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A Rocq Formalization of Simplicial Lagrange Finite Elements
No full textThe finite elements method is a popular method to numerically solve partial differential equations. In the long-term goal of proving its correctness, we focus here on the formal definition of what is a finite element: a record in the Rocq proof assistant with both values and proofs of validity, including the main one called unisolvence. We then instantiate this record with the most popular and useful, the simplicial Lagrange finite elements for evenly distributed nodes, for any dimension and any polynomial degree. These proofs require many results (definitions, lemmas, canonical structures) about finite families, affine spaces, multidimensional polynomials, in the context of finite or infinite-dimensional spaces
Minimax estimation of partially-observed vector autoregressions
No full textInternational audienceMulti-dimensional time series are a core ingredient of the statistical modeling toolkit, for which numerous estimation methods are known. But when observations are scarce or corrupted, the learning task becomes much harder. The question is: how much harder?In this paper, we study the properties of a partially-observed Vector AutoRegressive process, which is a state-space model endowed with a stochastic observation mechanism. Our goal is to estimate its transition matrix, but we only have access to a small and noisy subsample of the state components.We start by describing an estimator based on the Yule-Walker equation and the Dantzig selector, and we give an upper bound on its non-asymptotic error. Then, we provide a matching minimax lower bound, thus proving near-optimality of our estimator. The convergence rate we obtain sheds light on the role of several key parameters such as the sampling ratio, the amount of noise and the number of non-zero coefficients in the transition matrix, which can be dense in low dimension but is usually sparse in high dimension. These theoretical findings are commented and illustrated by numerical experiments on simulated data
Modelling the effect of volcanic outgassing of sulphur on early Martian surface temperatures using a 3-D Global Climate Model
No full textInternational audienceAround the time of the transition from the Late Noachian to the Early Hesperian eras (∼3.6 Gya), Mars was predicted to have been both volcanically active, and have sustained a climate warm enough to melt liquid water on its surface episodically despite a faint young sun. The effect of volcanic outgassing on the climate of early Mars and its ability to raise temperatures above the melting point of water has, however, been disputed, with a major uncertainty being the timescales over which the greenhouse effect of outgassed sulphur dioxide (SO 2 ) and hydrogen sulphide (H 2 S) can warm the atmosphere of Mars before they react to form H 2 SO 4 and S 8 aerosols which act to cool the surface of Mars. We have developed the first 3-D model of the Martian sulphur cycle from source to sink that includes outgassing of SO 2 , H 2 S and S 2 from the surface, the formation of H 2 SO 4 and S 8 through atmospheric chemistry, and the condensation and deposition of H 2 SO 4 and S 8 to the surface. We simulate the effect of a single large, day-long volcanic outgassing event on global surface temperatures, identifying the magnitude and duration of any net warming and cooling as a function of outgassing magnitude, atmospheric pressure, obliquity and aerosol particle size distribution. We confirm the results of Tian et al. (2010, EPSL 295, 412-418) and find that the persistence of the warming effect of volcanically outgassed SO 2 and H 2 S on the Martian atmosphere is only of the order of days to weeks for a surface pressure range of between 0.5 and 1.5 bars. Typical outgassing magnitudes result in a net cooling of the Martian surface over timescales of 3-4 years near the equator and several decades at the poles for plume neutral buoyancy heights within the troposphere. For very high magnitudes of outgassing, the rate of H 2 SO 4 cloud formation slows down due to the depletion of water vapour in the atmosphere, thereby slowing down the rate of cooling and providing a buffer against atmospheric collapse
The hidden dimension of low-carbon public transport policies: From biodiversity conservation to user preferences
No full textInternational audienceTransport infrastructures dedicated to low-carbon public transport are seen as a central tool in public policy strategies to mitigate climate change. Yet, the development of transport infrastructures has significant direct and indirect negative effects on biodiversity and social acceptability of these impacts remain little assessed. In this study, we analyse potential impacts of 20 tramway existing projects in France and social preferences with regard to their ecological and landscape integration. Using a discrete choice experiment on 1000 respondents, we show that users, even the most time constrained, are accepting an average travel time lengthening of 15 %, if tramway project integration retains a more wooded landscape, more diverse and abundant species and access to a natural area. We show that brief information provided on the state of biodiversity through framing encourages environmental consideration. We quantify the estimated impact of these projects on the naturalness of habitats and the buffer effect that project ecological integration could allow. These results highlight the non-negligible ecological impact of low-carbon transport infrastructures. They underline the need to consider climate change mitigation strategies in tandem with biodiversity preservation, while taking into account user preferences which affect the acceptability of the ecological and landscape integration of these projects
Asymptotic numerical hypocoercivity of the space-time discontinuous Galerkin method for Kolmogorov equation
No full textWe are concerned with discretisations of the classical Kolmogorov equation by a standard space-time discontinuous Galerkin method. Kolmogorov equation serves as simple, yet rich enough in the present context, model problem for a wide range of kinetic-type equations: although it involves diffusion in one of the two spatial dimensions only, the combined nature of the first order transport/drift term and the degenerate diffusion are sufficient to 'propagate dissipation' across the spatial domain in its entirety. This is a manifestation of the celebrated concept of hypocoercivity, a term coined and studied extensively by Villani in [27]. We show that the standard, classical, spacetime discontinuous Galerkin method, admits a corresponding hypocoercivity property at the discrete level, asymptotically for large times. To the best of our knowledge, this is the first result of this kind for any standard Galerkin scheme. This property is shown by proving one part of a discrete inf-sup-type stability result for the method in a family of norms dictated by a modified scalar product motivated by the theory in [27]. This family of norms contains the full gradient of the numerical solution, thereby allowing for a full spectral gap/Poincaré-type inequality at the discrete level, thus, showcasing a subtle, discretisation-parameter-dependent, numerical hypocoercivity property. Further, we show that the space-time discontinuous Galerkin method is inf-sup stable in the family of norms containing the full gradient of the numerical solution, which may be a result of independent interest
UNIT: Unsupervised Online Instance Segmentation through Time
No full textInternational audienceOnline object segmentation and tracking in Lidar point clouds enables autonomous agents to understand their surroundings and make safe decisions. Unfortunately, manual annotations for these tasks are prohibitively costly. We tackle this problem with the task of class-agnostic unsupervised online instance segmentation and tracking. To that end, we leverage an instance segmentation backbone and propose a new training recipe that enables the online tracking of objects. Our network is trained on pseudo-labels, eliminating the need for manual annotations. We conduct an evaluation using metrics adapted for temporal instance segmentation. Computing these metrics requires temporally-consistent instance labels. When unavailable, we construct these labels using the available 3D bounding boxes and semantic labels in the dataset. We compare our method against strong baselines and demonstrate its superiority across two different outdoor Lidar datasets
Incremental Reachability Index
No full textInternational audienceWe study the reachability problem in append-only DAGs: given two nodes u and v, is there a path from u to v? While the problem is linear in general, it can be answered faster by using a precomputed index, which gives a compressed representation of the transitive closure of the graph. Index algorithms are evaluated on three dimensions: the query time that the algorithm needs to answer whether there is a path from one node to another, the memory that the index uses per node, and the indexing time that is required to update the index when a node is added to the graph.In this paper, we combine Jagadish's static index [Jag90] with Felsner's online chain-decomposition algorithm [Fel97] to create an incremental index: data associated with a node is immutable, guaranteeing that queries are answered properly even if new nodes are inserted while the query is processed. Its query time is constant, but its index size is heavily dependent on the graph width, and as such is not competitive with recent indexing algorithms (2-hop, tree-chain, ...). We also propose a version of that incremental algorithm with a much lighter index. In the most compressed version, the query time becomes O(log n). However, constant-time queries can be retained depending on the desired time/memory trade-off
Modelling the poromechanical behaviour of class G cement paste: A multiphysics approach from early age to hardened state
No full textInternational audienceModelling cement-based materials from the early-age to the hardened state is crucial in numerous applications such as deep well cementing or 3D printing, which require comprehensive modelling of multiphysics couplings.To answer these requirements, a thermodynamically consistent time-dependent constitutive model based on the extent of hydration is developed in the framework of thermoporomechanics of partially saturated materials. Using minimal fitting, complex undrained oedometric tests on hydrating cement paste, combining effects of hydration progress, pore pressure evolution, elastic, viscous, and plastic deformations, are well reproduced numerically. In particular, the impact of early-age loading on the behaviour at a subsequent age, paramount in oil-well applications to understanding the consequences of pressurising the casing when the cement sheath is partially hydrated, is explained and quantitatively reproduced.</p
Reactive bromine in volcanic plumes confines the emission temperature and oxidation of magmatic gases at the atmospheric interface
No full textInternational audienceThe redox composition of volcanic gases relays substantial information about magmatic conditions and volcanic activity. Volcanic plume gas measurements are often interpreted assuming that magmatic gases are chemically inert on emission and near-source dilution in air. Conversely, many volcanic plumes contain high levels of bromine monoxide (BrO), which is produced by atmospheric oxidation of magmatic hydrogen bromide (HBr) emissions. We investigate the chemical kinetics of hot magmatic gases mixing with air. Our model reproduces and explains observations of volcanic plume BrO at Mt. Etna, evidencing that reduced gases [HBr, as well as carbon monoxide (CO) and hydrogen (H 2 )] can oxidize at the hot magma–air interface. The extent of oxidation is controlled by the magmatic gas temperature. Observations of BrO and H 2 in Mt. Etna plume indicate that magmatic gases enter air at several hundred kelvin below magmatic temperature, consistent with hypothesized decoupling of gas temperatures from magma prior to emission
Reference architecture and ontology framework for digital twin construction
No full textInternational audienceThe application of digital twins in building construction faces challenges due to limited guidance on the necessary data management layers. This paper addresses this gap by investigating how the reference architecture for Digital Twin Construction (DTC) should be structured to manage planning information, raw monitoring data, and derived knowledge, as well as its data schema to compare project plans with status. By defining platform requirements and using Design Science Research Methodology, a solution was implemented and validated using a case study based on the ConSLAM dataset. A plugin-based DTC reference architecture employing multiple RDF graphs linked to specialized databases and the DTC Ontology as the internal data schema are introduced. This architecture guides construction companies in data-driven decision-making during execution. It establishes a foundation for managing digital twins and fosters the development of domain-specific services that benefit from clear data structures, supporting a holistic digital twin adaptable to project-specific needs