Effective potential and stability of the rigid membrane

The calculation of the effective potential for fixed-end and toroidal rigid $p$-branes is performed in the one-loop as well as in the $1/d$ approximations. The analysis of the involved zeta-functions (of inhomogeneous Epstein type) which appear in the process of regularization is done in full detail. Assymptotic formulas (allowing only for exponentially decreasing errors of order $\leq 10^{-3}$) are found which carry all the dependences on the basic parameters of the theory explicitly. The behaviour of the effective potential (specified to the membrane case $p=2$) is investigated, and the extrema of this effective potential are obtained.Comment: 15 PAGE

Partition Functions for the Rigid String and Membrane at Any Temperature

Exact expressions for the partition functions of the rigid string and membrane at any temperature are obtained in terms of hypergeometric functions. By using zeta function regularization methods, the results are analytically continued and written as asymptotic sums of Riemann-Hurwitz zeta functions, which provide very good numerical approximations with just a few first terms. This allows to obtain systematic corrections to the results of Polchinski et al., corresponding to the limits $T\rightarrow 0$ and $T\rightarrow \infty$ of the rigid string, and to analyze the intermediate range of temperatures. In particular, a way to obtain the Hagedorn temperature for the rigid membrane is thus found.Comment: 20 pages, LaTeX file, UB-ECM-PF 93/

Renormalization group flows and continual Lie algebras

We study the renormalization group flows of two-dimensional metrics in sigma models and demonstrate that they provide a continual analogue of the Toda field equations based on the infinite dimensional algebra G(d/dt;1). The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time. We provide the general solution of the renormalization group flows in terms of free fields, via Backlund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches, which look like a cane in the infra-red region. Finally, we revisit the transition of a flat cone C/Z_n to the plane, as another special solution, and note that tachyon condensation in closed string theory exhibits a hidden relation to the infinite dimensional algebra G(d/dt;1) in the regime of gravity. Its exponential growth holds the key for the construction of conserved currents and their systematic interpretation in string theory, but they still remain unknown.Comment: latex, 73pp including 14 eps fig

Transverse momentum spectra of charged particles in proton-proton collisions at s=900\sqrt{s} = 900 GeV with ALICE at the LHC

The inclusive charged particle transverse momentum distribution is measured in proton-proton collisions at $\sqrt{s} = 900$ GeV at the LHC using the ALICE detector. The measurement is performed in the central pseudorapidity region $(|\eta|<0.8)$ over the transverse momentum range $0.15<p_{\rm T}<10$ GeV/$c$. The correlation between transverse momentum and particle multiplicity is also studied. Results are presented for inelastic (INEL) and non-single-diffractive (NSD) events. The average transverse momentum for $|\eta|<0.8$ is $\left<p_{\rm T}\right>_{\rm INEL}=0.483\pm0.001$ (stat.) $\pm0.007$ (syst.) GeV/$c$ and \left_{\rm NSD}=0.489\pm0.001 (stat.) $\pm0.007$ (syst.) GeV/$c$, respectively. The data exhibit a slightly larger $\left<p_{\rm T}\right>$ than measurements in wider pseudorapidity intervals. The results are compared to simulations with the Monte Carlo event generators PYTHIA and PHOJET.Comment: 20 pages, 8 figures, 2 tables, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/390

Global Retinoblastoma Presentation and Analysis by National Income Level

Importance: Early diagnosis of retinoblastoma, the most common intraocular cancer, can save both a child's life and vision. However, anecdotal evidence suggests that many children across the world are diagnosed late. To our knowledge, the clinical presentation of retinoblastoma has never been assessed on a global scale. Objectives: To report the retinoblastoma stage at diagnosis in patients across the world during a single year, to investigate associations between clinical variables and national income level, and to investigate risk factors for advanced disease at diagnosis. Design, Setting, and Participants: A total of 278 retinoblastoma treatment centers were recruited from June 2017 through December 2018 to participate in a cross-sectional analysis of treatment-naive patients with retinoblastoma who were diagnosed in 2017. Main Outcomes and Measures: Age at presentation, proportion of familial history of retinoblastoma, and tumor stage and metastasis. Results: The cohort included 4351 new patients from 153 countries; the median age at diagnosis was 30.5 (interquartile range, 18.3-45.9) months, and 1976 patients (45.4) were female. Most patients (n = 3685 84.7%) were from low-and middle-income countries (LMICs). Globally, the most common indication for referral was leukocoria (n = 2638 62.8%), followed by strabismus (n = 429 10.2%) and proptosis (n = 309 7.4%). Patients from high-income countries (HICs) were diagnosed at a median age of 14.1 months, with 656 of 666 (98.5%) patients having intraocular retinoblastoma and 2 (0.3%) having metastasis. Patients from low-income countries were diagnosed at a median age of 30.5 months, with 256 of 521 (49.1%) having extraocular retinoblastoma and 94 of 498 (18.9%) having metastasis. Lower national income level was associated with older presentation age, higher proportion of locally advanced disease and distant metastasis, and smaller proportion of familial history of retinoblastoma. Advanced disease at diagnosis was more common in LMICs even after adjusting for age (odds ratio for low-income countries vs upper-middle-income countries and HICs, 17.92 95% CI, 12.94-24.80, and for lower-middle-income countries vs upper-middle-income countries and HICs, 5.74 95% CI, 4.30-7.68). Conclusions and Relevance: This study is estimated to have included more than half of all new retinoblastoma cases worldwide in 2017. Children from LMICs, where the main global retinoblastoma burden lies, presented at an older age with more advanced disease and demonstrated a smaller proportion of familial history of retinoblastoma, likely because many do not reach a childbearing age. Given that retinoblastoma is curable, these data are concerning and mandate intervention at national and international levels. Further studies are needed to investigate factors, other than age at presentation, that may be associated with advanced disease in LMICs. © 2020 American Medical Association. All rights reserved