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A mathematical framework for modelling order book dynamics
No full text43 p.International audienceWe present a general framework for modelling the dynamics of limit order books, built on the combination of two modelling ingredients: the order flow, modelled as a general spatial point process, and market clearing, modelled via a deterministic 'mass transport' operator acting on distributions of buy and sell orders. At the mathematical level, this corresponds to a natural decomposition of the infinitesimal generator describing the evolution of the limit order book into two operators: the generator of the order flow and the clearing operator. Our model provides a flexible framework for modelling and simulating order book dynamics and studying various scaling limits of discrete order book models. We show that our framework includes previous models as special cases and yields insights into the interplay between order flow and price dynamics
Acting, Planning and Learning
No full textInternational audienceAI's next big challenge is to master the cognitive abilities needed by intelligent agents that perform actions. Such agents may be physical devices such as robots, or they may act in simulated or virtual environments through graphic animation or electronic web transactions. This book is about integrating and automating these essential cognitive abilities: planning what actions to undertake and under what conditions, acting (choosing what steps to execute, deciding how and when to execute them, monitoring their execution, and reacting to events), and learning about ways to act and plan. This comprehensive, coherent synthesis covers a range of state-of-the-art approaches and models – deterministic, probabilistic (including MDP and reinforcement learning), hierarchical, nondeterministic, temporal, spatial, and LLMs – and applications in robotics. The insights it provides into important techniques and research challenges will make it invaluable to researchers and practitioners in AI, robotics, cognitive science, and autonomous and interactive systems
A Max-Flow approach to Random Tensor Networks
No full textInternational audienceWe study the entanglement entropy of a random tensor network (RTN) using tools from free probability theory. Random tensor networks are simple toy models that help the understanding of the entanglement behavior of a boundary region in the ADS/CFT context. One can think of random tensor networks are specific probabilistic models for tensors having some particular geometry dictated by a graph (or network) structure. We first introduce our model of RTN, obtained by contracting maximally entangled states (corresponding to the edges of the graph) on the tensor product of Gaussian tensors (corresponding to the vertices of the graph). We study the entanglement spectrum of the resulting random spectrum along a given bipartition of the local Hilbert spaces. We provide the limiting eigenvalue distribution of the reduced density operator of the RTN state, in the limit of large local dimension. The limit value is described via a maximum flow optimization problem in a new graph corresponding to the geometry of the RTN and the given bipartition. In the case of series-parallel graphs, we provide an explicit formula for the limiting eigenvalue distribution using classical and free multiplicative convolutions. We discuss the physical implications of our results, allowing us to go beyond the semiclassical regime without any cut assumption, specifically in terms of finite corrections to the average entanglement entropy of the RTN
An overview of variance-based importance measures in the linear regression context: comparative analyses and numerical tests
No full textInternational audienceOne of the most fundamental issues in many socio-environmental studies is the identification of causal effects and influential variables related to phenomena of interest. In the context of regression analysis, importance measures are effective tools for feature selection and model interpretation, allowing for the ranking of the most influential regressors. In particular, variance-based importance measures (VIMs) are a prominent topic in the field of statistics, as well as in the emerging field of global sensitivity analysis. This is due to their accessible interpretation as variance shares of the explained variable. This work focuses on the linear regression model and aims to provide an updated overview of the most well-founded methods, mainly from comparative analyses and numerical tests on various toy cases. The paper also addresses some of the practical challenges that arise, including the case of dependent inputs and high input dimensionality. The practical relevance of these tools is demonstrated through empirical studies on simulated data and public datasets. The Supplementary Material also presents the use of VIMs in a classification context, specifically via the logistic linear regression model
Aging modeling and lifetime prediction of a proton exchange membrane fuel cell using an extended Kalman filter
No full textInternational audienceThis article presents a methodology that aims to model and to provide predictive capabilities for the lifetime of Proton Exchange Membrane Fuel Cell (PEMFC). The approach integrates parametric identification, dynamic modeling, and Extended Kalman Filtering (EKF). The foundation is laid with the creation of a representative aging database, emphasizing specific operating conditions. Electrochemical behavior is characterized through the identification of critical parameters. The methodology extends to capture the temporal evolution of the identified parameters. We also address challenges posed by the limiting current density through a differential analysis-based modeling technique and the detection of breakpoints. This approach, involving Monte Carlo simulations, is coupled with an EKF for predicting voltage degradation. The Remaining Useful Life (RUL) is also estimated. The results show that our approach accurately predicts future voltage and RUL with very low relative errors
In-situ Imaging of a Single-Atom Wave Packet in Continuous Space
No full text12 pages, 11 figuresInternational audienceThe wave nature of matter remains one of the most striking aspects of quantum mechanics. Since its inception, a wealth of experiments has demonstrated the interference, diffraction or scattering of massive particles. More recently, experiments with ever increasing control and resolution have allowed imaging the wavefunction of individual atoms. Here, we use quantum gas microscopy to image the in-situ spatial distribution of deterministically prepared single-atom wave packets as they expand in a plane. We achieve this by controllably projecting the expanding wavefunction onto the sites of a deep optical lattice and subsequently performing single-atom imaging. The protocol established here for imaging extended wave packets via quantum gas microscopy is readily applicable to the wavefunction of interacting many-body systems in continuous space, promising a direct access to their microscopic properties, including spatial correlation functions up to high order and large distances
M2.2.3 - High-resolution laser ablation of a copper layer for the fabrication of 3D-printed MEMS and microsensors
No full textarticle soumis après conférence Eurosensor 2025International audienc
Sufficient conditions for the absence of relaxation gaps in state-constrained optimal control
No full text9 page
Young measure relaxation gaps for controllable systems with smooth state constraints
No full textIn this article, we tackle the problem of the existence of a gap corresponding to Young measure relaxations for state-constrained optimal control problems. We provide a counterexample proving that a gap may occur in a very regular setting, namely for a smooth controllable system state constrained to the closed unit ball, provided that the Lagrangian density (i.e., the running cost) is non-convex in the control variables. The example is constructed in the setting of sub-Riemannian geometry with the core ingredient being an unusual admissible curve that exhibits a certain form of resistance to state-constrained approximation. Specifically, this curve cannot be approximated by neighboring admissible curves while obeying the state constraint due to the intricate nature of the dynamics near the boundary of the constraint set. Our example also presents an occupation measure relaxation gap.23 pages, 2 figure
PolExp growth for automorphisms of toral relatively hyperbolic groups
No full textLet be a toral relatively hyperbolic group, and let . We prove that, under iteration of , the conjugacy length of every element grows like for some and some algebraic integer . For a given , only finitely many values of and occur as varies in . The same statements hold for the growth of the word length . For hyperbolic, we generalize polynomial subgroups: we show that, for a given growth type other than , there is a malnormal family of quasiconvex subgroups such that a conjugacy class grows at most like if and only if is conjugate into one of the subgroups