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## Regularity at infinity of real mappings and a Morse-Sard theorem

Dias, L. R. G.; Ruas, Maria Aparecida Soares; Tibar, M.
Fonte: OXFORD UNIV PRESS; OXFORD Publicador: OXFORD UNIV PRESS; OXFORD
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
55.84%
We prove a new Morse-Sard-type theorem for the asymptotic critical values of semi-algebraic mappings and a new fibration theorem at infinity for C-2 mappings. We show the equivalence of three different types of regularity conditions which have been used in the literature in order to control the asymptotic behaviour of mappings. The central role of our picture is played by the p-regularity and its bridge toward the rho-regularity which implies topological triviality at infinity.; French grant; French grant [ANR-08-JCJC-0118-01]; CAPES [Proc. 2929/10-04]; CAPES; FAPESP; FAPESP [Proc. 2008/10563-4, Proc. 08/54222-6]; CNPq [Proc. 303774/2008-8]; CNPq

## Regularity at infinity and global fibrations of real algebraic maps; Regularidade no infinito e fibrações globais de aplicações algébricas reais

Dias, Luis Renato Gonçalves
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Relevância na Pesquisa
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Let f : 'K POT. ' be a 'C POT. 2' semi-algebraic mapping for K = R and a polynomial mapping for K = C. It is well-known that f is a locally trivial topological fibration over the complement of the bifurcation set B(f), also called atypical set. In this work, we consider the notion of t-regularity and 'ho E'-regularity to study the bifurcation set of semi-algebraic mappings f : 'R POT. n' 'ARROW' 'R POT. p' and polynomial mappings f : 'C POT. n' 'ARROW' 'C POT. p'. We show that t-regularity is equivalent to regularity conditions at infinity which have been used by Rabier (1997), Gaffney (1999), Kurdyka, Orro and Simon (2000) and Jelonek (2003) in order to control the asymptotic behaviour of mappings. In addition, we prove that t-regularity implies 'ho E'-regularity. The 'ho E'-regularity enables one to define the set of asymptotic non 'ho E'-regular values S(f) 'This contained' ' K POT. p', and the set 'A IND. 'ho E'' := f(Singf) U S(f). For 'C POT. 2' semi-algebraic mappings f : 'R POT. n' ARROW ' 'R POT. p' and polynomial mappings f : 'C POT. n' 'ARROW' 'C POT. p', based on a partial Thom stratification at infinity, we rove that S(f) and 'A IND. ho E' are closed real semi-algebraic sets of dimension at most p - 1 (real dimension at most 2p - 2...

## Critical points in logistic growth curves and treatment comparisons

de Souza Passos, Jose Raimundo; de Pinho, Sheila Zambello; de Carvalho, Lidia Raquel; Mischan, Martha Maria
Tipo: Artigo de Revista Científica Formato: 308-312
ENG
Relevância na Pesquisa
35.85%
Several biological phenomena have a behavior over time mathematically characterized by a strong increasing function in the early stages of development, then by a less pronounced growth, sometimes showing stability. The separation between these phases is very important to the researcher, since the maintenance of a less productive phase results in uneconomical activity. In this report we present methods of determining critical points in logistic functions that separate the early stages of growth from the asymptotic phase, with the aim of establishing a stopping critical point in the growth and on this basis determine differences in treatments. The logistic growth model is fitted to experimental data of imbibition of arariba seeds (Centrolobium tomentosum). To determine stopping critical points the following methods were used: i) accelerating growth function, ii) tangent at the inflection point, iii) segmented regression; iv) modified segmented regression; v) non-significant difference; and vi) non-significant difference by simulation. The analysis of variance of the abscissas and ordinates of the breakpoints was performed with the objective of comparing treatments and methods used to determine the critical points. The methods of segmented regression and of the tangent at the inflection point lead to early stopping points...

## Critical points in logistic growth curves and treatment comparisons

Passos,José Raimundo de Souza; Pinho,Sheila Zambello de; Carvalho,Lídia Raquel de; Mischan,Martha Maria
Fonte: São Paulo - Escola Superior de Agricultura "Luiz de Queiroz" Publicador: São Paulo - Escola Superior de Agricultura "Luiz de Queiroz"
Tipo: Artigo de Revista Científica Formato: text/html
Relevância na Pesquisa
35.85%
Several biological phenomena have a behavior over time mathematically characterized by a strong increasing function in the early stages of development, then by a less pronounced growth, sometimes showing stability. The separation between these phases is very important to the researcher, since the maintenance of a less productive phase results in uneconomical activity. In this report we present methods of determining critical points in logistic functions that separate the early stages of growth from the asymptotic phase, with the aim of establishing a stopping critical point in the growth and on this basis determine differences in treatments. The logistic growth model is fitted to experimental data of imbibition of araribá seeds (Centrolobium tomentosum). To determine stopping critical points the following methods were used: i) accelerating growth function, ii) tangent at the inflection point, iii) segmented regression; iv) modified segmented regression; v) non-significant difference; and vi) non-significant difference by simulation. The analysis of variance of the abscissas and ordinates of the breakpoints was performed with the objective of comparing treatments and methods used to determine the critical points. The methods of segmented regression and of the tangent at the inflection point lead to early stopping points...

## Reconsidering the asymptotic null distribution of likelihood ratio tests for genetic linkage in multivariate variance components models under complete pleiotropy

Han, Summer S.; Chang, Joseph T.
Fonte: Oxford University Press Publicador: Oxford University Press
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
35.91%
Accurate knowledge of the null distribution of hypothesis tests is important for valid application of the tests. In previous papers and software, the asymptotic null distribution of likelihood ratio tests for detecting genetic linkage in multivariate variance components models has been stated to be a mixture of chi-square distributions with binomial mixing probabilities. For variance components models under the complete pleiotropy assumption, we show by simulation and by theoretical arguments based on the geometry of the parameter space that all aspects of the previously stated asymptotic null distribution are incorrect—both the binomial mixing probabilities and the chi-square components. Correcting the null distribution gives more conservative critical values than previously stated, yielding P values that can easily be 10 times larger. The true mixing probabilities give the highest probability to the case where all variance parameters are estimated positive, and the mixing components show severe departures from chi-square distributions. Thus, the asymptotic null distribution has complex features that raise challenges for the assessment of significance of multivariate linkage findings. We propose a method to generate an asymptotic null distribution that is much faster than other empirical methods such as permutation...

## A Practical Comparison of the Bivariate Probit and Linear IV Estimators

Chiburis, Richard C.; Das, Jishnu; Lokshin, Michael
Fonte: Banco Mundial Publicador: Banco Mundial
Relevância na Pesquisa
35.84%
This paper presents asymptotic theory and Monte-Carlo simulations comparing maximum-likelihood bivariate probit and linear instrumental variables estimators of treatment effects in models with a binary endogenous treatment and binary outcome. The three main contributions of the paper are (a) clarifying the relationship between the Average Treatment Effect obtained in the bivariate probit model and the Local Average Treatment Effect estimated through linear IV; (b) comparing the mean-square error and the actual size and power of tests based on these estimators across a wide range of parameter values relative to the existing literature; and (c) assessing the performance of misspecification tests for bivariate probit models. The authors recommend two changes to common practices: bootstrapped confidence intervals for both estimators, and a score test to check goodness of fit for the bivariate probit model.

## Specification Tests of Parametric Dynamic Conditional Quantiles

Escanciano, Juan Carlos; Velasco, Carlos
Fonte: Center for Applied Economics and Policy Research Publicador: Center for Applied Economics and Policy Research
Tipo: Trabalho em Andamento Formato: 360981 bytes; application/pdf
EN_US
Relevância na Pesquisa
35.79%
This article proposes omnibus specification tests of parametric dynamic quantile regression models. Contrary to the existing procedures, we allow for a flexible and general specification framework where a possibly continuum of quantiles are simultaneously specified. This is the case for many econometric applications for both time series and cross section data which require a global diagnostic tool. We study the asymptotic distribution of the test statistics under fairly weak conditions on the serial dependence in the underlying data generating process. It turns out that the asymptotic null distribution depends on the data generating process and the hypothesized model. We propose a subsampling procedure for approximating the asymptotic critical values of the tests. An appealing property of the proposed tests is that they do not require estimation of the non-parametric (conditional) sparsity function. A Monte Carlo study compares the proposed tests and shows that the asymptotic results provide good approximations for small sample sizes. Finally, an application to some European stock indexes provides evidence that our methodology is a powerful and flexible alternative to standard backtesting procedures in evaluating market risk by using information from a range of quantiles in the lower tail of returns.

## Change point analysis of second order characteristics in non-stationary time series

Dette, Holger; Wu, Weichi; Zhou, Zhou
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.84%
An important assumption in the work on testing for structural breaks in time series consists in the fact that the model is formulated such that the stochastic process under the null hypothesis of "no change-point" is stationary. This assumption is crucial to derive (asymptotic) critical values for the corresponding testing procedures using an elegant and powerful mathematical theory, but it might be not very realistic from a practical point of view. This paper develops change point analysis under less restrictive assumptions and deals with the problem of detecting change points in the marginal variance and correlation structures of a non-stationary time series. A CUSUM approach is proposed, which is used to test the "classical" hypothesis of the form $H_0: \theta_1=\theta_2$ vs. $H_1: \theta_1 \not =\theta_2$, where $\theta_1$ and $\theta_2$ denote second order parameters of the process before and after a change point. The asymptotic distribution of the CUSUM test statistic is derived under the null hypothesis. This distribution depends in a complicated way on the dependency structure of the nonlinear non-stationary time series and a bootstrap approach is developed to generate critical values. The results are then extended to test the hypothesis of a {\it non relevant change point}...

## Reconsidering the asymptotic null distribution of likelihood ratio tests for genetic linkage in multivariate variance components models

Han, Summer S.; Chang, Joseph T.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.91%
Accurate knowledge of the null distribution of hypothesis tests is important for valid application of the tests. In previous papers and software, the asymptotic null distribution of likelihood ratio tests for detecting genetic linkage in multivariate variance components models has been stated to be a mixture of chi-square distributions with binomial mixing probabilities. Here we show, by simulation and by theoretical arguments based on the geometry of the parameter space, that all aspects of the previously stated asymptotic null distribution are incorrect--both the binomial mixing probabilities and the chi-square components. Correcting the null distribution gives more conservative critical values than previously stated, yielding P values that can easily be ten times larger. The true mixing probabilities give the highest probability to the case where all variance parameters are estimated positive, and the mixing components show severe departures from chi-square distributions. Thus, the asymptotic null distribution has complex features that raise challenges for the assessment of significance of multivariate linkage findings. We propose a method to generate an asymptotic null distribution that is much faster than other empirical methods such as gene-dropping...

## Dispersion Relation of a Ferrofluid Layer of Any Thickness and Viscosity in a Normal Magnetic Field; Asymptotic Regimes

Abou, Berengere; de Surgy, Gilles Neron; Wesfreid, Jose-Eduardo
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.81%
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.; Comment: 21 pages, 6 eps figures, Latex, to be published in Journal de Physique II

## Testing for Homogeneity in Mixture Models

Gu, Jiaying; Koenker, Roger; Volgushev, Stanislav
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.84%
Statistical models of unobserved heterogeneity are typically formalized as mixtures of simple parametric models and interest naturally focuses on testing for homogeneity versus general mixture alternatives. Many tests of this type can be interpreted as $C(\alpha)$ tests, as in Neyman (1959), and shown to be locally, asymptotically optimal. These $C(\alpha)$ tests will be contrasted with a new approach to likelihood ratio testing for general mixture models. The latter tests are based on estimation of general nonparametric mixing distribution with the Kiefer and Wolfowitz (1956) maximum likelihood estimator. Recent developments in convex optimization have dramatically improved upon earlier EM methods for computation of these estimators, and recent results on the large sample behavior of likelihood ratios involving such estimators yield a tractable form of asymptotic inference. Improvement in computation efficiency also facilitates the use of a bootstrap methods to determine critical values that are shown to work better than the asymptotic critical values in finite samples. Consistency of the bootstrap procedure is also formally established. We compare performance of the two approaches identifying circumstances in which each is preferred.

## Bifurcation set, M-tameness, Asymptotic critical values and Newton polyhedrons

Thang, Nguyen Tat
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.77%
Let $F=(F_1, F_2, ..., F_m): \mathbb{C}^n \to \mathbb{C}^m$ be a polynomial dominant mapping with $n>m$. In this paper we give the relations between the bifurcation set of $F$ and the set of values where $F$ is not M-tame as well as the set of generalized critical values of $F$. We also construct explicitly a proper subset of $\mathbb{C}^m$ in terms of the Newton polyhedrons of $F_1, F_2, ..., F_m$ and show that it contains the bifurcation set of $F$. In the case $m= n-1$ we show that $F$ is a locally $C^{\infty}$-trivial fibration if and only if it is a locally $C^0$-trivial fibration.; Comment: 12 pages; accepted for publication in Kodai M. J. Add comment in Remark 2.1, Remark 3.5 and correct Definition 3.2

## Counting Meromorphic Functions with Critical Points of Large Multiplicities

Panov, Dmitri; Zvonkine, Dimitri
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.8%
We study the number of meromorphic functions on a Riemann surface with given critical values and prescribed multiplicities of critical points and values. When the Riemann surface is $\CP^1$ and the function is a polynomial, we give an elementary way of finding this number. In the general case, we show that, as the multiplicities of critical points tend to infinity, the asymptotic for the number of meromorphic functions is given by the volume of some space of graphs glued from circles. We express this volume as a matrix integral.; Comment: 30 pages, 7 figures, a .tar.gz file

## Critical dynamics and effective exponents of magnets with extended impurities

Blavats'ka, V.; Dudka, M.; Folk, R.; Holovatch, Yu.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.89%
We investigate the asymptotic and effective static and dynamic critical behavior of (d=3)-dimensional magnets with quenched extended defects, correlated in $\epsilon_d$ dimensions (which can be considered as the dimensionality of the defects) and randomly distributed in the remaining $d-\epsilon_d$ dimensions. The field-theoretical renormalization group perturbative expansions being evaluated naively do not allow for the reliable numerical data. We apply the Chisholm-Borel resummation technique to restore convergence of the two-loop expansions and report the numerical values of the asymptotic critical exponents for the model A dynamics. We discuss different scenarios for static and dynamic effective critical behavior and give values for corresponding non-universal exponents.; Comment: 12 pages, 6 figures

## Effective and Asymptotic Critical Exponents of Weakly Diluted Quenched Ising Model: 3d Approach Versus $\epsilon^{1/2}$-Expansion

Folk, R.; Holovatch, Yu.; Yavors'kii, T.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.84%
We present a field-theoretical treatment of the critical behavior of three-dimensional weakly diluted quenched Ising model. To this end we analyse in a replica limit n=0 5-loop renormalization group functions of the $\phi^4$-theory with O(n)-symmetric and cubic interactions (H.Kleinert and V.Schulte-Frohlinde, Phys.Lett. B342, 284 (1995)). The minimal subtraction scheme allows to develop either the $\epsilon^{1/2}$-expansion series or to proceed in the 3d approach, performing expansions in terms of renormalized couplings. Doing so, we compare both perturbation approaches and discuss their convergence and possible Borel summability. To study the crossover effect we calculate the effective critical exponents providing a local measure for the degree of singularity of different physical quantities in the critical region. We report resummed numerical values for the effective and asymptotic critical exponents. Obtained within the 3d approach results agree pretty well with recent Monte Carlo simulations. $\epsilon^{1/2}$-expansion does not allow reliable estimates for d=3.; Comment: 35 pages, Latex, 9 eps-figures included. The reference list is refreshed and typos are corrected in the 2nd version

## Critical values of random analytic functions on complex manifolds

Feng, Renjie; Zelditch, Steve
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.86%

## Critical points in logistic growth curves and treatment comparisons

Passos, José Raimundo de Souza; Pinho, Sheila Zambello de; Carvalho, Lídia Raquel de; Mischan, Martha Maria
Fonte: Universidade de São Paulo. Escola Superior de Agricultura Luiz de Queiroz Publicador: Universidade de São Paulo. Escola Superior de Agricultura Luiz de Queiroz
Tipo: info:eu-repo/semantics/article; info:eu-repo/semantics/publishedVersion; ; ; ; ; Formato: application/pdf