A note on the convergence of parametrised non-resonant invariant manifolds

Truncated Taylor series representations of invariant manifolds are abundant in numerical computations. We present an aposteriori method to compute the convergence radii and error estimates of analytic parametrisations of non-resonant local invariant manifolds of a saddle of an analytic vector field, from such a truncated series. This enables us to obtain local enclosures, as well as existence results, for the invariant manifolds

On a computer-aided approach to the computation of Abelian integrals

An accurate method to compute enclosures of Abelian integrals is developed. This allows for an accurate description of the phase portraits of planar polynomial systems that are perturbations of Hamiltonian systems. As an example, it is applied to the study of bifurcations of limit cycles arising from a cubic perturbation of an elliptic Hamiltonian of degree four

Universal Equation for Efimov States

Efimov states are a sequence of shallow 3-body bound states that arise when the 2-body scattering length is large. Efimov showed that the binding energies of these states can be calculated in terms of the scattering length and a 3-body parameter by solving a transcendental equation involving a universal function of one variable. We calculate this universal function using effective field theory and use it to describe the three-body system of 4He atoms. We also extend Efimov's theory to include the effects of deep 2-body bound states, which give widths to the Efimov states.Comment: 8 pages, revtex4, 2 ps figures, table with numerical values of universal function adde

Reconstitution of lipoprotein(a) by infusion of human low density lipoprotein into transgenic mice expressing human apolipoprotein(a)

Lipoprotein(a) (Lp(a)) is an atherosclerosis-causing lipoprotein that circulates in human plasma as a complex of low density lipoprotein (LDL) and apolipoprotein(a) (apo(a)). It is not known whether apo(a) attaches to LDL within hepatocytes prior to secretion or in plasma subsequent to secretion. Here we describe the development of a line of mice expressing the human apo(a) transgene under the control of the murine transferrin promoter. The apo(a) was secreted into the plasma, but circulated free of lipoproteins. When human (h)-LDL was injected intravenously, the circulating apo(a) rapidly associated with the lipoproteins, as determined by nondenaturing gel electrophoresis. Human HDL and mouse LDL had no such effect. When h-VLDL was injected, there was a delayed association of apo(a) with the lipoprotein fraction which suggests that apo(a) preferentially associated with a metabolic product of VLDL. The complex of apo(a) with LDL formed both in vivo and in vitro was resistant to boiling in the presence of detergents and denaturants, but was resolved upon disulfide reduction. These studies suggest that apo(a) fails to associate with mouse lipoproteins due to structural differences between human and mouse LDL, and that Lp(a) formation can occur in plasma through the association of apo(a) with circulating LDL

Transgenic mice expressing high plasma concentrations of human apolipoprotein B100 and lipoprotein(a)

The B apolipoproteins, apo-B48 and apo-B100, are key structural proteins in those classes of lipoproteins considered to be atherogenic [e.g., chylomicron remnants, \u3b2-VLDL, LDL, oxidized LDL, and Lp(a)]. Here we describe the development of transgenic mice expressing high levels of human apo-B48 and apo-B100. A 79.5-kb human genomic DNA fragment containing the entire human apo-B gene was isolated from a P1 bacteriophage library and microinjected into fertilized mouse eggs. 16 transgenic founders expressing human apo-B were generated, and the animals with the highest expression had plasma apo-B100 levels nearly as high as those of normolipidemic humans ( 3c50 mg/dl). The human apo-B100 in transgenic mouse plasma was present largely in lipoproteins of the LDL class as shown by agarose gel electrophoresis, chromatography on a Superose 6 column, and density gradient ultracentrifugation. When the human apo-B transgenic founders were crossed with transgenic mice expressing human apo(a), the offspring that expressed both transgenes had high plasma levels of human Lp(a). Both the human apo-B and Lp(a) transgenic mice will be valuable resources for studying apo-B metabolism and the role of apo-B and Lp(a) in atherosclerosis

Universality in the Three-Body Problem for 4He Atoms

The two-body scattering length a for 4He atoms is much larger than their effective range r_s. As a consequence, low-energy few-body observables have universal characteristics that are independent of the interaction potential. Universality implies that, up to corrections suppressed by r_s/a, all low-energy three-body observables are determined by a and a three-body parameter \Lambda_*. We give simple expressions in terms of a and \Lambda_* for the trimer binding energy equation, the atom-dimer scattering phase shifts, and the rate for three-body recombination at threshold. We determine \Lambda_* for several 4He potentials from the calculated binding energy of the excited state of the trimer and use it to obtain the universality predictions for the other low-energy observables. We also use the calculated values for one potential to estimate the effective range corrections for the other potentials.Comment: 23 pages, revtex4, 6 ps figures, references added, universal expressions update

A tetragonal-to-monoclinic phase transition in a ferroelectric perovskite: the structure of PbZr(0.52)Ti(0.48)O3

The perovskite-like ferroelectric system PbZr(1-x)Ti(x)O3 (PZT) has a nearly vertical morphotropic phase boundary (MPB) around x=0.45-0.50. Recent synchrotron x-ray powder diffraction measurements by Noheda et al. [Appl. Phys. Lett. 74, 2059 (1999)] have revealed a new monoclinic phase between the previously-established tetragonal and rhombohedral regions. In the present work we describe a Rietveld analysis of the detailed structure of the tetragonal and monoclinic PZT phases on a sample with x= 0.48 for which the lattice parameters are respectively: at= 4.044 A, ct= 4.138 A, at 325 K, and am= 5.721 A, bm= 5.708 A, cm= 4.138 A, beta= 90.496 deg., at 20K. In the tetragonal phase the shifts of the atoms along the polar [001] direction are similar to those in PbTiO3 but the refinement indicates that there are, in addition, local disordered shifts of the Pb atoms of ~0.2 A perpendicular to the polar axis.. The monoclinic structure can be viewed as a condensation along one of the directions of the local displacements present in the tetragonal phase. It equally well corresponds to a freezing-out of the local displacements along one of the directions recently reported by Corker et al.[J. Phys. Condens. Matter 10, 6251 (1998)] for rhombohedral PZT. The monoclinic structure therefore provides a microscopic picture of the MPB region in which one of the "locally" monoclinic phases in the "average" rhombohedral or tetragonal structures freezes out, and thus represents a bridge between these two phases.Comment: REVTeX, 7 figures. Modifications after referee's suggestion: new figure (figure 5), comments in 2nd para. (Sect.III) and in 2nd & 3rd para. (Sect. IV-a), in the abstract: "...of ~0.2 A perpendicular to the polar axis.

Occlusion and Motion Reasoning for Long-Term Tracking

International audienceObject tracking is a reoccurring problem in computer vision. Tracking-by-detection approaches, in particular Struck (Hare et al., 2011), have shown to be competitive in recent evaluations. However, such approaches fail in the presence of long-term occlusions as well as severe viewpoint changes of the object. In this paper we propose a principled way to combine occlusion and motion reasoning with a tracking-by-detection approach. Occlusion and motion reasoning is based on state-of-the-art long-term trajectories which are labeled as object or background tracks with an energy-based formulation. The overlap between labeled tracks and detected regions allows to identify occlusions. The motion changes of the object between consecutive frames can be estimated robustly from the geometric relation between object trajectories. If this geometric change is significant, an additional detector is trained. Experimental results show that our tracker obtains state-of-the-art results and handles occlusion and viewpoints changes better than competing tracking methods