A geometric technique to generate lower estimates for the constants in the Bohnenblust--Hille inequalities

The Bohnenblust--Hille (polynomial and multilinear) inequalities were proved in 1931 in order to solve Bohr's absolute convergence problem on Dirichlet series. Since then these inequalities have found applications in various fields of analysis and analytic number theory. The control of the constants involved is crucial for applications, as it became evident in a recent outstanding paper of Defant, Frerick, Ortega-Cerd\'{a}, Ouna\"{\i}es and Seip published in 2011. The present work is devoted to obtain lower estimates for the constants appearing in the Bohnenblust--Hille polynomial inequality and some of its variants. The technique that we introduce for this task is a combination of the Krein--Milman Theorem with a description of the geometry of the unit ball of polynomial spaces on $\ell^2_\infty$.Comment: This preprint does no longer exist as a single manuscript. It is now part of the preprint entitled "The optimal asymptotic hypercontractivity constant of the real polynomial Bohnenblust-Hille inequality is 2" (arXiv reference 1209.4632

Energy dependence of ϕ meson production at forward rapidity in pp collisions at the LHC

The production of $\phi$ mesons has been studied in pp collisions at LHC energies with the ALICE detector via the dimuon decay channel in the rapidity region $2.5< y < 4$. Measurements of the differential cross section $\mathrm{d}^2\sigma /\mathrm{d}y \mathrm{d}p_{\mathrm {T}}$ are presented as a function of the transverse momentum ($p_{\mathrm {T}}$) at the center-of-mass energies $\sqrt{s}=5.02$, 8 and 13 TeV and compared with the ALICE results at midrapidity. The differential cross sections at $\sqrt{s}=5.02$ and 13 TeV are also studied in several rapidity intervals as a function of $p_{\mathrm {T}}$, and as a function of rapidity in three $p_{\mathrm {T}}$ intervals. A hardening of the $p_{\mathrm {T}}$-differential cross section with the collision energy is observed, while, for a given energy, $p_{\mathrm {T}}$ spectra soften with increasing rapidity and, conversely, rapidity distributions get slightly narrower at increasing $p_{\mathrm {T}}$. The new results, complementing the published measurements at $\sqrt{s}=2.76$ and 7 TeV, allow one to establish the energy dependence of $\phi$ meson production and to compare the measured cross sections with phenomenological models. None of the considered models manages to describe the evolution of the cross section with $p_{\mathrm {T}}$ and rapidity at all the energies.publishedVersio

ϒ production in p–Pb collisions at sNN=8.16 TeV

ϒproduction in p–Pbinteractions is studied at the centre-of-mass energy per nucleon–nucleon collision √sNN=8.16TeV with the ALICE detector at the CERN LHC. The measurement is performed reconstructing bottomonium resonances via their dimuon decay channel, in the centre-of-mass rapidity intervals 2.03 &lt;3.53and −4.46 &lt;−2.96, down to zero transverse momentum. In this work, results on the ϒ(1S) production cross section as a function of rapidity and transverse momentum are presented. The corresponding nuclear modification factor shows a suppression of the ϒ(1S) yields with respect to ppcollisions, both at forward and backward rapidity. This suppression is stronger in the low transverse momentum region and shows no significant dependence on the centrality of the interactions. Furthermore, the ϒ(2S) nuclear modification factor is evaluated, suggesting a suppression similar to that of the ϒ(1S). A first measurement of the ϒ(3S) has also been performed. Finally, results are compared with previous ALICE measurements in p–Pbcollisions at √sNN=5.02TeV and with theoretical calculations

Coherent psi (2S) photo-production in ultra-peripheral Pb-Pb collisions at root s(NN)=2.76TeV

We have performed the first measurement of the coherent psi(2S) photo-production cross section in ultraperipheral Pb-Pb collisions at the LHC. This charmonium excited state is reconstructed via the psi(2S) -> l(+)l(-) and ->(2S) -> J/psi pi(+)pi(-) decays, where the J/psi decays into two leptons. The analysis is based on an event sample corresponding to an integrated luminosity of about 22 mu b(-1). The cross section for coherent psi(2S) production in the rapidity interval -0.9 <y <0.9is d sigma(coh)(psi(2S))/dy = 0.83 +/- 0.19 (stat+syst) mb. The psi(2S) to J/psi coherent cross section ratio is 0.34(-0.07)(+0.08)(stat+syst). The obtained results are compared to predictions from theoretical models. (C) 2015 CERN for the benefit of the ALICE Collaboration. Published by Elsevier B.V.Peer reviewe

Guidelines for the use and interpretation of assays for monitoring autophagy (3rd edition)

In 2008 we published the first set of guidelines for standardizing research in autophagy. Since then, research on this topic has continued to accelerate, and many new scientists have entered the field. Our knowledge base and relevant new technologies have also been expanding. Accordingly, it is important to update these guidelines for monitoring autophagy in different organisms. Various reviews have described the range of assays that have been used for this purpose. Nevertheless, there continues to be confusion regarding acceptable methods to measure autophagy, especially in multicellular eukaryotes. For example, a key point that needs to be emphasized is that there is a difference between measurements that monitor the numbers or volume of autophagic elements (e.g., autophagosomes or autolysosomes) at any stage of the autophagic process versus those that measure fl ux through the autophagy pathway (i.e., the complete process including the amount and rate of cargo sequestered and degraded). In particular, a block in macroautophagy that results in autophagosome accumulation must be differentiated from stimuli that increase autophagic activity, defi ned as increased autophagy induction coupled with increased delivery to, and degradation within, lysosomes (inmost higher eukaryotes and some protists such as Dictyostelium ) or the vacuole (in plants and fungi). In other words, it is especially important that investigators new to the fi eld understand that the appearance of more autophagosomes does not necessarily equate with more autophagy. In fact, in many cases, autophagosomes accumulate because of a block in trafficking to lysosomes without a concomitant change in autophagosome biogenesis, whereas an increase in autolysosomes may reflect a reduction in degradative activity. It is worth emphasizing here that lysosomal digestion is a stage of autophagy and evaluating its competence is a crucial part of the evaluation of autophagic flux, or complete autophagy. Here, we present a set of guidelines for the selection and interpretation of methods for use by investigators who aim to examine macroautophagy and related processes, as well as for reviewers who need to provide realistic and reasonable critiques of papers that are focused on these processes. These guidelines are not meant to be a formulaic set of rules, because the appropriate assays depend in part on the question being asked and the system being used. In addition, we emphasize that no individual assay is guaranteed to be the most appropriate one in every situation, and we strongly recommend the use of multiple assays to monitor autophagy. Along these lines, because of the potential for pleiotropic effects due to blocking autophagy through genetic manipulation it is imperative to delete or knock down more than one autophagy-related gene. In addition, some individual Atg proteins, or groups of proteins, are involved in other cellular pathways so not all Atg proteins can be used as a specific marker for an autophagic process. In these guidelines, we consider these various methods of assessing autophagy and what information can, or cannot, be obtained from them. Finally, by discussing the merits and limits of particular autophagy assays, we hope to encourage technical innovation in the field

Measurement of charged jet production cross sections and nuclear modification in p-Pb collisions at root s(NN)=5.02 TeV

Charged jet production cross sections in p-Pb collisions at root s(NN) = 5.02 TeV measured with the ALICE detector at the LHC are presented. Using the anti-k(T) algorithm, jets have been reconstructed in the central rapidity region from charged particles with resolution parameters R = 0.2 and R = 0.4. The reconstructed jets have been corrected for detector effects and the underlying event background. To calculate the nuclear modification factor, R-pPb, of charged jets in p-Pb collisions, a pp reference was constructed by scaling previously measured charged jet spectra at root s = 7 TeV. In the transverse momentum range 20Peer reviewe

Systematic studies of correlations between different order flow harmonics in Pb-Pb collisions at root s(NN)=2.76 TeV

The correlations between event-by-event fluctuations of anisotropic flow harmonic amplitudes have been measured in Pb-Pb collisions at root s(NN) = 2.76 TeV with the ALICE detector at the Large Hadron Collider. The results are reported in terms of multiparticle correlation observables dubbed symmetric cumulants. These observables are robust against biases originating from nonflow effects. The centrality dependence of correlations between the higher order harmonics (the quadrangular v(4) and pentagonal v(5) flow) and the lower order harmonics (the elliptic v(2) and triangular v(3) flow) is presented. The transverse momentum dependences of correlations between v(3) and v(2) and between v(4) and v(2) are also reported. The results are compared to calculations from viscous hydrodynamics and a multiphase transport (AMPT) model calculations. The comparisons to viscous hydrodynamic models demonstrate that the different order harmonic correlations respond differently to the initial conditions and the temperature dependence of the ratio of shear viscosity to entropy density (eta/s). Asmall average value of eta/s is favored independent of the specific choice of initial conditions in the models. The calculations with the AMPT initial conditions yield results closest to the measurements. Correlations among the magnitudes of v(2), v(3), and v(4) show moderate p(T) dependence in midcentral collisions. This might be an indication of possible viscous corrections to the equilibrium distribution at hadronic freeze-out, which might help to understand the possible contribution of bulk viscosity in the hadronic phase of the system. Together with existing measurements of individual flow harmonics, the presented results provide further constraints on the initial conditions and the transport properties of the system produced in heavy-ion collisions

Two-particle differential transverse momentum and number density correlations in p-Pb collisions at 5.02 TeV and Pb-Pb collisions at 2.76 TeV at the CERN Large Hadron Collider

We present measurements of two-particle differential number correlation functions R2 and transverse momentum correlation functions P2, obtained from p-Pb collisions at 5.02 TeV and Pb-Pb collisions at 2.76 TeV. The results are obtained by using charged particles in the pseudorapidity range |\u3b7|<1.0 and transverse momentum range 0.2<2.0 GeV/c as a function of pair separation in pseudorapidity, |\u394\u3b7|, azimuthal angle \u394\u3c6, and for several charged-particle multiplicity classes. Measurements are carried out for like-sign and unlike-sign charged-particle pairs separately and combined to obtain charge-independent and charge-dependent correlation functions. We study the evolution of the width of the near-side peak of these correlation functions with collision centrality. Additionally, we study Fourier decompositions of the correlators in \u394\u3c6 as a function of pair separation |\u394\u3b7|. Significant differences in the dependence of their harmonic coefficients on multiplicity classes are found. These differences can be exploited, in theoretical models, to obtain further insight into charged-particle production and transport in heavy-ion collisions. Moreover, an upper limit of nonflow contributions to flow coefficients vn measured in Pb-Pb collisions based on the relative strength of Fourier coefficients measured in p-Pb interactions is estimated