996-01-01
In this paper we present the analytic form of the heavy-quark coefficient functions for deep-inelastic lepton-hadron scattering in the kinematical regime Q^2 \\gg m^2 . Here Q^2 and m^2 stand for the masses squared of the virtual photon and heavy quark respectively. The calculations have been performed up to next-to-leading order in the strong coupling constant \\alpha_s using operator product expansion techniques. Apart from a check on earlier calculations, which however are only accessible via large computer programs, the asymptotic forms of the coefficient functions are useful for charm production at HERA when the condition Q^2 \\gg m_c^2 is satisfied. Furthermore the analytical expressions can also be used when one applies the variable heavy flavour scheme up to next-to-leading order in \\alpha_s.
Heavy quark coefficient functions at asymptotic values Q2>>m2
In this paper we present the analytic form of the heavy quark coefficient functions for deep inelastic lepton-hadron scattering in the kinematical regime Q2>>m2. Here Q2 and m2 stand for the masses squared of the virtual photon and heavy quark, respectively. The calculations have been performed up to next-to-leading order in the strong coupling constant αs using operator product expansion techniques. Apart from a check on earlier calculations, which however are only accessible via large computer programs, the asymptotic forms of the coefficient functions are useful for charm production at HERA when the condition Q2>>m2c is satisfied. Furthermore, the analytical expressions can also be used when one applies the variable flavour number scheme up to next-to-leading order in αs. (orig.)
Czabarka, Eva; Johnson, Virginia; Kupczok, Anne; Szekely, Laszlo A
2011-01-01
P.L. Erdos and L.A. Szekely [Adv. Appl. Math. 10(1989), 488-496] gave a bijection between rooted semilabeled trees and set partitions. L.H. Harper's results [Ann. Math. Stat. 38(1967), 410-414] on the asymptotic normality of the Stirling numbers of the second kind translates into asymptotic normality of rooted semilabeled trees with given number of vertices, when the number of internal vertices varies. The Erdos-Szekely bijection specializes to a bijection between phylogenetic trees and set partitions with classes of size \\geq 2. We consider modified Stirling numbers of the second kind that enumerate partitions of a fixed set into a given number of classes of size \\geq 2, and obtain their asymptotic normality as the number of classes varies. The Erdos- Szekely bijection translates this result into the asymptotic normality of the number of phylogenetic trees with given number of vertices, when the number of leaves varies. We also obtain asymptotic normality of the number of phylogenetic trees with given number...
Uniform Asymptotic Normality of the Matrix-variate Beta-distribution
Kai Can LI; He TANG
2012-01-01
With the upper bound of Kullback-Leibler distance between a matrix variate Beta-distribution and a normal distribution,this paper gives the conditions under which a matrix-variate Betadistribution will approach uniformly and asymptotically a normal distribution.
A note on asymptotic normality in the thermodynamic limit at low densities
Jensen, J.L.
1991-01-01
We consider a continuous statistical mechanical system with a pair interaction in a region λ tending to infinity. For low densities asymptotic normality of the canonical statistic is proved, both in the grand canonical ensemble and in the canonical ensemble. The results are illustrated through th...
An asymptotically normal G-estimate for the Anderson-Fisher discriminant function
Girko, V.L.; Pavlenko, T.V. [Kiev State Univ. (Ukraine)
1994-06-05
Conditions under which a G-estimate of the Anderson-Fisher discriminant function is asymptotically normal are investigated. This estimate decreases by an order of magnitude the quantity of observations needed for a given level of accuracy on the part of an estimate and is thus of significant interest for practical applications. 3 refs.
Fisher information and asymptotic normality in system identification for quantum Markov chains
This paper deals with the problem of estimating the coupling constant θ of a mixing quantum Markov chain. For a repeated measurement on the chain's output we show that the outcomes' time average has an asymptotically normal (Gaussian) distribution, and we give the explicit expressions of its mean and variance. In particular, we obtain a simple estimator of θ whose classical Fisher information can be optimized over different choices of measured observables. We then show that the quantum state of the output together with the system is itself asymptotically Gaussian and compute its quantum Fisher information, which sets an absolute bound to the estimation error. The classical and quantum Fisher information are compared in a simple example. In the vicinity of θ=0 we find that the quantum Fisher information has a quadratic rather than linear scaling in output size, and asymptotically the Fisher information is localized in the system, while the output is independent of the parameter.
Invariant Measures and Asymptotic Gaussian Bounds for Normal Forms of Stochastic Climate Model
Yuan YUAN; Andrew J.MAJDA
2011-01-01
The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive high dimensional climate models is an important topic for atmospheric low-frequency variability, climate sensitivity, and improved extended range forecasting. Recently, techniques from applied mathematics have been utilized to systematically derive normal forms for reduced stochastic climate models for low-frequency variables. It was shown that dyad and multiplicative triad interactions combine with the climatological linear operator interactions to produce a normal form with both strong nonlinear cubic dissipation and Correlated Additive and Multiplicative (CAM) stochastic noise. The probability distribution functions (PDFs) of low frequency climate variables exhibit small but significant departure from Gaussianity but have asymptotic tails which decay at most like a Gaussian. Here, rigorous upper bounds with Gaussian decay are proved for the invariant measure of general normal form stochastic models. Asymptotic Gaussian lower bounds are also established under suitable hypotheses.
Coefficient of restitution of sports balls: A normal drop test
Dynamic behaviour of bodies during impact is investigated through impact experiment, the simplest being a normal drop test. Normally, a drop test impact experiment involves measurement of kinematic data; this includes measurement of incident and rebound velocity in order to calculate a coefficient of restitution (COR). A high speed video camera is employed for measuring the kinematic data where speed is calculated from displacement of the bodies. Alternatively, sensors can be employed to measure speeds, especially for a normal impact where there is no spin of the bodies. This paper compares experimental coefficients of restitution (COR) for various sports balls, namely golf, table tennis, hockey and cricket. The energy loss in term of measured COR and effects of target plate are discussed in relation to the material and construction of these sports balls.
Consistency rates and asymptotic normality of the high risk conditional for functional data
Rabhi Abbes
2015-12-01
Full Text Available The maximum of the conditional hazard function is a parameter of great importance in seismicity studies, because it constitutes the maximum risk of occurrence of an earthquake in a given interval of time. Using the kernel nonparametric estimates of the first derivative of the conditional hazard function, we establish uniform convergence properties and asymptotic normality of an estimate of the maximum in the context of independence data.
Local asymptotic normality in {\\delta}-neighborhoods of standard generalized Pareto processes
Aulbach, Stefan
2011-01-01
De Haan and Pereira (2006) provided models for spatial extremes in the case of stationarity, which depend on just one parameter {\\beta} > 0 measuring tail dependence, and they proposed different estimators for this parameter. This framework was supplemented in Falk (2011) by establishing local asymptotic normality (LAN) of a corresponding point process of exceedances above a high multivariate threshold, yielding in particular asymptotic efficient estimators. The estimators investigated in these papers are based on a finite set of points t1,...,td, at which observations are taken. We generalize this approach in the context of functional extreme value theory (EVT). This more general framework allows estimation over some spatial parameter space, i.e., the finite set of points t1,...,td is replaced by t in [a,b]. In particular, we derive efficient estimators of {\\beta} based on those processes in a sample of iid processes in C[0,1] which exceed a given threshold function.
Behring, A.; Bierenbaum, I.; Blümlein, J.; De Freitas, A.; Klein, S.; Wißbrock, F.
2014-09-01
We calculate the logarithmic contributions to the massive Wilson coefficients for deep-inelastic scattering in the asymptotic region $Q^2 \\gg m^2$ to 3-loop order in the fixed-flavor number scheme and present the corresponding expressions for the massive operator matrix elements needed in the variable flavor number scheme. Explicit expressions are given both in Mellin-$N$ space and $z$-space.
Bitencourt, Ana Carla P; Littlejohn, Robert G; Anderson, Roger; Aquilanti, Vincenzo
2014-01-01
The Wigner $3j$ symbols of the quantum angular momentum theory are related to the vector coupling or Clebsch-Gordan coefficients and to the Hahn and dual Hahn polynomials of the discrete orthogonal hyperspherical family, of use in discretization approximations. We point out the important role of the Regge symmetries for defining the screen where images of the coefficients are projected, and for discussing their asymptotic properties and semiclassical behavior. Recursion relationships are formulated as eigenvalue equations, and exploited both for computational purposes and for physical interpretations.
A Relation between the Anomalous Dimensions and OPE Coefficients in Asymptotic Free Field Theories
Sonoda, Hidenori; Su, Wang-Chang
1996-01-01
In asymptotic free field theories we show that part of the OPE of the trace of the stress-energy tensor and an arbitrary composite field is determined by the anomalous dimension of the composite field. We take examples from the two-dimensional O(N) non-linear sigma model.
Fisher informations and local asymptotic normality for continuous-time quantum Markov processes
Catana, Catalin; Bouten, Luc; Guţă, Mădălin
2015-09-01
We consider the problem of estimating an arbitrary dynamical parameter of an open quantum system in the input-output formalism. For irreducible Markov processes, we show that in the limit of large times the system-output state can be approximated by a quantum Gaussian state whose mean is proportional to the unknown parameter. This approximation holds locally in a neighbourhood of size {t}-1/2 in the parameter space, and provides an explicit expression of the asymptotic quantum Fisher information in terms of the Markov generator. Furthermore we show that additive statistics of the counting and homodyne measurements also satisfy local asymptotic normality and we compute the corresponding classical Fisher informations. The general theory is illustrated with the examples of a two-level system and the atom maser. Our results contribute towards a better understanding of the statistical and probabilistic properties of the output process, with relevance for quantum control engineering, and the theory of non-equilibrium quantum open systems.
Asymptotic behavior of a delay predator-prey system with stage structure and variable coefficients
Javier A. Hernandez-Pinzon
2008-10-01
Full Text Available In this paper, we establish a global attractor for a Lotka-Volterra type reaction-diffusion predator-prey model with stage structure for the predator, delay due to maturity and variable coefficients. This attractor is found by the method of upper and lower solutions and is given in terms of bounds for the coefficients.
Castello-Branco, K. H. C.; Abdalla, E.
2003-01-01
Following the monodromy technique performed by Motl and Neitzke, we consider the analytic determination of the highly damped (asymptotic) quasi-normal modes of small Schwarzschild-de Sitter (SdS) black holes. We comment the result as compared to the recent numerical data of Konoplya and Zhidenko.
Null distribution of multiple correlation coefficient under mixture normal model
Hydar Ali; Nagar, Daya K.
2002-01-01
The multiple correlation coefficient is used in a large variety of statistical tests and regression problems. In this article, we derive the null distribution of the square of the sample multiple correlation coefficient, R2, when a sample is drawn from a mixture of two multivariate Gaussian populations. The moments of 1−R2 and inverse Mellin transform have been used to derive the density of R2.
Castello-Branco, K H
2003-01-01
We consider perturbations of Schwarzschild-de Sitter (SdS) black holes. Following the analysis performed by Motl and Neitzke, we analytically study the perturbation equation continued to the complex plane and compute the associated monodromy. We show that the SdS case has features similar to those of asymptotically flat Schwarzschild and deduce an analytic expression for the asymptotic, highly damped quasi-normal mode spectrum. For the case of near-extreme SdS black holes our results are qualitatively supported by very recent numerical data.
Heavy quark coefficient functions at asymptotic values $Q^2 \\gg m^2$
Buza, M.; Matiounine, Y.; Smith, J.; Migneron, R.; van Neerven, W. L.
1996-01-01
In this paper we present the analytic form of the heavy-quark coefficient functions for deep-inelastic lepton-hadron scattering in the kinematical regime $Q^2 \\gg m^2$ . Here $Q^2$ and $m^2$ stand for the masses squared of the virtual photon and heavy quark respectively. The calculations have been performed up to next-to-leading order in the strong coupling constant $\\alpha_s$ using operator product expansion techniques. Apart from a check on earlier calculations, which however are only acces...
De Marco, Stefano
2011-01-01
We study smoothness of densities for the solutions of SDEs whose coefficients are smooth and nondegenerate only on an open domain $D$. We prove that a smooth density exists on $D$ and give upper bounds for this density. Under some additional conditions (mainly dealing with the growth of the coefficients and their derivatives), we formulate upper bounds that are suitable to obtain asymptotic estimates of the density for large values of the state variable ("tail" estimates). These results specify and extend some results by Kusuoka and Stroock [J. Fac. Sci. Univ. Tokyo Sect. IA Math. 32 (1985) 1--76], but our approach is substantially different and based on a technique to estimate the Fourier transform inspired from Fournier [Electron. J. Probab. 13 (2008) 135--156] and Bally [Integration by parts formula for locally smooth laws and applications to equations with jumps I (2007) The Royal Swedish Academy of Sciences]. This study is motivated by existing models for financial securities which rely on SDEs with non-...
Asymptotic normalization coefficients from the (14)C(d,p)(15)C reaction
Mukhamedzhanov, A.; Burjan, Václav; Gulino, M.; Hons, Zdeněk; Kroha, Václav; McCleskey, M.; Mrázek, Jaromír; Nguyen, N.; Nunes, FM.; Piskoř, Štěpán; Romano, S.; Sergi, M. L.; Spitaleri, C.; Tribble, R. E.
2011-01-01
Roč. 84, č. 2 (2011), 024616/1-024616/6. ISSN 0556-2813 R&D Projects: GA MŠk LC07050; GA ČR GAP203/10/0310 Institutional research plan: CEZ:AV0Z10480505 Keywords : NUCLEI Subject RIV: CA - Inorganic Chemistry Impact factor: 3.308, year: 2011
王德辉
2007-01-01
This paper is concerned with the distributional properties of a median unbiased estimator of ARCH(0,1) coefficient. The exact distribution of the estimator can be easily derived, however its practical calculations are too heavy to implement,even though the middle range of sample sizes. Since the estimator is shown to have asymptotic normality, asymptotic expansions for the distribution and the percentiles of the estimator are derived as the refinements. Accuracies of expansion formulas are evaluated numerically, and the results of which show that we can effectively use the expansion as a fine approximatioh of the distribution with rapid calculations. Derived expansion are applied to testing hypothesis of stationarity, and an implementation for a real data set is illustrated.
Asymptotic normality with small relative errors of posterior probabilities of half-spaces
Dudley, R. M.; Haughton, D.
2002-01-01
Let $\\Theta$ be a parameter space included in a finite-dimensional Euclidean space and let $A$ be a half-space. Suppose that the maximum likelihood estimate $\\theta_n$ of $\\theta$ is not in $A$ (otherwise, replace $A$ by its complement) and let $\\Delta$ be the maximum log likelihood (at $\\theta_n$) minus the maximum log likelihood over the boundary $\\partial A$. It is shown that under some conditions, uniformly over all half-spaces $A$, either the posterior probability of $A$ is asymptotic to...
Fujikoshi, Yasunori; Shimizu, Ryoichi
1989-01-01
This paper deals with the distribution of $\\mathbf{X} = \\sum^{1/2}\\mathbf{Z}$, where $\\mathbf{Z}: p \\times 1$ is distributed as $N_p(0, I_p), \\sum$ is a positive definite random matrix and $\\mathbf{Z}$ and $\\sum$ are independent. Assuming that $\\sum = I_p + BB'$, we obtain an asymptotic expansion of the distribution function of $\\mathbf{X}$ and its error bound, which is useful in the situation where $\\sum$ tends to $I_p$. A stronger version of the expansion is also given. The results are appl...
Behring, A.; Bluemlein, J.; Freitas, A. de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Bierenbaum, I. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Klein, S. [RWTH Aachen Univ. (Germany). Inst. fuer Theoretische Teilchenphysik und Kosmologie; Wissbrock, F. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation
2014-03-15
We calculate the logarithmic contributions to the massive Wilson coefficients for deep-inelastic scattering in the asymptotic region Q{sup 2} >> m{sup 2} to 3-loop order in the fixed-flavor number scheme and present the corresponding expressions for the massive operator matrix elements needed in the variable flavor number scheme. Explicit expressions are given both in Mellin-N space and z-space.
Behring, A; Blümlein, J; De Freitas, A; Klein, S; Wißbrock, F
2014-01-01
We calculate the logarithmic contributions to the massive Wilson coefficients for deep-inelastic scattering in the asymptotic region $Q^2 \\gg m^2$ to 3-loop order in the fixed-flavor number scheme and present the corresponding expressions for the massive operator matrix elements needed in the variable flavor number scheme. Explicit expressions are given both in Mellin-$N$ space and $z$-space.
Behring, A.; Bluemlein, J.; Freitas, A. de [Deutsches Elektronen Synchrotron, DESY, Zeuthen (Germany); Bierenbaum, I. [Universitaet Hamburg, II. Institut fuer Theoretische Physik, Hamburg (Germany); Klein, S. [RWTH Aachen University, Institut fuer Theoretische Teilchenphysik und Kosmologie, Aachen (Germany); Wissbrock, F. [Deutsches Elektronen Synchrotron, DESY, Zeuthen (Germany); Johannes Kepler University, Research Institute for Symbolic Computation (RISC), Linz (Austria); IHES, Bures-sur-Yvette (France)
2014-09-15
We calculate the logarithmic contributions to the massive Wilson coefficients for deep-inelastic scattering in the asymptotic region Q{sup 2} >> m{sup 2} to 3-loop order in the fixed flavor number scheme and present the corresponding expressions for the massive operator matrix elements needed in the variable flavor number scheme. Explicit expressions are given in Mellin N-space. (orig.)
Comparison of RNFL thickness and RPE-normalized RNFL attenuation coefficient for glaucoma diagnosis
Vermeer, K. A.; van der Schoot, J.; Lemij, H. G.; de Boer, J. F.
2013-03-01
Recently, a method to determine the retinal nerve fiber layer (RNFL) attenuation coefficient, based on normalization on the retinal pigment epithelium, was introduced. In contrast to conventional RNFL thickness measures, this novel measure represents a scattering property of the RNFL tissue. In this paper, we compare the RNFL thickness and the RNFL attenuation coefficient on 10 normal and 8 glaucomatous eyes by analyzing the correlation coefficient and the receiver operator curves (ROCs). The thickness and attenuation coefficient showed moderate correlation (r=0.82). Smaller correlation coefficients were found within normal (r=0.55) and glaucomatous (r=0.48) eyes. The full separation between normal and glaucomatous eyes based on the RNFL attenuation coefficient yielded an area under the ROC (AROC) of 1.0. The AROC for the RNFL thickness was 0.9875. No statistically significant difference between the two measures was found by comparing the AROC. RNFL attenuation coefficients may thus replace current RNFL thickness measurements or be combined with it to improve glaucoma diagnosis.
On asymptotic normality of pseudo likelihood estimates for pairwise interaction processes
Jensen, Jens Ledet; Künsch, Hans R.
1994-01-01
We consider point processes defined through a pairwise interaction potential and admitting a two-dimensional sufficient statistic. It is shown that the pseudo maximum likelihood estimate can be stochastically normed so that the limiting distribution is a standard normal distribution. This result...... is true irrespectively of the possible existence of phase transitions. The work here is an extension of the work Guyon and Künsch (1992, Lecture Notes in Statist., 74, Springer, New York) and is based on viewing a point process interchangeably as a lattice field. © 1994 The Institute of Statistical...
SONG Weixing; CHENG Ping
2002-01-01
In the distribution family with common support and the one side truncated distribution family, Bickle, I. A. Ibragimov and R. Z. Hasminskii proved two important convolution theorems. As to the two-side truncated case, we also proved a convolution theorem, which plays an extraordinary role in the efficiency theory. In this paper, we will study another kind of two-side truncated distribution family, and prove a convolution result with normal form. On the basis of this convolution result, a new kind of efficiency concept is given; meanwhile, we will show that MLE is an efficient estimate in this distribution family.
SONGWeixing; CHENGPing
2002-01-01
In the distribution family with common support and the one side truncated distribution family,Bickle,I.A.Ibragimov and R.Z.Hasminskii proved two important convolution theorems.As to the two-side truncated case,we also proved a convolution theorem,which plays an extraordinary role in the efficency theory.In this paper,we will study another kind of two-side truncated distribution family,and prove a convolution result with normal form.On the basis of this convolution result,a new kind of efficiency concept is given;meanwhile,we will show that MLE is an efficient estimate in this distribution family.
Franco, Antonio; Trapp, Stefan
2008-01-01
calculated by the software ACD/Labs®. The Henderson-Hasselbalch equation was applied to calculate dissociation. Regressions were developed to predict separately for the neutral and the ionic molecule species the distribution coefficient (Kd) normalized to organic carbon (KOC) from log KOW and pKa. The log......The sorption of organic electrolytes to soil was investigated. A dataset consisting of 164 electrolytes, composed of 93 acids, 65 bases, and six amphoters, was collected from literature and databases. The partition coefficient log KOW of the neutral molecule and the dissociation constant pKa were...
Jinhong YOU; CHEN Min; Gemai CHEN
2004-01-01
Consider a semiparametric regression model with linear time series errors Yκ = x′κβ + g(tκ) + εκ,1 ≤ k ≤ n, where Yκ's are responses, xκ= (xκ1,xκ2,…,xκp)′and tκ ∈ T( ) R are fixed design points, β = (β1,β2,…… ,βp)′ is an unknown parameter vector, g(.) is an unknown bounded real-valued function defined on a compact subset T of the real line R, and εκ is a linear process given by εκ = ∑∞j=0 ψjeκ-j, ψ0 = 1, where ∑∞j=0 |ψj| ＜∞, and ej, j = 0,±1,±2,…, are I.I.d, random variables. In this paper we establish the asymptotic normality of the least squares estimator ofβ, a smooth estimator of g(·), and estimators of the autocovariance and autocorrelation functions of the linear process εκ.
The effect of age on apparent diffusion coefficient values in normal spleen: A preliminary study
Aim: To investigate and characterize the effect of age on apparent diffusion coefficient (ADC) values in normal spleen. Materials and methods: A population of 127 patients (age range 10–79 years, mean age 44.4 years) without magnetic resonance imaging findings in abdominal scans, was selected over a 5-year period. The ADC values of the spleen were analysed in all ages, and dependency of ADC values on age was characterized using Spearman's correlation coefficient test. Results: A reduction of ADC values with ageing was found in the spleen (r = −0.702, p < 0.001). Conclusions: The ADC values of the spleen decline with age. This should be taken into consideration when disease is diagnosed
The linear attenuation coefficients for normal (adipose and glandular) and neoplastic (benign and malignant) breast tissues were measured using monoenergetic X-ray beams at the energy range of 8-30 keV, combining narrow beam geometry and high energy resolution obtained using a diffracted X-ray beam. The measured values are compared with predicted ones calculated according to the mixture rule and with previous experimental data showing a good agreement within the experimental uncertainties. Our results show that there is some degree of overlap among glandular, benign and malignant values. Nevertheless, significant differences (p < 0.05) exist in the linear attenuation coefficient between glandular and malignant at energies below 28 keV. Finally, a fitting procedure was applied to values for each group (mean and extremes values) in order to summarize all data.
Apparent diffusion coefficients of normal uterus in premenopausal women with 3 T MRI
Aim: To investigate the apparent diffusion coefficient (ADC) values of the normal uterine cervical zonal structures (cervical epithelium, the junctional zone, and myometrium) during different phases of the menstrual cycle among premenopausal women in different age groups. Materials and methods: Seventy healthy women, who were divided into three age groups (group A, 24 women in their twenties; group B, 23 women in their thirties; group C, 23 women in their forties), underwent 3 T magnetic resonance imaging (MRI) with T2-weighted and diffusion-weighted imaging (DWI) during the mid-proliferative and the mid-secretory phases. Results: The ADC values of each cervical zonal structure were significantly different from one another (p 0.05). Conclusion: ADC values of normal cervical epithelium and the junctional zone change with different phases of the menstrual cycle, which should be taken into consideration when early cervical disease is detected, when monitoring treatment response, and differentiating early tumour recurrence
Garcia-Sanchez, L. [Laboratory of Environmental Modelling, IRSN, Centre de Cadarache, bat. 159, BP 3, F-13115 Saint-Paul-lez-Durance Cedex (France)], E-mail: laurent.garcia-sanchez@irsn.fr; Konoplev, A.V. [SPA Typhoon, Centre for Environmental Chemistry, 82 Lenin Avenue, 249039 Obninsk (Russian Federation)
2009-09-15
Radionuclide wash-off is the transport of activity by flowing water over the soil surface (runoff). To complete existing reviews on long-term removal rates, this paper focuses on short-term wash-off fluxes, quantified in the literature by soil-runoff transfer factors called normalized liquid and solid entrainment coefficients (noted K{sub l}*, K{sub s}*). Compiled data concerned essentially {sup 137}Cs and {sup 90}Sr wash-off measured under simulated rainfalls on small experimental plots after Chernobyl fallout in the exclusion zone. K{sub l}* and K{sub s}* values span approximately one order of magnitude. Their validity is limited to a season, and their representativeness is limited by restricted studied situations, notably dominant unsoluble forms in fallout, light soils and intense rainfalls. Formulas based on a simplified representation of the soil-runoff system were proposed to generalize the existing values for other conditions. However, their implementation requires a more systematic compilation of the available information, including decisive influence factors such as the fraction of exchangeable form, distribution coefficient, suspended matter enrichment ratio. Entrainment coefficients K{sub l}* and K{sub s}* were mathematically related to the transfer function approach. The proposed relationships proved their complementarity in terms of time support and captured fluctuations. Both approaches should be used in assessments to estimate average fluxes and their variability.
Garcia-Sanchez, L; Konoplev, A V
2009-09-01
Radionuclide wash-off is the transport of activity by flowing water over the soil surface (runoff). To complete existing reviews on long-term removal rates, this paper focuses on short-term wash-off fluxes, quantified in the literature by soil-runoff transfer factors called normalized liquid and solid entrainment coefficients (noted K(l)(*), K(s)(*)). Compiled data concerned essentially (137)Cs and (90)Sr wash-off measured under simulated rainfalls on small experimental plots after Chernobyl fallout in the exclusion zone. K(l)(*) and K(s)(*) values span approximately one order of magnitude. Their validity is limited to a season, and their representativeness is limited by restricted studied situations, notably dominant unsoluble forms in fallout, light soils and intense rainfalls. Formulas based on a simplified representation of the soil-runoff system were proposed to generalize the existing values for other conditions. However, their implementation requires a more systematic compilation of the available information, including decisive influence factors such as the fraction of exchangeable form, distribution coefficient, suspended matter enrichment ratio. Entrainment coefficients K(l)(*) and K(s)(*) were mathematically related to the transfer function approach. The proposed relationships proved their complementarity in terms of time support and captured fluctuations. Both approaches should be used in assessments to estimate average fluxes and their variability. PMID:18950908
Naganawa, Shinji; Sato, Chiho; Ishigaki, Takeo [Nagoya University School of Medicine, Department of Radiology, Nagoya (Japan); Kumada, Hisashi; Miura, Shunichi [Toyohashi Municipal hospital, Department of Radiology, Toyohashi, Aich (Japan); Takizawa, Osamu [Siemens-Asahi Medical Technologies Ltd, Tokyo (Japan)
2005-01-01
A relation between apparent diffusion coefficient (ADC) values and tumor cellular density has been reported. The purpose of this study was to measure the ADC values of cervical cancers in the uterus and compare them with those of normal cervical tissues, and to test whether ADC could differentiate between normal and malignant cervical tissues in the uterus. Twelve consecutive female patients with cervical cancer of the uterus and ten female patients with other pelvic abnormalities were included in this study. ADC was measured at 1.5 T with b-factors of 0, 300 and 600 s/mm{sup 2} using single-shot echo-planar diffusion-weighted imaging and a parallel imaging technique. The mean ADC value of cervical cancer lesions was 1.09{+-}0.20 x 10{sup -3} mm{sup 2}/s, and that of normal cervix tissue was 1.79{+-}0.24 x 10{sup -3} mm{sup 2}/s (P<0.0001). In nine patients treated by chemotherapy and/or radiation therapy, the mean ADC value of the cervical cancer lesion increased significantly after therapy (P<0.001). The present study showed, with a small number of patients, that ADC measurement has a potential ability to differentiate between normal and cancerous tissue in the uterine cervix. Further study is necessary to determine the accuracy of ADC measurement in monitoring the treatment response. (orig.)
Apparent diffusion coefficient values of normal testis and variations with age
Athina C Tsili
2014-06-01
Full Text Available The usefulness of diffusion-weighted magnetic resonance imaging (DWI in the evaluation of scrotal pathology has recently been reported. A standard reference of normal testicular apparent diffusion coefficient (ADC values and their variations with age is necessary when interpreting normal testicular anatomy and pathology. We evaluated 147 normal testes using DWI, including 71 testes from 53 men aged 20-39 years (group 1, 67 testes from 42 men aged 40-69 years (group 2 and nine testes from six men older than 70 years (group 3. DWI was performed along the axial plane, using a single shot, multislice spin-echo planar diffusion pulse sequence and b-values of 0 and 900 s mm−2 . The mean and standard deviation of the ADC values of normal testicular parenchyma were calculated for each age group separately. Analysis of variance (ANOVA followed by post hoc analysis (Dunnett T3 was used for statistical purposes. The ADC values (× 10−3 mm 2 s−1 of normal testicular tissue were different among age groups (group 1: 1.08 ± 0.13; group 2: 1.15 ± 0.15 and group 3: 1.31 ± 0.22. ANOVA revealed differences in mean ADC among age groups (F = 11.391, P < 0.001. Post hoc analysis showed differences between groups 1 and 2 (P = 0.008 and between groups 1 and 3 (P = 0.043, but not between groups 2 and 3 (P = 0.197. Our findings suggest that ADC values of normal testicular tissue increase with advancing age.
Photon linear attenuation coefficients and water content of normal and pathological breast tissues
Normal and pathological breast tissue samples were scanned using a Photon Transmission Tomography (PTT) technique in order to determine their averaged photon linear attenuation coefficients (μ). Subsequent to being freeze-dried the samples were examined, using a high purity germanium detector (HPGe) and the γ-rays of energy 59.5 keV from an americium source, and the results were corrected for the water reduction by the use of the Mixture Rule. The ratio of our experimental findings to the published data for μ for various breast tissues were 88, 96 and 88% for adipose, glandular and tumour tissues, respectively. The mean accuracy in our study, investigated relative to standard chemical compounds, was about 3%. The water content of each tissue type was determined as the weight loss during the freeze drying process. This work was initiated in order to evaluate the suitability of new tissue substitute materials for mammography applications. (Author)
We compute the 3-loop fermion-loop corrections to the asymptotic heavy flavor Wilson coefficients of the structure function F2(x,Q2) and of Transversity in the asymptotic region Q2 >>m2∝Ci Nf TF2 and first contributions ∝Ci TF2, with i=F,A. The computation is based on a factorization theorem of the massive Wilson coefficients into massive operator matrix elements and the massless Wilson coefficients. Our method is based on direct integration, avoiding the integration-by-parts technique, which is advantageous due to the compactness of the intermediate and final results. We also obtain the corresponding contributions to the 3-loop anomalous dimensions and confirm results in the literature.
Bernard, Simon; Marrelec, Guillaume; Laugier, Pascal; Grimal, Quentin
2015-06-01
Resonant ultrasound spectroscopy is an experimental technique for measuring the stiffness of anisotropic solid materials. The free vibration resonant frequencies of a specimen are measured and the stiffness coefficients of the material adjusted to minimize the difference between experimental and predicted frequencies. An issue of this inverse approach is that the measured frequencies are not easily paired with their predicted counterpart, leading to ambiguities in the definition of the objective function. In the past, this issue has been overcome through trial-and-error methods requiring the experimentalist to find the correct pairing, or through involved experimental methods measuring the shapes of the normal vibration modes in addition to their frequencies. The purpose of this work is to show, through a Bayesian formulation, that the inverse problem can be solved automatically and without requiring additions to the usual experimental setup. The pairing of measured and predicted frequencies is considered unknown, and the joint posterior probability distribution of pairing and stiffness is sampled using Markov chain Monte Carlo. The method is illustrated on two published data sets. The first set includes the exact pairing, allowing validation of the method. The second application deals with attenuative materials, for which many predicted modes cannot be observed, further complicating the inverse problem. In that case, introduction of prior information through Bayesian formulation reduces ambiguities.
Phillip Burgers
Full Text Available For a century, researchers have used the standard lift coefficient C(L to evaluate the lift, L, generated by fixed wings over an area S against dynamic pressure, ½ρv(2, where v is the effective velocity of the wing. Because the lift coefficient was developed initially for fixed wings in steady flow, its application to other lifting systems requires either simplifying assumptions or complex adjustments as is the case for flapping wings and rotating cylinders.This paper interprets the standard lift coefficient of a fixed wing slightly differently, as the work exerted by the wing on the surrounding flow field (L/ρ·S, compared against the total kinetic energy required for generating said lift, ½v(2. This reinterpreted coefficient, the normalized lift, is derived from the work-energy theorem and compares the lifting capabilities of dissimilar lift systems on a similar energy footing. The normalized lift is the same as the standard lift coefficient for fixed wings, but differs for wings with more complex motions; it also accounts for such complex motions explicitly and without complex modifications or adjustments. We compare the normalized lift with the previously-reported values of lift coefficient for a rotating cylinder in Magnus effect, a bat during hovering and forward flight, and a hovering dipteran.The maximum standard lift coefficient for a fixed wing without flaps in steady flow is around 1.5, yet for a rotating cylinder it may exceed 9.0, a value that implies that a rotating cylinder generates nearly 6 times the maximum lift of a wing. The maximum normalized lift for a rotating cylinder is 1.5. We suggest that the normalized lift can be used to evaluate propellers, rotors, flapping wings of animals and micro air vehicles, and underwater thrust-generating fins in the same way the lift coefficient is currently used to evaluate fixed wings.
Aim: To compare the efficacy of apparent diffusion coefficient (ADC) and normalized ADC (nADC) for estimating the histological grade of vesical urothelial carcinoma and to identify an optimal reference for nADC calculation. Materials and methods: Thirty patients with histologically confirmed vesical urothelial carcinomas underwent preoperative diffusion-weighted magnetic resonance imaging (DW-MRI) of the pelvis. nADC of the tumour was calculated as ADC (tumour)/ADC (reference) using urine in the bladder lumen, and the obturator internus and gluteus maximus muscles as reference. Receiver operating characteristic (ROC) curves were constructed and compared to identify an optimal reference for nADC calculation. Results: Both ADC and nADC of low-grade tumours (1.112 ± 0.159 × 10−3 mm2/s, 0.403 ± 0.047 × 10−3 mm2/s) were significantly (p < 0.001) higher than those of high-grade tumours (0.772 ± 0.091 × 10−3 mm2/s, 0.276 ± 0.033 × 10−3 mm2/s). The area under the nADC ROC curve using urine as reference was significantly (p = 0.000) larger (0.995) than those using obturator internus (0.960) and gluteus maximus (0.945). Conclusions: nADC is superior to ADC for estimating the histological grade of bladder carcinoma using urine in the bladder lumen as an optimal reference for nADC calculation. - Highlights: • We use a new non-invasive method in bladder cancer preoperative pathological grade evaluation. • We first use the normalized ADC value in bladder cancer. • Normalized ADC value was confirmed to be more reliable than ADC value
Abou, B; Wesfreid, J E; Abou, Berengere; Surgy, Gilles Neron de; Wesfreid, Jose-Eduardo
1997-01-01
We have calculated the general dispersion relationship for surface waves on a ferrofluid layer of any thickness and viscosity, under the influence of a uniform vertical magnetic field. The amplification of these waves can induce an instability called peaks instability (Rosensweig instability). The expression of the dispersion relationship requires that the critical magnetic field and the critical wavenumber of the instability depend on the thickness of the ferrofluid layer. The dispersion relationship has been simplified into four asymptotic regimes: thick or thin layer and viscous or inertial behaviour. The corresponding critical values are presented. We show that a typical parameter of the ferrofluid enables one to know in which regime, viscous or inertial, the ferrofluid will be near the onset of instability.
Skákala, Jozef
2012-01-01
We analyze the largely accepted formulas for the asymptotic quasi-normal frequencies of the non-extremal Reissner-Nordström black hole, (for the electromagnetic-gravitational/scalar perturbations). We focus on the question of whether the gap in the spacing in the imaginary part of the QNM frequencies has a well defined limit as n goes to infinity and if so, what is the value of the limit. The existence and the value of this limit has a crucial importance from the point of view of the currently popular Maggiore's conjecture, which represents a way of connecting the asymptotic behavior of the quasi-normal frequencies to the black hole thermodynamics. With the help of previous results and insights we will prove that the gap in the imaginary part of the frequencies does not converge to any limit, unless one puts specific constraints on the ratio of the two surface gravities related to the two spacetime horizons. Specifically the constraints are that the ratio of the surface gravities must be rational and such that it is given by two relatively prime integers n ± whose product is an even number. If the constraints are fulfilled the limit of the sequence is still not guaranteed to exist, but if it exists its value is given as the lowest common multiplier of the two surface gravities. At the end of the paper we discuss the possible implications of our results.
Aditya Kumar
2013-01-01
Full Text Available The influence of applied normal load and roughness on the tribological behavior between the indenter and sample surface during nanoindentation-based scratching has been experimentally investigated by using different surfaces (fused silica and diamond-like carbon featuring various degrees of roughness. At a sufficiently low applied normal load, wherein the contact is elastic, the friction coefficient is constant. However, at increased normal loads the contact involves plastic deformation and the friction coefficient increases with increasing normal load. The critical load range for a transition from predominantly elastic to plastic contact, between the indenter and sample surface, increases with increasing size of indenter and decreases with roughness. Distinct differences between the present experimental results and the existing theoretical models/predictions are discussed.
Asymptotics for spherical needlets
Baldi, P.; Kerkyacharian, G.; Marinucci, D.; Picard, D.
We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially decaying tails. We show that, for random fields on the sphere, the needlet coefficients are asymptotically uncorrelated for any fixed angular distance. This property is used to derive CLT and functional CLT convergence results for polynomial functionals of the needlet coefficients: here the asymptotic theory is considered in the high-frequency sense. Our proposals emerge from strong empirical motivations, especially in connection with the analysis of cosmological data sets.
Basak, A. K.; Celis, J.-P.; Vardavoulias, M.; Matteazzi, P.
2014-02-01
Alumina dispersed FeCuAl-based nanostructured cermet coatings were deposited from nanostructured powders by atmospheric plasma spraying on low carbon steel substrates. Nanostructuring was retained in the deposited coatings which exhibit up to four distinctive phases as revealed by electron microscopy. In this study, the friction behavior of the distinctive phases at nano-normal load scale was investigated alongside their contribution to the overall friction behavior at macro-normal load scale. Friction behavior at nano-normal load scale was investigated by lateral force microscopy, whereas conventional tribometers were used for investigations at micro and macro-normal loads. It appeared that, the friction measured at nano-normal loads on individual phases is dictated by both composition and hardness of the corresponding phases, and thus influences the overall friction behavior of the coatings at macro-normal loads. Moreover, the coefficient of friction at macro-normal loads differs from the one at nano-normal loads, and deviates from Amonton's friction law.
Kazemi, M. R.; Jafari, A A
2016-01-01
In this paper, we use the method of modified signed log-likelihood ratio test for the problem of testing the equality of correlation coefficients in two independent bivariate normal distributions. We compare this method with two other %competing approaches, Fisher's Z-transform and generalized test variable, using a Monte Carlo simulation. It indicates that the proposed method is better than the other approaches, in terms of the actual sizes and powers especially when the sample sizes are une...
Werner, Charles L.; Wegmueller, Urs; Small, David L.; Rosen, Paul A.
1994-01-01
Terrain slopes, which can be measured with Synthetic Aperture Radar (SAR) interferometry either from a height map or from the interferometric phase gradient, were used to calculate the local incidence angle and the correct pixel area. Both are required for correct thematic interpretation of SAR data. The interferometric correlation depends on the pixel area projected on a plane perpendicular to the look vector and requires correction for slope effects. Methods for normalization of the backscatter and interferometric correlation for ERS-1 SAR are presented.
Dettmann, Carl P.
2002-01-01
Recent advances in the periodic orbit theory of stochastically perturbed systems have permitted a calculation of the escape rate of a noisy chaotic map to order 64 in the noise strength. Comparison with the usual asymptotic expansions obtained from integrals and with a previous calculation of the electrostatic potential of exactly selfsimilar fractal charge distributions, suggests a remarkably accurate form for the late terms in the expansion, with parameters determined independently from the...
We tested the feasibility of a simple method for assessment of prostate cancer (PCa) aggressiveness using diffusion-weighted magnetic resonance imaging (MRI) to calculate apparent diffusion coefficient (ADC) ratios between prostate cancer and healthy prostatic tissue. The requirement for institutional review board approval was waived. A set of 20 standardized core transperineal saturation biopsy specimens served as the reference standard for placement of regions of interest on ADC maps in tumorous and normal prostatic tissue of 22 men with PCa (median Gleason score: 7; range, 6–9). A total of 128 positive sectors were included for evaluation. Two diagnostic ratios were computed between tumor ADCs and normal sector ADCs: the ADC peripheral ratio (the ratio between tumor ADC and normal peripheral zone tissue, ADC-PR), and the ADC central ratio (the ratio between tumor ADC and normal central zone tissue, ADC-CR). The performance of the two ratios in detecting high-risk tumor foci (Gleason 8 and 9) was assessed using the area under the receiver operating characteristic curve (AUC). Both ADC ratios presented significantly lower values in high-risk tumors (0.48 ± 0.13 for ADC-CR and 0.40 ± 0.09 for ADC-PR) compared with low-risk tumors (0.66 ± 0.17 for ADC-CR and 0.54 ± 0.09 for ADC-PR) (p < 0.001) and had better diagnostic performance (ADC-CR AUC = 0.77, sensitivity = 82.2%, specificity = 66.7% and ADC-PR AUC = 0.90, sensitivity = 93.7%, specificity = 80%) than stand-alone tumor ADCs (AUC of 0.75, sensitivity = 72.7%, specificity = 70.6%) for identifying high-risk lesions. The ADC ratio as an intrapatient-normalized diagnostic tool may be better in detecting high-grade lesions compared with analysis based on tumor ADCs alone, and may reduce the rate of biopsies
Aim: To investigate and characterize the effect of age on apparent diffusion coefficient (ADC) values in the normal adult pancreas using diffusion-weighted magnetic resonance imaging (DWI). Materials and methods: Five hundred and fifty-nine adult patients without pancreatic disease, ranging from 20–81 years of age (mean 50.9 years; 436 men, 123 women), were included in this study. Breath-hold single-shot echo-planar DWI (b-values = 0, 500 s/mm2) was employed to determine the ADCs across all patients. Dependency of ADCs on age was characterized using a Spearman rank-order correlation test. Results: Across the age spectrum, there was no significant correlation between ADC and age (p = 0.409). Conclusion: The findings of the present study suggest that the effect of age on ADCs can be excluded from the diagnosis of pancreatic diseases and design of future studies using breath-hold single-shot DWI and ADCs (as calculated with b-values of 0 and 500 s/mm2)
Asymptotic expansions for the Gaussian unitary ensemble
Haagerup, Uffe; Thorbjørnsen, Steen
2012-01-01
Let g : R ¿ C be a C8-function with all derivatives bounded and let trn denote the normalized trace on the n × n matrices. In Ref. 3 Ercolani and McLaughlin established asymptotic expansions of the mean value ¿{trn(g(Xn))} for a rather general class of random matrices Xn, including the Gaussian...... Unitary Ensemble (GUE). Using an analytical approach, we provide in the present paper an alternative proof of this asymptotic expansion in the GUE case. Specifically we derive for a random matrix Xn that where k is an arbitrary positive integer. Considered as mappings of g, we determine the coefficients...... aj(g), j ¿ N, as distributions (in the sense of L. Schwarts). We derive a similar asymptotic expansion for the covariance Cov{Trn[f(Xn)], Trn[g(Xn)]}, where f is a function of the same kind as g, and Trn = n trn. Special focus is drawn to the case where and for ¿, µ in C\\R. In this case the mean and...
Mukhamedzhanov, A. M.; Bém, Pavel; Burjan, Václav; Gagliardi, C. A.; Goldberg, V.Z.; Hons, Zdeněk; La Cognata, M.; Kroha, Václav; Mrázek, Jaromír; Novák, Jan; Piskoř, Štěpán; Pizzone, R. G.; Plunkett, A.; Romano, S.; Šimečková, Eva; Spitareli, C.; Trache, L.; Tribble, R. E.; Veselý, František; Vincour, Jiří
2008-01-01
Roč. 78, č. 1 (2008), 015804/1-015804/8. ISSN 0556-2813 R&D Projects: GA ČR GA202/05/0302; GA MŠk LC07050 Institutional research plan: CEZ:AV0Z10480505 Keywords : ANC Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 3.124, year: 2008
Tang, X. D.; Azhari, A.; FU, CB.; Gagliardi, C. A.; Mukhamedzhanov, A. M.; Pirlepesov, F.; Trache, L.; Tribble, R. E.; Burjan, Václav; Kroha, Václav; Carstoiu, F.; Irgaziev, BF.
2004-01-01
Roč. 69, č. 5 (2004), 055807. ISSN 0556-2813 R&D Projects: GA ČR GA202/01/0709; GA MŠk ME 385 Institutional research plan: CEZ:AV0Z1048901 Keywords : coupled-channels calculations * cross-section Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 3.125, year: 2004
Highlights: → Some concrete were determined photon radiation absorbent for 0.663 keV. → It was concluded that barite was effective. → As known, colemanite was good absorbent to prevent for neutron transmission. → As a neutron absorbent, colemanite would be preferred to normal aggregate. - Abstract: Accurate measurements have been made to determine radiation transmission of concretes produced with barite, colemanite and normal aggregate by using beam transmission method for 0.663 MeV γ-rays energy of 137Cs radioactive isotopes by using NaI(Tl) scintillation detector. Linear and mass attenuation coefficients of thirteen heavy- and four normal-weight concretes were calculated. It was determined that the linear attenuation coefficient (μ, cm-1) decreased with colemanite concentration and increased with barite concentration in both type of the concretes. Mass attenuation coefficient values of our concretes were compared with the values proposed by the United States National Institute of Standards and Technology (NIST).
Macarini, Luca; Stoppino, Luca Pio; Milillo, Paola; Ciuffreda, Pierpaolo; Fortunato, Francesca; Vinci, Roberta
2010-01-01
The purpose of the study was to assess the capability and the reliability of apparent diffusion coefficient (ADC) measurements in the evaluation of different benign renal abnormalities. Twenty-five healthy volunteers and 31 patients, divided into seven different groups (A-G) according to pathology, underwent diffusion-weighted magnetic resonance imaging (DW MRI) of the kidneys using 1.5-T system. DW images were obtained in the axial plane with a spin-echo echo planar imaging single-shot sequence with three b values (0, 300, and 600 s/mm²). Before acquisition of DW sequences, we performed in each patient a morphological study of the kidneys. ADC was 2.40±0.20×10⁻³ mm² s⁻¹ in volunteers. A significant difference was found between Groups A (cysts=3.39±0.51×10⁻³ mm² s⁻¹) and B (acute/chronic renal failure=1.38±0.40×10⁻³ mm² s⁻¹) and between Groups A and C (chronic pyelonephritis=1.53±0.21×10⁻³ mm² s⁻¹) (P.05). A considerable correlation between glomerular filtration rate and ADC was found (P=.04). In conclusion, significant differences were detected among different patient groups, and this suggests that ADC measurements can be useful in differentiating normal renal parenchyma from most commonly encountered nonmalignant renal lesions. PMID:21092872
Trending Time-Varying Coefficient Models With Serially Correlated Errors
Cai, Zongwu
2003-01-01
In this paper we study time-varying coefficient models with time trend function and serially correlated errors to characterize nonlinear, nonstationary and trending phenomenon in time series. Compared with the Nadaraya-Watson method, the local linear approach is developed to estimate the time trend and coefficient functions. The consistency of the proposed estimators is obtained without any specification of the error distribution and the asymptotic normality of the proposed estimators is esta...
Inference on multivariate heteroscedastic time varying random coefficient models
Giraitis, Liudas; Kapetanios, George; Yates, Tony
2015-01-01
In this paper we introduce the general setting of a multivariate time series autoregressive model with stochastic time-varying coefficients and time-varying conditional variance of the error process. This allows modeling VAR dynamics for non-stationary times series and estimation of time varying parameter processes by well-known rolling regression estimation techniques. We establish consistency, convergence rates and asymptotic normality for kernel estimators of the paths of coefficient proce...
Burgers, Phillip; Alexander, David E.
2012-01-01
For a century, researchers have used the standard lift coefficient CL to evaluate the lift, L, generated by fixed wings over an area S against dynamic pressure, ½ρv 2, where v is the effective velocity of the wing. Because the lift coefficient was developed initially for fixed wings in steady flow, its application to other lifting systems requires either simplifying assumptions or complex adjustments as is the case for flapping wings and rotating cylinders. This paper interprets the standard ...
The linear attenuation coefficients for normal (adipose and glandular), peripheral normal (adjacent to neoplasia) and neoplastic (carcinomas and fibroadenomas) breast tissues were determined using a polienergetic x-ray beam at the energy range of 10 to 45 keV, combining narrow beam geometry and high energy resolution obtained using a Si(Li) detector. The obtained results show that the linear attenuation coefficient for adipose and peripheral normal breast tissues are smaller than those obtained for others tissues at ali energies, whereas the values obtained for the different neoplastic groups are similar. The measured values are compared with previous experimental data and with theoretical predictions, calculated according to the mixture rule, showing a good agreement. (author)
Efficient Quantile Estimation for Functional-Coefficient Partially Linear Regression Models
Zhangong ZHOU; Rong JIANG; Weimin QIAN
2011-01-01
The quantile estimation methods are proposed for functional-coefficient partially linear regression (FCPLR) model by combining nonparametric and functional-coefficient regression (FCR) model.The local linear scheme and the integrated method are used to obtain local quantile estimators of all unknown functions in the FCPLR model.These resulting estimators are asymptotically normal,but each of them has big variance.To reduce variances of these quantile estimators,the one-step backfitting technique is used to obtain the efficient quantile estimators of all unknown functions,and their asymptotic normalities are derived.Two simulated examples are carried out to illustrate the proposed estimation methodology.
Super-b4 coefficients in supergravity
For covariantly chiral superfields coupled to background Yang-Mills superfields and defined on a curved superspace background, the superfield analogue of the heat kernel associated with the differential operator appearing in the quadratic part of the action is defined. The super-b4 coefficient in the asymptotic expansion of the kernel is computed using a system of superspace normal coordinates. These coefficients are shown to determine the one-loop trace supermultiplet and the one-loop logarithmic divergence for pure supergravity. (author)
EFFICIENT ESTIMATION OF FUNCTIONAL-COEFFICIENT REGRESSION MODELS WITH DIFFERENT SMOOTHING VARIABLES
Zhang Riquan; Li Guoying
2008-01-01
In this article, a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different co-efficient functions is defined. First step, by the local linear technique and the averaged method, the initial estimates of the coefficient functions are given. Second step, based on the initial estimates, the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure. The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions. Two simulated examples show that the procedure is effective.
Asymptotic Efficiency in OLEDS
Nelson, Mitchell C
2015-01-01
Asymptotic efficiency (high output without droop) was recently reported for OLEDS in which a thin emitter layer is located at the anti-node in a resonant microcavity. Here we extend our theoretical analysis to treat multi-mode devices with isotropic emitter orientation. We recover our efficiency equations for the limiting cases with an isotropic emitter layer located at the anti-node where output is linear in current, and for an isotropic emitter located at the node where output can exhibit second order losses with an overall efficiency coefficient that depends on loss terms in competition with a cavity factor. Additional scenarios are described where output is driven by spontaneous emission, or mixed spontaneous and stimulated emission, with stimulated emission present in a loss mode, potentially resulting in cavity driven droop or output clamping, and where the emitter layer is a host-guest system.
In the extraction cycles of Purex process of nuclear fuel reprocessing zirconium is of particular importance because it is one of the most readily extractable of longer-lived fission products, and therefore one frequently contaminates uranium or plutonium product solutions. Theoretical and experimental studies have been initiated to find out a suitable distribution coefficient co-relation of Zr(IV). The present paper describes calculations of distribution coefficient of Zr(IV) between aqueous nitrate solutions and 30 vol% TBP/NPH. The correlation functions are described as a mathematical model in which equilibrium constants are expressed as a function of total nitrate salting strength by a quadratic polynomial. A generalized least-squares techniques has been used to determine equilibrium constants of Zr(IV) and its variation with the medium composition in solvent extraction equilibria by minimizing the difference between observed and calculated distribution coefficients using experimental data. The results presented here shall be useful for the flowsheet simulation of extraction cycles of Purex process
Asymptotic expansions for high-contrast linear elasticity
Poveda, Leonardo A.
2015-03-01
We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study the convergence of the expansion in the H1 norm. © 2015 Elsevier B.V.
陈桂景; Sa,AKME
2000-01-01
This paper presents the large properties of‘regression quantiles' in linear models, establishing the strong consistency and asymptotic normality in similar form,modifying and extending the results about minimum l1 - norm estimates in linear models obtained by Chen, X.R., et al. (1990,1992).The results in this paper improve the corresponding results obtained by Koenker & Bassett(1978),Gutenburnner & Jure cková(1992),Jure cková & Prochazka(1994),and so on.%论证了线性模型中回归分位点估计量的强相合性及渐近正态性等大样本性质，这些结果推广了陈希孺等(1990，1992)的有关定理，改进了Koenker与Basstee(1978)，Gutenburnner与Jureckova(1992)，以及Jureckovo与Prochazka(1994)等人的有关成果。
Asymptotically Safe Dark Matter
Sannino, Francesco; Shoemaker, Ian M.
2015-01-01
We introduce a new paradigm for dark matter (DM) interactions in which the interaction strength is asymptotically safe. In models of this type, the coupling strength is small at low energies but increases at higher energies, and asymptotically approaches a finite constant value. The resulting...... searches are the primary ways to constrain or discover asymptotically safe dark matter....
Robust asymptotic sampling theory for correlations in pedigrees.
Keen, K J; Elston, Robert C
2003-10-30
Methods to unravel the genetic determinants of non-Mendelian diseases lie at the next frontier of statistical approaches for human genetics. It is generally agreed that, before proceeding with segregation or linkage analysis, the trait under study ought to be shown to exhibit familial correlation. By coding dichotomous traits as binary variables, a single robust approach in the estimation of pedigree correlations, rather than two distinct approaches, can be used to assess the potential heritability of a trait, and, latterly, to examine the mode of inheritance. The asymptotic theory to conduct hypothesis tests and confidence intervals for correlations among different members of nuclear families is well established but is applicable only if the nuclear families are independent. As a further contribution to the literature, we derive the asymptotic sampling distribution of correlations between random variables among arbitrary pairs of members in extended families for the Pearson product-moment estimator with generalized weights. This derivation is done without assuming normality of the traits. The sampling distribution is shown to be asymptotically normal to first order, and hence large-sample hypothesis tests and confidence intervals with estimates of the variances and correlation coefficients are proposed. Discussion concludes with an example and a suggestion for future research. PMID:14518025
Comparison of Spearman's rho and Kendall's tau in Normal and Contaminated Normal Models
Xu, Weichao; Hung, Y S; Zou, Yuexian
2010-01-01
This paper analyzes the performances of the Spearman's rho (SR) and Kendall's tau (KT) with respect to samples drawn from bivariate normal and bivariate contaminated normal populations. The exact analytical formulae of the variance of SR and the covariance between SR and KT are obtained based on the Childs's reduction formula for the quadrivariate normal positive orthant probabilities. Close form expressions with respect to the expectations of SR and KT are established under the bivariate contaminated normal models. The bias, mean square error (MSE) and asymptotic relative efficiency (ARE) of the three estimators based on SR and KT to the Pearson's product moment correlation coefficient (PPMCC) are investigated in both the normal and contaminated normal models. Theoretical and simulation results suggest that, contrary to the opinion of equivalence between SR and KT in some literature, the behaviors of SR and KT are strikingly different in the aspects of bias effect, variance, mean square error, and asymptotic...
Kobryn, A E; Tokarchuk, M V
1999-01-01
An Enskog-Landau kinetic equation for a many-component system of charged hard spheres is proposed. It has been obtained from the Liouville equation with modified boundary conditions by the method of nonequilibrium statistical operator. On the basis of this equation the normal solutions and transport coefficients such as bulk kappa and shear eta viscosities, thermal conductivity lambda, mutual diffusion D^{\\alpha\\beta} and thermal diffusion D_T^\\alpha have been obtained for a binary mixture in the first approximation using the Chapman-Enskog method. Numerical calculations of all transport coefficients for mixtures Ar-Kr, Ar-Xe, Kr-Xe with different concentrations of compounds have been evaluated for the cases of absence and presence of long-range Coulomb interactions. The results are compared with those obtained from other theories and experiment.
Asymptotic Solutions of Serial Radial Fuel Shuffling
Xue-Nong Chen
2015-12-01
Full Text Available In this paper, the mechanism of traveling wave reactors (TWRs is investigated from the mathematical physics point of view, in which a stationary fission wave is formed by radial fuel drifting. A two dimensional cylindrically symmetric core is considered and the fuel is assumed to drift radially according to a continuous fuel shuffling scheme. A one-group diffusion equation with burn-up dependent macroscopic coefficients is set up. The burn-up dependent macroscopic coefficients were assumed to be known as functions of neutron fluence. By introducing the effective multiplication factor keff, a nonlinear eigenvalue problem is formulated. The 1-D stationary cylindrical coordinate problem can be solved successively by analytical and numerical integrations for associated eigenvalues keff. Two representative 1-D examples are shown for inward and outward fuel drifting motions, respectively. The inward fuel drifting has a higher keff than the outward one. The 2-D eigenvalue problem has to be solved by a more complicated method, namely a pseudo time stepping iteration scheme. Its 2-D asymptotic solutions are obtained together with certain eigenvalues keff for several fuel inward drifting speeds. Distributions of the neutron flux, the neutron fluence, the infinity multiplication factor kinf and the normalized power are presented for two different drifting speeds.
Asymptotics and Borel summability
Costin, Ovidiu
2008-01-01
Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, transseries, and exponential asymptotics. He provides complete mathematical rigor while supplementing it with heuristic material and examples, so that some proofs may be omitted by applications-oriented readers.To give a sense of how new methods are us
On asymptotic extension dimension
Repovš, Dušan; Zarichnyi, Mykhailo
2011-01-01
The aim of this paper is to introduce an asymptotic counterpart of the extension dimension defined by Dranishnikov. The main result establishes a relation between the asymptotic extensional dimension of a proper metric space and extension dimension of its Higson corona.
Spectral Expansion for the Asymptotically Spectral Periodic Differential Operators
O. A. Veliev
2016-01-01
In this paper we investigate the spectral expansion for the asymptotically spectral differential operators generated in all real line by ordinary differential expression of arbitrary order with periodic matrix-valued coefficients
ASYMPTOTIC QUANTIZATION OF PROBABILITY DISTRIBUTIONS
Klaus P(o)tzelberger
2003-01-01
We give a brief introduction to results on the asymptotics of quantization errors.The topics discussed include the quantization dimension,asymptotic distributions of sets of prototypes,asymptotically optimal quantizations,approximations and random quantizations.
Asymptotic Resource Usage Bounds
Albert E.; Alonso D.; Arenas P.; Genaim S.; Puebla G.
2009-01-01
When describing the resource usage of a program, it is usual to talk in asymptotic terms, such as the well-known “big O” notation, whereby we focus on the behaviour of the program for large input data and make a rough approximation by considering as equivalent programs whose resource usage grows at the same rate. Motivated by the existence of non-asymptotic resource usage analyzers, in this paper, we develop a novel transformation from a non-asymptotic cost function (which can be produced by ...
O' Flynn, Elizabeth A.M.; Morgan, Veronica A.; Giles, Sharon L. [Cancer Research UK and ESPSRC Cancer Imaging Centre, Clinical Magnetic Resonance Group, Surrey (United Kingdom); deSouza, Nandita M. [Royal Marsden NHS Foundation Trust, Clinical Magnetic Resonance Group, Institute of Cancer Research, Surrey (United Kingdom)
2012-07-15
To establish the reproducibility of apparent diffusion coefficient (ADC) measurements in normal fibroglandular breast tissue and to assess variation in ADC values with phase of the menstrual cycle and menopausal status. Thirty-one volunteers (13 premenopausal, 18 postmenopausal) underwent magnetic resonance twice (interval 11-22 days) using diffusion-weighted MRI. ADC{sub total} and a perfusion-insensitive ADC{sub high} (omitting b = 0) were calculated. Reproducibility and inter-observer variability of mean ADC values were assessed. The difference in mean ADC values between the two phases of the menstrual cycle and the postmenopausal breast were evaluated. ADC{sub total} and ADC{sub high} showed good reproducibility (r% = 17.6, 22.4). ADC{sub high} showed very good inter-observer agreement (kappa = 0.83). The intraclass correlation coefficients (ICC) were 0.93 and 0.91. Mean ADC values were significantly lower in the postmenopausal breast (ADC{sub total} 1.46 {+-} 0.3 x 10{sup -3} mm{sup 2}/s, ADC{sub high} 1.33 {+-} 0.3 x 10{sup -3} mm{sup 2}/s) compared with the premenopausal breast (ADC{sub total} 1.84 {+-} 0.26 x 10{sup -3} mm{sup 2}/s, ADC{sub high} 1.77 {+-} 0.26 x 10{sup -3} mm{sup 2}/s; both P < 0.001). No significant difference was seen in ADC values in relation to menstrual cycle (ADC{sub total} P = 0.2, ADC{sub high} P = 0.24) or between postmenopausal women taking or not taking oestrogen supplements (ADC{sub total} P = 0.6, ADC{sub high} P = 0.46). ADC values in fibroglandular breast tissue are reproducible. Lower ADC values within the postmenopausal breast may reduce diffusion-weighted contrast and have implications for accurately detecting tumours. (orig.)
Nonstandard asymptotic analysis
Berg, Imme
1987-01-01
This research monograph considers the subject of asymptotics from a nonstandard view point. It is intended both for classical asymptoticists - they will discover a new approach to problems very familiar to them - and for nonstandard analysts but includes topics of general interest, like the remarkable behaviour of Taylor polynomials of elementary functions. Noting that within nonstandard analysis, "small", "large", and "domain of validity of asymptotic behaviour" have a precise meaning, a nonstandard alternative to classical asymptotics is developed. Special emphasis is given to applications in numerical approximation by convergent and divergent expansions: in the latter case a clear asymptotic answer is given to the problem of optimal approximation, which is valid for a large class of functions including many special functions. The author's approach is didactical. The book opens with a large introductory chapter which can be read without much knowledge of nonstandard analysis. Here the main features of the t...
Bousso, Raphael
2016-01-01
We show that known entropy bounds constrain the information carried off by radiation to null infinity. We consider distant, planar null hypersurfaces in asymptotically flat spacetime. Their focussing and area loss can be computed perturbatively on a Minkowski background, yielding entropy bounds in terms of the energy flux of the outgoing radiation. In the asymptotic limit, we obtain boundary versions of the Quantum Null Energy Condition, of the Generalized Second Law, and of the Quantum Bousso Bound.
Asymptotically Safe Dark Matter
Sannino, Francesco
2014-01-01
We introduce a new paradigm for dark matter interactions according to which the interaction strength is asymptotically safe. In models of this type, the interaction strength is small at low energies but increases at higher energies towards a finite constant value of the coupling. The net effect is to partially offset direct detection constraints without affecting thermal freeze-out at higher energies. High-energy collider and indirect annihilation searches are the primary ways to constrain or discover asymptotically safe dark matter.
Asymptotic Fitness Distribution in the Bak-Sneppen Model of Biological Evolution with Four Species
Schlemm, Eckhard
2012-08-01
We suggest a new method to compute the asymptotic fitness distribution in the Bak-Sneppen model of biological evolution. As applications we derive the full asymptotic distribution in the four-species model, and give an explicit linear recurrence relation for a set of coefficients determining the asymptotic distribution in the five-species model.
Asymptotic fitness distribution in the Bak-Sneppen model of biological evolution with four species
Schlemm, Eckhard
2012-01-01
We suggest a new method to compute the asymptotic fitness distribution in the Bak-Sneppen model of biological evolution. As applications we derive the full asymptotic distribution in the four-species model, and give an explicit linear recurrence relation for a set of coefficients determining the asymptotic distribution in the five-species model.
Andrić, Filip; Šegan, Sandra; Dramićanin, Aleksandra; Majstorović, Helena; Milojković-Opsenica, Dušanka
2016-08-01
Soil-water partition coefficient normalized to the organic carbon content (KOC) is one of the crucial properties influencing the fate of organic compounds in the environment. Chromatographic methods are well established alternative for direct sorption techniques used for KOC determination. The present work proposes reversed-phase thin-layer chromatography (RP-TLC) as a simpler, yet equally accurate method as officially recommended HPLC technique. Several TLC systems were studied including octadecyl-(RP18) and cyano-(CN) modified silica layers in combination with methanol-water and acetonitrile-water mixtures as mobile phases. In total 50 compounds of different molecular shape, size, and various ability to establish specific interactions were selected (phenols, beznodiazepines, triazine herbicides, and polyaromatic hydrocarbons). Calibration set of 29 compounds with known logKOC values determined by sorption experiments was used to build simple univariate calibrations, Principal Component Regression (PCR) and Partial Least Squares (PLS) models between logKOC and TLC retention parameters. Models exhibit good statistical performance, indicating that CN-layers contribute better to logKOC modeling than RP18-silica. The most promising TLC methods, officially recommended HPLC method, and four in silico estimation approaches have been compared by non-parametric Sum of Ranking Differences approach (SRD). The best estimations of logKOC values were achieved by simple univariate calibration of TLC retention data involving CN-silica layers and moderate content of methanol (40-50%v/v). They were ranked far well compared to the officially recommended HPLC method which was ranked in the middle. The worst estimates have been obtained from in silico computations based on octanol-water partition coefficient. Linear Solvation Energy Relationship study revealed that increased polarity of CN-layers over RP18 in combination with methanol-water mixtures is the key to better modeling of
Quasi-extended asymptotic functions
The class F of ''quasi-extended asymptotic functions'' is introduced. It contains all extended asymptotic functions as well as some new asymptotic functions very similar to the Schwartz distributions. On the other hand, every two quasiextended asymptotic functions can be multiplied as opposed to the Schwartz distributions; in particular, the square delta2 of an asymptotic function delta similar to Dirac's delta-function, is constructed as an example
On the Asymptotic Accuracy of Efron's Bootstrap
Singh, Kesar
1981-01-01
In the non-lattice case it is shown that the bootstrap approximation of the distribution of the standardized sample mean is asymptotically more accurate than approximation by the limiting normal distribution. The exact convergence rate of the bootstrap approximation of the distributions of sample quantiles is obtained. A few other convergence rates regarding the bootstrap method are also studied.
Zero bias transformation and asymptotic expansions
Jiao, Ying
2012-01-01
Let W be a sum of independent random variables. We apply the zero bias transformation to deduce recursive asymptotic expansions for $\\mathbb {E}[h(W)]$ in terms of normal expectations, or of Poisson expectations for integer-valued random variables. We also discuss the estimates of remaining errors.
On the Asymptotic Distribution of Signal Fraction
Volobouev, Igor
2016-01-01
Condition of the asymptotic normality of the signal fraction estimate by maximum likelihood is derived under the null hypothesis of no signal. Consequences of this condition for determination of signal significance taking in to account the look elsewhere effect are discussed.
Puschnigg, Michael
1996-01-01
The aim of cyclic cohomology theories is the approximation of K-theory by cohomology theories defined by natural chain complexes. The basic example is the approximation of topological K-theory by de Rham cohomology via the classical Chern character. A cyclic cohomology theory for operator algebras is developed in the book, based on Connes' work on noncommutative geometry. Asymptotic cyclic cohomology faithfully reflects the basic properties and features of operator K-theory. It thus becomes a natural target for a Chern character. The central result of the book is a general Grothendieck-Riemann-Roch theorem in noncommutative geometry with values in asymptotic cyclic homology. Besides this, the book contains numerous examples and calculations of asymptotic cyclic cohomology groups.
A large part of physics consists of learning which asymptotic methods to apply where, yet physicists are not always taught asymptotics in a systematic way. Asymptotology is given using an example from aerodynamics, and a rent Phys. Rev. Letter Comment is used as a case study of one subtle way things can go wrong. It is shown that the application of local analysis leads to erroneous conclusions regarding the existence of a continuous spectrum in a simple test problem, showing that a global analysis must be used. The final section presents results on a more sophisticated example, namely the WKBJ solution of Mathieu equation. 13 refs., 2 figs
Jones, D S
1997-01-01
Many branches of science and engineering involve applications of mathematical analysis. An important part of applied analysis is asymptotic approximation which is, therefore, an active area of research with new methods and publications being found constantly. This book gives an introduction to the subject sufficient for scientists and engineers to grasp the fundamental techniques, both those which have been known for some time and those which have been discovered more recently. The asymptotic approximation of both integrals and differential equations is discussed and the discussion includes hy
Asymptotic freedom, asymptotic flatness and cosmology
Holographic RG flows in some cases are known to be related to cosmological solutions. In this paper another example of such correspondence is provided. Holographic RG flows giving rise to asymptotically-free β-functions have been analyzed in connection with holographic models of QCD. They are shown upon Wick rotation to provide a large class of inflationary models with logarithmically-soft inflaton potentials. The scalar spectral index is universal and depends only on the number of e-foldings. The ratio of tensor to scalar power depends on the single extra real parameter that defines this class of models. The Starobinsky inflationary model as well as the recently proposed models of T-inflation are members of this class. The holographic setup gives a completely new (and contrasting) view to the stability, naturalness and other problems of such inflationary models
Line Complexity Asymptotics of Polynomial Cellular Automata
Stone, Bertrand
2016-01-01
Cellular automata are discrete dynamical systems that consist of patterns of symbols on a grid, which change according to a locally determined transition rule. In this paper, we will consider cellular automata that arise from polynomial transition rules, where the symbols in the automaton are integers modulo some prime $p$. We are principally concerned with the asymptotic behavior of the line complexity sequence $a_T(k)$, which counts, for each $k$, the number of coefficient strings of length...
Tao Hu; Heng-jian Cui; Xing-wei Tong
2009-01-01
This article considers a semiparametric varying-coefficient partially linear regression model with current status data. The semiparametric varying-coefficient partially linear regression model which is a gen-eralization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estima-tor for the unknown smooth function is obtained and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are conducted to examine the small-sample properties of the proposed estimates and a real dataset is used to illustrate our approach.
Litim, Daniel F.; Sannino, Francesco
2014-01-01
We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet ...
Cristallini, Achille
2016-07-01
A new and intriguing machine may be obtained replacing the moving pulley of a gun tackle with a fixed point in the rope. Its most important feature is the asymptotic efficiency. Here we obtain a satisfactory description of this machine by means of vector calculus and elementary trigonometry. The mathematical model has been compared with experimental data and briefly discussed.
Asymptotic distributions in the projection pursuit based canonical correlation analysis
无
2010-01-01
In this paper, associations between two sets of random variables based on the projection pursuit (PP) method are studied. The asymptotic normal distributions of estimators of the PP based canonical correlations and weighting vectors are derived.
We have developed a magnetic resonance (MR) spin echo method to obtain diffusion weighted imaging using motion probing gradient (MPG) pulses in orthogonal direction before and after a 180 degree pulse. Phantom models containing water, acetone, cupric sulfate and agar, and normal brains of Wistar rats and puppies were examined. MRI was performed using a SISCO SIS 200/400 MRI/MRS experimental system for small animals (4.7 tesla, 400 mm bore). The apparent diffusion coefficient (ADC) values, given in mm2/sec, were 2.19±0.02 x 10-3 in water, 4.51±0. 18 x 10-3 in acetone, and the ADC of water was independent on longitudinal (T1) or transverse (T2) relaxation time. Time-dependent ADC changes were not demonstrated, however position-dependent ADC changes were significant. It is therefore important to set the sample at the same position for repeated MRI studies and for the evaluation of the time course of experimental studies. Mean ADC values of rat brains were 0.65 x 10-3 for cortex, 0.69 x 10-3 for caudate-putamen, 0.69 x 10-3 (perpendicular to axon) for corpus callosum, 1.11 x 10-3 (parallel to axon) for optic nerve, and 1.38 x 10-3 (parallel to axon) for trigeminal nerve. Those of puppies were 1.14- 1.42 x 10-3 for gray matter, 1.17 (parallel to axon) and 0.89 (perpendicular to axon) x 10-3 for white matter, 1.66 (parallel to axon) and 0.57 (perpendicular to axon) x 10-3 for internal capsule, and 0.91-0.95 x 10-3 for thalamus. On the in vivo ADC maps, white matter tracts successfully showed anisotropic diffusion. This technique has promising implications for the evaluation of the time course of cerebral damage and degenerative changes. (author)
Xuemei HU; Feng LIU; Zhizhong WANG
2009-01-01
The authors propose a V_(N,P) test statistic for testing finite-order serial correlation in a semiparametric varying coefficient partially linear errors-in-variables model. The test statistic is shown to have asymptotic normal distribution under the null hypothesis of no serial correlation. Some Monte Carlo experiments are conducted to examine the finite sample performance of the proposed V_(N,P) test statistic. Simulation results confirm that the proposed test performs satisfactorily in estimated size and power.
Asymptotic Behavior of Mean Partitions in Consensus Clustering
Jain, Brijnesh
2015-01-01
Although consistency is a minimum requirement of any estimator, little is known about consistency of the mean partition approach in consensus clustering. This contribution studies the asymptotic behavior of mean partitions. We show that under normal assumptions, the mean partition approach is consistent and asymptotic normal. To derive both results, we represent partitions as points of some geometric space, called orbit space. Then we draw on results from the theory of Fr\\'echet means and sto...
Optimistic Agents are Asymptotically Optimal
Sunehag, Peter; Hutter, Marcus
2012-01-01
We use optimism to introduce generic asymptotically optimal reinforcement learning agents. They achieve, with an arbitrary finite or compact class of environments, asymptotically optimal behavior. Furthermore, in the finite deterministic case we provide finite error bounds.
ASYMPTOTICS OF MEAN TRANSFORMATION ESTIMATORS WITH ERRORS IN VARIABLES MODEL
CUI Hengjian
2005-01-01
This paper addresses estimation and its asymptotics of mean transformation θ = E[h(X)] of a random variable X based on n iid. Observations from errors-in-variables model Y = X + v, where v is a measurement error with a known distribution and h(.) is a known smooth function. The asymptotics of deconvolution kernel estimator for ordinary smooth error distribution and expectation extrapolation estimator are given for normal error distribution respectively. Under some mild regularity conditions, the consistency and asymptotically normality are obtained for both type of estimators. Simulations show they have good performance.
Asymptotic Flatness in Rainbow Gravity
Hackett, Jonathan
2005-01-01
A construction of conformal infinity in null and spatial directions is constructed for the Rainbow-flat space-time corresponding to doubly special relativity. From this construction a definition of asymptotic DSRness is put forward which is compatible with the correspondence principle of Rainbow gravity. Furthermore a result equating asymptotically flat space-times with asymptotically DSR spacetimes is presented.
Coarse geometry and asymptotic dimension
Grave, Bernd
2006-01-01
We consider asymptotic dimension of coarse spaces. We analyse coarse structures induced by metrisable compactifications. We calculate asymptotic dimension of coarse cell complexes. We calculate the asymptotic dimension of certain negatively curved spaces, e.g. for complete, simply connected manifolds with bounded, strictly negative sectional curvature.
Asymptotically hyperbolic connections
Fine, Joel; Krasnov, Kirill; Scarinci, Carlos
2015-01-01
General Relativity in 4 dimensions can be equivalently described as a dynamical theory of SO(3)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analog of the Fefferman-Graham expansion in the language of connections. As in the metric setup, one can solve the arising "evolution" equations order by order in the expansion in powers of the radial coordinate. The solution in the connection setting is arguably simpler, and very straightforward algebraic manipulations allow one to see how the obstruction appears at third order in the expansion. Another interesting feature of the connection formulation is that the "counter terms" required in the computation of the renormalised volume all combine into the Chern-Simons functional of the restriction of the connection to the boundary. As the Chern-Simons invariant is only defined modulo large gauge transformations, the requirement that the path integral over asymptotically hyperbolic connections is well-d...
Local heat kernel asymptotics for nonminimal differential operators
The method for computing the local coefficients in the asymptotical heat kernel expansion is extended to the case of nonminimal differential operators. The lowest expansion coefficients are calculated for the second-order nonminimal operators on oneforms over a riemannian space in arbitrary dimensions. Unlike the coefficients for the minimal second-order operators those for nonminimal ones turn out to be essentially dependent on the space dimension. (orig.)
Another Asymptotic Notation : "Almost"
Mondal, Nabarun; Ghosh, Partha P.
2013-01-01
Asymptotic notations are heavily used while analysing runtimes of algorithms. Present paper argues that some of these usages are non trivial, therefore incurring errors in communication of ideas. After careful reconsidera- tion of the various existing notations a new notation is proposed. This notation has similarities with the other heavily used notations like Big-Oh, Big Theta, while being more accurate when describing the order relationship. It has been argued that this notation is more su...
Frequency-dependent seismic reflection coefficient for discriminating gas reservoirs
The asymptotic equation of wave propagation in fluid-saturated porous media is available for calculating the normal reflection coefficient within a seismic frequency band. This frequency-dependent reflection coefficient is expressed in terms of a dimensionless parameter ε, which is the product of the reservoir fluid mobility (i.e. inverse viscosity), fluid density and the frequency of the signal. In this paper, we apply this expression to the Xinchang gas field, China, where reservoirs are in super-tight sands with very low permeability. We demonstrate that the variation in the reflection coefficient at a gas–water contact as a transition zone within a sand formation is observable within the seismic frequency band. Then, we conduct seismic inversion to generate attributes which first indicate the existence of fluid (either gas or water), and then discriminate a gas reservoir from a water reservoir
Marklund, Mette; Christensen, Robin; Torp-Pedersen, Søren; Thomsen, Carsten; Nolsøe, Christian P
2007-01-01
containing oral contraceptives (ECOC) was recorded. Post-processing with automated subtraction, manually traced ROI (region of interest) and recording of the SI was performed. A random coefficient model was applied. RESULTS: We found an SI increase of 24.2% and 40% following the low and high dose...
Asymptotic sampling distribution of inverse coeﬃcient of variation and its applications: revisited
Ahmed N. Albatineh
2013-12-01
Full Text Available Sharma and Krishna (1994 derived mathematically an appealing asymptotic confidence interval for the population signal-to-noise ratio (SNR. In this paper, an evaluation of the performance of this interval using monte carlo simulations using randomly generated data from normal, log-normal, $\\chi^2$, Gamma, and Weibull distributions three of which are discussed in Sharma and Krishna (1994. Simulations revealed that its performance, as measured by coverage probability, is totally dependent on the amount of noise introduced. A proposal for using ranked set sampling (RSS instead of simple random sampling (SRS improved its performance. It is recommended against using this confidence interval for data from a log-normal distribution. Moreover, this interval performs poorly in all other distributions unless the SNR is around one.Keywords: Signal-to-noise ratio, coefficient of variation, sampling distribution, confidence interval, ranked set sample, simple random sample.
Asymptotics for Nonlinear Transformations of Fractionally Integrated Time Series
无
2007-01-01
The asymptotic theory for nonlinear transformations of fractionally integrated time series is developed. By the use of fractional Occupation Times Formula, various nonlinear functions of fractionally integrated series such as ARFIMA time series are studied, and the asymptotic distributions of the sample moments of such functions are obtained and analyzed. The transformations considered in this paper includes a variety of functions such as regular functions, integrable functions and asymptotically homogeneous functions that are often used in practical nonlinear econometric analysis. It is shown that the asymptotic theory of nonlinear transformations of original and normalized fractionally integrated processes is different from that of fractionally integrated processes, but is similar to the asymptotic theory of nonlinear transformations of integrated processes.
Tang, X.; Azhari, A.; Changbo, Fu.; Gagliardi, C. A.; Mukhamedzhanov, A. M.; Pirlepesov, F.; Trache, R. E.; Tribble, R. E.; Burjan, Václav; Kroha, Václav; Carstoiu, F.
Texas : TAMU, 2003. s. 1-2. [Progress Report 2003. 00.09.2003, Texas] R&D Projects: GA AV ČR KSK1048102; GA MŠk ME 385; GA MŠk ME 643; GA ČR GA202/01/0709 Keywords : direct capture * S factor * R-matrix Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders
Hwang, W. -Y.; Matsumoto, Keiji
2001-01-01
We propose entanglement measures with asymptotic weak-monotonicity. We show that a normalized form of entanglement measures with the asymptotic weak-monotonicity are lower (upper) bound for the entanglement of cost (distillation).
Kartuzova, Olga; Kassemi, Mohammad
2015-01-01
In this paper, a computational model that describes pressure control phase of a typical MHTB experiment will be presented. The fidelity of the model will be assessed by comparing the models predictions with MHTB experimental data. In this paper CFD results for MHTB spray bar cooling case with 50 tank fill ratio will be presented and analyzed. Effect of accommodation coefficient for calculating droplet-ullage mass transfer will be evaluated.
Juna, Shazia; Huber, Anton
2015-01-01
Starch is a highly disperse material with broad distributions of molecular sizes and geometries. Its dissolution in aqueous media is difficult to achieve and it tends to form aggregates through both inter- and intra-molecular interactions. Asymmetrical flow field-flow fractionation (AF4) is a suitable technique for the separation of such macromolecular and colloidal systems. A major advantage of AF4 is the direct correlation of translational diffusion coefficients with retention time and expe...
Duality and asymptotic geometries
Boonstra, H J; Skenderis, K
1997-01-01
We consider a series of duality transformations that leads to a constant shift in the harmonic functions appearing in the description of a configuration of branes. This way, for several intersections of branes, we can relate the original brane configuration which is asymptotically flat to a geometry of the type $adS_k \\xx E^l \\xx S^m$. The implications of our results for supersymmetry enhancement, M(atrix) theory at finite N, and for supergravity theories in diverse dimensions are discussed.
New Inference Procedures for Semiparametric Varying-Coefficient Partially Linear Cox Models
Yunbei Ma
2014-01-01
Full Text Available In biomedical research, one major objective is to identify risk factors and study their risk impacts, as this identification can help clinicians to both properly make a decision and increase efficiency of treatments and resource allocation. A two-step penalized-based procedure is proposed to select linear regression coefficients for linear components and to identify significant nonparametric varying-coefficient functions for semiparametric varying-coefficient partially linear Cox models. It is shown that the penalized-based resulting estimators of the linear regression coefficients are asymptotically normal and have oracle properties, and the resulting estimators of the varying-coefficient functions have optimal convergence rates. A simulation study and an empirical example are presented for illustration.
Estimation of Semi-Varying Coefficient Model with Surrogate Data and Validation Sampling
Ya-zhao L(U); Ri-quan ZHANG; Zhen-sheng HUANG
2013-01-01
In this paper,we investigate the estimation of semi-varying coefficient models when the nonlinear covariates are prone to measurement error.With the help of validation sampling,we propose two estimators of the parameter and the coefficient functions by combining dimension reduction and the profile likelihood methods without any error structure equation specification or error distribution assumption.We establish the asymptotic normality of proposed estimators for both the parametric and nonparametric parts and show that the proposed estimators achieves the best convergence rate.Data-driven bandwidth selection methods are also discussed.Simulations are conducted to evaluate the finite sample property of the estimation methods proposed.
Asymptotic Symmetries from finite boxes
Andrade, Tomas
2015-01-01
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a "box." This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the Anti-de Sitter and Poincar\\'e asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2+1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS$_3$ and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.
Asymptotic symmetries from finite boxes
Andrade, Tomás; Marolf, Donald
2016-01-01
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a 'box.' This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the anti-de Sitter and Poincaré asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2 + 1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS3 and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.
Robust methods and asymptotic theory in nonlinear econometrics
Bierens, Herman J
1981-01-01
This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate ...
The asymptotic distribution of maxima in bivariate samples
Campbell, J. W.; Tsokos, C. P.
1973-01-01
The joint distribution (as n tends to infinity) of the maxima of a sample of n independent observations of a bivariate random variable (X,Y) is studied. A method is developed for deriving the asymptotic distribution of the maxima, assuming that X and Y possess asymptotic extreme-value distributions and that the probability element dF(x,y) can be expanded in a canonical series. Applied both to the bivariate normal distribution and to the bivariate gamma and compound correlated bivariate Poisson distributions, the method shows that maxima from all these distributions are asymptotically uncorrelated.
Regular Variation and Smile Asymptotics
Benaim, Shalom; Friz, Peter
2006-01-01
We consider risk-neutral returns and show how their tail asymptotics translate directly to asymptotics of the implied volatility smile, thereby sharpening Roger Lee's celebrated moment formula. The theory of regular variation provides the ideal mathematical framework to formulate and prove such results. The practical value of our formulae comes from the vast literature on tail asymptotics and our conditions are often seen to be true by simple inspection of known results.
Heavy Flavor DIS Wilson coefficients in the asymptotic regime
Bierenbaum, Isabella; Blumlein, Johannes; Klein, Sebastian; Ablinger, J.; Hasselhuhn, A.(Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, Linz, A-4040, Austria); Schneider, C; Wissbrock, F.
2010-01-01
We report on results for the heavy flavor contributions to $F_2(x,Q^2)$ in the limit $Q^2\\gg m^2$ at {\\sf NNLO}. By calculating the massive $3$--loop operator matrix elements, we account for all but the power suppressed terms in $m^2/Q^2$. Recently, the calculation of fixed Mellin moments of all $3$--loop massive operator matrix elements has been finished. We present new all--$N$ results for the $O(n_f)$--terms, thereby confirming the corresponding parts of the $3$--loop anomalous dimensions....
Heavy flavor DIS Wilson coefficients in the asymptotic regime
Ablinger, J.; Schneider, C. [Linz Univ. (AT). Research Inst. for Symbolic Computation (RISC); Bierenbaum, I. [CSIC-Universitat de Valencia (Spain). Inst. de Fisica Corpuscular; Bluemlein, J.; Hasselhuhn, A.; Wissbrock, F. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Klein, S. [RWTH Aachen (Germany). Inst. fuer Theoretische Teilchenphysik und Kosmologie
2010-07-15
We report on results for the heavy flavor contributions to F{sub 2}(x,Q{sup 2}) in the limit Q{sup 2}>>m{sup 2} at NNLO. By calculating the massive 3-loop operator matrix elements, we account for all but the power suppressed terms in m{sup 2}/Q{sup 2}. Recently, the calculation of fixed Mellin moments of all 3-loop massive operator matrix elements has been finished. We present new all-N results for the O(n{sub f})-terms, thereby confirming the corresponding parts of the 3-loop anomalous dimensions. Additionally, we report on first genuine 3-loop results of the ladder-type diagrams for general values of the Mellin variable N. (orig.)
Heavy flavor DIS Wilson coefficients in the asymptotic regime
We report on results for the heavy flavor contributions to F2(x,Q2) in the limit Q2>>m2 at NNLO. By calculating the massive 3-loop operator matrix elements, we account for all but the power suppressed terms in m2/Q2. Recently, the calculation of fixed Mellin moments of all 3-loop massive operator matrix elements has been finished. We present new all-N results for the O(nf)-terms, thereby confirming the corresponding parts of the 3-loop anomalous dimensions. Additionally, we report on first genuine 3-loop results of the ladder-type diagrams for general values of the Mellin variable N. (orig.)
Research on temperature profiles of honeycomb regenerator with asymptotic analysis
AI Yuan-fang; MEI Chi; HUANG Guo-dong; JIANG Shao-jian; CHEN Hong-rong
2006-01-01
An asymptotic semi-analytical method for heat transfer in counter-flow honeycomb regenerator is proposed. By introducing a combined heat-transfer coefficient between the gas and solid phase, a heat transfer model is built based on the thin-walled assumption. The dimensionless thermal equation is deduced by considering solid heat conduction along the passage length. The asymptotic analysis is used for the small parameter of heat conduction term in equation. The first order asymptotic solution to temperature distribution under weak solid heat conduction is achieved after Laplace transformation through the multiple scales method and the symbolic manipulation function in MATLAB. Semi-analytical solutions agree with tests and finite-difference numerical results. It is proved possible for the asymptotic analysis to improve the effectiveness, economics and precision of thermal research on regenerator.
Extended asymptotic functions - some examples
Several examples of extended asymptotic functions are exposed. These examples will illustrate the notions introduced in another paper but at the same time they have a significance as realizations of some Schwartz disctibutions: delta(x), H(x), P(1/xsup(n)), etc. The important thing is that the asymptotic functions of these examples (which, on their part, are realizations of the above-mentioned distributions) can be multiplied in the class of the asymptotic functions as opposed to the theory of Schwartz distributions. Some properties of the set of all extended asymptotic functions are considered which are essential for the next step of this approach
Unified treatment of the asymptotics of asymmetric kernel density estimators
Hoffmann, Till; Jones, Nick S.
2015-01-01
We extend balloon and sample-smoothing estimators, two types of variable-bandwidth kernel density estimators, by a shift parameter and derive their asymptotic properties. Our approach facilitates the unified study of a wide range of density estimators which are subsumed under these two general classes of kernel density estimators. We demonstrate our method by deriving the asymptotic bias, variance, and mean (integrated) squared error of density estimators with gamma, log-normal, Birnbaum-Saun...
Sharp asymptotic results for simplified mutation-selection algorithms
Bérard, J.; Bienvenüe, A
2003-01-01
We study the asymptotic behavior of a mutation--selection genetic algorithm on the integers with finite population of size $p\\ge 1$. The mutation is defined by the steps of a simple random walk and the fitness function is linear. We prove that the normalized population satisfies an invariance principle, that a large-deviations principle holds and that the relative positions converge in law. After $n$ steps, the population is asymptotically around $\\sqrt{n}$ times the posi...
Asymptotic Enumeration of RNA Structures with Pseudoknots
Jin, Emma Y
2007-01-01
In this paper we present the asymptotic enumeration of RNA structures with pseudoknots. We develop a general framework for the computation of exponential growth rate and the sub exponential factors for $k$-noncrossing RNA structures. Our results are based on the generating function for the number of $k$-noncrossing RNA pseudoknot structures, ${\\sf S}_k(n)$, derived in \\cite{Reidys:07pseu}, where $k-1$ denotes the maximal size of sets of mutually intersecting bonds. We prove a functional equation for the generating function $\\sum_{n\\ge 0}{\\sf S}_k(n)z^n$ and obtain for $k=2$ and $k=3$ the analytic continuation and singular expansions, respectively. It is implicit in our results that for arbitrary $k$ singular expansions exist and via transfer theorems of analytic combinatorics we obtain asymptotic expression for the coefficients. We explicitly derive the asymptotic expressions for 2- and 3-noncrossing RNA structures. Our main result is the derivation of the formula ${\\sf S}_3(n) \\sim \\frac{10.4724\\cdot 4!}{n(n...
On asymptotics for difference equations
Rafei, M.
2012-01-01
In this thesis a class of nonlinear oscillator equations is studied. Asymptotic approximations of first integrals for nonlinear difference equations are constructed by using the recently developed perturbation method based on invariance vectors. The asymptotic approximations of the solutions of the
Strong and ratio asymptotics for Laguerre polynomials revisited
Deaño, Alfredo; Huertas, Edmundo J.; Marcellán, Francisco
2013-01-01
In this paper we consider the strong asymptotic behavior of Laguerre polynomials in the complex plane. The leading behavior is well known from Perron and Mehler-Heine formulas, but higher order coefficients, which are important in the context of Krall-Laguerre or Laguerre-Sobolev-type orthogonal polynomials, are notoriously difficult to compute. In this paper, we propose the use of an alternative expansion, due to Buchholz, in terms of Bessel functions of the first kind. The coefficients in t...
Objective: The purpose of this study is to discuss the diagnostic accuracy of normalized liver ADC using the spleen and renal cortex as reference organs for the diagnosis of liver fibrosis. Methods: Forty three patients with liver disease (chronic liver disease group) at compensated stage and 10 healthy volunteers (control group) were retrospectively assessed with diffusion-weighted imaging at a 3.0 T MR unit. Liver ADC, spleen ADC, renal ADC and normalized ADC (defined as the ratio of liver ADC to spleen ADC or renal cortex ADC, S-ADC and R-ADC for short) were measured in patients stratified by fibrosis stage. Spearman analysis was used to see the correlation between fibrosis stages and ADC, one-way ANOVA was used to compare the ADCs in different fibrosis stages. Logistic regression analysis was used to determine the performance of ADC for prediction of liver fibrosis, and show the area under the curve (AUC), sensitivity and specificity choosing the optimal cutoff value that maximized the Youden index. Results: Ten volunteers belonged to S0 stage. From S0 to S4 stage, there were 2, 5, 9, 12 and 15 patients, correspondingly, liver ADC were (1.37±0.13) ×10-3, (1.33±0.16) ×10-3, (1.17±0.16) ×10-3, (1.23±0.14) ×10-3 and (1.12 ±0.11) × 10-3 mm2/s, S-ADC were 1.86 ±0.18, 1.68 ±0.12, 1.34 ±0.14, 1.48 ±0.15 and 1.34±0.10, R-ADC were 0.71 ±0.08, 0.68 ±0.12, 0.61 ±0.09, 0.64 ±0.11 and 0.60 ±0.08 respectively, and the differences among them were significant (F=6.48, 18.70 and 3.04, P<0.05). The correlation between fibrosis stage and S-ADC was stronger than between fibrosis stage and liver ADC, R-ADC (r=-0.71, -0.51, -0.41; P<0.01). S-ADC was superior to liver ADC and R-ADC for detection of S2, S3 and S4 fibrosis stage (Youden index: 0.91, 0.58, and 0.59). Conclusion: Spleen normalized liver ADC improves diagnostic accuracy for detection of liver fibrosis than liver ADC and renal normalized liver ADC. (authors)
Zhang, Hao; Han, Hao; Wang, Jing; Ma, Jianhua; Liu, Yan; Moore, William; Liang, Zhengrong
2014-01-01
Purpose: Repeated computed tomography (CT) scans are required for some clinical applications such as image-guided interventions. To optimize radiation dose utility, a normal-dose scan is often first performed to set up reference, followed by a series of low-dose scans for intervention. One common strategy to achieve the low-dose scan is to lower the x-ray tube current and exposure time (mAs) or tube voltage (kVp) setting in the scanning protocol, but the resulted image quality by the conventi...
Asymptotic Phase for Stochastic Oscillators
Thomas, Peter J.; Lindner, Benjamin
2014-12-01
Oscillations and noise are ubiquitous in physical and biological systems. When oscillations arise from a deterministic limit cycle, entrainment and synchronization may be analyzed in terms of the asymptotic phase function. In the presence of noise, the asymptotic phase is no longer well defined. We introduce a new definition of asymptotic phase in terms of the slowest decaying modes of the Kolmogorov backward operator. Our stochastic asymptotic phase is well defined for noisy oscillators, even when the oscillations are noise dependent. It reduces to the classical asymptotic phase in the limit of vanishing noise. The phase can be obtained either by solving an eigenvalue problem, or by empirical observation of an oscillating density's approach to its steady state.
Purpose: To prospectively investigate the effect on signal intensity (SI) of healthy breast parenchyma on magnetic resonance mammography (MRM) when doubling the contrast dose from 0.1 to 0.2 mmol/kg bodyweight. Materials and methods: Informed consent and institutional review board approval were obtained. Twenty-five healthy female volunteers (median age: 24 years (range: 21-37 years) and median bodyweight: 65 kg (51-80 kg)) completed two dynamic MRM examinations on a 0.6 T open scanner. The inter-examination time was 24 h (23.5-25 h). The following sequences were applied: axial T2W TSE and an axial dynamic T1W FFED, with a total of seven frames. At day 1, an i.v. gadolinium (Gd) bolus injection of 0.1 mmol/kg bodyweight (Omniscan) (low) was administered. On day 2, the contrast dose was increased to 0.2 mmol/kg (high). Injection rate was 2 mL/s (day 1) and 4 mL/s (day 2). Any use of estrogen containing oral contraceptives (ECOC) was recorded. Post-processing with automated subtraction, manually traced ROI (region of interest) and recording of the SI was performed. A random coefficient model was applied. Results: We found an SI increase of 24.2% and 40% following the low and high dose, respectively (P < 0.0001); corresponding to a 65% (95% CI: 37-99%) SI increase, indicating a moderate saturation. Although not statistically significant (P = 0.06), the results indicated a tendency, towards lower maximal SI in the breast parenchyma of ECOC users compared to non-ECOC users. Conclusion: We conclude that the contrast dose can be increased from 0.1 to 0.2 mmol/kg bodyweight, if a better contrast/noise relation is desired but increasing the contrast dose above 0.2 mmol/kg bodyweight is not likely to improve the enhancement substantially due to the moderate saturation observed. Further research is needed to determine the impact of ECOC on the relative enhancement ratio, and further studies are needed to determine if a possible use of ECOC should be considered a compromising
Conformal Phase Diagram of Complete Asymptotically Free Theories
Pica, Claudio; Sannino, Francesco
2016-01-01
We investigate the ultraviolet and infrared fixed point structure of gauge-Yukawa theories featuring a single gauge coupling, Yukawa coupling and scalar self coupling. Our investigations are performed using the two loop gauge beta function, one loop Yukawa beta function and one loop scalar beta function. We provide the general conditions that the beta function coefficients must abide for the theory to be completely asymptotically free while simultaneously possessing an infrared stable fixed point. We also uncover special trajectories in coupling space along which some couplings are both asymptotically safe and infrared conformal.
Asymptotic structure of isolated systems
The main methods to formulate asymptotic flatness conditions are introduced and motivation and basic ideas are emphasized. Any asymptotic flatness condition proposed up to now describes space-times which behave somehow like Minkowski space, and a very explicit exposition of the structure at infinity of Minkowski space is given. This structure is used to describe the asymptotic behaviour of fields on Minkowski space in a frame-dependent way. The definition of null infinity for curved space-time according to Penrose is given and attempts to define spacelike infinity are outlined. The conformal bundle approach to the formulation of asymptotic behaviour is described and its relation to null and spacelike infinity is given, as far as known. (Auth.)
Asymptotic algebra of quantum electrodynamics
Herdegen, Andrzej
2004-01-01
The Staruszkiewicz quantum model of the long-range structure in electrodynamics is reviewed in the form of a Weyl algebra. This is followed by a personal view on the asymptotic structure of quantum electrodynamics.
Exponential asymptotics and gravity waves
Chapman, S. J.; Vanden-Broeck, J.
2006-01-01
The problem of irrotational inviscid incompressible free-surface flow is examined in the limit of small Froude number. Since this is a singular perturbation, singularities in the flow field (or its analytic continuation) such as stagnation points, or corners in submerged objects or on rough beds, lead to a divergent asymptotic expansion, with associated Stokes lines. Recent techniques in exponential asymptotics are employed to observe the switching on of exponentially small gravity waves acro...
Asymptotic behavior of atomic momentals
Thakkar, Ajit J.
1987-05-01
Knowledge of the large and small momentum transfer behavior of the electron momentum distribution is an important ingredient in the analysis of experimental isotropic Compton profiles. This behavior ultimately rests upon the asymptotic behavior of atomic momentals (momentum space orbitals). The small momentum Maclaurin expansion and the large momentum asymptotic expansion of atomic momentals with arbitrary angular momentum quantum number are derived in this paper. Their implications for momentum densities and Compton profiles are derived and discussed.
Detailed ultraviolet asymptotics for AdS scalar field perturbations
Evnin, Oleg
2016-01-01
We present a range of methods suitable for accurate evaluation of the leading asymptotics for integrals of products of Jacobi polynomials in limits when the degrees of some or all polynomials inside the integral become large. The structures in question have recently emerged in the context of effective descriptions of small amplitude perturbations in anti-de Sitter (AdS) spacetime. The limit of high degree polynomials corresponds in this situation to effective interactions involving extreme short-wavelength modes, whose dynamics is crucial for the turbulent instabilities that determine the ultimate fate of small AdS perturbations. We explicitly apply the relevant asymptotic techniques to the case of a self-interacting probe scalar field in AdS and extract a detailed form of the leading large degree behavior, including closed form analytic expressions for the numerical coefficients appearing in the asymptotics.
Estimation of the average correlation coefficient for stratified bivariate data.
Rubenstein, L M; Davis, C S
1999-03-15
If the relationship between two ordered categorical variables X and Y is influenced by a third categorical variable with K levels, the Cochran-Mantel-Haenszel (CMH) correlation statistic QC is a useful stratum-adjusted summary statistic for testing the null hypothesis of no association between X and Y. Although motivated by and developed for the case of K I x J contingency tables, the correlation statistic QC is also applicable when X and Y are continuous variables. In this paper we derive a corresponding estimator of the average correlation coefficient for K I x J tables. We also study two estimates of the variance of the average correlation coefficient. The first is a restricted variance based on the variances of the observed cell frequencies under the null hypothesis of no association. The second is an unrestricted variance based on an asymptotic variance derived by Brown and Benedetti. The estimator of the average correlation coefficient works well in tables with balanced and unbalanced margins, for equal and unequal stratum-specific sample sizes, when correlation coefficients are constant over strata, and when correlation coefficients vary across strata. When the correlation coefficients are zero, close to zero, or the cell frequencies are small, the confidence intervals based on the restricted variance are preferred. For larger correlations and larger cell frequencies, the unrestricted confidence intervals give superior performance. We also apply the CMH statistic and proposed estimators to continuous non-normal data sampled from bivariate gamma distributions. We compare our methods to statistics for data sampled from normal distributions. The size and power of the CMH and normal theory statistics are comparable. When the stratum-specific sample sizes are small and the distributions are skewed, the proposed estimator is superior to the normal theory estimator. When the correlation coefficient is zero or close to zero, the restricted confidence intervals
Ekström, Joakim
2011-01-01
Spearman’s rank correlation coefficient is shown to be a deterministic transformation of the empirical polychoric correlation coefficient. The transformation is a homeomorphism under given marginal probabilities, and has a fixed point at zero. Moreover, the two measures of association for ordinal variables are asymptotically equivalent, in a certain sense. If the ordinal variables arise from discretizations, such as groupings of values into categories, Spearman’s rank correlation coefficient ...
Superradiant instabilities of asymptotically anti-de Sitter black holes
Green, Stephen R.; Hollands, Stefan; Ishibashi, Akihiro; Wald, Robert M.
2016-06-01
We study the linear stability of asymptotically anti-de Sitter black holes in general relativity in spacetime dimension d≥slant 4. Our approach is an adaptation of the general framework of Hollands and Wald, which gives a stability criterion in terms of the sign of the canonical energy, { E }. The general framework was originally formulated for static or stationary and axisymmetric black holes in the asymptotically flat case, and the stability analysis for that case applies only to axisymmetric perturbations. However, in the asymptotically anti-de Sitter case, the stability analysis requires only that the black hole have a single Killing field normal to the horizon and there are no restrictions on the perturbations (apart from smoothness and appropriate behavior at infinity). For an asymptotically anti-de Sitter black hole, we define an ergoregion to be a region where the horizon Killing field is spacelike; such a region, if present, would normally occur near infinity. We show that for black holes with ergoregions, initial data can be constructed such that { E }\\lt 0, so all such black holes are unstable. To obtain such initial data, we first construct an approximate solution to the constraint equations using the WKB method, and then we use the Corvino–Schoen technique to obtain an exact solution. We also discuss the case of charged asymptotically anti-de Sitter black holes with generalized ergoregions.
Asymptotic Properties of Criteria for Selection of Variables in Multiple Regression
Nishii, Ryuei
1984-01-01
In normal linear regression analysis, many model selection rules proposed from various viewpoints are available. For the information criteria AIC, FPE, $C_p$, PSS and BIC, the asymptotic distribution of the selected model and the asymptotic quadratic risk based on each criterion are explicitly obtained.
ASYMPTOTIC PROPERTIES OF MLE FOR WEIBULL DISTRIBUTION WITH GROUPED DATA
XUE Hongqi; SONG Lixin
2002-01-01
A grouped data model for Weibull distribution is considered. Under mild con-ditions, the maximum likelihood estimators(MLE) are shown to be identifiable, strongly consistent, asymptotically normal, and satisfy the law of iterated logarithm. Newton iter- ation algorithm is also considered, which converges to the unique solution of the likelihood equation. Moreover, we extend these results to a random case.
Asymptotics for Kernel Estimation of Slicing Average Third-Moment Estimation
Li-ping Zhu; Li-xing Zhu
2006-01-01
To estimate central dimension-reduction space in multivariate nonparametric regression, Sliced Inverse Regression[7] (SIR), Sliced Average Variance Estimation[4] (SAVE) and Slicing Average Third-moment Estimation[14] (SAT) have been developed. Since slicing estimation has very different asymptotic behavior for SIR and SAVE, the relevant study has been made case by case, when the kernel estimators of SIR and SAVE share similar asymptotic properties. In this paper, we also investigate kernel estimation of SAT. We prove the asymptotic normality, and show that, compared with the existing results, the kernel smoothing for SIR, SAVE and SAT has very similar asymptotic behavior.
Baez, J C; Egan, G F; Baez, John C.; Egan, Greg
2002-01-01
The Riemannian 10j symbols are spin networks that assign an amplitude to each 4-simplex in the Barrett-Crane model of Riemannian quantum gravity. This amplitude is a function of the areas of the 10 faces of the 4-simplex, and Barrett and Williams have shown that one contribution to its asymptotics comes from the Regge action for all non-degenerate 4-simplices with the specified face areas. However, we show numerically that the dominant contribution comes from degenerate 4-simplices. As a consequence, one can compute the asymptotics of the Riemannian 10j symbols by evaluating a `degenerate spin network', where the rotation group SO(4) is replaced by the Euclidean group of isometries of R^3. We conjecture formulas for the asymptotics of a large class of Riemannian and Lorentzian spin networks, including the Lorentzian 10j symbols, in terms of these degenerate spin networks.
Asymptotics for restricted integer compositions
Malandro, Martin E
2011-01-01
We study the compositions of an integer n where the part sizes of the compositions are restricted to lie in a finite set. We obtain asymptotic formulas for the number of such compositions, the total and average number of parts among all such compositions, and the total and average number of times a particular part size appears among all such compositions. Several of our asymptotics have the additional property that their absolute errors---not just their percentage errors---go to 0 as n goes to infinity. Along the way we also obtain recurrences and generating functions for calculating several of these quantities. Our asymptotic formulas come from the meromorphic analysis of our generating functions. Our results also apply to questions about certain kinds of tilings and rhythm patterns.
Asymptotic analysis and boundary layers
Cousteix, Jean
2007-01-01
This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general comprehensive presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows. The advantages of SCEM are discussed in comparison with the standard Method of Matched Asymptotic Expansions. In particular, for the first time, the theory of Interactive Boundary Layer is fully justified. With its chapter summaries, detailed derivations of results, discussed examples and fully worked out problems and solutions, the book is self-contained. It is written on a mathematical level accessible to graduate and post-graduate students of engineering and physics with a good knowledge in fluid mechanics. Researchers and practitioners will estee...
Second virial coefficients of dipolar hard spheres
Philipse, A.P.; Kuipers, B.W.M.
2010-01-01
An asymptotic formula is reported for the second virial coefficient B2 of a dipolar hard-sphere (DHS) fluid, in zero external field, for strongly coupled dipolar interactions. This simple formula, together with the one for the weak-coupling B2, provides an accurate prediction of the second virial co
Asymptotic risks of Viterbi segmentation
Kuljus, Kristi
2010-01-01
We consider the maximum likelihood (Viterbi) alignment of a hidden Markov model (HMM). In an HMM, the underlying Markov chain is usually hidden and the Viterbi alignment is often used as the estimate of it. This approach will be referred to as the Viterbi segmentation. The goodness of the Viterbi segmentation can be measured by several risks. In this paper, we prove the existence of asymptotic risks. Being independent of data, the asymptotic risks can be considered as the characteristics of the model that illustrate the long-run behavior of the Viterbi segmentation.
ASYMPTOTIC METHODS OF STATISTICAL CONTROL
Orlov A. I.
2014-10-01
Full Text Available Statistical control is a sampling control based on the probability theory and mathematical statistics. The article presents the development of the methods of statistical control in our country. It discussed the basics of the theory of statistical control – the plans of statistical control and their operational characteristics, the risks of the supplier and the consumer, the acceptance level of defectiveness and the rejection level of defectiveness. We have obtained the asymptotic method of synthesis of control plans based on the limit average output level of defectiveness. We have also developed the asymptotic theory of single sampling plans and formulated some unsolved mathematical problems of the theory of statistical control
Asymptotic perturbation theory of waves
Ostrovsky, Lev
2014-01-01
This book is an introduction to the perturbation theory for linear and nonlinear waves in dispersive and dissipative media. The main focus is on the direct asymptotic method which is based on the asymptotic expansion of the solution in series of one or more small parameters and demanding finiteness of the perturbations; this results in slow variation of the main-order solution. The method, which does not depend on integrability of basic equations, is applied to quasi-harmonic and non-harmonic periodic waves, as well as to localized waves such as solitons, kinks, and autowaves. The basic theor
Asymptotic freedom for nonrelativistic confinement
Some aspects of asymptotic freedom are discussed in the context of a simple two-particle nonrelativistic confining potential model. In this model, asymptotic freedom follows from the similarity of the free-particle and bound state radial wave functions at small distances and for the same angular momentum and the same large energy. This similarity, which can be understood using simple quantum mechanical arguments, can be used to show that the exact response function approaches that obtained when final state interactions are ignored. A method of calculating corrections to this limit is given, and explicit examples are given for the case of a harmonic oscillator
Comment on Asymptotically Safe Inflation
Tye, S -H Henry
2010-01-01
We comment on Weinberg's interesting analysis of asymptotically safe inflation (arXiv:0911.3165). We find that even if the gravity theory exhibits an ultraviolet fixed point, the energy scale during inflation is way too low to drive the theory close to the fixed point value. We choose the specific renormalization groupflow away from the fixed point towards the infrared region that reproduces the Newton's constant and today's cosmological constant. We follow this RG flow path to scales below the Planck scale to study the stability of the inflationary scenario. Again, we find that some fine tuning is necessary to get enough efolds of infflation in the asymptotically safe inflationary scenario.
Asymptotically free SU(5) models
The behaviour of Yukawa and Higgs effective charges of the minimal SU(5) unification model is investigated. The model includes ν=3 (or more, up to ν=7) generations of quarks and leptons and, in addition, the 24-plet of heavy fermions. A number of solutions of the renorm-group equations are found, which reproduce the known data about quarks and leptons and, due to a special choice of the coupling constants at the unification point are asymptotically free in all charges. The requirement of the asymptotical freedom leads to some restrictions on the masses of particles and on their mixing angles
Cube Root Asymptotics: Maximal Scores and Irregular Histograms
Moss, Jonas
2015-01-01
Estimators with cube root asymptotics are typically the result of M-estimation with non-smooth objective functions. Aside from being inefficient, they are hard to calculate, have intractable limiting distributions, and are unamenable to the bootstrap. Manski's maximum score estimator and irregular histograms receive special attention. We investigate the geometry, algorithmics and robustness properties of Manski's maximum score estimator, a semiparametric estimator of the coefficients in the b...
Asymptotics of weighted random sums
Corcuera, José Manuel; Nualart, David; Podolskij, Mark
2014-01-01
In this paper we study the asymptotic behaviour of weighted random sums when the sum process converges stably in law to a Brownian motion and the weight process has continuous trajectories, more regular than that of a Brownian motion. We show that these sums converge in law to the integral of the...
Ruin problems and tail asymptotics
Rønn-Nielsen, Anders
The thesis Ruin Problems and Tail Asymptotics provides results on ruin problems for several classes of Markov processes. For a class of diffusion processes with jumps an explicit expression for the joint Laplace transform of the first passage time and the corresponding undershoot is derived. An...
Asymptotic expansions of Jacobi functions
The author presents an asymptotic expansion of the Jacobi polynomials which is based on the fact, that these polynomials are special hypergeometric functions. He uses an integral representation of these functions and expands the integrand in a power series. He derives explicit error bounds on this expansion. (HSI)
Thermodynamics of asymptotically safe theories
Rischke, Dirk H.; Sannino, Francesco
2015-01-01
We investigate the thermodynamic properties of a novel class of gauge-Yukawa theories that have recently been shown to be completely asymptotically safe, because their short-distance behaviour is determined by the presence of an interacting fixed point. Not only do all the coupling constants freeze...
Inverse scattering at fixed energy on asymptotically hyperbolic Liouville surfaces
Daudé, Thierry; Kamran, Niky; Nicoleau, Francois
2015-12-01
In this paper, we study an inverse scattering problem on Liouville surfaces having two asymptotically hyperbolic ends. The main property of Liouville surfaces consists of the complete separability of the Hamilton-Jacobi equations for the geodesic flow. An important related consequence is the fact that the stationary wave equation can be separated into a system of radial and angular ODEs. The full scattering matrix at fixed energy associated to a scalar wave equation on asymptotically hyperbolic Liouville surfaces can be thus simplified by considering its restrictions onto the generalized harmonics corresponding to the angular separated ODE. The resulting partial scattering matrices consists in a countable set of 2 × 2 matrices whose coefficients are the so called transmission and reflection coefficients. It is shown that the reflection coefficients are nothing but generalized Weyl-Titchmarsh (WT) functions for the radial ODE in which the generalized angular momentum is seen as the spectral parameter. Using the complex angular momentum method and recent results on 1D inverse problem from generalized WT functions, we show that the knowledge of the reflection operators at a fixed non-zero energy is enough to determine uniquely the metric of the asymptotically hyperbolic Liouville surface under consideration.
Mel'nikov, A. V.
1996-10-01
Contents Introduction Chapter I. Basic notions and results from contemporary martingale theory §1.1. General notions of the martingale theory §1.2. Convergence (a.s.) of semimartingales. The strong law of large numbers and the law of the iterated logarithm Chapter II. Stochastic differential equations driven by semimartingales §2.1. Basic notions and results of the theory of stochastic differential equations driven by semimartingales §2.2. The method of monotone approximations. Existence of strong solutions of stochastic equations with non-smooth coefficients §2.3. Linear stochastic equations. Properties of stochastic exponentials §2.4. Linear stochastic equations. Applications to models of the financial market Chapter III. Procedures of stochastic approximation as solutions of stochastic differential equations driven by semimartingales §3.1. Formulation of the problem. A general model and its relation to the classical one §3.2. A general description of the approach to the procedures of stochastic approximation. Convergence (a.s.) and asymptotic normality §3.3. The Gaussian model of stochastic approximation. Averaged procedures and their effectiveness Chapter IV. Statistical estimation in regression models with martingale noises §4.1. The formulation of the problem and classical regression models §4.2. Asymptotic properties of MLS-estimators. Strong consistency, asymptotic normality, the law of the iterated logarithm §4.3. Regression models with deterministic regressors §4.4. Sequential MLS-estimators with guaranteed accuracy and sequential statistical inferences Bibliography
Uniform asymptotics for the full moment conjecture of the Riemann zeta function
Hiary, Ghaith A
2011-01-01
Conrey, Farmer, Keating, Rubinstein, and Snaith recently conjectured formulas for the full asymptotics of the moments of $L$-functions. In the case of the Riemann zeta function, their conjecture states that the $2k$-th absolute moment of zeta on the critical line is asymptotically given by a certain $2k$-fold residue integral. This residue integral can be expressed as a polynomial of degree $k^2$, whose coefficients are given in exact form by elaborate and complicated formulas. In this article, uniform asymptotics for roughly the first $k$ coefficients of the moment polynomial are derived. Numerical data to support our asymptotic formula are presented. An application to bounding the maximal size of the zeta function is considered.
On Asymptotically Efficient Estimation in Semiparametric Models
Schick, Anton
1986-01-01
A general method for the construction of asymptotically efficient estimates in semiparametric models is presented. It improves and modifies Bickel's (1982) construction of adaptive estimates and obtains asymptotically efficient estimates under conditions weaker than those in Bickel.
On transfinite extension of asymptotic dimension
Radul, Taras
2006-01-01
We prove that a transfinite extension of asymptotic dimension asind is trivial. We introduce a transfinite extension of asymptotic dimension asdim and give an example of metric proper space which has transfinite infinite dimension.
Asymptotic Parameter Estimation for a Class of Linear Stochastic Systems Using Kalman-Bucy Filtering
Xiu Kan
2012-01-01
Full Text Available The asymptotic parameter estimation is investigated for a class of linear stochastic systems with unknown parameter θ:dXt=(θα(t+β(tXtdt+σ(tdWt. Continuous-time Kalman-Bucy linear filtering theory is first used to estimate the unknown parameter θ based on Bayesian analysis. Then, some sufficient conditions on coefficients are given to analyze the asymptotic convergence of the estimator. Finally, the strong consistent property of the estimator is discussed by comparison theorem.
Asymptotic Parameter Estimation for a Class of Linear Stochastic Systems Using Kalman-Bucy Filtering
Xiu Kan; Huisheng Shu; Yan Che
2012-01-01
The asymptotic parameter estimation is investigated for a class of linear stochastic systems with unknown parameter θ:dXt=(θα(t)+β(t)Xt)dt+σ(t)dWt. Continuous-time Kalman-Bucy linear filtering theory is first used to estimate the unknown parameter θ based on Bayesian analysis. Then, some sufficient conditions on coefficients are given to analyze the asymptotic convergence of the estimator. Finally, the strong consistent property of the estimator is discussed by comparison theorem.
Asymptotic expansions of integral means and applications to the ratio of gamma functions
Elezović, Neven; Vukšić, Lenka
2013-01-01
Integral means are important class of bivariate means. In this paper we prove the very general algorithm for calculation of coefficients in asymptotic expansion of integral mean. It is based on explicit solving the equation of the form $B(A(x))=C(x)$, where $B$ and $C$ have known asymptotic expansions. The results are illustrated by calculation of some important integral means connected with gamma and digamma functions.
Asymptotic analysis and numerical modeling of mass transport in tubular structures
Cardone, G; Sirakov, Y
2009-01-01
In the paper the flow in a thin tubular structure is considered. The velocity of the flow stands for a coefficient in the diffusion-convection equation set in the thin structure. An asymptotic expansion of solution is constructed. This expansion is used further for justification of an asymptotic domain decomposition strategy essentially reducing the memory and the time of the code. A numerical solution obtained by this strategy is compared to the numerical solution obtained by a direct FEM computation.
Exact and asymptotic results for insurance risk models with surplus-dependent premiums
Albrecher, Hansjörg; Palmowski, Zbigniew; Regensburger, Georg; Rosenkranz, Markus
2011-01-01
In this paper we develop a symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance portfolio. The analysis is based on boundary problems for linear ordinary differential equations with variable coefficients. The algebraic structure of the Green's operators allows us to develop an intuitive way of tackling the asymptotic behavior of the solutions, leading to exponential-type expansions and Cram\\'er-type asymptotics. Furthermore, we obtain closed-form solutions for more specific cases of premium functions in the compound Poisson risk model.
Asymptotic functions and multiplication of distributions
Considered is a new type of generalized asymptotic functions, which are not functionals on some space of test functions as the Schwartz distributions. The definition of the generalized asymptotic functions is given. It is pointed out that in future the particular asymptotic functions will be used for solving some topics of quantum mechanics and quantum theory
Hydrodynamics, resurgence and trans-asymptotics
Basar, Gokce
2015-01-01
The second-order hydrodynamical description of a homogeneous conformal plasma that undergoes a boost- invariant expansion is given by a single nonlinear ordinary differential equation, whose resurgent asymptotic properties we study, developing further the recent work of Heller and Spalinski [Phys. Rev. Lett. 115, 072501 (2015)]. Resurgence clearly identifies the non-hydrodynamic modes that are exponentially suppressed at late times, analogous to the quasi-normal-modes in gravitational language, organizing these modes in terms of a trans-series expansion. These modes are analogs of instantons in semi-classical expansions, where the damping rate plays the role of the instanton action. We show that this system displays the generic features of resurgence, with explicit quantitative relations between the fluctuations about different orders of these non-hydrodynamic modes. The imaginary part of the trans-series parameter is identified with the Stokes constant, and the real part with the freedom associated with init...
Motion Parallax is Asymptotic to Binocular Disparity
Stroyan, Keith
2010-01-01
Researchers especially beginning with (Rogers & Graham, 1982) have noticed important psychophysical and experimental similarities between the neurologically different motion parallax and stereopsis cues. Their quantitative analysis relied primarily on the "disparity equivalence" approximation. In this article we show that retinal motion from lateral translation satisfies a strong ("asymptotic") approximation to binocular disparity. This precise mathematical similarity is also practical in the sense that it applies at normal viewing distances. The approximation is an extension to peripheral vision of (Cormac & Fox's 1985) well-known non-trig central vision approximation for binocular disparity. We hope our simple algebraic formula will be useful in analyzing experiments outside central vision where less precise approximations have led to a number of quantitative errors in the vision literature.
Superradiant instabilities of asymptotically anti-de Sitter black holes
Green, Stephen R; Ishibashi, Akihiro; Wald, Robert M
2015-01-01
We study the linear stability of asymptotically anti-de Sitter black holes in general relativity in spacetime dimension $d\\ge4$. Our approach is an adaptation of the general framework of Hollands and Wald, which gives a stability criterion in terms of the sign of the canonical energy, $\\mathcal{E}$. The general framework was originally formulated for static or stationary and axisymmetric black holes in the asymptotically flat case, and the stability analysis for that case applies only to axisymmetric perturbations. However, in the asymptotically anti-de Sitter case, the stability analysis requires only that the black hole have a single Killing field normal to the horizon and there are no restrictions on the perturbations (apart from smoothness and appropriate behavior at infinity). For an asymptotically anti-de Sitter black hole, we define an ergoregion to be a region where the horizon Killing field is spacelike; such a region, if present, would normally occur near infinity. We show that for black holes with ...
Asymptotic structure of isolated systems
I discuss the general ideas underlying the subject of ''asymptotics'' in general relativity and describe the current status of the concepts resulting from these ideas. My main concern will be the problem of consistency. By this I mean the question as to whether the geometric assumptions inherent in these concepts are compatible with the dynamics of the theory, as determined by Einstein's equations. This rather strong bias forces me to leave untouched several issues related to asymptotics, discussed in the recent literature, some of which are perhaps thought equally, or more important, by other workers in the field. In addition I shall, for coherence of presentation, mainly consider Einstein's equations in vacuo. When attention is confined to small neighbourhoods of null and spacelike infinity, this restriction is not important, but is surely relevant for more global issues. (author)
Asymptotic safety goes on shell
It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector and a new cut-off scheme. We find a nontrivial fixed point, with a value of the cosmological constant that is independent of the gauge-fixing parameters. (paper)
Asymptotic safety goes on shell
Benedetti, Dario
2012-01-01
It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector and a new cut-off scheme. We find a nontrivial fixed point, with a value of the cosmological constant that is independent of the gauge-fixing parameters.
Asymptotic analysis of Hoppe trees
Leckey, Kevin
2012-01-01
We introduce and analyze a random tree model associated to Hoppe's urn. The tree is built successively by adding nodes to the existing tree when starting with the single root node. In each step a node is added to the tree as a child of an existing node where these parent nodes are chosen randomly with probabilities proportional to their weights. The root node has weight $\\vartheta>0$, a given fixed parameter, all other nodes have weight 1. This resembles the stochastic dynamic of Hoppe's urn. For $\\vartheta=1$ the resulting tree is the well-studied random recursive tree. We analyze the height, internal path length and number of leaves of the Hoppe tree with $n$ nodes as well as the depth of the last inserted node asymptotically as $n\\to \\infty$. Mainly expectations, variances and asymptotic distributions of these parameters are derived.
Asymptotics of the filtration problem for suspension in porous media
Kuzmina Ludmila Ivanovna
2015-01-01
Full Text Available The mechanical-geometric model of the suspension filtering in the porous media is considered. Suspended solid particles of the same size move with suspension flow through the porous media - a solid body with pores - channels of constant cross section. It is assumed that the particles pass freely through the pores of large diameter and are stuck at the inlet of pores that are smaller than the particle size. It is considered that one particle can clog only one small pore and vice versa. The particles stuck in the pores remain motionless and form a deposit. The concentrations of suspended and retained particles satisfy a quasilinear hyperbolic system of partial differential equations of the first order, obtained as a result of macro-averaging of micro-stochastic diffusion equations. Initially the porous media contains no particles and both concentrations are equal to zero; the suspension supplied to the porous media inlet has a constant concentration of suspended particles. The flow of particles moves in the porous media with a constant speed, before the wave front the concentrations of suspended and retained particles are zero. Assuming that the filtration coefficient is small we construct an asymptotic solution of the filtration problem over the concentration front. The terms of the asymptotic expansions satisfy linear partial differential equations of the first order and are determined successively in an explicit form. It is shown that in the simplest case the asymptotics found matches the known asymptotic expansion of the solution near the concentration front.
Asymptotic Analysis of Fiber-Reinforced Composites of Hexagonal Structure
Kalamkarov, Alexander L.; Andrianov, Igor V.; Pacheco, Pedro M. C. L.; Savi, Marcelo A.; Starushenko, Galina A.
2016-08-01
The fiber-reinforced composite materials with periodic cylindrical inclusions of a circular cross-section arranged in a hexagonal array are analyzed. The governing analytical relations of the thermal conductivity problem for such composites are obtained using the asymptotic homogenization method. The lubrication theory is applied for the asymptotic solution of the unit cell problems in the cases of inclusions of large and close to limit diameters, and for inclusions with high conductivity. The lubrication method is further generalized to the cases of finite values of the physical properties of inclusions, as well as for the cases of medium-sized inclusions. The analytical formulas for the effective coefficient of thermal conductivity of the fiber-reinforced composite materials of a hexagonal structure are derived in the cases of small conductivity of inclusions, as well as in the cases of extremely low conductivity of inclusions. The three-phase composite model (TPhM) is applied for solving the unit cell problems in the cases of the inclusions with small diameters, and the asymptotic analysis of the obtained solutions is performed for inclusions of small sizes. The obtained results are analyzed and illustrated graphically, and the limits of their applicability are evaluated. They are compared with the known numerical and asymptotic data in some particular cases, and very good agreement is demonstrated.
Asymptotic Excisions of Metric Spaces and Ideals of Asymptotic Coarse Roe Algebras
LI Jin-xiu; WANG Qin
2006-01-01
We introduce in this note the notions of asymptotic excision of proper metric spaces and asymptotic equivalence relation for subspaces of metric spaces, which are relevant in characterizing spatial ideals of the asymptotic coarse Roe algebras. We show that the lattice of the asymptotic equivalence classes of the subspaces of a proper metric space is isomorphic to the lattice of the spatial ideals of the asymptotic Roe algebra. For asymptotic excisions of the metric space, we also establish a Mayer-Vietoris sequence in K-theory of the asymptotic coarse Roe algebras.
Exponential asymptotics and capillary waves
Chapman, S. J.; Vanden-Broeck, J.
2002-01-01
Recently developed techniques in exponential asymptotics beyond all orders are employed on the problem of potential flows with a free surface and small surface tension, in the absence of gravity. Exponentially small capillary waves are found to be generated on the free surface where the equipotentials from singularities in the flow (for example, stagnation points and corners) meet it. The amplitude of these waves is determined, and the implications are considered for many quite general flows....
Asymptotic safety: A simple example
We use the Gross-Neveu model in 2f expansion where the model is known to be renormalizable to all orders. In this limit, the fixed-point action as well as all universal critical exponents can be computed analytically. As asymptotic safety has become an important scenario for quantizing gravity, our description of a well-understood model is meant to provide for an easily accessible and controllable example of modern nonperturbative quantum field theory.
Asymptotic algebra for charged particles and radiation
A C*-algebra of asymptotic fields which properly describes the infrared structure in quantum electrodynamics is proposed. The algebra is generated by the null asymptotic of electromagnetic field and the time asymptotic of charged matter fields which incorporate the corresponding Coulomb fields. As a consequence Gauss' law is satisfied in the algebraic setting. Within this algebra the observables can be identified by the principle of gauge invariance. A class of representations of the asymptotic algebra is constructed which resembles the Kulish-Faddeev treatment of electrically charged asymptotic fields. (orig.)
Sieve M-estimation for semiparametric varying-coefficient partially linear regression model
无
2010-01-01
This article considers a semiparametric varying-coefficient partially linear regression model.The semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable.A sieve M-estimation method is proposed and the asymptotic properties of the proposed estimators are discussed.Our main object is to estimate the nonparametric component and the unknown parameters simultaneously.It is easier to compute and the required computation burden is much less than the existing two-stage estimation method.Furthermore,the sieve M-estimation is robust in the presence of outliers if we choose appropriate ρ(·).Under some mild conditions,the estimators are shown to be strongly consistent;the convergence rate of the estimator for the unknown nonparametric component is obtained and the estimator for the unknown parameter is shown to be asymptotically normally distributed.Numerical experiments are carried out to investigate the performance of the proposed method.
The clustering coefficient of a scale-free random graph
Eggemann, N.; Noble, S D
2009-01-01
We consider a random graph process in which, at each time step, a new vertex is added with m out-neighbours, chosen with probabilities proportional to their degree plus a strictly positive constant. We show that the expectation of the clustering coefficient of the graph process is asymptotically proportional to log n/n. Bollob\\'as and Riordan have previously shown that when the constant is zero, the same expectation is asymptotically proportional to ((log n)^2)/n.
Conformal symmetries of gravity from asymptotic methods: further developments
Lambert, Pierre-Henry
2014-01-01
In this thesis, the symmetry structure of gravitational theories at null infinity is studied further, in the case of pure gravity in four dimensions and also in the case of Einstein-Yang-Mills theory in $d$ dimensions with and without a cosmological constant. The first part of this thesis is devoted to the presentation of asymptotic methods (symmetries, solution space and surface charges) applied to gravity in the case of the BMS gauge in three and four spacetime dimensions. The second part of this thesis contains the original contributions. Firstly, it is shown that the enhancement from Lorentz to Virasoro algebra also occurs for asymptotically flat spacetimes defined in the sense of Newman-Unti. As a first application, the transformation laws of the Newman-Penrose coefficients characterizing solution space of the Newman-Unti approach are worked out, focusing on the inhomogeneous terms that contain the information about central extensions of the theory. These transformations laws make the conformal structure...
ASYMPTOTIC PROPERTIES OF MLE FOR WEIBULL DISTRIBUTION WITH GROUPED DATA
XUEHongqi; SONGLixin
2002-01-01
A grouped data model for weibull distribution is considered.Under mild conditions .the maximum likelihood estimators(MLE)are shown to be identifiable,strongly consistent,asymptotically normal,and satisfy the law of iterated logarithm .Newton iteration algorthm is also condsidered,which converges to the unique solution of the likelihood equation.Moreover,we extend these results to a random case.
Asymptotic black hole quasinormal frequencies
Motl, Lubos; Neitzke, Andrew
2003-01-01
We give a new derivation of the quasinormal frequencies of Schwarzschild black holes in d greater than or equal to 4 and Reissner-Nordstrom black holes in d = 4, in the limit of infinite damping. For Schwarzschild in d greater than or equal to 4 we find that the asymptotic real part is THawkinglog(3) for scalar perturbations and for some gravitational perturbations; this confirms a result previously obtained by other means in the case d = 4. For Reissner-Nordstrom in d = 4 w...
Asymptotics of robust utility maximization
Knispel, Thomas
2012-01-01
For a stochastic factor model we maximize the long-term growth rate of robust expected power utility with parameter $\\lambda\\in(0,1)$. Using duality methods the problem is reformulated as an infinite time horizon, risk-sensitive control problem. Our results characterize the optimal growth rate, an optimal long-term trading strategy and an asymptotic worst-case model in terms of an ergodic Bellman equation. With these results we propose a duality approach to a "robust large deviations" criterion for optimal long-term investment.
Asymptotics for Associated Random Variables
Oliveira, Paulo Eduardo
2012-01-01
The book concerns the notion of association in probability and statistics. Association and some other positive dependence notions were introduced in 1966 and 1967 but received little attention from the probabilistic and statistics community. The interest in these dependence notions increased in the last 15 to 20 years, and many asymptotic results were proved and improved. Despite this increased interest, characterizations and results remained essentially scattered in the literature published in different journals. The goal of this book is to bring together the bulk of these results, presenting
Degree and clustering coefficient in sparse random intersection graphs
Bloznelis, Mindaugas
2013-01-01
We establish asymptotic vertex degree distribution and examine its relation to the clustering coefficient in two popular random intersection graph models of Godehardt and Jaworski [Electron. Notes Discrete Math. 10 (2001) 129–132]. For sparse graphs with a positive clustering coefficient, we examine statistical dependence between the (local) clustering coefficient and the degree. Our results are mathematically rigorous. They are consistent with the empirical observation of Foudalis et al. [In...
A new approach to bootstrap inference in functional coefficient models
Herwartz, Helmut; Xu, Fang
2007-01-01
We introduce a new, factor based bootstrap approach which is robust under heteroskedastic error terms for inference in functional coefficient models. Modeling the functional coefficient parametrically, the bootstrap approximation of an F statistic is shown to hold asymptotically. In simulation studies with both parametric and nonparametric functional coefficients, factor based bootstrap inference outperforms the wild bootstrap and pairs bootstrap approach according to its size features. Apply...
Asymptotic black hole quasinormal frequencies
Motl, L; Motl, Lubos; Neitzke, Andrew
2003-01-01
We give a simple derivation of the quasinormal frequencies of Schwarzschild black holes in d>=4 and non-extremal Reissner-Nordstrom black holes in d=4, in the limit of infinite damping. For Schwarzschild in d=4 the asymptotic real part of the frequency is (T_Hawking)log(1+2cos(pi.j)), where j is the spin of the perturbation; this confirms a result previously obtained by other means. For Schwarzschild in d>4 we find that the asymptotic real part is (T_Hawking)log(3) for scalar perturbations. For non-extremal Reissner-Nordstrom in d=4 we find a specific but generally aperiodic behavior for the quasinormal frequencies, both for scalar perturbations and for axial electromagnetic-gravitational perturbations; there is nevertheless a hint that the value (T_Hawking)log(2) may be special in this case. The formulae are obtained by studying the monodromy of the perturbation analytically continued to the complex plane.
Asymptotically Free Gauge Theories. I
Wilczek, Frank; Gross, David J.
1973-07-01
Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization group techniques and their application to scaling phenomena. The renormalization group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large space-like momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3)xSU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken, and that the severe infrared singularities prevent the occurrence of non-color singlet physical states. The deep inelastic structure functions, as well as the electron position total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive lightcone or parton model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.
The maximum drag reduction asymptote
Choueiri, George H.; Hof, Bjorn
2015-11-01
Addition of long chain polymers is one of the most efficient ways to reduce the drag of turbulent flows. Already very low concentration of polymers can lead to a substantial drag and upon further increase of the concentration the drag reduces until it reaches an empirically found limit, the so called maximum drag reduction (MDR) asymptote, which is independent of the type of polymer used. We here carry out a detailed experimental study of the approach to this asymptote for pipe flow. Particular attention is paid to the recently observed state of elasto-inertial turbulence (EIT) which has been reported to occur in polymer solutions at sufficiently high shear. Our results show that upon the approach to MDR Newtonian turbulence becomes marginalized (hibernation) and eventually completely disappears and is replaced by EIT. In particular, spectra of high Reynolds number MDR flows are compared to flows at high shear rates in small diameter tubes where EIT is found at Re Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n° [291734].
Asymptotic safety goes on shell
Benedetti, Dario
2011-01-01
It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge-dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector, and a new cut-off scheme. We find a non-trivial fixed point, with a value of the cosmological constant which is independent of the gauge-fixing parameters.
Efficient estimation of price adjustment coefficients
Lyhagen, Johan
1999-01-01
The price adjustment coefficient model of Amihud and Mendelson (1987) is shown to be suitable for estimation by the Kalman filter. A techique that, under some commonly used conditions, is asymptotically efficient. By Monte Carlo simulations it is shown that both bias and mean squared error are much smaler compared to the estimator proposed by Damodaran and Lim (1991) and Damodaran (1993). A test for the adeqacy of the model is also proposed. Using data from four minor, the nordic countries ex...
Asymptotic conservation laws in field theory
Anderson, Ian M.; Torre, Charles G.
1996-01-01
A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription which does not rely upon the existence of Noether identities or any Lagrangian or Hamiltonian formalisms. The resulting general expressions of the conservation laws enjoy important invariance properties and synthesize all known asymptotic conservation...
Asymptotically Plane Wave Spacetimes and their Actions
Witt, Julian Le; Ross, Simon F.
2008-01-01
We propose a definition of asymptotically plane wave spacetimes in vacuum gravity in terms of the asymptotic falloff of the metric, and discuss the relation to previously constructed exact solutions. We construct a well-behaved action principle for such spacetimes, using the formalism developed by Mann and Marolf. We show that this action is finite on-shell and that the variational principle is well-defined for solutions of vacuum gravity satisfying our asymptotically plane wave falloff condi...
Asymptotics of near unit roots (in Russian)
Stanislav Anatolyev; Nikolay Gospodinov
2012-01-01
Sometimes the conventional asymptotic theory yields that the limiting distribution changes discontinuously, or that the asymptotic distribution does not approximate accurately the actual finite-sample distribution. In such situations one finds useful an asymptotic tool of drifting parameterizations where certain parameters are allowed to depend explicitly on the sample size. It proves useful, among other things, for impulse response analysis and forecasting of strongly dependent processes at ...
Asymptotic independence and a network traffic model
Maulik, Krishanu; Resnick, Sidney; Rootzén, Holger
2002-01-01
The usual concept of asymptotic independence, as discussed in the context of extreme value theory, requires the distribution of the coordinatewise sample maxima under suitable centering and scaling to converge to a product measure. However, this definition is too broad to conclude anything interesting about the tail behavior of the product of two random variables that are asymptotically independent. Here we introduce a new concept of asymptotic independence which allows u...
Exponential asymptotic stability for linear volterra equations
John A. D. Appleby
2000-01-01
This note studies the exponential asymptotic stability of the zero solution of the linear Volterra equation x˙ (t) = Ax(t) + t 0 K(t − s)x(s) ds by extending results in the paper of Murakami “Exponential Asymptotic Stability for scalar linear Volterra Equations”, Differential and Integral Equations, 4, 1991. In particular, when K isi ntegrable and has entries which do not change sign, and the equation has a uniformly asymptotically stable solution, exponential asympto...
Asymptotic behaviour of pion-pion total cross-sections
We derive a sum rule which shows that the Froissart-Martin bound for the asymptotic behaviour of the ππ total cross sections at high energies, if modulated by the Lukaszuk-Martin coefficient of the leading log2 s behaviour, cannot be an optimal bound in QCD. We next compute the total cross sections for π+π−, π±π0 and π0π0 scattering within the framework of the constituent chiral quark model (CχQM) in the limit of a large number of colours Nc and discuss their asymptotic behaviours. The same ππ cross sections are also discussed within the general framework of Large-Nc QCD and we show that it is possible to make an Ansatz for the isospin I=1 and I=0 spectrum which satisfy the Froissart-Martin bound with coefficients which, contrary to the Lukaszuk-Martin coefficient, are not singular in the chiral limit and have the correct Large-Nc counting. We finally propose a simple phenomenological model which matches the low energy behaviours of the σπ±π0total(s) cross section predicted by the CχQM with the high energy behaviour predicted by the Large-Nc Ansatz. The magnitude of these cross sections at very high energies is of the order of those observed for the pp and pp-bar scattering total cross sections
Ultraviolet asymptotics and singular dynamics of AdS perturbations
Craps, Ben; Vanhoof, Joris
2015-01-01
Important insights into the dynamics of spherically symmetric AdS-scalar field perturbations can be obtained by considering a simplified time-averaged theory accurately describing perturbations of amplitude epsilon on time-scales of order 1/epsilon^2. The coefficients of the time-averaged equations are complicated expressions in terms of the AdS scalar field mode functions, which are in turn related to the Jacobi polynomials. We analyze the behavior of these coefficients for high frequency modes. The resulting asymptotics can be useful for understanding the properties of the finite-time singularity in solutions of the time-averaged theory recently reported in the literature. We highlight, in particular, the gauge dependence of this asymptotics, with respect to the two most commonly used gauges. The harsher growth of the coefficients at large frequencies in higher-dimensional AdS suggests strengthening of turbulent instabilities in higher dimensions. In the course of our derivations, we arrive at recursive rel...
Supersymmetric asymptotic safety is not guaranteed
Intriligator, Kenneth; Sannino, Francesco
It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety in...... supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those of...
Why are tensor field theories asymptotically free?
Rivasseau, Vincent
2015-01-01
In this pedagogic letter we explain the combinatorics underlying the generic asymptotic freedom of tensor field theories. We focus on simple combinatorial models with a $1/p^2$ propagator and quartic interactions and on the comparison between the intermediate field representations of the vector, matrix and tensor cases. The transition from asymptotic freedom (tensor case) to asymptotic safety (matrix case) is related to the crossing symmetry of the matrix vertex whereas in the vector case, the lack of asymptotic freedom ("Landau ghost"), as in the ordinary scalar case, is simply due to the absence of any wave function renormalization at one loop.
Numerical Asymptotic Solutions Of Differential Equations
Thurston, Gaylen A.
1992-01-01
Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.
Asymptotic Chi-Square Tests for a Large Class of Factor Analysis Models
Amemiya, Yasuo; Anderson, T W
1990-01-01
Three types of asymptotic $\\chi^2$ goodness-of-fit tests derived under the normal assumption have been used widely in factor analysis. Asymptotic behavior of the test statistics is investigated here for the factor analysis model with linearly or nonlinearly restricted factor loadings under weak assumptions on the factor vector and the error vector. In particular the limiting $\\chi^2$ result for the three tests is shown to hold for the factor vector, either fixed or random with any distributio...
Airy asymptotics: the logarithmic derivative and its reciprocal
Kearney, Michael J [Faculty of Engineering and Physical Sciences, University of Surrey, Guildford, Surrey, GU2 7XH (United Kingdom); Martin, Richard J [AHL, Man Investments Limited, Sugar Quay, Lower Thames Street, London, EC3R 6DU (United Kingdom)], E-mail: m.j.kearney@surrey.ac.uk
2009-10-23
We consider the asymptotic expansion of the logarithmic derivative of the Airy function Ai'(z)/Ai(z), and also its reciprocal Ai(z)/Ai'(z), as |z| {yields} {infinity}. We derive simple, closed-form solutions for the coefficients which appear in these expansions, which are of interest since they are encountered in a wide variety of problems. The solutions are presented as Mellin transforms of given functions; this fact, together with the methods employed, suggests further avenues for research.
Renormalization constants and asymptotic behaviour in quantum electrodynamics
Using dimensional regularization a field theory contains at least one parameter less than the dimension of a mass. The Callan-Symanzik equations for the renormalization constants then become soluble entirely in terms of the coefficient functions. Explicit expressions are obtained for all the renormalization constants in Quantum Electrodynamics. At nonexceptional momenta the infrared behaviour and the three leading terms in the asymptotic expansion of any Greens function are controlled by the Callan-Symanzik equations. For the propagators the three leading terms are computed explicitly in terms of functions of α only. The gauge dependence of the electron propagator in momentum space is solved explicitly in all orders of perturbation theory. (Auth.)