Spectral analysis of the biharmonic operator subject to Neumann boundary conditions on dumbbell domains

We consider the biharmonic operator subject to homogeneous boundary conditions of Neumann type on a planar dumbbell domain which consists of two disjoint domains connected by a thin channel. We analyse the spectral behaviour of the operator, characterizing the limit of the eigenvalues and of the eigenprojections as the thickness of the channel goes to zero. In applications to linear elasticity, the fourth order operator under consideration is related to the deformation of a free elastic plate, a part of which shrinks to a segment. In contrast to what happens with the classical second order case, it turns out that the limiting equation is here distorted by a strange factor depending on a parameter which plays the role of the Poisson coefficient of the represented plate.Comment: To appear in "Integral Equations and Operator Theory

Brick Walls and AdS/CFT

We discuss the relationship between the bulk-boundary correspondence in Rehren's algebraic holography (and in other 'fixed-background' approaches to holography) and in mainstream 'Maldacena AdS/CFT'. Especially, we contrast the understanding of black-hole entropy from the viewpoint of QFT in curved spacetime -- in the framework of 't Hooft's 'brick wall' model -- with the understanding based on Maldacena AdS/CFT. We show that the brick-wall modification of a Klein Gordon field in the Hartle-Hawking-Israel state on 1+2-Schwarzschild AdS (BTZ) has a well-defined boundary limit with the same temperature and entropy as the brick-wall-modified bulk theory. One of our main purposes is to point out a close connection, for general AdS/CFT situations, between the puzzle raised by Arnsdorf and Smolin regarding the relationship between Rehren's algebraic holography and mainstream AdS/CFT and the puzzle embodied in the 'correspondence principle' proposed by Mukohyama and Israel in their work on the brick-wall approach to black hole entropy. Working on the assumption that similar results will hold for bulk QFT other than the Klein Gordon field and for Schwarzschild AdS in other dimensions, and recalling the first author's proposed resolution to the Mukohyama-Israel puzzle based on his 'matter-gravity entanglement hypothesis', we argue that, in Maldacena AdS/CFT, the algebra of the boundary CFT is isomorphic only to a proper subalgebra of the bulk algebra, albeit (at non-zero temperature) the (GNS) Hilbert spaces of bulk and boundary theories are still the 'same' -- the total bulk state being pure, while the boundary state is mixed (thermal). We also argue from the finiteness of its boundary (and hence, on our assumptions, also bulk) entropy at finite temperature, that the Rehren dual of the Maldacena boundary CFT cannot itself be a QFT and must, instead, presumably be something like a string theory.Comment: 54 pages, 3 figures. Arguments strengthened in the light of B.S. Kay `Instability of Enclosed Horizons' arXiv:1310.739

Holographic View on Quantum Correlations and Mutual Information between Disjoint Blocks of a Quantum Critical System

In (d+1) dimensional Multiscale Entanglement Renormalization Ansatz (MERA) networks, tensors are connected so as to reproduce the discrete, (d + 2) holographic geometry of Anti de Sitter space (AdSd+2) with the original system lying at the boundary. We analyze the MERA renormalization flow that arises when computing the quantum correlations between two disjoint blocks of a quantum critical system, to show that the structure of the causal cones characteristic of MERA, requires a transition between two different regimes attainable by changing the ratio between the size and the separation of the two disjoint blocks. We argue that this transition in the MERA causal developments of the blocks may be easily accounted by an AdSd+2 black hole geometry when the mutual information is computed using the Ryu-Takayanagi formula. As an explicit example, we use a BTZ AdS3 black hole to compute the MI and the quantum correlations between two disjoint intervals of a one dimensional boundary critical system. Our results for this low dimensional system not only show the existence of a phase transition emerging when the conformal four point ratio reaches a critical value but also provide an intuitive entropic argument accounting for the source of this instability. We discuss the robustness of this transition when finite temperature and finite size effects are taken into account.Comment: 21 pages, 5 figures. Abstract and Figure 1 has been modified. Minor modifications in Section 1 and Section

Gevrey local solvability in locally integrable structures

We consider a locally integrable real-analytic structure, and we investigate the local solvability in the category of Gevrey functions and ultradistributions of the complex d' naturally induced by the de Rham complex. We prove that the so-called condition Y(q) on the signature of the Levi form, for local solvability of d' u=f, is still necessary even if we take f in the classes of Gevrey functions and look for solutions u in the corresponding spaces of ultradistributions.Comment: 12 page

Two-Loop Soft Corrections and Resummation of the Thrust Distribution in the Dijet Region

The thrust distribution in electron-positron annihilation is a classical precision QCD observable. Using renormalization group (RG) evolution in Laplace space, we perform the resummation of logarithmically enhanced corrections in the dijet limit, $T\to 1$ to next-to-next-to-leading logarithmic (NNLL) accuracy. We independently derive the two-loop soft function for the thrust distribution and extract an analytical expression for the NNLL resummation coefficient $g_3$. To combine the resummed expressions with the fixed-order results, we derive the $\log(R)$-matching and $R$-matching of the NNLL approximation to the fixed-order NNLO distribution.Comment: 50 pages, 12 figures, 1 table. Few minor changes. Version accepted for publication in JHE

Cluster-like headache and idiopathic intracranial hypertension: a case report.

Cluster headache (CH) is a well-defined primary headache syndrome, but cases of symptomatic headache with clinical features of CH have been previously reported. Idiopathic Intracranial Hypertension (IIH) is a secondary headache disorder characterized by headache and visual symptoms, without clinical, radiological or laboratory evidence of intracranial pathology. Both papilloedema and IIH-related headache are typically bilateral, however asymmetrical or even unilateral localizations are described in literature. We report the case of a previously headache-free woman who presented cluster-like headache and asymmetrical papilloedema related to IIH. In our opinion the asymmetrical presentation supports, in this case, the hypothesis of cavernous sinus involvement in the IIH-related cluster-like headache pathogenesis

Evidence for an excess of B -> D(*) Tau Nu decays

Based on the full BaBar data sample, we report improved measurements of the ratios R(D(*)) = B(B -> D(*) Tau Nu)/B(B -> D(*) l Nu), where l is either e or mu. These ratios are sensitive to new physics contributions in the form of a charged Higgs boson. We measure R(D) = 0.440 +- 0.058 +- 0.042 and R(D*) = 0.332 +- 0.024 +- 0.018, which exceed the Standard Model expectations by 2.0 sigma and 2.7 sigma, respectively. Taken together, our results disagree with these expectations at the 3.4 sigma level. This excess cannot be explained by a charged Higgs boson in the type II two-Higgs-doublet model. We also report the observation of the decay B -> D Tau Nu, with a significance of 6.8 sigma.Comment: Expanded section on systematics, text corrections, improved the format of Figure 2 and included the effect of the change of the Tau polarization due to the charged Higg

Passive experimental autoimmune encephalomyelitis in C57BL/6 with MOG: evidence of involvement of B cells

Experimental autoimmune encephalomyelitis (EAE) is the most relevant animal model to study demyelinating diseases such as multiple sclerosis. EAE can be induced by active (active EAE) or passive (at-EAE) transfer of activated T cells in several species and strains of rodents. However, histological features of at-EAE model in C57BL/6 are poorly described. The aim of this study was to characterize the neuroinflammatory and neurodegenerative responses of at-EAE in C57BL/6 mice by histological techniques and compare them with that observed in the active EAE model. To develop the at-EAE, splenocytes from active EAE female mice were harvested and cultured in presence of MOG 35-55 and IL-12, and then injected intraperitoneally in recipient female C57BL6/J mice. In both models, the development of EAE was similar except for starting before the onset of symptoms and presenting a higher EAE cumulative score in the at-EAE model. Spinal cord histological examination revealed an increased glial activation as well as more extensive demyelinating areas in the at-EAE than in the active EAE model. Although inflammatory infiltrates composed by macrophages and T lymphocytes were found in the spinal cord and brain of both models, B lymphocytes were significantly increased in the at-EAE model. The co-localization of these B cells with IgG and their predominant distribution in areas of demyelination would suggest that IgG-secreting B cells are involved in the neurodegenerative processes associated with at-EAE

An international multicenter retrospective study of Pseudomonas aeruginosa nosocomial pneumonia: Impact of multidrug resistance

Introduction: Pseudomonas aeruginosa nosocomial pneumonia (Pa-NP) is associated with considerable morbidity, prolonged hospitalization, increased costs, and mortality. Methods: We conducted a retrospective cohort study of adult patients with Pa-NP to determine 1) risk factors for multidrug-resistant (MDR) strains and 2) whether MDR increases the risk for hospital death. Twelve hospitals in 5 countries (United States, n = 3; France, n = 2; Germany, n = 2; Italy, n = 2; and Spain, n = 3) participated. We compared characteristics of patients who had MDR strains to those who did not and derived regression models to identify predictors of MDR and hospital mortality. Results: Of 740 patients with Pa-NP, 226 patients (30.5%) were infected with MDR strains. In multivariable analyses, independent predictors of multidrug-resistance included decreasing age (adjusted odds ratio [AOR] 0.91, 95% confidence interval [CI] 0.96-0.98), diabetes mellitus (AOR 1.90, 95% CI 1.21-3.00) and ICU admission (AOR 1.73, 95% CI 1.06-2.81). Multidrug-resistance, heart failure, increasing age, mechanical ventilation, and bacteremia were independently associated with in-hospital mortality in the Cox Proportional Hazards Model analysis. Conclusions: Among patients with Pa-NP the presence of infection with a MDR strain is associated with increased in-hospital mortality. Identification of patients at risk of MDR Pa-NP could facilitate appropriate empiric antibiotic decisions that in turn could lead to improved hospital survival