On Legendrian Embbeddings into Open Book Decompositions

We study Legendrian embeddings of a compact Legendrian submanifold $L$ sitting in a closed contact manifold $(M,\xi)$ whose contact structure is supported by a (contact) open book $\mathcal{OB}$ on $M$. We prove that if $\mathcal{OB}$ has Weinstein pages, then there exist a contact structure $\xi'$ on $M$, isotopic to $\xi$ and supported by $\mathcal{OB}$, and a contactomorphism $f:(M,\xi) \to (M,\xi')$ such that the image $f(L)$ of any such submanifold can be Legendrian isotoped so that it becomes disjoint from the closure of a page of $\mathcal{OB}$.Comment: 14 pages, 4 figures. Major corrections made. arXiv admin note: substantial text overlap with arXiv:1003.220

Statistical Confirmation of a Stellar Upper Mass Limit

We derive the expectation value for the maximum stellar mass (m_max) in an ensemble of N stars, as a function of the IMF upper-mass cutoff (m_up) and N. We statistically demonstrate that the upper IMF of the local massive star census observed thus far in the Milky Way and Magellanic Clouds clearly exhibits a universal upper mass cutoff around 120 - 200 M_sun for a Salpeter IMF, although the result is more ambiguous for a steeper IMF.Comment: PDF, 5 pages, 4 figures. Accepted to the Astrophysical Journal Letter

Proteostasis and ageing: insights from long-lived mutant mice

The global increase in life expectancy is creating significant medical, social and economic challenges to current and future generations. Consequently, there is a need to identify the fundamental mechanisms underlying the ageing process. This knowledge should help develop realistic interventions capable of combatting age-related disease, and thus improving late-life health and vitality. While several mechanisms have been proposed as conserved lifespan determinants, the loss of proteostasis- where proteostasis is defined here as the maintenance of the proteome- appears highly relevant to both ageing and disease. Several studies have shown that multiple proteostatic mechanisms, including the endoplasmic reticulum (ER)-induced unfolded protein response (UPR), the ubiquitin-proteasome system (UPS) and autophagy, all appear indispensable for longevity in many long-lived invertebrate mutants. Similarly, interspecific comparisons suggest that proteostasis may be an important lifespan determinant in vertebrates. Over the last 20 years a number of long-lived mouse mutants have been described, many of which carry single-gene mutations within the growth-hormone, insulin/IGF-1 or mTOR signalling pathways. However, we still do not know how these mutations act mechanistically to increase lifespan and healthspan, and accordingly whether mechanistic commonality occurs between different mutants. Recent evidence supports the premise that the successful maintenance of the proteome during ageing may be linked to the increased lifespan and healthspan of long-lived mouse mutants

The star formation process in the Magellanic Clouds

The Magellanic Clouds offer unique opportunities to study star formation both on the global scales of an interacting system of gas-rich galaxies, as well as on the scales of individual star-forming clouds. The interstellar media of the Small and Large Magellanic Clouds and their connecting bridge, span a range in (low) metallicities and gas density. This allows us to study star formation near the critical density and gain an understanding of how tidal dwarfs might form; the low metallicity of the SMC in particular is typical of galaxies during the early phases of their assembly, and studies of star formation in the SMC provide a stepping stone to understand star formation at high redshift where these processes can not be directly observed. In this review, I introduce the different environments encountered in the Magellanic System and compare these with the Schmidt-Kennicutt law and the predicted efficiencies of various chemo-physical processes. I then concentrate on three aspects that are of particular importance: the chemistry of the embedded stages of star formation, the Initial Mass Function, and feedback effects from massive stars and its ability to trigger further star formation.Comment: 12pages, 5figures, invited review at the IAUS 256, The Magellanic System: Stars, Gas, and Galaxies, eds. Jacco van Loon, Joana Oliveir

Towards DIB mapping in galaxies beyond 100 Mpc. A radial profile of the λ\lambda5780.5 diffuse interstellar band in AM 1353-272 B

Diffuse Interstellar Bands (DIBs) are non-stellar weak absorption features of unknown origin found in the spectra of stars viewed through one or several clouds of Interstellar Medium (ISM). Research of DIBs outside the Milky Way is currently very limited. Specifically spatially resolved investigations of DIBs outside of the Local Group is, to our knowledge, inexistent. Here, we explore the capability of the high sensitivity Integral Field Spectrograph, MUSE, as a tool to map diffuse interstellar bands at distances larger than 100 Mpc. We use MUSE commissioning data for AM 1353-272 B, the member with highest extinction of the "The Dentist's Chair", an interacting system of two spiral galaxies. High signal-to-noise spectra were created by co-adding the signal of many spatial elements distributed in a geometry of concentric elliptical half-rings. We derived decreasing radial profiles for the equivalent width of the $\lambda$5780.5 DIB both in the receding and approaching side of the companion galaxy up to distances of $\sim$4.6 kpc from the center of the galaxy. Likewise, interstellar extinction, as derived from the Halpha/Hbeta line ratio displays a similar trend, with decreasing values towards the external parts. This translates into an intrinsic correlation between the strength of the DIB and the extinction within AM 1353-272 B consistent with the current existing global trend between these quantities when using measurements for both Galactic and extragalactic sight lines. Mapping of DIB strength in the Local Universe as up to now only done for the Milky Way seems feasible. This offers a new approach to study the relationship between DIBs and other characteristics and species of the ISM in different conditions as those found in our Galaxy to the use of galaxies in the Local Group and/or single sightlines towards supernovae, quasars and galaxies outside the Local Group.Comment: 4 pages, 4 figures, accepted for publication as a Letter in Astronomy and Astrophysics; Received 10 February 2015 / Accepted 20 February 2015 ; English corrections include

The Phase Diagram of 1-in-3 Satisfiability Problem

We study the typical case properties of the 1-in-3 satisfiability problem, the boolean satisfaction problem where a clause is satisfied by exactly one literal, in an enlarged random ensemble parametrized by average connectivity and probability of negation of a variable in a clause. Random 1-in-3 Satisfiability and Exact 3-Cover are special cases of this ensemble. We interpolate between these cases from a region where satisfiability can be typically decided for all connectivities in polynomial time to a region where deciding satisfiability is hard, in some interval of connectivities. We derive several rigorous results in the first region, and develop the one-step--replica-symmetry-breaking cavity analysis in the second one. We discuss the prediction for the transition between the almost surely satisfiable and the almost surely unsatisfiable phase, and other structural properties of the phase diagram, in light of cavity method results.Comment: 30 pages, 12 figure

Fibroblasts derived from long-lived insulin receptor substrate 1 null mice are not resistant to multiple forms of stress

Reduced signalling through the insulin/insulin-like growth factor-1 signalling (IIS) pathway is a highly conserved lifespan determinant in model organisms. The precise mechanism underlying the effects of the IIS on lifespan and health is currently unclear, although cellular stress resistance may be important. We have previously demonstrated that mice globally lacking insulin receptor substrate 1 (Irs1−/−) are long-lived and enjoy a greater period of their life free from age-related pathology compared with wild-type (WT) controls. In this study, we show that primary dermal fibroblasts and primary myoblasts derived from Irs1−/− mice are no more resistant to a range of oxidant and nonoxidant chemical stressors than cells derived from WT mice