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Intersections pose critical challenges in traffic management, where maintaining operational constraints and ensuring safety are essential for efficient flow. This paper investigates the effect of intervention timing in management strategies on maintaining operational constraints at intersections while ensuring safe separation distance, avoiding collisions, and minimizing delay. We introduce control regions, represented as circles around the intersection, which refers to the timing of interventions by a centralized control system when agents approach the intersection. We use a mixed-integer linear programming (MILP) approach to optimize the system's performance. To analyze the effectiveness of early and late control measures, a simulation study is conducted, focusing on the safe, efficient, and robust management of agent movement within the control regions.

With advancements in technology, commercial aircraft formation flying is becoming increasingly feasible as an efficient and environmentally friendly flight method. However, gaps remain in practical implementation, particularly in collision avoidance for aircraft formations. Existing avoidance algorithms mainly focus on single aircraft or UAV swarms, lacking comprehensive studies on the complex interactions within commercial aircraft formations. To address this, this paper proposes an optimization model designed to generate safe and effective collision avoidance solutions for commercial aircraft formations. This model demonstrates avoidance paths for formations facing intruders and offers insights for developing formation flight strategies. This study explores response strategies for commercial aircraft formations encountering intruders, considering the difficulty of pilot maneuvers. The findings provide theoretical support for the practical implementation of commercial formation flying and may advance the adoption of this technology.

Recent evidence supporting reionisation ending at redshift z<6 includes the rapid redshift evolution of the mean free path for Lyman-limit photons through the intergalactic medium at 510 discovered with JWST., Comment: 17 pages, 14 figures, accepted to MNRAS

Electricity price forecasting (EPF) plays a major role for electricity companies as a fundamental entry for trading decisions or energy management operations. As electricity can not be stored, electricity prices are highly volatile which make EPF a particularly difficult task. This is all the more true when dramatic fortuitous events disrupt the markets. Trading and more generally energy management decisions require risk management tools which are based on probabilistic EPF (PEPF). In this challenging context, we argue in favor of the deployment of highly adaptive black-boxes strategies allowing to turn any forecasts into a robust adaptive predictive interval, such as conformal prediction and online aggregation, as a fundamental last layer of any operational pipeline. We propose to investigate a novel data set containing the French electricity spot prices during the turbulent 2020-2021 years, and build a new explanatory feature revealing high predictive power, namely the nuclear availability. Benchmarking state-of-the-art PEPF on this data set highlights the difficulty of choosing a given model, as they all behave very differently in practice, and none of them is reliable. However, we propose an adequate conformalisation, OSSCP-horizon, that improves the performances of PEPF methods, even in the most hazardous period of late 2021. Finally, we emphasize that combining it with online aggregation significantly outperforms any other approaches, and should be the preferred pipeline, as it provides trustworthy probabilistic forecasts.

Advanced machine learning algorithms require platforms that are extremely robust and equipped with rich sensory feedback to handle extensive trial-and-error learning without relying on strong inductive biases. Traditional robotic designs, while well-suited for their specific use cases, are often fragile when used with these algorithms. To address this gap -- and inspired by the vision of enabling curiosity-driven baby robots -- we present a novel robotic limb designed from scratch. Our design has a hybrid soft-hard structure, high redundancy with rich non-contact sensors (exclusively cameras), and easily replaceable failure points. Proof-of-concept experiments using two contemporary reinforcement learning algorithms on a physical prototype demonstrate that our design is able to succeed in a simple target-finding task even under simulated sensor failures, all with minimal human oversight during extended learning periods. We believe this design represents a concrete step toward more tailored robotic designs for achieving general-purpose, generally intelligent robots., Comment: 6 pages in main text + 2 pages of references, 8 figures in main text, 1 table in main text; source code available at https://github.com/dylanashley/robot-limb-testai

We introduce a new class of quadratic functions based on a hierarchy of linear time-varying (LTV) dynamical systems. These quadratic functions in the higher order space can be also seen as a non-homogeneous polynomial Lyapunov functions for the original system, i.e the first system in the hierarchy. These non-homogeneous polynomials are used to obtain accurate outer approximation for the reachable set given the initial condition and less conservative bounds for the impulse response peak of linear, possibly time-varying systems. In addition, we pose an extension to the presented approach to construct invariant sets that are not necessarily Lyapunov functions. The introduced methods are based on elementary linear systems theory and offer very much flexibility in defining arbitrary polynomial Lyapunov functions and invariant sets for LTV systems.

A method for constructing homogeneous Lyapunov functions of degree 1 from polynomial invariant sets is presented for linear time varying systems, homogeneous dynamic systems and the class of nonlinear systems that can be represented as such. The method allows the development of Lyapunov functions that are not necessarily symmetric about the origin, unlike the polynomial, homogeneous Lyapunov functions discussed in the prior literature. The work is illustrated by very simple examples.

High-$Q$ whispering gallery mode microresonators are cornerstones to develop compact coherent sources like single frequency lasers or frequency combs. This work reports a detailed characterization of a whispering gallery mode microsphere in the near ultraviolet. Light coupling in the resonator is obtain thanks to a robust angle-polished fiber allowing to investigate the different coupling regimes. An intrinsic $Q_0$-factor of $2.2 \times 10^8$ and a finesse of $7.3 \times 10^4$ are reported at a wavelength of 420 nm. Physical mechanisms contributing to the $Q_0$-factor are discussed and routes to improve the performances are drawn. Such high-$Q$ factor and high finesse are key ingredients to ease the study of photonic devices based on WGM microresonators., Comment: 6 pages, 6 figures

Introductory state-space linear control courses focus on linear, time-invariant systems and spend intense efforts by introducing system realizations that allow the student to grasp fundamental concepts, among which controllability, observability, and controller and observer design. This note describes a graphical mechanism to transform a system expressed in observability form into its observer form based on elementary block diagram manipulations, a technique whose pedagogical usefulness tends to be overlooked. Given the well-known duality principle in linear systems with respect to controllability and observability, the proposed graphical mechanism is applicable to transform from controllability to controller realization., Comment: 18 pages, 6 figures, 6 tables

Quadratic Lyapunov function has been widely used in the analysis of linear time invariant (LTI) systems ever since it has shown that the existence of such quadratic Lyapunov function certifies the stability of the LTI system. In this work, the problem of finding upper and lower bounds for the $L_{\infty}$-induced norm of the LTI system is considered. Quadratic Lyapunov functions are used to find the star norm, the best upper on the $L_{\infty}$-induced norm, by bounding the unit peak input reachable sets by inescapable ellipsoids. Instead, a more general class of homogeneous Lyapunov functions is used to get less conservative upper bounds on the $L_{\infty}$-induced norm and better conservative approximations for the reachable sets than those obtained using standard quadratic Lyapunov functions. The homogeneous Lyapunov function for the LTI system is considered to be a quadratic Lyapunov function for a higher-order system obtained by Lifting the LTI system via Kronecker product. Different examples are provided to show the significant improvements on the bounds obtained by using Homogeneous Lyapunov functions.

Uncertainty quantification of predictive models is crucial in decision-making problems. Conformal prediction is a general and theoretically sound answer. However, it requires exchangeable data, excluding time series. While recent works tackled this issue, we argue that Adaptive Conformal Inference (ACI, Gibbs and Cand{\`e}s, 2021), developed for distribution-shift time series, is a good procedure for time series with general dependency. We theoretically analyse the impact of the learning rate on its efficiency in the exchangeable and auto-regressive case. We propose a parameter-free method, AgACI, that adaptively builds upon ACI based on online expert aggregation. We lead extensive fair simulations against competing methods that advocate for ACI's use in time series. We conduct a real case study: electricity price forecasting. The proposed aggregation algorithm provides efficient prediction intervals for day-ahead forecasting. All the code and data to reproduce the experiments is made available.