Monogamy of entanglement between cones

International audienceA separable quantum state shared between parties $A$ and $B$ can be symmetrically extended to a quantum state shared between party $A$ and parties $B_1,\ldots ,B_k$ for every $k\in\mathbf{N}$. Quantum states that are not separable, i.e., entangled, do not have this property. This phenomenon is known as "monogamy of entanglement". We show that monogamy is not only a feature of quantum theory, but that it characterizes the minimal tensor product of general pairs of convex cones $\mathsf{C}_A$ and $\mathsf{C}_B$: The elements of the minimal tensor product $\mathsf{C}_A\otimes_{\min} \mathsf{C}_B$ are precisely the tensors that can be symmetrically extended to elements in the maximal tensor product $\mathsf{C}_A\otimes_{\max} \mathsf{C}^{\otimes_{\max} k}_B$ for every $k\in\mathbf{N}$. Equivalently, the minimal tensor product of two cones is the intersection of the nested sets of $k$-extendible tensors. It is a natural question when the minimal tensor product $\mathsf{C}_A\otimes_{\min} \mathsf{C}_B$ coincides with the set of $k$-extendible tensors for some finite $k$. We show that this is universally the case for every cone $\mathsf{C}_A$ if and only if $\mathsf{C}_B$ is a polyhedral cone with a base given by a product of simplices. Our proof makes use of a new characterization of products of simplices up to affine equivalence that we believe is of independent interest

What about thematic information? An analysis of the multidimensional visualization of individual mobility

International audienceThis paper reviews the literature on the visualization of individual mobility data, with a focus on thematic integration. It emphasizes the importance of visualization in understanding mobility patterns within a population and how it helps mobility experts to address domain-specific questions. We analyze 38 papers published between 2010 and 2024 in GIS and VIS venues that describe visualizations of multidimensional data related to individual movements in urban environments, concentrating on individual mobility rather than traffic data. Our primary aim is to report advances in interactive visualization for individual mobility analysis, particularly regarding the representation of thematic information about people's motivations for mobility. Our findings indicate that the thematic dimension is only partially represented in the literature, despite its critical significance in transportation. This gap often stems from the challenge of identifying data sources that inherently provide this information, necessitating visualization designers and developers to navigate multiple, heterogeneous data sources. We identify the strengths and limitations of existing visualizations and suggest potential research directions for the field

„Was dabey überhaupt zu beobachten ist, das kann man mit wenig Worten sagen.“ Überlegungen zur semantischen und pragmatischen Entwicklung des Adverbs überhaupt

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Rapture of the deep: highs and lows of sparsity in a world of depths

Promoting sparsity in deep networks is a natural way to control their complexity, and a timely endeavor, since practical neural model sizes have grown to unprecedented levels. The lessons from sparsity in linear inverse problems also bear the promise of many other benefits beyond such computational aspects, from statistical significance to explainability. Can these promises be fulfilled? Can we safely leverage the know-how of sparsity-promoting regularizers for inverse problems to harness sparsity in deeper contexts, linear or not? This article surveys the curses and blessings of deep sparsity. After reminding the main lessons from inverse problems, we tour a number of results that challenge their immediate deep extensions, both from a mathematical and a computational perspective. In particular, we highlight that l1 regularization does not always lead to sparsity, and that optimization with a prescribed set of allowed nonzero coefficients can be NP-hard. We emphasize the role ofrescaling-invariances in these phenomena, and the need to favor structured sparsity to keep sparse network training problems under control, ensure their stability, and actually enable efficient network implementations on GPUs. We finally outline the promises and challenges of a flexible family of so-called Kronecker sparsity structures, which extend the classical butterfly structure and appear in many classical scientific computing applications and that have recently emerged also in deep learning

All, most, some? On diffeomorphisms of the interval that are distorted and/or conjugate to powers of themselves

32 pages, 3 figuresWe study the problem of conjugating a diffeomorphism of the interval to (positive) powers of itself. Although this is always possible for homeomorphisms, the smooth setting is rather interesting. Besides the obvious obstruction given by hyperbolic fixed points, several other aspects need to be considered. As concrete results we show that, in class $C^1$, if we restrict to the (closed) subset of diffeomorphisms having only parabolic fixed points, then the set of diffeomorphisms that are conjugate to their powers is dense, but its complement is generic. In higher regularity, however, the complementary set contains an open and dense set. The text is complemented with several remarks and results concerning distortion elements of the group of diffeomorphisms of the interval in several regularities

Suspensions of attractive microcapsules: A noncolloidal fragile gel?

International audienceWe investigated the rheological properties of suspensions of attractive microcapsules, which formed a weak gel at volume fractions ϕ as low as 0.1. These microcapsules, measuring 100 μm in diameter, were constructed with a droplet of positively charged chitosan solution protected by a membrane formed through the complexation of chitosan with a negatively charged surfactant. Iso-density matched suspensions were achieved by dispersing these microcapsules in silicone oils. Plate-plate rheometry revealed that these suspensions displayed a yield stress ranging from about 0.1 to 3 Pa for ϕ increasing from 0.1 to 0.5. At much higher stresses, the suspension viscosity was almost shear independent. Furthermore, these suspensions exhibited a frequency sweep signature akin to attractive colloidal suspensions, with a shear elastic modulus plateauing at low frequencies, indicative of an elastic microstructure within the suspensions. Remarkably, a degree of microstructural anisotropy, reminiscent of fragile matter, was evidenced by the transient fluidization of the suspension when the direction of applied stress, which remained below the yield stress, was reversed. Beyond the yield stress, both symmetric and asymmetric stress reversal experiments demonstrated that the suspension structure was influenced by the applied stress. It changed from an anisotropic and fragile network at low stress levels to a dispersion of isolated particles at high stress levels. We concluded that suspensions of attractive microcapsules could be classified as a fragile particulate gel, whose microstructure depends on the stress and its direction

Modeling the magnetocaloric effect and critical behavior near the ferromagnetic–paramagnetic transition temperature in Zn 0.5-x Ni x Mg 0.5 Fe 2 O 4 (x = 0, 0.125 and 0.250) spinel ferrites

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Choix, Présentation et annotation de textes de consolation du premier XVIIe siècle ( Théophile de Viau, Tristan L'Hermite, Malherbe)

International audienceThe volume édits a collection of texts on consolation, classified by topic, period, or practices. My work involved selecting, editing, and presenting the practice of consolation for four lyric texts: Théophile de Viau, "Consolation à M. de L.," 1621; Tristan, "Consolation à Monsieur de Gournay sur la perte de deux de ses enfants," Epitaph-Tombeau 10, La Lyre, 1643; Malherbe, "Vers de Malherbe à madame la comtesse sur la mort de sa fille," [1599]Le volume propose d'éditer un ensemble de textes sur la consolation, classées par topique, période ou pratiques. Mon travail a consisté à choisir, éditer et présenter la pratique de la consolation pour 4 textes lyriques: Théophile de Viau, « Consolation à M. de L. », 1621, Tristan, « Consolation à Monsieur de Gournay sur la perte de deux de ses enfans », épitaphe-tombeau 10., La Lyre, 1643; Malherbe, "Vers de Malherbe à madame la comtesse sur la mort de sa fille", [1599] 

Une goutte de sang

Alm@e Linguae n°2 Un@ Editions / PUPPATraduction inédite du récit La gota de sangre (1911) de Emilia Pardo Bazán, premier récit policier long de l'histoire du genre en Espagn

Predicting coarse-grained representations of biogeochemical cycles from metabarcoding data

Taxonomic analysis of environmental microbial communities is now routinely performed thanks to advances in DNA sequencing. Determining the role of these communities in global biogeochemical cycles requires the identification of their metabolic functions, such as hydrogen oxidation, sulfur reduction, and carbon fixation. These functions can be directly inferred from metagenomics data, but in many environmental applications metabarcoding is still the method of choice. The reconstruction of metabolic functions from metabarcoding data and their integration into coarse-grained representations of geobiochemical cycles remains a difficult bioinformatics problem today. Results We developed a pipeline, called Tabigecy, which exploits taxonomic affiliations to predict metabolic functions constituting biogeochemical cycles. In a first step, Tabigecy uses the tool EsMeCaTa to predict consensus proteomes from input affiliations. To optimise this process, we generated a precomputed database containing information about 2,404 taxa from UniProt. The consensus proteomes are searched using bigecyhmm, a newly developed Python package relying on Hidden Markov Models to identify key enzymes involved in metabolic function of biogeochemical cycles. The metabolic functions are then projected on coarse-grained representation of the cycles. We applied Tabigecy to two salt cavern datasets and validated its predictions with microbial activity and hydrochemistry measurements performed on the samples. The results highlight the utility of the approach to investigate the impact of microbial communities on geobiochemical processes