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Geometric theory of constrained Schrödinger dynamics with application to time-dependent density-functional theory on a finite lattice
No full textTime-dependent density-functional theory (TDDFT) is a central tool for studying the dynamical electronic structure of molecules and solids, yet aspects of its mathematical foundations remain insufficiently understood. In this work, we revisit the foundations of TDDFT within a finite-dimensional setting by developing a general geometric framework for Schrödinger dynamics subject to prescribed expectation values of selected observables. We show that multiple natural definitions of such constrained dynamics arise from the underlying geometry of the state manifold. The conventional TDDFT formulation emerges from demanding stationarity of the action functional, while an alternative, purely geometric construction leads to a distinct form of constrained Schrödinger evolution that has not been previously explored. This alternative dynamics may provide a more mathematically robust route to TDDFT and may suggest new strategies for constructing nonadiabatic approximations. Applying the theory to interacting fermions on finite lattices, we derive novel Kohn--Sham schemes in which the density constraint is enforced via an imaginary potential or, equivalently, a nonlocal Hermitian operator. Numerical illustrations for the Hubbard dimer demonstrate the behavior of these new approaches
Scaling limits of solitons in the box-ball system
No full textInternational audienceWe study the space-time scaling limits of solitons in the box-ball system with random initial distribution. In particular, we show that any recentered tagged soliton converges to a Brownian motion in the diffusive space-time scale, and also prove the large deviation principle for the tagged soliton under certain shift-ergodic invariant distributions, including Bernoulli product measures and two-sided Markov distributions. Furthermore, in the diffusive space-time scaling, we show that two tagged solitons converge to the same Brownian motion even if they are macroscopically far apart
Graph functional dependencies: Analysis and translation to PG-schema
No full textInternational audienceOfficially published as an ISO/IEC standard in April 2024, the Graph Query Language (GQL) aims to establish itself as the standard language for querying graph data, much like SQL is for relational data. The graph database community has also recently introduced additional specifications, such as PG-Key and, later, PG-Schema, to define graph schemas and dependencies. At the same time, several proposals have emerged in the literature to express Functional Dependency constraints in graph data. Given the wide range of Graph Dependencies presented in the literature, the first contribution of this article is a survey of Graph Functional Dependencies in existing proposals, highlighting the most significant ones, their differences, and their relative expressiveness. In a second contribution, we align with the goals of the graph database community by proposing mappings to translate different kinds of Graph Functional Dependencies from the literature into PG-Schema-compliant dependencies. These mappings are implemented within a publicly available tool PG-FD, which to our knowledge, is the first solution capable of transforming Graph Dependencies into the PG-Schema standard while fully preserving their semantics
A characterization of Generalized functions of Bounded Deformation
No full textInternational audienceWe show that Dal Maso's GBD space, introduced for tackling crack growth in linearized elasticity, can be defined by simple conditions in a finite number of directions of slicing.</div
Learning To Sample From Diffusion Models Via Inverse Reinforcement Learning
No full textDiffusion models generate samples through an iterative denoising process, guided by a neural network. While training the denoiser on real-world data is computationally demanding, the sampling procedure itself is more flexible. This adaptability serves as a key lever in practice, enabling improvements in both the quality of generated samples and the efficiency of the sampling process. In this work, we introduce an inverse reinforcement learning framework for learning sampling strategies without retraining the denoiser. We formulate the diffusion sampling procedure as a discretetime finite-horizon Markov Decision Process, where actions correspond to optional modifications of the sampling dynamics. To optimize action scheduling, we avoid defining an explicit reward function. Instead, we directly match the target behavior expected from the sampler using policy gradient techniques. We provide experimental evidence that this approach can improve the quality of samples generated by pretrained diffusion models and automatically tune sampling hyperparameters
Demand response control structure in imperfectly competitive power markets: Independent or integrated?
No full textInternational audienceThis article investigates different types of actors controlling demand response (DR) operations under Cournot competition. Analytical results linking shiftable load level, market equilibrium, and welfare are obtained for DR operated either by an independent aggregator (price-taker or price-maker), by end-consumers’ suppliers, or within the portfolio of generators. An application to a 2035 French power system with detailed flexible appliances constraints is also proposed. Results show that supplier-integrated DR yields the greatest price reductions and lowest shiftable load withholding, while DR integrated with baseload producers has the weakest effects on prices and may worsen welfare losses compared to a perfectly competitive market. While DR deployment consistently improves welfare and lowers prices, the extent depends on the control structure. Independent aggregation and supplier integration deliver similar welfare gains but shift surplus toward consumers, whereas integration within generators results in up to a 6€/MWh higher producer surplus compared to the other structures. Policy implications highlight the importance of DR deployment overall but caution against DR integration exclusively within baseload generators’ portfolios due to limited market benefits
Multi-Objective Categorical Deep Q-Networks
No full textInternational audienceMotivated by recent advances in distributional reinforcement learning on the one hand and Multi-Objective Reinforcement Learning (MORL) on the other, we propose MO-CDQN, a value based algorithms that, given a possibly non-linear scalarization function, learn the policy with maximal expected scalarized return. Leveraging the Kantorovich-Rubenstein duality we prove the theoretical validity of our method for Lipschitz-continuous scalarization function. We establish that the state-action return distributions learned by our algorithm converge to a fixed point whose expected scalarized return is optimal. Our approach is then extended to propose a first valuebased multi-policy algorithm for solving MORL problems under the expected scalarized return criterion. The proposed algorithms are tested on several environments from the MO-gymnasium benchmark. The results are promising and show that, on the one hand, our algorithm learns policies better than those obtained by existing approaches in the literature while requiring fewer interactions with the environments. On the other hand, given a set of scalarization functions, our multi-policy takes advantage of its off-policy nature to successfully optimize several policies concurrently and efficiently provide a set of policies each one optimal for a given scalarization function.</div
The index of a pair of pure states and the interacting integer quantum Hall effect
No full textInternational audienceWe introduce the index of a pair of pure states on a unital C*-algebra, which is a generalization of the notion of the index of a pair of projections on a Hilbert space. We then show that the Hall conductance associated with an invertible state of a two-dimensional interacting electronic system which is symmetric under charge transformation may be written as the index , where is obtained from by inserting a unit of magnetic flux. This exhibits the integrality and continuity properties of the Hall conductance in the context of general topological features of
Entropic Mirror Monte Carlo
No full textImportance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions in highdimensional spaces, the efficiency of importance sampling critically depends on the choice of the proposal distribution. In this paper, we propose a novel adaptive scheme for the construction of efficient proposal distributions. Our algorithm promotes efficient exploration of the target distribution by combining global sampling mechanisms with a delayed weighting procedure. The proposed weighting mechanism plays a key role by enabling rapid resampling in regions where the proposal distribution is poorly adapted to the target. Our sampling algorithm is shown to be geometrically convergent under mild assumptions and is illustrated through various numerical experiments
Impact Evaluation of Parental Education Campaign on Child Development in Nepal
No full textThis study assesses the impacts of a parental education community training on childdevelopment in Nepal. Relying on a sample of approximately 1,000 households, we randomlyvary the access to the intervention. A few months after the end of the intervention, children inthe treatment group exhibit significantly higher scores on early childhood development indicators—both overall and across linguistic, motor, and cognitive domains. In turn, the interventionhas no sizable effects on anthropometric outcomes. Mechanism analysis reveals that the programimproves parental knowledge about child development and enhances the quality of parent-childinteractions