The space of solutions to the Hessian one equation in the finitely punctured plane

We construct the space of solutions to the elliptic Monge-Ampere equation det(D^2 u)=1 in the plane R^2 with n points removed. We show that, modulo equiaffine transformations and for n>1, this space can be seen as an open subset of R^{3n-4}, where the coordinates are described by the conformal equivalence classes of once punctured bounded domains in the complex plane of connectivity n-1. This approach actually provides a constructive procedure that recovers all such solutions to the Monge-Ampere equation, and generalizes a theorem by K. Jorgens.Comment: 14 pages, 3 figure

New insights in the origin and evolution of the old, metal-rich open cluster NGC 6791

NGC 6791 is one of the most studied open clusters, it is massive ($\sim5000\,M_{\odot}$), located at the solar circle, old ($~8\,$Gyr) and yet the most metal-rich cluster (${\rm [Fe/H]}\simeq0.4$) known in the Milky Way. By performing an orbital analysis within a Galactic model including spiral arms and a bar, we found that it is plausible that NGC 6791 formed in the inner thin disc or in the bulge, and later displaced by radial migration to its current orbit. We apply different tools to simulate NGC 6791, including direct $N$-body summation in time-varying potentials, to test its survivability when going through different Galactic environments. In order to survive the 8 Gyr journey moving on a migrating orbit, NGC 6791 must have been more massive, $M_0 \geq 5\times10^4 M_{\odot}$, when formed. We find independent confirmation of this initial mass in the stellar mass function, which is observed to be flat; this can only be explained if the average tidal field strength experienced by the cluster is stronger than what it is at its current orbit. Therefore, the birth place and journeys of NGC 6791 are imprinted in its chemical composition, in its mass loss, and in its flat stellar mass function, supporting its origin in the inner thin disc or in the bulge.Comment: 14 pages, 10 Figures, 3 Tables. Accepted for publication in MNRA

Estudios de imagen en el diagnóstico de los hemangiomas y malformaciones vasculares

The diagnosis of haemangiomata and cutaneous vascular malformations is based on clinical history and physical exploration. Imaging studies might be necessary to clarify and confirm the diagnosis, and in order to analyse the extent of the lesions by permitting an evaluation of their non-visible component as well as the affection of neighbouring structures. Finally, they also play an important role when it comes to planning and directing treatment, whether surgical or endovascular. The imaging techniques employed for haemangiomas and vascular malformations include: plain films ultrasound (Doppler), computerised tomography (Angio-CT), magnetic resonance (Angio-MR) and the angiographic techniques (arteriography, phlebography)

Contribution of speckle noise in near-infrared spectroscopy measurements

Near-infrared spectroscopy (NIRS) is widely used in biomedical optics with applications ranging from basic science, such as in functional neuroimaging, to clinical, as in pulse oximetry. Despite the relatively low absorption of tissue in the near-infrared, there is still a significant amount of optical attenuation produced by the highly scattering nature of tissue. Because of this, designers of NIRS systems have to balance source optical power and source–detector separation to maximize the signal-to-noise ratio (SNR). However, theoretical estimations of SNR neglect the effects of speckle. Speckle manifests as fluctuations of the optical power received at the detector. These fluctuations are caused by interference of the multiple random paths taken by photons in tissue. We present a model for the NIRS SNR that includes the effects of speckle. We performed experimental validations with a NIRS system to show that it agrees with our model. Additionally, we performed computer simulations based on the model to estimate the contribution of speckle noise for different collection areas and source–detector separations. We show that at short source–detector separation, speckle contributes most of the noise when using long coherence length sources. Considering this additional noise is especially important for hybrid applications that use NIRS and speckle contrast simultaneously, such as in diffuse correlation spectroscopy.R01 EB025145 - NIBIB NIH HHS; R24 NS104096 - NINDS NIH HHSPublished versio

Effect of aeration on steady-state conditions in non- and partially aerated low-loaded biofilter

Excessive growth of biomass and retention of solids associated with air bubbles lead to bed clogging, which affects the biofilters' performance. Two experiments were carried out in a submerged biofilter at the flow velocity of 0.5 m h(-1), for an organic loading rate of 51 g C m(-3) h(-1) and a nitrogen loading rate of 13 g NH4-N m(-3) h(-1), one with the biofilter not aerated, the other with the biofilter partially aerated. The results showed that the higher head losses occurred in the upper section of the biofilter, where there was a greater biomass development and a higher removal of organic carbon, ammonia and solids, with the maximum allowed head loss being reached in 16 and 8 days. In any case, the steady-state conditions were achieved after 2 days and were interrupted on the tenth day of experiment E1 and on the fifth day of experiment E2. This allowed defining different operating cycles that enabled an average organic removal rate of 12.7 g C m(-3) h(-1) (27 %) and an average ammonia removal rate of 1.1 g NH4-N m(-3) h(-1) (9 %) without aeration, and of 35.8 g C m(-3) h(-1) (76 %) and 6.3 g NH4-N m(-3) h(-1) (51 %) with aeration. Regardless of the aeration conditions, more than 90 % of TOC and NH4-N removal occurred in the upper section. After the backwashing cycle, the biofilter returned to steady-state conditions in 6 h (without aeration) and 7 h (with aeration)