Inscribed Radius Bounds for Lower Ricci Bounded Metric Measure Spaces with Mean Convex Boundary

Consider an essentially nonbranching metric measure space with the measure contraction property of Ohta and Sturm, or with a Ricci curvature lower bound in the sense of Lott, Sturm and Villani. We prove a sharp upper bound on the inscribed radius of any subset whose boundary has a suitably signed lower bound on its generalized mean curvature. This provides a nonsmooth analog to a result of Kasue (1983) and Li (2014). We prove a stability statement concerning such bounds and - in the Riemannian curvature-dimension (RCD) setting - characterize the cases of equality

Best practices for HPM-assisted performance engineering on modern multicore processors

Many tools and libraries employ hardware performance monitoring (HPM) on modern processors, and using this data for performance assessment and as a starting point for code optimizations is very popular. However, such data is only useful if it is interpreted with care, and if the right metrics are chosen for the right purpose. We demonstrate the sensible use of hardware performance counters in the context of a structured performance engineering approach for applications in computational science. Typical performance patterns and their respective metric signatures are defined, and some of them are illustrated using case studies. Although these generic concepts do not depend on specific tools or environments, we restrict ourselves to modern x86-based multicore processors and use the likwid-perfctr tool under the Linux OS.Comment: 10 pages, 2 figure

Radiative transfer modelling of parsec-scale dusty warped discs

Warped discs have been found on (sub-)parsec scale in some nearby Seyfert nuclei, identified by their maser emission. Using dust radiative transfer simulations we explore their observational signatures in the infrared in order to find out whether they can partly replace the molecular torus. Strong variations of the brightness distributions are found, depending on the orientation of the warp with respect to the line of sight. Whereas images at short wavelengths typically show a disc-like and a point source component, the warp itself only becomes visible at far-infrared wavelengths. A similar variety is visible in the shapes of the spectral energy distributions. Especially for close to edge-on views, the models show silicate feature strengths ranging from deep absorption to strong emission for variations of the lines of sight towards the warp. To test the applicability of our model, we use the case of the Circinus galaxy, where infrared interferometry has revealed a highly elongated emission component matching a warped maser disc in orientation and size. Our model is for the first time able to present a physical explanation for the observed dust morphology as coming from the AGN heated dust. As opposed to available torus models, a warped disc morphology produces a variety of silicate feature shapes for grazing lines of sight, close to an edge-on view. This could be an attractive alternative to a claimed change of the dust composition for the case of the nearby Seyfert 2 galaxy NGC 1068, which harbours a warped maser disc as well.Comment: accepted by MNRA

The life cycle of starbursting circumnuclear gas discs

High-resolution observations from the sub-mm to the optical wavelength regime resolve the central few 100pc region of nearby galaxies in great detail. They reveal a large diversity of features: thick gas and stellar discs, nuclear starbursts, in- and outflows, central activity, jet interaction, etc. Concentrating on the role circumnuclear discs play in the life cycles of galactic nuclei, we employ 3D adaptive mesh refinement hydrodynamical simulations with the RAMSES code to self-consistently trace the evolution from a quasi-stable gas disc, undergoing gravitational (Toomre) instability, the formation of clumps and stars and the disc's subsequent, partial dispersal via stellar feedback. Our approach builds upon the observational finding that many nearby Seyfert galaxies have undergone intense nuclear starbursts in their recent past and in many nearby sources star formation is concentrated in a handful of clumps on a few 100pc distant from the galactic centre. We show that such observations can be understood as the result of gravitational instabilities in dense circumnuclear discs. By comparing these simulations to available integral field unit observations of a sample of nearby galactic nuclei, we find consistent gas and stellar masses, kinematics, star formation and outflow properties. Important ingredients in the simulations are the self-consistent treatment of star formation and the dynamical evolution of the stellar distribution as well as the modelling of a delay time distribution for the supernova feedback. The knowledge of the resulting simulated density structure and kinematics on pc scale is vital for understanding inflow and feedback processes towards galactic scales.Comment: accepted by MNRA

The complexity of parsec-scaled dusty tori in AGN

Warm gas and dust surround the innermost regions of active galactic nuclei (AGN). They provide the material for accretion onto the super-massive black hole and they are held responsible for the orientation-dependent obscuration of the central engine. The AGN-heated dust distributions turn out to be very compact with sizes on scales of about a parsec in the mid-infrared. Only infrared interferometry currently provides the necessary angular resolution to directly study the physical properties of this dust. Size estimates for the dust distributions derived from interferometric observations can be used to construct a size--luminosity relation for the dust distributions. The large scatter about this relation suggests significant differences between the dust tori in the individual galaxies, even for nuclei of the same class of objects and with similar luminosities. This questions the simple picture of the same dusty doughnut in all AGN. The Circinus galaxy is the closest Seyfert 2 galaxy. Because its mid-infrared emission is well resolved interferometrically, it is a prime target for detailed studies of its nuclear dust distribution. An extensive new interferometric data set was obtained for this galaxy. It shows that the dust emission comes from a very dense, disk-like structure which is surrounded by a geometrically thick, similarly warm dust distribution as well as significant amounts of warm dust within the ionisation cone.Comment: 8 pages, 3 figures, to appear in the proceedings of the conference "The central kiloparsec in Galactic Nuclei: Astronomy at High Angular Resolution 2011", open access Journal of Physics: Conference Series (JPCS), published by IOP Publishin

The Muscle-Brain Axis and Neurodegenerative Diseases: The Key Role of Mitochondria in Exercise-Induced Neuroprotection.

Regular exercise is associated with pronounced health benefits. The molecular processes involved in physiological adaptations to exercise are best understood in skeletal muscle. Enhanced mitochondrial functions in muscle are central to exercise-induced adaptations. However, regular exercise also benefits the brain and is a major protective factor against neurodegenerative diseases, such as the most common age-related form of dementia, Alzheimer's disease, or the most common neurodegenerative motor disorder, Parkinson's disease. While there is evidence that exercise induces signalling from skeletal muscle to the brain, the mechanistic understanding of the crosstalk along the muscle-brain axis is incompletely understood. Mitochondria in both organs, however, seem to be central players. Here, we provide an overview on the central role of mitochondria in exercise-induced communication routes from muscle to the brain. These routes include circulating factors, such as myokines, the release of which often depends on mitochondria, and possibly direct mitochondrial transfer. On this basis, we examine the reported effects of different modes of exercise on mitochondrial features and highlight their expected benefits with regard to neurodegeneration prevention or mitigation. In addition, knowledge gaps in our current understanding related to the muscle-brain axis in neurodegenerative diseases are outlined

GCIRS 7, a pulsating M1 supergiant at the Galactic centre. Physical properties and age

The stellar population in the central parsec of the Galaxy is dominated by an old (several Gyr) population, but young, massive stars dominate the luminosity function. We have studied the most luminous of these stars, GCIRS 7, in order to constrain the age of the recent star formation event in the Galactic Centre and to characterise it as an interferometric reference for observations of the Galactic Centre with the instrument GRAVITY, which will equip the Very Large Telescope Interferometer in the near future. We present the first H-band interferometric observations of GCIRS 7, obtained using the PIONIER visitor instrument on the VLTI using the four 8.2-m unit telescopes. In addition, we present unpublished K-band VLTI/AMBER data, build JHKL light-curves based on data spanning 4 decades, and measured the star's effective temperature using SINFONI spectroscopy. GCIRS 7 is marginally resolved at H-band (in 2013: uniform-disk diameter=1.076+/-0.093mas, R=960+/-92Rsun at 8.33+/-0.35kpc). We detect a significant circumstellar contribution at K-band. The star and its environment are variable in brightness and in size. The photospheric H-band variations are well modelled with two periods: P0~470+/-10 days (amplitude ~0.64mag) and long secondary period LSP~2700-2850 days (~1.1mag). As measured from CO equivalent width, =3600+/-195K. The size, periods, luminosity (=-8.44+/-0.22) and effective temperature are consistent with an M1 supergiant with an initial mass of 22.5+/-2.5Msun and an age of 6.5-10Myr (depending on rotation). This age is in remarkable agreement with most estimates for the recent star formation event in the central parsec. Caution should be taken when using this star as an interferometric reference as it is variable in size, is surrounded by a variable circumstellar environment and large convection cells may form on its photosphere.Comment: Accepted for publication in A&A. 10 pages, 12 figure

Resolving the nucleus of Centaurus A at mid-IR wavelengths

We have observed Centaurus A with the MID-infrared Interferometric instrument (MIDI) at the Very Large Telescope Interferometer (VLTI) at resolutions of 7 - 15 mas (at 12.5 micron) and filled gaps in the (u,v) coverage in comparison to earlier measurements. We are now able to describe the nuclear emission in terms of geometric components and derive their parameters by fitting models to the interferometric data. With simple geometrical models, the best fit is achieved for an elongated disk with flat intensity profile with diameter 76 +/- 9 mas x 35 +/- 2 mas (1.41 +/- 0.17 pc x 0.65 +/- 0.03 pc) whose major axis is oriented at a position angle (PA) of 10.1 +/- 2.2 degrees east of north. A point source contributes 47 +/- 11 % of the nuclear emission at 12.5 micron. There is also evidence that neither such a uniform nor a Gaussian disk are good fits to the data. This indicates that we are resolving more complicated small-scale structure in AGNs with MIDI, as has been seen in Seyfert galaxies previously observed with MIDI. The PA and inferred inclination i = 62.6 +2.1/-2.6 degrees of the dust emission are compared with observations of gas and dust at larger scales.Comment: Accepted for the PASA special issue on Centaurus