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Differentiable Generalized Sliced Wasserstein Plans
No full textInternational audienceOptimal Transport (OT) has attracted significant interest in the machine learning community, not only for its ability to define meaningful distances between probability distributions -- such as the Wasserstein distance -- but also for its formulation of OT plans. Its computational complexity remains a bottleneck, though, and slicing techniques have been developed to scale OT to large datasets. Recently, a novel slicing scheme, dubbed min-SWGG, lifts a single one-dimensional plan back to the original multidimensional space, finally selecting the slice that yields the lowest Wasserstein distance as an approximation of the full OT plan. Despite its computational and theoretical advantages, min-SWGG inherits typical limitations of slicing methods: (i) the number of required slices grows exponentially with the data dimension, and (ii) it is constrained to linear projections. Here, we reformulate min-SWGG as a bilevel optimization problem and propose a differentiable approximation scheme to efficiently identify the optimal slice, even in high-dimensional settings. We furthermore define its generalized extension for accommodating to data living on manifolds. Finally, we demonstrate the practical value of our approach in various applications, including gradient flows on manifolds and high-dimensional spaces, as well as a novel sliced OT-based conditional flow matching for image generation -- where fast computation of transport plans is essential
Density and unitarity of the Burau representation from a non-semisimple TQFT
No full textInternational audienceWe study the density of the Burau representation from the perspective of a non-semisimple TQFT at a fourth root of unity. This gives a TQFT construction of Squier's Hermitian form on the Burau representation with possibly mixed signature. We prove that the image of the braid group in the space of possibly indefinite unitary representations is dense. We also argue for the potential applications of non-semisimple TQFTs toward topological quantum computation
Strong mixing for the periodic Lorentz gas flow with infinite horizon
No full textInternational audienceWe establish strong mixing for the Z d-periodic, infinite horizon, Lorentz gas flow for continuous observables with compact support. The essential feature of this natural class of observables is that their support may contain points with infinite free flights. Dealing with such a class of functions is a serious challenge and there is no analogue of it in the finite horizon case. The mixing result for the aforementioned class of functions is obtained via new results: 1) mixing for continuous observables with compact support consisting of configurations at a bounded time from the closest collision; 2) a tightness-type result that allows us to control the configurations with long free flights. To prove 1), we establish a mixing local limit theorem for the Sinai billiard flow with infinite horizon, previously an open question
Accounting for meteorological and load data uncertainty in the optimal design of off-grid hybrid renewable energy systems
No full textInternational audienceThis study presents a methodological contribution to the optimal design of an off-grid hybrid renewable energy systems (HRES) producing both electricity and drinking water. Beyond simulating the operation of a system combining solar photovoltaic and wind generation with battery and hydrogen storage , the work focuses on a critical yet often overlooked issue: the uncertainty associated with meteorological and consumption input data. A multi-objective optimization model, implemented in Julia, is used to determine system configurations that minimize the cost of energy and water while maximizing the share of renewable energy. The analysis demonstrates that the selection of input data has a significant influence on system design results. A methodology is proposed to identify the most favorable and most unfavorable input datasets. A novel shortage indicator is introduced to quantify energy deficits during periods when renewable production is insufficient to meet demand. This indicator enables interpretation of the underlying causes of cost and sizing variations, by linking them to storage requirements. The methodology is applied to the island of Molène (France) using meteorological and consumption data from 2018 to 2023. The results highlight the strong sensitivity of system design to input variability, and provide a framework for robust analysis and planning under uncertainty
Relationship Analysis Between Helicopter Gearbox Bearing Condition Indicators and Oil Temperature Through Dynamic ARDL and Wavelet Coherence Techniques
No full textInternational audienceThis study investigates the dynamic relationship between bearing gearbox condition indicators (BGCIs) and the lubrication oil temperature within the framework of health and usage monitoring system (HUMS) applications. Using the dynamic autoregressive distributed lag (DARDL) simulation model, we quantified both the short- and long-term responses of condition indicators to shocks in oil temperature, offering a robust framework for a counterfactual analysis. To complement the time-domain perspective, we applied a wavelet coherence analysis (WCA) to explore time–frequency co-movements and phase relationships between the condition indicators under varying operational regimes. The DARDL results revealed that the ball energy, cage energy, and inner and outer race indicators significantly increased in response to the oil temperature in the long run. The WCA results further confirmed the positive association between oil temperature and the condition indicators under examination, aligning with the DARDL estimations. The DARDL model revealed that the ball energy and the inner race energy have statistically significant long-term effects on the oil temperature, with p-values < 0.01. The adjusted R2 of 0.785 and the root mean square error (MSE) of 0.008 confirm the model’s robustness. The wavelet coherence analysis showed strong time–frequency correlations, especially in the 8–16 scale range, while the frequency-domain causality (FDC) tests confirmed a bidirectional influence between the oil temperature and several condition indicators. The FDC analysis showed that the oil temperature significantly affected the BGCIs, with evidence of feedback effects, suggesting a mutual dependency. These findings contribute to the advancement of predictive maintenance frameworks in HUMSs by providing practical insights for enhancing system reliability and optimizing maintenance schedules. The integration of dynamic econometric approaches demonstrates a robust methodology for monitoring critical mechanical components and encourages further research in broader aerospace and industrial contexts
Generalized differentiation in Wasserstein space and application to multiagent control problem
No full textSeveral concepts of generalized differentiation in Wasserstein space have been proposed in order to deal with the intrinsic nonsmoothness arising in the context of optimization problems in Wasserstein spaces. In this paper we introduce a concept of admissible variation encompassing some of the most popular definitions as special cases, and using it to derive a comparison principle for viscosity solutions of an Hamilton Jacobi Bellman equation following from an optimal control of a multiagent systems
Cu-25Cr composites processed by in situ alloying in electron beam powder bed fusion
No full textInternational audienceDue to their high thermal and electrical conductivity and high resistance to arc erosion, Cu-Cr alloys (Cr >10 wt %) are used as electrical contacts in medium voltage vacuum circuit breakers. Such electrical contacts are industrially processed using solid-state sintering (SSS) from pure Cu and Cr powders or vacuum arc remelting (VAR). In this work, we confirm the possibility of fabricating dense Cu-25Cr samples with a refined and relatively homogeneous microstructure by electron beam powder bed fusion (EB-PBF) using elemental powder blending. The as-printed microstructure is characterized using SEM imaging and EBSD analysis while the mechanical, electrical, and thermal are probed to establish the microstructure-property relationships of the EB-PBF Cu-25Cr composite. The properties of the EB-PBF composite are systematically compared to their VAR counterparts. The as-printed microstructure results from the presence of a metastable miscibility gap that refines the microstructure (micron-sized Cr particles) by an order of magnitude compared to the VAR. The fine EB-PBF microstructure shows superior mechanical properties (hardness, yield strength and ultimate tensile strength), enhanced electrical conductivity, and equivalent thermal conductivity with respect to its VAR counterpart. The microstructureproperty relationships are discussed in light of the mechanisms affecting the mechanical, electrical, and thermal properties of metal matrix composites. This work demonstrates the interest in producing Cu-Cr electrical contacts by additive manufacturing
Faraday waves and period tripling in a horizontal circular tank
No full textInternational audienceUnderstanding wave kinematics is crucial for analysing the thermodynamic effects of sloshing, which can lead to pressure drops in non-isothermal cryogenic fuel tanks. In the research reported here, Faraday waves in a horizontal circular tank (partially filled with water) under vertical excitation are investigated. The tank geometry is referred to as a horizontal circular tank throughout, with its circular face oriented perpendicular to the horizontal plane. Firstly, this paper addresses the eigenvalue problem through linear potential flow theory, in order to provide theoretical evidence of Faraday waves in horizontal circular tanks, the impact the density ratio has on the eigenvalues is then considered. Secondly, an experimental investigation testing multiple liquid fill levels is conducted. A soft-spring nonlinear response is demonstrated throughout the parameter space. The results showed larger sloshing amplitudes for low fill levels and smaller sloshing amplitudes for high fill levels. Asymmetry between anti-nodes at the container sidewalls and through the tank centreline are evident for low fill levels. Moreover, the sloshing wave amplitude at which breaking waves occur is smaller for high fill level conditions. Finally, period tripling was observed for all fill levels tested, confirming nonlinear mode interactions before the onset to wave breaking
Local adaptation of life-history traits in a seasonal environment
No full textInternational audiencePopulations are often spread across a spatially heterogeneous landscape, connected by migration. Consequently, the question arises whether divergent selective forces created by spatial heterogeneity can overcome the homogenizing force of migration and loss of diversity through genetic drift to favour different traits across space. The resulting population differentiation due to divergent selection is known as local adaptation. While local adaptation has been studied in a variety of settings, it remains unclear under what conditions local adaptation of certain life-history traits can arise. Life-history traits, such as those determining an organism's fecundity (the parameter r) and ability to compete for resources (the parameter K) demonstrate unique eco-evolutionary feedback loops due to their direct relationship to individual fitness. Classic ecological theory holds that in a constant environment, long-term evolution maximizes the population's competitive ability. Divergent selective pressures on life-history traits requires complex environmental differences, such as heterogeneous patterns of seasonality. We consider life-history evolution in a Lotka-Volterra model with three types of seasonal perturbations: repeated sudden crashes in population size, fluctuating death rates, and fluctuating resource levels. We show that fluctuating resources cannot change the evolutionary outcome, but that sufficiently harsh population crashes or fluctuating death rates favour increased fecundity over competitive ability. Our results quantify what we expect qualitatively based on early life-history theory. Finally, we apply deterministic and stochastic modelling to study local adaptation of an island population to periodic population crashes in an island-mainland model. We find that local adaptation favouring r-selected individuals again arises when conditions are sufficiently harsh, but not so harsh that the island population cannot be sustained in the absence of migration
Geopolitical Risk, Inflation, and Commodity Shocks in MENA: Evidence from a VECM-HAC-DCC Framework
No full textThis paper examines how macro conditions shape equity returns across 13 Middle East and North Africa markets using monthly data from January 2016 to June 2025. A compact VECM-HAC-DCC framework preserves long-run relations, controls for heteroskedasticity, and maps time variation in correlations. At the 5 percent level, geopolitical risk predicts standardized returns in 4 of 13 markets and remains after false-discovery control in two oil-exporting, USD-pegged markets. Inflation predicts only in Turkey and survives FDR. A commodity factor extracted from oil and gold is episodic, with significance concentrated in Jordan. Dynamic-correlation paths reveal regimes aligned with identifiable stress periods. The evidence translates into implementable guidance: add a geopolitical-risk overlay in oil-exporting, USD-pegged markets, condition allocation on inflation regimes in Turkey, and monitor correlation regimes where average predictability is weak