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A Zoo of Continuity Properties in Constructive Type Theory
No full textInternational audienceContinuity principles stating that all functions are continuous play a central role in some schools of constructive mathematics. However, there are different ways to formalise the property of being continuous in constructive foundations. We analyse these continuity properties from the perspective of constructive reverse mathematics. We work in constructive type theory, which can be seen as a minimal foundation for constructive reverse mathematics. We treat continuity of functions F : (Q → A) → R, i.e. with question type Q, answer type A, and result type R. Concretely, we discuss continuity defined via moduli, making the relevant list L : LQ of questions explicit, dialogue trees, making the question answer process explicit as inductive tree, and tree functions, making the question answer process explicit as function. We prove equivalences where possible and isolate necessary and sufficient axioms for equivalence proofs. Many of the results we discuss are already present in the works of Hancock, Pattinson, Ghani, Kawai, Fujiwara, Brede, Herbelin, Escardó, and others. Our main contribution is their formulation over a uniform foundation, the observation that no choice axioms are necessary, the generalisation to arbitrary types from natural numbers where possible, and a mechanisation in the Coq proof assistant.</div
Biographical Feature: In memoriam Pierre Tiollais (1934–2024)
No full textInternational audiencePierre Tiollais, a French physician-biologist who cloned and sequenced the genome of hepatitis B virus (HBV) and developed a recombinant hepatitis B vaccine, died on 5 August 2024, at the age of 89. Pierre had his wife Irène and his son Romain close by his side through the difficult times since he had been ill. Born on 8 December 1934 in Rennes, Brittany, to pharmacist parents, Pierre remained attached to his native province, which in France is characterized by a strong anthropological particularism, throughout his life and always proudly defined himself as a Breton
Visual mental imagery in typical imagers and in aphantasia: A millimeter-scale 7-T fMRI study
No full textInternational audienceMost of us effortlessly describe visual objects, whether seen or remembered. Yet, around 4% of people report congenital aphantasia: they struggle to visualize objects despite being able to describe their visual appearance. What neural mechanisms create this disparity between subjective experience and objective performance? Aphantasia can provide novel insights into conscious processing and awareness. We used ultra-high field 7T fMRI to establish the neural circuits involved in visual mental imagery and perception, and to elucidate the neural mechanisms associated with the processing of internally generated visual information in the absence of imagery experience in congenital aphantasia. Ten typical imagers and 10 aphantasic individuals performed imagery and perceptual tasks in five domains: object shape, object color, written words, faces, and spatial relationships. In typical imagers, imagery tasks activated left-hemisphere frontoparietal areas, the relevant domain-preferring areas in the ventral temporal cortex partly overlapping with the perceptual domain-preferring areas, and a domain-general area in the left fusiform gyrus (the Fusiform Imagery Node). The results were valid for each individual participant. In aphantasic individuals, imagery activated similar visual areas, but there was reduced functional connectivity between the Fusiform Imagery Node and frontoparietal areas. Our results unveil the domain-general and domain-specific circuits of visual mental imagery, their functional disorganization in aphantasia, and support the general hypothesis that conscious visual experience- whether perceived or imagined- depends on the integrated activity of high-level visual cortex and frontoparietal networks
The refractory-to-ice ratio in comet 67P: implications on the composition of the comet-forming region of the protoplanetary disk
No full textComets, asteroids, and other small bodies are thought to be remnants of the original planetesimal population of the Solar System. As such, their physical, chemical, and isotopic properties hold crucial details on how and where they formed and how they evolved. Yet, placing precise constraints on the formation region of these bodies has been challenging. Data from spacecraft missions have a particularly high potential of addressing the question of the origin of the visited bodies. ESA's Rosetta mission to comet 67P/Churyumov-Gerasimenko returned data from the comet for two years on its journey around the Sun. This extensive data set has revolutionised our view on comets and still holds unsolved problems. We use the Rosetta/ROSINA (Rosetta Orbiter Spectrometer for Ion and Neutral Analysis) measurement of the volatile/ice composition and the Rosetta/COSIMA (COmetary Secondary Ion Mass Analyzer) measurements of the refractory composition of comet 67P. These measurements are combined using a Monte Carlo method. The refractory-to-ice ratio is a free parameter that is constrained a posteriori. Using only the composition, we constrain the refractory-to-ice ratio to 0.5<χ<1.7, and derive the bulk elemental abundances for 67P of H, C, N, O, Na, Mg, Al, S, K, Ar, Ca, Cr, Mn, Fe, Kr, and Xe. We find the noble gas xenon in near solar elemental abundance in comet 67P. Krypton is slightly depleted, while argon is heavily depleted. Comet 67P is enriched in all three noble gases by up to 2.5 orders of magnitude compared to CI chondrites. We show this is consistent with a formation region between 25 and 35 au in a protoplanetary disk region with temperatures between 30 and 40 K and with the trapping of dust for a long time in rings of the protoplanetary disk
Migrations humaines et évolution linguistique. Les parcours des créoles et du français: Leçon inaugurale prononcée au Collège de France le jeudi 28 mars 2024
No full textInternational audienceLoin d’être immuables, les langues ne cessent de se transformer au gré des contacts entre les peuples. Les migrations humaines sont à ce titre un facteur important d’évolution linguistique. Celles des Européens vers les colonies, à partir du XVe siècle, ont donné naissance à de nouvelles variétés et, en particulier, à des créoles. L’histoire de ces parlers apparus au cours de l’époque moderne mérite que l’on s’y attarde, tant leurs processus d’émergence et de différenciation font écho à ceux des langues romanes.Cette leçon inaugurale entreprend d’analyser les dynamiques évolutives des créoles et du français, mettant en évidence les enjeux sociaux, politiques et économiques qui les traversent. Questionnant les préjugés des philologues du XIXe siècle et jusqu’aux idées reçues qui persistent de nos jours, elle montre que la déconstruction des représentations coloniales de la formation des créoles est indispensable pour faire avancer la compréhension du développement des langues romanes
Objects of Desire, Desire for Objects: Inaugural lecture delivered at the Collège de France on Thursday 30 March 2017
No full textInternational audienceAt the museum, this means seeing the objects where they are, and simultaneously seeing them where they no longer are, that is to say, in the regions from which they were taken. It means enjoying the beauty and the knowledge that have been accumulated in our cities over centuries, but enjoying them with full awareness of the conditions in which these objects were collected, in asymmetrical economic, military and epistemological contexts. It means rendering visible, in order to master them better, the internal contradictions and the glaring tensions that have been at work in the very idea of museums since its origin. It means paying close attention, in this context, to the gazes and voices of the dispossessed
Laser, Offspring and Powerful Enabler of Quantum Science
No full textInternational audienceAmong all the inventions that quantum physics has produced, the laser holds a particularly important place, both for the rich story of successive discoveries that led to its birth, and for the role it has played in fundamental and applied research. I recall here the lineage of theoretical discoveries and experiments that have marked this history, restricting myself to the contribution of lasers to blue sky science and leaving apart its well-known role in various domains of technology. This story started from advances in the old quantum theory, from Einstein’s theoretical description of stimulated emission to O. Stern’s experimental discovery of the spatial quantization of the electron spin. Nuclear magnetic resonance, atomic clocks, optical pumping, and masers followed and the pace of discoveries accelerated with the appearance of the laser in 1960. This extraordinary light source has since enabled breakthroughs in fundamental physics and opened up fields of research that could not even have been imagined at the time of its birth. I was fortunate to begin my career in physics at this crossroad of atomic physics and optics. I give in this article my personal view of the great adventures in fundamental research in which I participated as an actor or spectator, from the cooling and trapping of atoms by light, to the physics of quantum gases of bosons and fermions, the manipulation of individual quantum particles and quantum simulations. Many other areas of fundamental physics, which I will only mention briefly, owe their development to lasers and further advances are still to be expected in the years to come
