Existence and concentration of ground state solutions for a critical nonlocal Schr\"odinger equation in R2\R^2

We study the following singularly perturbed nonlocal Schr\"{o}dinger equation -\vr^2\Delta u +V(x)u =\vr^{\mu-2}\Big[\frac{1}{|x|^{\mu}}\ast F(u)\Big]f(u) \quad \mbox{in} \quad \R^2, where $V(x)$ is a continuous real function on $\R^2$, $F(s)$ is the primitive of $f(s)$, $0<\mu<2$ and \vr is a positive parameter. Assuming that the nonlinearity $f(s)$ has critical exponential growth in the sense of Trudinger-Moser, we establish the existence and concentration of solutions by variational methods.Comment: 3

Surgical treatment of sporadic vestibular schwannoma in a series of 1006 patients. Trattamento chirurgico degli schwannomi vestibolari: risultati su una serie di 1006 pazienti

La gestione dello schwannoma vestibolare (SV) sporadico si è gradualmente evoluta negli ultimi decenni. Lo scopo di questo studio è di analizzare l’evoluzione negli esiti chirurgici dell’exeresi di queste lesioni, realizzata da un team neurotologico tra il 1990 e il 2006, attraverso differenti approcci. È stata eseguita una revisione retrospettica monocentrica dei dati clinici di 1006 pazienti. Al fine di valutare eventuali modifiche e progressi, il periodo di 17 anni è stato diviso in tre periodi, ciascuno comprendente rispettivamente 268 SV (1990- 1996), 299 SV (1997-2001), e 439 SV (2002-2006). Il follow-up medio è stato di 5,9 ± 2,4 anni. Complessivamente l’asportazione totale è stata ottenuta nel 99,4% dei casi. Il tasso di mortalità è stato dello 0,3%, la meningite e la perdita di liquido cefalo rachidiano (LCR) sono stati osservati nel 1,2% e il 9% dei casi, rispettivamente. La frequenza della perdita di LCR è diminuita dal 11,6% al 7,1% tra il primo e dell’ultimo periodo (p &lt; 0,01) e la revisione chirurgica dal 3,4% al 0,9% (p &lt; 0,05). Il nervo facciale è stato anatomicamente conservato nel 97,7% dei casi. Ad un anno, una buona funzione del nervo facciale è stata osservata nel 85,1% dei pazienti (I e II grado HouseBrackmann), con una variazione tra il primo e l’ultimo periodo che andava dal 78,4% al 87,6% (p &lt; 0,05). Ad un anno post-operatorio la conservazione dell’udito è stata ottenuta nel 61,6% dei pazienti, passando dal 50,9% del primo periodo, al 69,0% del periodo piú recente (p &lt; 0,05) (classe A + B + C dalla classificazione AAO-HNS). L’udito utile (classe A + B) è stato conservato nel 33,5% dei casi complessivamente, con percentuali comprese tra il 21,8% e 42% nel primo e nell’ultimo periodo rispettivamente (p &lt; 0,01). Gli esiti chirurgici dell’asportazion dello schwannoma vestibolare sporadico sono migliorati negli anni per quanto riguarda i risultati funzionali del nervo facciale, la conservazione dell’udito, le perdite di liquido cefalorachidiano, principalmente grazie all’esperienza del team neurotologico. I risultati funzionali dopo la rimozione microchirurgica completa SV di grandi dimensioni dipendono dall’ esperienza maturata sulle lesioni di piccole dimensioniThe management of sporadic vestibular schwannoma (VS) has evolved in the last decades. The aim of this study was to analyse the evolution in surgical outcomes of VSs operated by a neurotological team between 1990 and 2006 by different approaches. A monocentric retrospective review of medical charts of 1006 patients was performed. In order to assess eventual changes and progress, the 17-years period was divided in three periods, each one comprehending 268 VS (1990-1996), 299 VS (1997-2001), and 439 VS (2002-2006). Mean follow-up was 5.9 ± 2.4 years. Overall, complete VS removal was achieved in 99.4% of cases. Mortality rate was 0.3%, meningitis and CSF leaks were observed in 1.2 % and 9 % of the cases, respectively. CSF leakage decreased from 11.6% to 7.1% between the first and last period (p &lt; 0.01) as well as revision surgery from 3.4 % to 0.9 % (p &lt; 0.05). Facial nerve was anatomically preserved in 97.7% of cases. At one year, a good facial nerve function was observed in 85.1% of patients (grade I and II of House-Brackmann grading scale), which ranged between the first and last period from 78.4% to 87.6% (p &lt;0.05). At one year, hearing preservation was obtained in 61.6% of patients, which increased from the first period to the last one from 50.9% to 69.0% (p &lt; 0.05) (class A+B+C from the AAO-HNS classification). Useful hearing (class A+B) was observed in 33.5% of cases overall, with 21.8% and 42% in the first and last period, respectively (p &lt; 0.01). Surgical outcomes of sporadic vestibular schwannoma have improved concerning facial nerve function outcomes, hearing preservation and cerebrospinal fluid (CSF) leaks, mainly due to the neuro-otological team's experience. Functional results after complete microsurgical removal of large VS depend on experience gained on small VS removal

Quantum-inspired computational imaging

Computational imaging combines measurement and computational methods with the aim of forming images even when the measurement conditions are weak, few in number, or highly indirect. The recent surge in quantum-inspired imaging sensors, together with a new wave of algorithms allowing on-chip, scalable and robust data processing, has induced an increase of activity with notable results in the domain of low-light flux imaging and sensing. We provide an overview of the major challenges encountered in low-illumination (e.g., ultrafast) imaging and how these problems have recently been addressed for imaging applications in extreme conditions. These methods provide examples of the future imaging solutions to be developed, for which the best results are expected to arise from an efficient codesign of the sensors and data analysis tools.Y.A. acknowledges support from the UK Royal Academy of Engineering under the Research Fellowship Scheme (RF201617/16/31). S.McL. acknowledges financial support from the UK Engineering and Physical Sciences Research Council (grant EP/J015180/1). V.G. acknowledges support from the U.S. Defense Advanced Research Projects Agency (DARPA) InPho program through U.S. Army Research Office award W911NF-10-1-0404, the U.S. DARPA REVEAL program through contract HR0011-16-C-0030, and U.S. National Science Foundation through grants 1161413 and 1422034. A.H. acknowledges support from U.S. Army Research Office award W911NF-15-1-0479, U.S. Department of the Air Force grant FA8650-15-D-1845, and U.S. Department of Energy National Nuclear Security Administration grant DE-NA0002534. D.F. acknowledges financial support from the UK Engineering and Physical Sciences Research Council (grants EP/M006514/1 and EP/M01326X/1). (RF201617/16/31 - UK Royal Academy of Engineering; EP/J015180/1 - UK Engineering and Physical Sciences Research Council; EP/M006514/1 - UK Engineering and Physical Sciences Research Council; EP/M01326X/1 - UK Engineering and Physical Sciences Research Council; W911NF-10-1-0404 - U.S. Defense Advanced Research Projects Agency (DARPA) InPho program through U.S. Army Research Office; HR0011-16-C-0030 - U.S. DARPA REVEAL program; 1161413 - U.S. National Science Foundation; 1422034 - U.S. National Science Foundation; W911NF-15-1-0479 - U.S. Army Research Office; FA8650-15-D-1845 - U.S. Department of the Air Force; DE-NA0002534 - U.S. Department of Energy National Nuclear Security Administration)Accepted manuscrip

Naked Singularities as Particle Accelerators II

We generalize here our earlier results on particle acceleration by naked singularities. We showed recently[1] that the naked singularities that form due to gravitational collapse of massive stars provide a suitable environment where particles could get accelerated and collide at arbitrarily high center of mass energies. However, we focussed there only on the spherically symmetric gravitational collapse models, which were also assumed to be self-similar. In this paper, we broaden and generalize the result to all gravitational collapse models leading to the formation of a naked singularity as final state of collapse, evolving from a regular initial data, without making any prior restrictive assumptions about the spacetime symmetries such as above. We show that when the particles interact and collide near the Cauchy horizon, the energy of collision in the center of mass frame will be arbitrarily high, thus offering a window to the Planck scale physics. We also consider the issue of various possible physical mechanisms of generation of such very high energy particles from the vicinity of naked singularity. We then construct a model of gravitational collapse to a timelike naked singularity to demonstrate the working of these ideas, where the pressure is allowed to be negative but the energy conditions are respected. We show that a finite amount of mass-energy density has to be necessarily radiated away from the vicinity of the naked singularity as the collapse evolves. Therefore the nature of naked singularities, both at classical and quantum level could play an important role in the process of particle acceleration, explaining the occurrence of highly energetic outgoing particles in the vicinity of Cauchy horizon that participate in extreme high energy collisions.Comment: 13 pages, 5 figures, Accepted for publication in Phys. Rev. D, Reference and Acknowledgments adde

Contraints on Matter from Asymptotic Safety

Recent studies of the ultraviolet behaviour of pure gravity suggest that it admits a non-Gaussian attractive fixed point, and therefore that the theory is asymptotically safe. We consider the effect on this fixed point of massless minimally coupled matter fields. The existence of a UV attractive fixed point puts bounds on the type and number of such fields.Comment: 5 pages, 2 figures, revtex4; introduction expande

Sharp estimates on the first eigenvalue of the p-Laplacian with negative Ricci lower bound

We complete the picture of sharp eigenvalue estimates for the p-Laplacian on a compact manifold by providing sharp estimates on the first nonzero eigenvalue of the nonlinear operator $\Delta_p$ when the Ricci curvature is bounded from below by a negative constant. We assume that the boundary of the manifold is convex, and put Neumann boundary conditions on it. The proof is based on a refined gradient comparison technique and a careful analysis of the underlying model spaces.Comment: Sign mistake fixed in the proof of the gradient comparison theorem (theorem 5.1 pag 10), and some minor improvements aroun

Magnetic field in a young circumbinary disk

We use polarization observations of a circumbinary disk to investigate how the polarization properties change at distinct frequency bands. Our goal is to discern the main mechanism responsible for the polarization through comparison between our observations and model predictions. We used ALMA to perform full polarization observations at 97.5 GHz, 233 GHz and 343.5 GHz. The target is the Class I object BHB07-11, which is the youngest object in the Barnard 59 protocluster. Complementary VLA observations at 34.5 GHz revealed a binary system within the disk. We detect an extended and structured polarization pattern remarkably consistent among all three bands. The distribution of polarized intensity resembles a horseshoe shape with polarization angles following this morphology. From the spectral index between bands 3 and 7, we derive a dust opacity index $\beta \sim 1$ consistent with maximum grain sizes larger than expected to produce self-scattering polarization in each band. The polarization morphology do not match predictions from self-scattering. On the other hand, marginal correspondence is seen between our maps and predictions from radiation field assuming the brightest binary component as main radiation source. Molecular line data from BHB07-11 indicates disk rotation. We produced synthetic polarization maps from a rotating magnetized disk model assuming combined poloidal and toroidal magnetic field components. The magnetic field vectors (i. e., the polarization vectors rotated by 90\degr) are better represented by a model with poloidal magnetic field strength about 3 times the toroidal one. The similarity of our polarization patterns among the three bands provides a strong evidence against self-scattering and radiation fields. On the other hand, our data are reasonably well reproduced by a model of disk with toroidal magnetic field components slightly smaller than poloidal ones.Comment: 8 pages, 8 figures, accepted for publication in Astronomy & Astrophysic

Path-integral over non-linearly realized groups and Hierarchy solutions

The technical problem of deriving the full Green functions of the elementary pion fields of the nonlinear sigma model in terms of ancestor amplitudes involving only the flat connection and the nonlinear sigma model constraint is a very complex task. In this paper we solve this problem by integrating, order by order in the perturbative loop expansion, the local functional equation derived from the invariance of the SU(2) Haar measure under local left multiplication. This yields the perturbative definition of the path-integral over the non-linearly realized SU(2) group.Comment: 26 page

Physiological and Social Stress on Cognitive Performance

Humans are highly social creatures and this provides us with a number of benefits, such as protection and support, but it also brings new avenues for stress from social sources. Basic and translational neuroendocrine research has yielded a rich set of findings and a general understanding of how acute and chronic stress can result in reduced health, earlier aging, and earlier death. Although stress can be indexed by level of cortisol, the major stress hormone in humans, many interrelated physiological systems are involved in a stress response, including the cardio and vascular systems. Research toward greater understanding of stress buffering mechanisms holds value for improved human health in the face of entrenched social stressors. In particular, acute and chronic stress have consistently been found to impair cognitive performance, Many adults in high stress environments also face a changing social landscape during college years: changes in living partners, less control over noise, sleep, exercise, and nutrition. In this pilot investigation, we are interested in measuring the influences of acute stress on cognitive performance and whether social support, a factor that is modifiable, would be protective on the multi-systems relationships between stress and cognition. Broadly, we found (1) that higher levels of cortisol measured in saliva was associated with a faster return to resting levels of salivary cortisol (a measure of flexible, adaptive functioning of the central HPA stress system) after the stressor is removed and may also be associated with lower cortisol in the initial response to the stressor. In parallel, we found (2) that higher levels of cortisol were associated with impaired cognitive performance after the stress task, (3) finally, we found that those reporting high social support showed faster recovery to baseline in the cardiovascular systems and greater social support produced some buffering of stress response on their post-stress cognitive performance