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

Carnot-Caratheodory metric and gauge fluctuation in Noncommutative Geometry

Gauge fields have a natural metric interpretation in terms of horizontal distance. The latest, also called Carnot-Caratheodory or subriemannian distance, is by definition the length of the shortest horizontal path between points, that is to say the shortest path whose tangent vector is everywhere horizontal with respect to the gauge connection. In noncommutative geometry all the metric information is encoded within the Dirac operator D. In the classical case, i.e. commutative, Connes's distance formula allows to extract from D the geodesic distance on a riemannian spin manifold. In the case of a gauge theory with a gauge field A, the geometry of the associated U(n)-vector bundle is described by the covariant Dirac operator D+A. What is the distance encoded within this operator ? It was expected that the noncommutative geometry distance d defined by a covariant Dirac operator was intimately linked to the Carnot-Caratheodory distance dh defined by A. In this paper we precise this link, showing that the equality of d and dh strongly depends on the holonomy of the connection. Quite interestingly we exhibit an elementary example, based on a 2 torus, in which the noncommutative distance has a very simple expression and simultaneously avoids the main drawbacks of the riemannian metric (no discontinuity of the derivative of the distance function at the cut-locus) and of the subriemannian one (memory of the structure of the fiber).Comment: published version with additional figures to make the proof more readable. Typos corrected in this ultimate versio

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

Twisted Hopf symmetries of canonical noncommutative spacetimes and the no-pure-boost principle

We study the twisted-Hopf-algebra symmetries of observer-independent canonical spacetime noncommutativity, for which the commutators of the spacetime coordinates take the form [x^{mu},x^{nu}]=i theta^{mu nu} with observer-independent (and coordinate-independent) theta^{mu nu}. We find that it is necessary to introduce nontrivial commutators between transformation parameters and spacetime coordinates, and that the form of these commutators implies that all symmetry transformations must include a translation component. We show that with our noncommutative transformation parameters the Noether analysis of the symmetries is straightforward, and we compare our canonical-noncommutativity results with the structure of the conserved charges and the "no-pure-boost" requirement derived in a previous study of kappa-Minkowski noncommutativity. We also verify that, while at intermediate stages of the analysis we do find terms that depend on the ordering convention adopted in setting up the Weyl map, the final result for the conserved charges is reassuringly independent of the choice of Weyl map and (the corresponding choice of) star product.Comment: 12 page

Line element in quantum gravity: the examples of DSR and noncommutative geometry

We question the notion of line element in some quantum spaces that are expected to play a role in quantum gravity, namely non-commutative deformations of Minkowski spaces. We recall how the implementation of the Leibniz rule forbids to see some of the infinitesimal deformed Poincare transformations as good candidates for Noether symmetries. Then we recall the more fundamental view on the line element proposed in noncommutative geometry, and re-interprete at this light some previous results on Connes' distance formula.Comment: some references added. Proceedings of the Second Workshop on Quantum Gravity and Noncommutative Geometry, Universidade Lusofona, Lisbon 22-24 September 200

Conformal mapping of Unruh temperature

Thanks to a local interpetation of the KMS condition, the mapping from (unbounded) wedge regions of Minkowski space-time to (bounded) double-cone regions is extended to the Unruh temperature associated to relevant observers in both regions. A previous result, the diamond's temperature, is shown to be proportional to the inverse of the conformal factor (Weyl rescaling of the metric) of this map. One thus explains from a mathematical point of view why an observer with finite lifetime experiences the vacuum as a thermal state whatever his acceleration, even vanishing.Comment: Paper shortened and reorganized. To be published in Modern Physics Letters

Aspirin and the risk of colorectal and other digestive tract cancers: an updated meta-analysis through 2019

Aspirin has been associated with a reduced risk of colorectal cancer, and possibly of a few other digestive tract cancers. The quantification of risk reduction and the optimal dose and duration of aspirin use for the prevention of colorectal and other digestive tract cancers remains unclear

Museums and the making of textile histories: Past, present, and future

Many different types of museums collect, document, and preserve textiles, interpreting them through temporary and semi-permanent exhibitions, publications, and web- site interventions – sometimes independently, sometimes as part of a broader histo- ry of art and design, science and technology, social history and anthropology, local history or world cultures (for example, see the range and approaches in major fash- ion capitals such as London, Paris, Milan, New York with a long tradition of textile production as well as consumption, and in manufacturing cities such as Krefeld, Lyon, Manchester). Nonetheless, textile-focused events seldom receive great public attention or crit- ical acclaim, with the possible exceptions of innovative temporary exhibitions such as Jean-Paul Leclercq, “Jouer la Lumière” (Paris, Les Arts Décoratifs, 2001); Thomas P. Campbell, “Tapestry in the Renaissance: Art and Magnificence” (New York, The Metropolitan Museum of Art, 2002); Amelia Peck et al., “Interwoven Globe. The Worldwide Textile Trade, 1500-1800” (New York, The Metropolitan Museum of Art, 2013-2014); John Styles, “Threads of Feeling” (London, The Foundling Hospital, 2010-2011; Colonial Williamsburg, 2014).1 The aims of this debate are to draw on the different cultural experiences and disciplinary backgrounds of participants: – To generate discussion over the role of museums in making and representing tex- tile histories. Museums are not only depositories of textile objects, but also write or make both public and academic history through displays and publications. But how does their work relate to university research and dissemination, feed such research, or react to it? How might interactions between museums and universities in different regions and cultures be developed in the future? – To consider where innovative museum work is being undertaken (locally, region- ally, nationally, internationally), wherein lies its innovation, and how it might suggest directions for the future (in collecting, interpretation, etc.). By interpreta- tion, I mean any analogue or digital explanation that contextualizes the objects on display. – To suggest that the most dynamic study of objects from 1500 to the present is no longer limited to art historians – indeed, that the focus in art history on textiles that belong within a well-established tradition of connoisseurship (in which tap- estries and high-end commissions for wall-hangings dominate) is being challenged by the adoption of a more inclusive approach among historians, design historians, and historians of material culture. [Lesley Miller] EAN: 978-2-917902-31-

Gone in 2s:a deep dive intoperfection analysing thecollaborative maintenance pitstopof Formula 1

Purpose–The paper aims to convert into useable guidelines, the knowledge related to human factors andtasks’organisation, which are embedded in one of the most exciting maintenance actions that are carried out,the pitstop in Formula 1 races.Design/methodology/approach–The paper opted for a fault tree analysis (FTA) to de-construct all the sub-tasks and their possible deviations from desirable situations and to evaluate the most relevant informationneeded for carrying out the pitstop operation. Besides, the SHELL model was applied in a second stage toevaluate the interaction between human being and human interfaces with other components of the system.Once this set of information was crystallised, the research translated it into useable guidelines for organisingindustrial maintenance actions using the same approach and possible reaching the same results.Findings–The results of this study is a structured set of guidelines that encompasses the most paramountaspects that should be considered for setting correct maintenance actions. They represent a“guide”forincluding the different angles that are included during these operations.Research limitations/implications–The guidelines are potentially applicable to every maintenance operation.The guidelines should be tested on different working domains to check their applicability besides the racing world.Practical implications–This study is a reverse engineering work for creating a scheme to include intomaintenance operations aspects such as crew athlete-like fitness, training, technology, organisational issues,safety, ergonomics and psychology.Originality/value–The value of the paper is deconstructing the results of one of the most successful andprepared maintenance action. The paper takes a different approach in proposing how to structure and createmaintenance solutions. The difference in approaches between the maintenance during the pitstop of Formula 1car and industrial applications enhances the gap that needs still to be filled for further improving maintenanceactions out of the racing world

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