Higher order Lagrangian systems: Geometric structures, Dynamics, and Constraints

In order to study the connections between Lagrangian and Hamiltonian formalisms constructed from aperhaps singularhigher-order Lagrangian, some geometric structures are constructed. Intermediate spaces between those of Lagrangian and Hamiltonian formalisms, partial Ostrogradskiis transformations and unambiguous evolution operators connecting these spaces are intrinsically defined, and some of their properties studied. Equations of motion, constraints, and arbitrary functions of Lagrangian and Hamiltonian formalisms are thoroughly studied. In particular, all the Lagrangian constraints are obtained from the Hamiltonian ones. Once the gauge transformations are taken into account, the true number of degrees of freedom is obtained, both in the Lagrangian and Hamiltonian formalisms, and also in all the intermediate formalisms herein defined.

Motion estimation using higher-order statistics

The objective of this paper is to introduce a fourth-order cost function of the displaced frame difference (DFD) capable of estimatingmotion even for small regions or blocks. Using higher than second-orderstatistics is appropriate in case the image sequence is severely corruptedby additive Gaussian noise. Some results are presented and compared to those obtained from the mean kurtosis and the mean square error of the DFD.

Wigner higher-order spectra: definition, properties, computation and application to transient signal analysis

The Wigner higher order moment spectra (WHOS)are defined as extensions of the Wigner-Ville distribution (WD)to higher order moment spectra domains. A general class oftime-frequency higher order moment spectra is also defined interms of arbitrary higher order moments of the signal as generalizations of the Cohen’s general class of time-frequency representations. The properties of the general class of time-frequency higher order moment spectra can be related to theproperties of WHOS which are, in fact, extensions of the properties of the WD. Discrete time and frequency Wigner higherorder moment spectra (DTF-WHOS) distributions are introduced for signal processing applications and are shown to beimplemented with two FFT-based algorithms. One applicationis presented where the Wigner bispectrum (WB), which is aWHOS in the third-order moment domain, is utilized for thedetection of transient signals embedded in noise. The WB iscompared with the WD in terms of simulation examples andanalysis of real sonar data. It is shown that better detectionschemes can be derived, in low signal-to-noise ratio, when theWB is applied.

On the number of higher order Delaunay triangulations

"Vegeu el resum a l'inici del document del fitxer adjunt."

The impact of labour market status on second and higher-order births. A comparative study of Denmark, Italy, Spain and United Kingdom

This paper investigates the effects of women‘s labour force participation on fertility, as well as the effects of the combined labour force participation of both members of a couple. It specifically focuses on such dimensions as unemployment, earnings, temporary contracts and part-time jobs, and it shows that their effects differ in accordance with national institutions and labour market regulations. Event-history methods and a longitudinal sample of the European Community Household Panel are used in the analyses, concerning the years 1993-2000. The results show that labour market insecurity of one or both members of a couple has a particularly strong impact in reducing birth rates in the Southern European countries studied. The more conventional model of men’s employment combined with housewifery has a positive impact on second or higher order births in United Kingdom, Spain and Italy, while in Denmark the effect is the opposite. These differences are consistent with different national models of combining parental responsibilities and participation by gender across the life course.

Dynamic higher order expectations

In models where privately informed agents interact, agents may need to formhigher order expectations, i.e. expectations of other agents' expectations. This paper develops a tractable framework for solving and analyzing linear dynamic rational expectationsmodels in which privately informed agents form higher order expectations. The frameworkis used to demonstrate that the well-known problem of the infinite regress of expectationsidentified by Townsend (1983) can be approximated to an arbitrary accuracy with a finitedimensional representation under quite general conditions. The paper is constructive andpresents a fixed point algorithm for finding an accurate solution and provides weak conditions that ensure that a fixed point exists. To help intuition, Singleton's (1987) asset pricingmodel with disparately informed traders is used as a vehicle for the paper.

A Variant of Higher-Order Anti-Unification

We present a rule-based Huet’s style anti-unification algorithm for simply-typed lambda-terms in ɳ long β normal form, which computes a least general higher-order pattern generalization. For a pair of arbitrary terms of the same type, such a generalization always exists and is unique modulo α equivalence and variable renaming. The algorithm computes it in cubic time within linear space. It has been implemented and the code is freely available

Higher-order colored-noise effects in multivariable systems

We extend the partial resummation technique of Fokker-Planck terms for multivariable stochastic differential equations with colored noise. As an example, a model system of a Brownian particle with colored noise is studied. We prove that the asymmetric behavior found in analog simulations is due to higher-order terms which are left out in that technique. On the contrary, the systematic ¿-expansion approach can explain the analog results.

The role of intramolecular barriers on the glass transition of polymers: computer simulations versus mode coupling theory

We present computer simulations of a simple bead-spring model for polymer melts with intramolecular barriers. By systematically tuning the strength of the barriers, we investigate their role on the glass transition. Dynamic observables are analyzed within the framework of the mode coupling theory (MCT). Critical nonergodicity parameters, critical temperatures, and dynamic exponents are obtained from consistent fits of simulation data to MCT asymptotic laws. The so-obtained MCT λ-exponent increases from standard values for fully flexible chains to values close to the upper limit for stiff chains. In analogy with systems exhibiting higher-order MCT transitions, we suggest that the observed large λ-values arise form the interplay between two distinct mechanisms for dynamic arrest: general packing effects and polymer-specific intramolecular barriers. We compare simulation results with numerical solutions of the MCT equations for polymer systems, within the polymer reference interaction site model (PRISM) for static correlations. We verify that the approximations introduced by the PRISM are fulfilled by simulations, with the same quality for all the range of investigated barrier strength. The numerical solutions reproduce the qualitative trends of simulations for the dependence of the nonergodicity parameters and critical temperatures on the barrier strength. In particular, the increase in the barrier strength at fixed density increases the localization length and the critical temperature. However the qualitative agreement between theory and simulation breaks in the limit of stiff chains. We discuss the possible origin of this feature.

Reaction-diffusion waves of advance in the transition to agricultural economics

In a previous paper [J.Fort and V.Méndez, Phys. Rev. Lett. 82, 867 (1999)], the possible importance of higher-order terms in a human population wave of advance has been studied. However, only a few such terms were considered. Here we develop a theory including all higher-order terms. Results are in good agreement with the experimental evidence involving the expansion of agriculture in Europe

Initial convergence of the perturbation series expansion for vibrational nonlinear optical properties

Initial convergence of the perturbation series expansion for vibrational nonlinear optical (NLO) properties was analyzed. The zero-point vibrational average (ZPVA) was obtained through first-order in mechanical plus electrical anharmonicity. Results indicated that higher-order terms in electrical and mechanical anharmonicity can make substantial contributions to the pure vibrational polarizibility of typical NLO molecules

Electronic and vibrational contributions to first hyperpolarizability of donor-acceptor-substituted azobenzene

In this study we report on the electronic and vibrational (hyper)polarizabilities of donor–acceptorsubstituted azobenzene. It is observed that both electronic and vibrational contributions to the electricdipole first hyperpolarizability of investigated photoactive molecule substantially depend on the conformation. The contributions to the nuclear relaxation first hyperpolarizability are found to be quite important in the case of two considered isomers (cis and trans). Although the double-harmonic term is found to be the largest in terms of magnitude, it is shown that the total value of the nuclear relaxation contribution to vibrational first hyperpolarizability is a result of subtle interplay of higher-order contributions. As a part of the study, we also assess the performance of long-range-corrected densityfunctional theory in determining vibrational contributions to electric dipole (hyper)polarizabilities. In most cases, the applied long-range-corrected exchange correlation potentials amend the drawbacks of their conventional counterparts

Signatures of CP violation in the presence of multiple b-pair production at hadron colliders

We calculate the production of two b-quark pairs in hadron collisions. Sources of multiple pairs are multiple interactions and higher order perturbative QCD mechanisms. We subsequently investigate the competing effects of multiple b-pair production on measurements of CP violation: (i) the increase in event rate with multiple b-pair cross sections which may reach values of the order of 1 b in the presence of multiple interactions and (ii) the dilution of b versus b tagging efficiency because of the presence of events with four B mesons. The impact of multiple B-meson production is small unless the cross section for producing a single pair exceeds 1 mb. We show that even for larger values of the cross section the competing effects (i) and (ii) roughly compensate so that there is no loss in the precision with which CP-violating CKM angles can be determined.

Perturbation theory and locality in the Field-Antifield formalism

The BatalinVilkovisky formalism is studied in the framework of perturbation theory by analyzing the antibracket BecchiRouetStoraTyutin (BRST) cohomology of the proper solution S0. It is concluded that the recursive equations for the complete proper solution S can be solved at any order of perturbation theory. If certain conditions on the classical action and on the gauge generators are imposed the solution can be taken local.

On the relationship between connections and the asymptotic properties of predictive distributions

In a recent paper, Komaki studied the second-order asymptotic properties of predictive distributions, using the Kullback-Leibler divergence as a loss function. He showed that estimative distributions with asymptotically efficient estimators can be improved by predictive distributions that do not belong to the model. The model is assumed to be a multidimensional curved exponential family. In this paper we generalize the result assuming as a loss function any f divergence. A relationship arises between alpha connections and optimal predictive distributions. In particular, using an alpha divergence to measure the goodness of a predictive distribution, the optimal shift of the estimate distribution is related to alpha-covariant derivatives. The expression that we obtain for the asymptotic risk is also useful to study the higher-order asymptotic properties of an estimator, in the mentioned class of loss functions.