In this paper, we mainly focus on the numerical solution of high-dimensional stochastic optimal control problem driven by fully-coupled forward-backward stochastic differential equations (FBSDEs in short) through deep learning. We first transform the problem into a stochastic Stackelberg differential game problem (leader-follower problem), then a bi-level optimization method is developed where the leader's cost functional and the follower's cost functional are optimized alternatively via deep neural networks. As for the numerical results, we compute two examples of the investment-consumption problem solved through stochastic recursive utility models, and the results of both examples demonstrate the effectiveness of our proposed algorithm.
Segmentation models based on deep neural networks demonstrate strong generalization for medical image segmentation. However, they often exhibit overconfidence or underconfidence, leading to unreliable confidence scores for segmentation masks, especially in ambiguous regions. This limits the reliability of fully automatic segmentation in ambiguous regions. Motivated by the learning-to-defer (L2D) paradigm, we introduce Deferred-Seg, a pixel-wise Human-AI collaborative deferral framework that learns whether to retain model predictions or defer difficult pixels or regions to expert branches. DeferredSeg extends the base segmentor with an aggregated deferral predictor and additional routing channels that dynamically route each pixel to either the base segmentor or human expert. To train this routing efficiently, we introduce a pixel-wise surrogate collaboration loss that supervises deferral decisions. In addition, we introduce a spatial-coherence loss that aligns the aggregated expert-assignment probability with the learned routing decisions, encouraging locally consistent deferral patterns. Beyond single-expert deferral, we further extend the framework to a multi-expert setting by introducing multiple experts with different reliability profiles for collaborative decision-making. To mitigate overloading or underutilization of individual experts, we further design a load-balancing penalty that discourages routing collapse and promotes more balanced utilization across expert branches. We evaluate DeferredSeg on multiple medical segmentation benchmarks using MedSAM and CENet as the base segmentors, and further compare it with an expert-assisted patch-correction baseline. Experimental results show that DeferredSeg consistently improves System-level segmentation performance while selectively deferring difficult pixels or regions to more reliable expert branches. Moreover, the proposed framework is backbone-compatible and can be instantiated with different segmentation architectures that provide intermediate feature representations.
To optimize the ignition and combustion performance of nanosecond pulsed surface dielectric barrier discharge (nSDBD) electrodes for NH3/air mixtures, an experimental investigation was conducted by varying the number of radial copper strips (number of conductive areas: CAN = 6, 9, 12) and width (width of conductive areas: CAW = 1 mm, 2 mm, 3 mm) on the powered electrode. Experiments were performed in a constant-volume combustion chamber under an NH3/air mixture with an initial temperature of 363 K, initial pressure of 2 bar, and an excess air ratio (lambda) of 1.0. Diagnostics were implemented using high-speed camera and pressure sensors, with nanosecond pulse parameters set to 100 pulses and a pulse repetition frequency of 20 kHz. The regulatory effects of electrode structural parameters on flame kernel development, flame propagation, and combustion characteristics were systematically analyzed. The results indicate that the CAN and CAW directly govern the flame kernel morphology and evolution by modulating the distribution of discharge energy. Under the optimal configuration of CAN = 6 and CAW = 3 mm, the electric field distribution is uniform with moderate energy density, leading to the stable generation of active free radicals (e.g., O, OH, H). Consequently, the synchronization of flame kernel ignition is maximized, with a consistent, stable number of 6 initial kernels, without obvious fusion or extinction. This configuration significantly compresses the flame development time (FDT = 8.5 ms) and flame rise time (FRT = 26.5 ms). Additionally, the combustion pressure peak occurs earliest (at 54 ms), and the cumulative heat release rate increases the fastest in the early stage. The findings demonstrate that the nSDBD electrode with CAN = 6 and CAW = 3 mm achieves efficient regulation of combustion performance in NH3/air mixtures by leveraging multi-scale synergy among "electric field distribution-energy deposition-active species generation-flame kernel development-combustion timing". This study provides critical technical parameters and theoretical support for the optimal design of ignition systems in ammonia-fueled engines.
An r-uniform hypergraph is called t-union-free if any two distinct subsets of at most t edges have distinct union. The study of union-free hypergraphs has multiple origins and a long history, dating back to the works of Kautz and Singleton (1964) in coding theory, Bollobás and Erdős (1976) in combinatorics, and Hwang and Sós (1987) in group testing. Let U_t(n,r) denote the maximum number of edges in an n-vertex t-union-free r-uniform hypergraph. In this paper, we determine the asymptotic behavior of U_t(n,r), up to a lower order term, for almost all t≥ 3 and r≥ 3. This significantly advances the understanding of this extremal function, as previously, only the asymptotics of U_2(n,3) and U_2(n,4) were known. As a key ingredient of our proof, we establish the existence of near-optimal locally sparse induced hypergraph packings, which is of independent interest.
Several sources of flexibility in transmission and, especially, distribution networks are being unlocked by advances in information and communication technologies, aggregators, and new flexibility markets. However, maximizing benefits for both transmission and distribution system operators in a coordinated way requires new algorithms, modeling tools, and modernization of regulatory frameworks. Such approaches must account for uncertainties, the physical and operational constraints of flexibility providers and the grid itself, constraints on information exchange, and scalability, including computational requirements and time constraints. Given the diverse contexts and jurisdictions around the world, there is no single recipe for achieving coordination, but important trends and shared challenges are emerging. This paper surveys the complexities of coordination from technical, market, and technological perspectives, and outlines current practices, proposed approaches, and future research directions to effectively manage, coordinate, model, and leverage flexibility across voltage levels.
