On Pythagoras' theorem for products of spectral triples

We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some unitality condition. We show that these inequalities are optimal, and provide non-unital counter-examples inspired by K-homology.Comment: Paper slightly shortened to match the published version; Lett. Math. Phys. 201

Is life a thermal horizon ?

This talk aims at questioning the vanishing of Unruh temperature for an inertial observer in Minkovski spacetime with finite lifetime, arguing that in the non eternal case the existence of a causal horizon is not linked to the non-vanishing of the acceleration. This is illustrated by a previous result, the diamonds temperature, that adapts the algebraic approach of Unruh effect to the finite case.Comment: Proceedings of the conference DICE 2006, Piombino september 200

De Sitter Thermodynamics from Diamonds's Temperature

The thermal time hypothesis proposed by Rovelli [1] regards the physical basis for the flow of time as thermodynamical and provides a definition of the temperature for some special cases. We verify this hypothesis in the case of de Sitter spacetime by relating the uniformly accelerated observer in de Sitter spacetime to the diamond in Minkowski spacetime. Then, as an application of it, we investigate the thermal effect for the uniformly accelerated observer with a finite lifetime in dS spacetime, which generalizes the corresponding result for the case of Minkowski spacetime [2]. Furthermore, noticing that a uniformly accelerated dS observer with a finite lifetime corresponds to a Rindler observer with a finite lifetime in the embedding Minkowski spacetime, we show that the global-embedding-Minkowski-spacetime (GEMS) picture of spacetime thermodynamics is valid in this case. This is a rather nontrivial and unexpected generalization of the GEMS picture, as well as a further verification of both the thermal time hypothesis and the GEMS picture.Comment: 10 pages, 3 figures, LaTeX; v2: reorganized with a new section added concerning a generalization of the GEMS picture from our result; v3: version with minor corrections, to appear in JHE

Minimal length in quantum space and integrations of the line element in Noncommutative Geometry

We question the emergence of a minimal length in quantum spacetime, comparing two notions that appeared at various points in the literature: on the one side, the quantum length as the spectrum of an operator L in the Doplicher Fredenhagen Roberts (DFR) quantum spacetime, as well as in the canonical noncommutative spacetime; on the other side, Connes' spectral distance in noncommutative geometry. Although on the Euclidean space the two notions merge into the one of geodesic distance, they yield distinct results in the noncommutative framework. In particular on the Moyal plane, the quantum length is bounded above from zero while the spectral distance can take any real positive value, including infinity. We show how to solve this discrepancy by doubling the spectral triple. This leads us to introduce a modified quantum length d'_L, which coincides exactly with the spectral distance d_D on the set of states of optimal localization. On the set of eigenstates of the quantum harmonic oscillator - together with their translations - d'_L and d_D coincide asymptotically, both in the high energy and large translation limits. At small energy, we interpret the discrepancy between d'_L and d_D as two distinct ways of integrating the line element on a quantum space. This leads us to propose an equation for a geodesic on the Moyal plane.Comment: 29 pages, 2 figures. Minor corrections to match the published versio

Case mix at the European Institute of Oncology: first report of the Tumour Registry, 2000–2002

Introduction: An institutional and centralized hospital-based tumour registry (TR) is the ideal supporting tool for the organization and management of clinical data in a comprehensive cancer centre. The purpose of this paper is to describe the development of the TR at the European Institute of Oncology (IEO) in Milan, Italy, from its origin to its current applications. Material and methods: After a series of meetings with members of administrative, clinical, research and informatics departments, the TR was activated in March 2006 with the aim to collect data on all the individuals referring to the Institute, with or at risk of developing a tumour. It was implemented on an Oracle\u2122-based interface. A minimum data set of variables was defined and data collection was divided into four forms, which together gather all the relevant data on patients, tumours, treatments and subsequent events. Results: After a 6-month pilot period, which involved the training of the tumour registrars, adjustments to the structure of the registry, development of data quality control procedure and finalization of the operative protocol, from September 2006 the data collection has been fully operative. Five registrars have been chronologically entering data of all individuals who visited the IEO for the first time since 1st January 2000. As of March 2009, data on 69,637 individuals and 43,567 tumours has been reviewed, recoded and registered in the TR. Twenty-two percent of the tumours (n=9,578) were first invasive primaries, diagnosed and treated in IEO; the most common sites were breast (n=4,972), lung (n=627), intestines (n=479) and prostate (n=376). Conclusion: The IEO TR has been proven functional and reliable in monitoring the activity of the Hospital, allowing extraction of data from any subpopulation with characteristics of interest. The structured and centralized TR represents an important tool for our research-oriented Institution

Lung response to prone positioning in mechanically-ventilated patients with COVID-19

Background: Prone positioning improves survival in moderate-to-severe acute respiratory distress syndrome (ARDS) unrelated to the novel coronavirus disease (COVID-19). This benefit is probably mediated by a decrease in alveolar collapse and hyperinflation and a more homogeneous distribution of lung aeration, with fewer harms from mechanical ventilation. In this preliminary physiological study we aimed to verify whether prone positioning causes analogue changes in lung aeration in COVID-19. A positive result would support prone positioning even in this other population. Methods: Fifteen mechanically-ventilated patients with COVID-19 underwent a lung computed tomography in the supine and prone position with a constant positive end-expiratory pressure (PEEP) within three days of endotracheal intubation. Using quantitative analysis, we measured the volume of the non-aerated, poorly-aerated, well-aerated, and over-aerated compartments and the gas-to-tissue ratio of the ten vertical levels of the lung. In addition, we expressed the heterogeneity of lung aeration with the standardized median absolute deviation of the ten vertical gas-to-tissue ratios, with lower values indicating less heterogeneity. Results: By the time of the study, PEEP was 12 (10–14) cmH2O and the PaO2:FiO2 107 (84–173) mmHg in the supine position. With prone positioning, the volume of the non-aerated compartment decreased by 82 (26–147) ml, of the poorly-aerated compartment increased by 82 (53–174) ml, of the normally-aerated compartment did not significantly change, and of the over-aerated compartment decreased by 28 (11–186) ml. In eight (53%) patients, the volume of the over-aerated compartment decreased more than the volume of the non-aerated compartment. The gas-to-tissue ratio of the ten vertical levels of the lung decreased by 0.34 (0.25–0.49) ml/g per level in the supine position and by 0.03 (− 0.11 to 0.14) ml/g in the prone position (p < 0.001). The standardized median absolute deviation of the gas-to-tissue ratios of those ten levels decreased in all patients, from 0.55 (0.50–0.71) to 0.20 (0.14–0.27) (p < 0.001). Conclusions: In fifteen patients with COVID-19, prone positioning decreased alveolar collapse, hyperinflation, and homogenized lung aeration. A similar response has been observed in other ARDS, where prone positioning improves outcome. Therefore, our data provide a pathophysiological rationale to support prone positioning even in COVID-19

Relative entropy and the Bekenstein bound

Elaborating on a previous work by Marolf et al, we relate some exact results in quantum field theory and statistical mechanics to the Bekenstein universal bound on entropy. Specifically, we consider the relative entropy between the vacuum and another state, both reduced to a local region. We propose that, with the adequate interpretation, the positivity of the relative entropy in this case constitutes a well defined statement of the bound in flat space. We show that this version arises naturally from the original derivation of the bound from the generalized second law when quantum effects are taken into account. In this formulation the bound holds automatically, and in particular it does not suffer from the proliferation of the species problem. The results suggest that while the bound is relevant at the classical level, it does not introduce new physical constraints semiclassically.Comment: 12 pages, 1 figure, minor changes and references adde

Diamonds's Temperature: Unruh effect for bounded trajectories and thermal time hypothesis

We study the Unruh effect for an observer with a finite lifetime, using the thermal time hypothesis. The thermal time hypothesis maintains that: (i) time is the physical quantity determined by the flow defined by a state over an observable algebra, and (ii) when this flow is proportional to a geometric flow in spacetime, temperature is the ratio between flow parameter and proper time. An eternal accelerated Unruh observer has access to the local algebra associated to a Rindler wedge. The flow defined by the Minkowski vacuum of a field theory over this algebra is proportional to a flow in spacetime and the associated temperature is the Unruh temperature. An observer with a finite lifetime has access to the local observable algebra associated to a finite spacetime region called a "diamond". The flow defined by the Minkowski vacuum of a (four dimensional, conformally invariant) quantum field theory over this algebra is also proportional to a flow in spacetime. The associated temperature generalizes the Unruh temperature to finite lifetime observers. Furthermore, this temperature does not vanish even in the limit in which the acceleration is zero. The temperature associated to an inertial observer with lifetime T, which we denote as "diamond's temperature", is 2hbar/(pi k_b T).This temperature is related to the fact that a finite lifetime observer does not have access to all the degrees of freedom of the quantum field theory.Comment: One reference correcte

Expected performance of the ASTRI-SST-2M telescope prototype

ASTRI (Astrofisica con Specchi a Tecnologia Replicante Italiana) is an Italian flagship project pursued by INAF (Istituto Nazionale di Astrofisica) strictly linked to the development of the Cherenkov Telescope Array, CTA. Primary goal of the ASTRI program is the design and production of an end-to-end prototype of a Small Size Telescope for the CTA sub-array devoted to the highest gamma-ray energy region. The prototype, named ASTRI SST-2M, will be tested on field in Italy during 2014. This telescope will be the first Cherenkov telescope adopting the double reflection layout in a Schwarzschild-Couder configuration with a tessellated primary mirror and a monolithic secondary mirror. The collected light will be focused on a compact and light-weight camera based on silicon photo-multipliers covering a 9.6 deg full field of view. Detailed Monte Carlo simulations have been performed to estimate the performance of the planned telescope. The results regarding its energy threshold, sensitivity and angular resolution are shown and discussed.Comment: In Proceedings of the 33rd International Cosmic Ray Conference (ICRC2013), Rio de Janeiro (Brazil). All CTA contributions at arXiv:1307.223