Let $\Omega\subset\mathbb{R}^N$, $N\geq 1$, be an open bounded connected set. We consider the indefinite weighted eigenvalue problem $-\Delta u =\lambda m u$ in Ω with $\lambda \in \mathbb{R}$, $m\in L^\infty(\Omega)$ and with homogeneous Neumann boundary conditions. We study weak* continuity, convexity and Gâteaux differentiability of the map $m\mapsto1/\lambda_1(m)$, where $\lambda_1(m)$ is the principal eigenvalue. Then, denoting by $\mathcal{G}(m_0)$ the class of rearrangements of a fixed weight m0, under the assumptions that m0 is positive on a set of positive Lebesgue measure and $\int_\Omega m_0\,dx \lt 0$, we prove the existence and a characterization of minimizers of $\lambda_1(m)$ and the non-existence of maximizers. Finally, we show that, if Ω is a cylinder, then every minimizer is monotone with respect to the direction of the generatrix. In the context of the population dynamics, this kind of problems arise from the question of determining the optimal spatial location of favourable and unfavourable habitats for a population to survive.

The assessment of soil–structure interaction (SSI) under dynamic loading conditions remains a challenging task due to the complexities of modeling this system and the interplay of SSI effects, which is also characterized by uncertainties across varying loading scenarios. This field of research encompasses a wide range of engineering structures, including underground tunnels. In this study, a surrogate model based on a regression ensemble model has been developed for real-time assessment of underground tunnels under dynamic loads. The surrogate model utilizes synthetic data generated using Latin hypercube sampling, significantly reducing the required dataset size while maintaining accuracy. The synthetic dataset is constructed using an accurate numerical model that integrates the two-and-a-half-dimensional singular boundary method for modeling wave propagation in the soil with the finite element method for structural modeling. This hybrid approach allows for a precise representation of the dynamic interaction between tunnels and the surrounding soil. The validation and optimization algorithms are evaluated for two problems: underground railway tunnels with circular and rectangular cross-sections, both embedded in a homogenous full-space medium. Both geometrical and material characteristics of the underground tunnel are incorporated into the optimization process. The optimization target is to minimize elastic wave propagation in the surrounding soil. The results demonstrate that the proposed optimization framework, which combines the Bayesian optimization algorithm with surrogate models, effectively explores trade-offs among multiple design parameters. This enables the design of underground railway tunnels that achieve an optimal balance between elastic wave propagation performance, material properties, and geometric constraints.

Maintaining high-complexity aircraft requires resilient and data-driven maintenance planning. This article presents the efficient task allocation and packing problem solver (ETTAPS), a novel framework that integrates predictive analytics and optimisation models to generate adaptive maintenance schedules. ETTAPS employs a trial-and-error approach to optimise maintenance intervals, leveraging a branch-and-cut solver combined with first-fit decreasing (FFD) task grouping to minimise costs and enhance aircraft availability. Additionally, a random forest model, retrained using a rolling 24-month data window, continuously refines predictions, leading to progressive cost reductions and improved system reliability over multiple maintenance cycles. Our results demonstrate that ETTAPS significantly reduces maintenance costs and increases aircraft availability by efficiently grouping tasks and incorporating real-world constraints, such as mechanic skill levels, task dependencies and resource limitations. The framework addresses key gaps in MSG-3 and certification analysis, improving task scheduling efficiency and ensuring long-term operational resilience. Furthermore, ETTAPS lays the groundwork for integration with digital twins, real-time anomaly detection and flight planning systems, supporting a more intelligent and proactive approach to aircraft maintenance. This research advances resilience and sustainable aviation maintenance planning by optimising costs, reducing downtime and proactively adapting to operational demands. By aligning with Industry 4.0 and aviation sustainability goals for 2050, ETTAPS contributes to the next generation of intelligent maintenance systems.

The proportional–integral–derivative (PID) controller remains widely used in industrial applications today due to its simplicity and ease of implementation. However, tuning the controller’s gains is crucial for achieving desired performance. This study compares the performance of PID controllers within a cascade control architecture designed for both position and attitude control of a quadcopter. Particle swarm optimisation (PSO), grey wolf optimisation (GWO), artificial bee colony (ABC), and differential evaluation (DE) methods are employed to optimally tune the PID parameters. A set of PID gains is determined offline by minimising various modified multi-objective functions based on different fitness measures: IAE, ISE, ITAE and ITSE. These measures are adapted as fitness functions for position and attitude control. A simulation study is conducted to determine which fitness function yields the optimal PID gains, as evidenced by the lowest values of the objective functions. In these simulations, two different desired trajectories are designed, and the controllers are applied to ensure the quadcopter tracks these trajectories accurately. Additionally, to test the robustness of the flight control architecture and the finely tuned PID controllers against various environmental effects and parametric uncertainties, several case scenarios are also explored.

While researchers often study message features like moral content in text, such as party manifestos and social media posts, their quantification remains a challenge. Conventional human coding struggles with scalability and intercoder reliability. While dictionary-based methods are cost-effective and computationally efficient, they often lack contextual sensitivity and are limited by the vocabularies developed for the original applications. In this paper, we present an approach to construct “vec-tionaries” that boost validated dictionaries with word embeddings through nonlinear optimization. By harnessing semantic relationships encoded by embeddings, vec-tionaries improve the measurement of message features from text, especially those in short format, by expanding the applicability of original vocabularies to other contexts. Importantly, a vec-tionary can produce additional metrics to capture the valence and ambivalence of a message feature beyond its strength in texts. Using moral content in tweets as a case study, we illustrate the steps to construct the moral foundations vec-tionary, showcasing its ability to process texts missed by conventional dictionaries and to produce measurements better aligned with crowdsourced human assessments. Furthermore, additional metrics from the vec-tionary unveiled unique insights that facilitated predicting downstream outcomes such as message retransmission.

Minimizing an adversarial surrogate risk is a common technique for learning robust classifiers. Prior work showed that convex surrogate losses are not statistically consistent in the adversarial context – or in other words, a minimizing sequence of the adversarial surrogate risk will not necessarily minimize the adversarial classification error. We connect the consistency of adversarial surrogate losses to properties of minimizers to the adversarial classification risk, known as adversarial Bayes classifiers. Specifically, under reasonable distributional assumptions, a convex surrogate loss is statistically consistent for adversarial learning iff the adversarial Bayes classifier satisfies a certain notion of uniqueness.

The muscular restructuring and loss of function that occurs during a transfemoral amputation surgery has a great impact on the gait and mobility of the individual. The hip of the residual limb adopts a number of functional roles that would previously be controlled by lower joints. In the absence of active plantar flexors, swing initiation must be achieved through an increased hip flexion moment. The high activity of the residual limb is a major contributor to the discomfort and fatigue experienced by individuals with transfemoral amputations during walking. In other patient populations, both passive and active hip exosuits have been shown to positively affect gait mechanics. We believe an exosuit configured to aid with hip flexion could be well applied to individuals with transfemoral amputation. In this article, we model the effects of such a device during whole-body, subject-specific kinematic simulations of level ground walking. The device is simulated for 18 individuals of K2 and K3 Medicare functional classification levels. A user-specific device profile is generated via a three-axis moment-matching optimization using an interior-point algorithm. We employ two related cost functions that reflect an active and passive form of the device. We hypothesized that the optimal device configuration would be highly variable across subjects but that variance within mobility groups would be lower. From the results, we partially accept this hypothesis, as some parameters had high variance across subjects. However, variance did not consistently trend down when dividing into mobility groups, highlighting the need for user-specific design.