Association between obstructive apnea syndrome during sleep and damages to anterior labyrinth: Our experience

The obstructive sleep apnea syndrome is a chronic condition characterized by frequent episodes of collapse of the upper airways during sleep. It can be considered a multisystem disease. Among the districts involved, even the auditory system was seen to be concerned. It was enrolled a population of 20 patients after polysomnographic diagnosis of OSAS (Apnea Hypopnea Index > 10) and a control group of 28 healthy persons (Apnea Hypopnea Index < 5). Each patient has been subjected to Pure Tone Audiometry, Tympanometry, study of Acoustic Reflex, Otoacoustic Emissions and Auditory Brainstem Response. Moreover they were submitted to endoscopy of upper airway with Muller Maneuver and Epworth Sleepiness Scale (ESS). The values of ESS was 13.5 in OSAS group and 5.4 in control group. The tone audiometry is worse in all frequencies analyzed in OSAS patients, but within the normal range for both groups analyzed by 250 to 1000 Hertz. Otoacoustic emissions show a reduced reproducibility and a lower signal/ noise ratio in OSAS group (P <0.01)

Branching Structures in Elastic Shape Optimization

Fine scale elastic structures are widespread in nature, for instances in plants or bones, whenever stiffness and low weight are required. These patterns frequently refine towards a Dirichlet boundary to ensure an effective load transfer. The paper discusses the optimization of such supporting structures in a specific class of domain patterns in 2D, which composes of periodic and branching period transitions on subdomain facets. These investigations can be considered as a case study to display examples of optimal branching domain patterns. In explicit, a rectangular domain is decomposed into rectangular subdomains, which share facets with neighbouring subdomains or with facets which split on one side into equally sized facets of two different subdomains. On each subdomain one considers an elastic material phase with stiff elasticity coefficients and an approximate void phase with orders of magnitude softer material. For given load on the outer domain boundary, which is distributed on a prescribed fine scale pattern representing the contact area of the shape, the interior elastic phase is optimized with respect to the compliance cost. The elastic stress is supposed to be continuous on the domain and a stress based finite volume discretization is used for the optimization. If in one direction equally sized subdomains with equal adjacent subdomain topology line up, these subdomains are consider as equal copies including the enforced boundary conditions for the stress and form a locally periodic substructure. An alternating descent algorithm is employed for a discrete characteristic function describing the stiff elastic subset on the subdomains and the solution of the elastic state equation. Numerical experiments are shown for compression and shear load on the boundary of a quadratic domain.Comment: 13 pages, 6 figure

Motion of a droplet for the Stochastic mass conserving Allen-Cahn equation

We study the stochastic mass-conserving Allen-Cahn equation posed on a smoothly bounded domain of R2 with additive, spatially smooth, space-time noise. This equation describes the stochastic motion of a small almost semicircular droplet attached to domain's boundary and moving towards a point of locally maximum curvature. We apply It^o calculus to derive the stochastic dynamics of the center of the droplet by utilizing the approximately invariant manifold introduced by Alikakos, Chen and Fusco [2] for the deterministic problem. In the stochastic case depending on the scaling, the motion is driven by the change in the curvature of the boundary and the stochastic forcing. Moreover, under the assumption of a su ciently small noise strength, we establish stochastic stability of a neighborhood of the manifold of boundary droplet states in the L2- and H1-norms, which means that with overwhelming probability the solution stays close to the manifold for very long time-scales

On the structure of phase transition maps for three or more coexisting phases

This paper is partly based on a lecture delivered by the author at the ERC workshop "Geometric Partial Differential Equations" held in Pisa in September 2012. What is presented here is an expanded version of that lecture.Comment: 23 pages, 6 figure

The Mediterranean island states : Malta and Cyprus

The 2004 European Union enlargement also included the Mediterranean island-states of Cyprus and Malta, two former British colonies and members of the British Commonwealth. The islands share a number of similarities but they are also dissimilar in uniquely distinct ways. The membership applications of both states initially presented the EU with a number of political difficulties. With respect to Cyprus, many member states would have preferred to see the island join the Union after the ‘Cyprus Problem’ had been settled. As for Malta, the island showed a very high degree of Euroskepticism. It froze its application in 1996 but reactivated it in 1998. Apart from this skepticism the island’s neutral status, enshrined in the Constitution could present insurmountable problems.peer-reviewe

Droplet minimizers for the Gates-Lebowitz-Penrose free energy functional

We study the structure of the constrained minimizers of the Gates-Lebowitz-Penrose free-energy functional ${\mathcal F}_{\rm GLP}(m)$, non-local functional of a density field $m(x)$, $x\in {\mathcal T}_L$, a $d$-dimensional torus of side length $L$. At low temperatures, ${\mathcal F}_{\rm GLP}$ is not convex, and has two distinct global minimizers, corresponding to two equilibrium states. Here we constrain the average density L^{-d}\int_{{\cal T}_L}m(x)\dd x to be a fixed value $n$ between the densities in the two equilibrium states, but close to the low density equilibrium value. In this case, a "droplet" of the high density phase may or may not form in a background of the low density phase, depending on the values $n$ and $L$. We determine the critical density for droplet formation, and the nature of the droplet, as a function of $n$ and $L$. The relation between the free energy and the large deviations functional for a particle model with long-range Kac potentials, proven in some cases, and expected to be true in general, then provides information on the structure of typical microscopic configurations of the Gibbs measure when the range of the Kac potential is large enough

Massive Star Cluster Formation and Destruction in Luminous Infrared Galaxies in GOALS

We present the results of a {\it Hubble Space Telescope} ACS/HRC FUV, ACS/WFC optical study into the cluster populations of a sample of 22 Luminous Infrared Galaxies in the Great Observatories All-Sky LIRG Survey. Through integrated broadband photometry we have derived ages and masses for a total of 484 star clusters contained within these systems. This allows us to examine the properties of star clusters found in the extreme environments of LIRGs relative to lower luminosity star-forming galaxies in the local Universe. We find that by adopting a Bruzual \& Charlot simple stellar population (SSP) model and Salpeter initial mass function, the age distribution of clusters declines as $dN/d\tau = \tau^{-0.9 +/- 0.3}$, consistent with the age distribution derived for the Antennae Galaxies, and interpreted as evidence for rapid cluster disruption occuring in the strong tidal fields of merging galaxies. The large number of $10^{6} M_{\odot}$ young clusters identified in the sample also suggests that LIRGs are capable of producing more high-mass clusters than what is observed to date in any lower luminosity star-forming galaxy in the local Universe. The observed cluster mass distribution of $dN/dM = M^{-1.95 +/- 0.11}$ is consistent with the canonical -2 power law used to describe the underlying initial cluster mass function (ICMF) for a wide range of galactic environments. We interpret this as evidence against mass-dependent cluster disruption, which would flatten the observed CMF relative to the underlying ICMF distribution.Comment: 63 pages, 58 Figures, 56 Tables, Accepted for publication in Ap

Ground state at high density

Weak limits as the density tends to infinity of classical ground states of integrable pair potentials are shown to minimize the mean-field energy functional. By studying the latter we derive global properties of high-density ground state configurations in bounded domains and in infinite space. Our main result is a theorem stating that for interactions having a strictly positive Fourier transform the distribution of particles tends to be uniform as the density increases, while high-density ground states show some pattern if the Fourier transform is partially negative. The latter confirms the conclusion of earlier studies by Vlasov (1945), Kirzhnits and Nepomnyashchii (1971), and Likos et al. (2007). Other results include the proof that there is no Bravais lattice among high-density ground states of interactions whose Fourier transform has a negative part and the potential diverges or has a cusp at zero. We also show that in the ground state configurations of the penetrable sphere model particles are superposed on the sites of a close-packed lattice.Comment: Note adde