UAV swarms have emerged as transformative systems for complex missions including wildfire surveillance ( Julian and Kochenderfer 2019), intelligence surveillance and reconnaissance ( Kolar 2020), situational awareness ( Scharre 2018), and cooperative interception ( Balhance et al. 2017). In these applications, trajectory optimization is the cornerstone for ensuring both mission success and operational s afety ( Sezer 2022; Qian et al. 2020; Sanchez-Lopez et al. 2020). Over the past decade, trajectory optimization techniques hav e evolved from sophisticated single-agent formulations to distributed multi-agent frameworks, driven by the increasing scale and complexity of swarm-based missions ( Saravanos et al. 2023). For individual UAV trajectory optimization, a variety of numerical m ethods have demonstrated strong performance. Pseudospectral methods achieve high-accuracy solution s by discretizing continuous-time problems ( Chai et al. 2017), while sequential quadratic programming (SQP) ( Hong et al. 2021) and sequential convex programming (SCP) ( Deligiannis et al. 2019) provide flexible tools for handling nonlinear dynamics and constraint s.

Contemporary machine learning models, including large language models, exhibit remarkable capabilities in static tasks yet falter in non-stationary environments due to rigid architectures that hinder continual adaptation and lifelong learning. Building upon the nested learning paradigm, which decomposes models into multi-level optimization problems with fixed update frequencies, this work proposes dynamic nested hierarchies as the next evolutionary step in advancing artificial intelligence and machine learning. Dynamic nested hierarchies empower models to autonomously adjust the number of optimization levels, their nesting structures, and update frequencies during training or inference, inspired by neuroplasticity to enable self-evolution without predefined constraints. This innovation addresses the anterograde amnesia in existing models, facilitating true lifelong learning by dynamically compressing context flows and adapting to distribution shifts. Through rigorous mathematical formulations, theoretical proofs of convergence, expressivity bounds, and sublinear regret in varying regimes, alongside empirical demonstrations of superior performance in language modeling, continual learning, and long-context reasoning, dynamic nested hierarchies establish a foundational advancement toward adaptive, general-purpose intelligence.

The advent of smart manufacturing is addressing the limitations of traditional centralized scheduling and inflexible production line configurations in the rubber tyre industry, especially in terms of coping with dynamic production demands. Contemporary tyre manufacturing systems form complex networks of tightly coupled subsystems pronounced nonlinear interactions and emergent dynamics. This complexity renders the effective coordination of multiple subsystems, posing an essential yet formidable task. For high-dimensional, multi-objective optimization problems in this domain, we introduce a deep reinforcement learning algorithm: Multi-path Differentiated Clipping Proximal Policy Optimization (MPD-PPO). This algorithm employs a multi-branch policy architecture with differentiated gradient clipping constraints to ensure stable and efficient high-dimensional policy updates. Validated through experiments on width and thickness control in rubber tyre film production, MPD-PPO demonstrates substantial improvements in both tuning accuracy and operational efficiency. The framework successfully tackles key challenges, including high dimensionality, multi-objective trade-offs, and dynamic adaptation, thus delivering enhanced performance and production stability for real-time industrial deployment in tyre manufacturing.

Shot assembly is a crucial step in film production and video editing, involving the sequencing and arrangement of shots to construct a narrative, convey information, or evoke emotions. Traditionally, this process has been manually executed by experienced editors. While current intelligent video editing technologies can handle some automated video editing tasks, they often fail to capture the creator's unique artistic expression in shot assembly. To address this challenge, we propose an energy-based optimization method for video shot assembly. Specifically, we first perform visual-semantic matching between the script generated by a large language model and a video library to obtain subsets of candidate shots aligned with the script semantics. Next, we segment and label the shots from reference videos, extracting attributes such as shot size, camera motion, and semantics. We then employ energy-based models to learn from these attributes, scoring candidate shot sequences based on their alignment with reference styles. Finally, we achieve shot assembly optimization by combining multiple syntax rules, producing videos that align with the assembly style of the reference videos. Our method not only automates the arrangement and combination of independent shots according to specific logic, narrative requirements, or artistic styles but also learns the assembly style of reference videos, creating a coherent visual sequence or holistic visual expression. With our system, even users with no prior video editing experience can create visually compelling videos. Project page: https://sobeymil.github.io/esa.com

Inverse problems lie at the heart of modern imaging science, with broad applications in areas such as medical imaging, remote sensing, and microscopy. Recent years have witnessed a paradigm shift in solving imaging inverse problems, where data-driven regularizers are used increasingly, leading to remarkably high-fidelity reconstruction. A particularly notable approach for data-driven regularization is to use learned image denoisers as implicit priors in iterative image reconstruction algorithms. This chapter presents a comprehensive overview of this powerful and emerging class of algorithms, commonly referred to as plug-and-play (PnP) methods. We begin by providing a brief background on image denoising and inverse problems, followed by a short review of traditional regularization strategies. We then explore how proximal splitting algorithms, such as the alternating direction method of multipliers (ADMM) and proximal gradient descent (PGD), can naturally accommodate learned denoisers in place of proximal operators, and under what conditions such replacements preserve convergence. The role of Tweedie's formula in connecting optimal Gaussian denoisers and score estimation is discussed, which lays the foundation for regularization-by-denoising (RED) and more recent diffusion-based posterior sampling methods. We discuss theoretical advances regarding the convergence of PnP algorithms, both within the RED and proximal settings, emphasizing the structural assumptions that the denoiser must satisfy for convergence, such as non-expansiveness, Lipschitz continuity, and local homogeneity. We also address practical considerations in algorithm design, including choices of denoiser architecture and acceleration strategies.

Ordinary differential equations (ODEs) are a conventional way to describe the observed dynamics of physical systems. Scientists typically hypothesize about dynamical behavior, propose a mathematical model, and compare its predictions to data. However, modern computing and algorithmic advances now enable purely data-driven learning of governing dynamics directly from observations. In data-driven settings, one learns the ODE's right-hand side (RHS). Dense measurements are often assumed, yet high temporal resolution is typically both cumbersome and expensive. Consequently, one usually has only sparsely sampled data. In this work we introduce ChaosODE (CODE), a Polynomial Chaos ODE Expansion in which we use an arbitrary Polynomial Chaos Expansion (aPCE) for the ODE's right-hand side, resulting in a global orthonormal polynomial representation of dynamics. We evaluate the performance of CODE in several experiments on the Lotka-Volterra system, across varying noise levels, initial conditions, and predictions far into the future, even on previously unseen initial conditions. CODE exhibits remarkable extrapolation capabilities even when evaluated under novel initial conditions and shows advantages compared to well-examined methods using neural networks (NeuralODE) or kernel approximators (KernelODE) as the RHS representer. We observe that the high flexibility of NeuralODE and KernelODE degrades extrapolation capabilities under scarce data and measurement noise. Finally, we provide practical guidelines for robust optimization of dynamics-learning problems and illustrate them in the accompanying code.

This paper presents a tractable algorithm for estimating an unknown Lipschitz function from noisy observations and establishes an upper bound on its convergence rate. The approach extends max-affine methods from convex shape-restricted regression to the more general Lipschitz setting. A key component is a nonlinear feature expansion that maps max-affine functions into a subclass of delta-convex functions, which act as universal ap-proximators of Lipschitz functions while preserving their Lipschitz constants. Leveraging this property, the estimator attains the minimax convergence rate (up to logarithmic factors) with respect to the intrinsic dimension of the data under squared loss and subgaussian distributions in the random design setting. The algorithm integrates adaptive partitioning to capture intrinsic dimension, a penalty-based regularization mechanism that removes the need to know the true Lipschitz constant, and a two-stage optimization procedure combining a convex initialization with local refinement. The framework is also straightforward to adapt to convex shape-restricted regression. Experiments demonstrate competitive performance relative to other theoretically justified methods, including nearest-neighbor and kernel-based regressors.

Appendix E), the variance across multiple runs is negligible, hence the ribbons are not observable.