Threshold quantile autoregressive models

We study in this article threshold quantile autoregressive processes. In particular we propose estimation and inference of the parameters in nonlinear quantile processes when the threshold parameter defining nonlinearities is known for each quantile, and also when the parameter vector is estimated consistently. We derive the asymptotic properties of the nonlinear threshold quantile autoregressive estimator. In addition, we develop hypothesis tests for detecting threshold nonlinearities in the quantile process when the threshold parameter vector is not identified under the null hypothesis. In this case we propose to approximate the asymptotic distribution of the composite test using a p-value transformation. This test contributes to the literature on nonlinearity tests by extending Hansen’s (Econometrica 64, 1996, pp.413-430) methodology for the conditional mean process to the entire quantile process. We apply the proposed methodology to model the dynamics of US unemployment growth after the Second World War. The results show evidence of important heterogeneity associated with unemployment, and strong asymmetric persistence on unemployment growth

Integrability of Lie systems and some of its applications in physics

The geometric theory of Lie systems will be used to establish integrability conditions for several systems of differential equations, in particular Riccati equations and Ermakov systems. Many different integrability criteria in the literature will be analyzed from this new perspective and some applications in physics will be given.Comment: 16 page

Torsional birefringence in metric-affine Chern-Simons gravity: gravitational waves in late-time cosmology

In the context of the metric-affine Chern-Simons gravity endowed with projective invariance, we derive analytical solutions for torsion and nonmetricity in the homogeneous and isotropic cosmological case, described by a flat Friedmann-Robertson-Walker metric. We describe in some details the general properties of the cosmological solutions in the presence of a perfect fluid, such as dynamical stability and the settling of big bounce points, and we discuss the structure of some specific solutions reproducing de Sitter and power law behaviours for the scale factor. Then, we focus on first-order perturbations in the de Sitter scenario, and we study the propagation of gravitational waves in the adiabatic limit, looking at tensor and scalar polarizations. In particular, we find that metric tensor modes couple to torsion tensor components, leading to the appearance, as in the metric version of Chern-Simons gravity, of birefringence, described by different dispersion relations for the left and right circularized polarization states. As a result, the purely tensor part of torsion propagates like a wave, while nonmetricity decouples and behaves like a harmonic oscillator. Finally, we discuss scalar modes, outlining as they decay exponentially in time and do not propagate.Comment: References adde

New records of the ectoparasitic flagellate Colpodella gonderi on non-Colpoda ciliates

Colpodella gonderi is the only ectoparasitic flagellate of ciliated protozoa described thus far. This investigation reveals new records of C. gonderi retrieved from soil samples in southern Scotland, UK. Of fourteen ciliates species identified in one single occasion, three of them, Colpoda steinii, Pseudoplatyophrya nana and Grossglockneria acuta, were infested with the parasite. These results provide further evidence that C. gonderi is not host-specific of the ciliate genus Colpoda

Testing linearity against threshold effects: uniform inference in quantile regression

This paper develops a uniform test of linearity against threshold effects in the quantile regression framework. The test is based on the supremum of the Wald process over the space of quantile and threshold parameters. We establish the limiting null distribution of the test statistic for stationary weakly dependent processes, and propose a simulation method to approximate the critical values. The proposed simulation method makes the test easy to implement. Monte Carlo experiments show that the proposed test has good size and reasonable power against non-linear threshold models

Quasars Clustering at z approx 3 on Scales less sim 10 h^{-1} Mpc

We test the hypothesis whether high redshift QSOs would preferentially appear in small groups or pairs, and if they are associated with massive, young clusters. We carried out a photometric search for \Ly emitters on scales $\lesssim 10 h^{-1}$ Mpc, in the fields of a sample of 47 $z\approx3$ known QSOs. Wide and narrow band filter color-magnitude diagrams were generated for each of the $6'.6\times6'.6$ fields. A total of 13 non resolved objects with a significant color excess were detected as QSO candidates at a redshift similar to that of the target. All the candidates are significantly fainter than the reference QSOs, with only 2 of them within 2 magnitudes of the central object. Follow-up spectroscopic observations have shown that 5, i.e., about 40% of the candidates, are QSOs at the same redshift of the target; 4 are QSOs at different z (two of them probably being a lensed pair at z = 1.47); 2 candidates are unresolved HII galaxies at z$\sim$0.3; one unclassified and one candidate turned out to be a CCD flaw. These data indicate that at least 10% of the QSOs at z$\sim$3 do have companions. We have also detected a number of resolved, rather bright \Ly Emitter Candidates. Most probably a large fraction of them might be bright galaxies with [OII] emission, at z$\approx$ 0.3. The fainter population of our candidates corresponds to the current expectations. Thus, there are no strong indication for the existence of an overdensity of \Ly galaxies brighter than m $\approx$ 25 around QSOs at $z\approx$ 3.Comment: 29 pages, 8 figures, tar gzip LaTex file, accepted to appear in Ap

Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras

Lie bialgebra contractions are introduced and classified. A non-degenerate coboundary bialgebra structure is implemented into all pseudo-orthogonal algebras $so(p,q)$ starting from the one corresponding to $so(N+1)$. It allows to introduce a set of Lie bialgebra contractions which leads to Lie bialgebras of quasi-orthogonal algebras. This construction is explicitly given for the cases $N=2,3,4$. All Lie bialgebra contractions studied in this paper define Hopf algebra contractions for the Drinfel'd-Jimbo deformations $U_z so(p,q)$. They are explicitly used to generate new non-semisimple quantum algebras as it is the case for the Euclidean, Poincar\'e and Galilean algebras.Comment: 26 pages LATE

Influence of Second-Order Effects on Thermoelastic Behaviour in the Proximity of Crack Tips on Titanium

The Stress Intensity Factor (SIF) is used to describe the stress state and the mechanical behaviour of a material in the presence of cracks. SIF can be experimentally assessed using contactless techniques such as Thermoelastic Stress Analysis (TSA). The classic TSA theory concerns the relationship between temperature and stress variations and was successfully applied to fracture mechanics for SIF evaluation and crack tip location. This theory is no longer valid for some materials, such as titanium and aluminium, where the temperature variations also depend on the mean stress. The objective of this work was to present a new thermoelastic equation that includes the mean stress dependence to investigate the thermoelastic effect in the proximity of crack tips on titanium. Westergaard’s equations and Williams’s series expansion were employed in order to express the thermoelastic signal, including the second-order effect. Tests have been carried out to investigate the differences in SIF evaluation between the proposed approach and the classical one. A first qualitative evaluation of the importance of considering second-order effects in the thermoelastic signal in proximity of the crack tip in two loading conditions at two different loading ratios, R = 0.1 and R = 0.5, consisted of comparing the experimental signal and synthetic TSA maps. Moreover, the SIF, evaluated with the proposed and classical approaches, was compared with values from the ASTM standard formulas. The new formulation demonstrates its improved capability for describing the stress distribution in the proximity of the crack tip. The effect of the correction cannot be neglected in either Williams’s or Westergaard’s model

Weyl-Underhill-Emmrich quantization and the Stratonovich-Weyl quantizer

Weyl-Underhill-Emmrich (WUE) quantization and its generalization are considered. It is shown that an axiomatic definition of the Stratonovich-Weyl (SW) quantizer leads to severe difficulties. Quantization on the cylinder within the WUE formalism is discussed.Comment: 15+1 pages, no figure