Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability into the light of Kolmogorov and Nekhoroshev theories

We investigate the long-time stability of the Sun-Jupiter-Saturn-Uranus system by considering a planar secular model, that can be regarded as a major refinement of the approach first introduced by Lagrange. Indeed, concerning the planetary orbital revolutions, we improve the classical circular approximation by replacing it with a solution that is invariant up to order two in the masses; therefore, we investigate the stability of the secular system for rather small values of the eccentricities. First, we explicitly construct a Kolmogorov normal form, so as to find an invariant KAM torus which approximates very well the secular orbits. Finally, we adapt the approach that is at basis of the analytic part of the Nekhoroshev's theorem, so as to show that there is a neighborhood of that torus for which the estimated stability time is larger than the lifetime of the Solar System. The size of such a neighborhood, compared with the uncertainties of the astronomical observations, is about ten times smaller.Comment: 31 pages, 2 figures. arXiv admin note: text overlap with arXiv:1010.260

Combinatorial Hopf algebras in quantum field theory I

This manuscript stands at the interface between combinatorial Hopf algebra theory and renormalization theory. Its plan is as follows: Section 1 is the introduction, and contains as well an elementary invitation to the subject. The rest of part I, comprising Sections 2-6, is devoted to the basics of Hopf algebra theory and examples, in ascending level of complexity. Part II turns around the all-important Faa di Bruno Hopf algebra. Section 7 contains a first, direct approach to it. Section 8 gives applications of the Faa di Bruno algebra to quantum field theory and Lagrange reversion. Section 9 rederives the related Connes-Moscovici algebras. In Part III we turn to the Connes-Kreimer Hopf algebras of Feynman graphs and, more generally, to incidence bialgebras. In Section10 we describe the first. Then in Section11 we give a simple derivation of (the properly combinatorial part of) Zimmermann's cancellation-free method, in its original diagrammatic form. In Section 12 general incidence algebras are introduced, and the Faa di Bruno bialgebras are described as incidence bialgebras. In Section 13, deeper lore on Rota's incidence algebras allows us to reinterpret Connes-Kreimer algebras in terms of distributive lattices. Next, the general algebraic-combinatorial proof of the cancellation-free formula for antipodes is ascertained; this is the heart of the paper. The structure results for commutative Hopf algebras are found in Sections 14 and 15. An outlook section very briefly reviews the coalgebraic aspects of quantization and the Rota-Baxter map in renormalization.Comment: 94 pages, LaTeX figures, precisions made, typos corrected, more references adde

Dusty Planetary Systems

Extensive photometric stellar surveys show that many main sequence stars show emission at infrared and longer wavelengths that is in excess of the stellar photosphere; this emission is thought to arise from circumstellar dust. The presence of dust disks is confirmed by spatially resolved imaging at infrared to millimeter wavelengths (tracing the dust thermal emission), and at optical to near infrared wavelengths (tracing the dust scattered light). Because the expected lifetime of these dust particles is much shorter than the age of the stars (>10 Myr), it is inferred that this solid material not primordial, i.e. the remaining from the placental cloud of gas and dust where the star was born, but instead is replenished by dust-producing planetesimals. These planetesimals are analogous to the asteroids, comets and Kuiper Belt objects (KBOs) in our Solar system that produce the interplanetary dust that gives rise to the zodiacal light (tracing the inner component of the Solar system debris disk). The presence of these "debris disks" around stars with a wide range of masses, luminosities, and metallicities, with and without binary companions, is evidence that planetesimal formation is a robust process that can take place under a wide range of conditions. This chapter is divided in two parts. Part I discusses how the study of the Solar system debris disk and the study of debris disks around other stars can help us learn about the formation, evolution and diversity of planetary systems by shedding light on the frequency and timing of planetesimal formation, the location and physical properties of the planetesimals, the presence of long-period planets, and the dynamical and collisional evolution of the system. Part II reviews the physical processes that affect dust particles in the gas-free environment of a debris disk and their effect on the dust particle size and spatial distribution.Comment: 68 pages, 25 figures. To be published in "Solar and Planetary Systems" (P. Kalas and L. French, Eds.), Volume 3 of the series "Planets, Stars and Stellar Systems" (T.D. Oswalt, Editor-in-chief), Springer 201

Superconductivity of bulk CaC6

We have obtained bulk samples of the graphite intercalation compound, CaC6, by a novel method of synthesis from highly oriented pyrolytic graphite. The crystal structure has been completely determined showing that it is the only member of the MC6, metal-graphite compounds, which has rhombohedral symmetry. We have clearly shown the occurrence of superconductivity in the bulk sample at 11.5K, using magnetization measurements.Comment: 8 pages of text + 4 figures = 12 page

The sub-arcsecond dusty environment of Eta Carinae

The core of the nebula surrounding Eta Carinae has been observed with the VLT Adaptive Optics system NACO and with the interferometer VLTI/MIDI to constrain spatially and spectrally the warm dusty environment and the central object. In particular, narrow-band images at 3.74 and 4.05 micron reveal the butterfly shaped dusty environment close to the central star with unprecedented spatial resolution. A void whose radius corresponds to the expected sublimation radius has been discovered around the central source. Fringes have been obtained in the Mid-IR which reveal a correlated flux of about 100Jy situated 0.3" south-east of the photocenter of the nebula at 8.7 micron, which corresponds with the location of the star as seen in other wavelengths. This correlated flux is partly attributed to the central object, and these observations provide an upper limit for the SED of the central source from 2.2 to 13.5 micron. Moreover, we have been able to spectrally disperse the signal from the nebula itself at PA=318 degree, i.e. in the direction of the bipolar nebula 310 degree) within the MIDI field of view of 3". A large amount of corundum (Al2O3) is discovered, peaking at 0.6-1.2" south-east from the star, whereas the dust content of the Weigelt blobs is dominated b silicates. We discuss the mechanisms of dust formation which are closely related to the geometry of this Butterfly nebulae

Preliminary Evidence for Cell Membrane Amelioration in Children with Cystic Fibrosis by 5-MTHF and Vitamin B12 Supplementation: A Single Arm Trial

Cystic fibrosis (CF) is one of the most common fatal autosomal recessive disorders in the Caucasian population caused by mutations of gene for the cystic fibrosis transmembrane conductance regulator (CFTR). New experimental therapeutic strategies for CF propose a diet supplementation to affect the plasma membrane fluidity and to modulate amplified inflammatory response. The objective of this study was to evaluate the efficacy of 5-methyltetrahydrofolate (5-MTHF) and vitamin B12 supplementation for ameliorating cell plasma membrane features in pediatric patients with cystic fibrosis.A single arm trial was conducted from April 2004 to March 2006 in an Italian CF care centre. 31 children with CF aged from 3 to 8 years old were enrolled. Exclusion criteria were diabetes, chronic infections of the airways and regular antibiotics intake. Children with CF were supplemented for 24 weeks with 5-methyltetrahydrofolate (5-MTHF, 7.5 mg /day) and vitamin B12 (0.5 mg/day). Red blood cells (RBCs) were used to investigate plasma membrane, since RBCs share lipid, protein composition and organization with other cell types. We evaluated RBCs membrane lipid composition, membrane protein oxidative damage, cation content, cation transport pathways, plasma and RBCs folate levels and plasma homocysteine levels at baseline and after 24 weeks of 5-MTHF and vitamin B12 supplementation. In CF children, 5-MTHF and vitamin B12 supplementation (i) increased plasma and RBC folate levels; (ii) decreased plasma homocysteine levels; (iii) modified RBC membrane phospholipid fatty acid composition; (iv) increased RBC K(+) content; (v) reduced RBC membrane oxidative damage and HSP70 membrane association.5-MTHF and vitamin B12 supplementation might ameliorate RBC membrane features of children with CF.ClinicalTrials.gov NCT00730509

Cellular binding partners of the human papillomavirus E6 protein

The high-risk strains of human papillomavirus (HR-HPV) are known to be causative agents of cervical cancer and have recently also been implicated in cancers of the oropharynx. E6 is a potent oncogene of HR-HPVs, and its role in the progression to malignancy has been and continues to be explored. E6 is known to interact with and subsequently inactivate numerous cellular proteins pivotal in the mediation of apoptosis, transcription of tumor suppressor genes, maintenance of epithelial organization, and control of cell proliferation. Binding of E6 to these proteins cumulatively contributes to the oncogenic potential of HPV. This paper provides an overview of these cellular protein partners of HR-E6, the motifs known to mediate oncoprotein binding, and the agents that have the potential to interfere with E6 expression and activity and thus prevent the subsequent progression to oncogenesis

First Scattered-light Images of the Gas-rich Debris Disk around 49 Ceti

We present the first scattered-light images of the debris disk around 49 Ceti, a ∼40 Myr A1 main-sequence star at 59 pc, famous for hosting two massive dust belts as well as large quantities of atomic and molecular gas. The outer disk is revealed in reprocessed archival Hubble Space Telescope NICMOS-F110W images, as well as new coronagraphic H-band images from the Very Large Telescope SPHERE instrument. The disk extends from 1.″1 (65 au) to 4.″6 (250 au) and is seen at an inclination of 73°, which refines previous measurements at lower angular resolution. We also report no companion detection larger than 3 M Jup at projected separations beyond 20 au from the star (0.″34). Comparison between the F110W and H-band images is consistent with a gray color of 49 Ceti's dust, indicating grains larger than 2 μm. Our photometric measurements indicate a scattering efficiency/infrared excess ratio of 0.2-0.4, relatively low compared to other characterized debris disks. We find that 49 Ceti presents morphological and scattering properties very similar to the gas-rich HD 131835 system. From our constraint on the disk inclination we find that the atomic gas previously detected in absorption must extend to the inner disk, and that the latter must be depleted of CO gas. Building on previous studies, we propose a schematic view of the system describing the dust and gas structure around 49 Ceti and hypothetical scenarios for the gas nature and origin.E.C. acknowledges support from NASA through Hubble Fellowship grant HST-HF2-51355 awarded by STScI, operated by AURA, Inc. under contract NAS5-26555, and support from HST-AR-12652, for research carried out at the Jet Propulsion Laboratory, California Institute of Technology. J.M. acknowledges ESO through the ESO fellowship program. M.B. acknowledges support from DFG project Kr 2164/15-1. G.M.K. is supported by the Royal Society as a Royal Society University Research Fellow. C.d.B. is supported by Mexican CONACyT research grant CB-2012-183007. L.M. acknowledges support by STFC through a graduate studentship. J.C.A. acknowledges support by the Programme National de Planétologie. We acknowledge support by the European Union through ERC grant 337569 for O.A. and C.A.G.G. and grant 279973 for M.W. and L.M