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The paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions $f(u)$ or $g(u)$, when the gradient $u_x$ of the solution is positive or negative, respectively. We study here the unstable case where $f(u)>g(u)$ for all $u\in {\mathbb R}$. Assuming that both $f$ and $g$ are strictly convex, solutions to the Riemann problem are constructed. Even for smooth initial data, examples show that infinitely many solutions can occur. For an initial data which is piecewise monotone, i.e., increasing or decreasing on a finite number of intervals, a global solution of the Cauchy problem is obtained. It is proved that such solution is unique under the additional requirement that the number of interfaces, where the flux switches between $f$ and $g$, remains as small as possible., Comment: 27 pages, 15 figures

The paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions $f(u)$ or $g(u)$, when the gradient $u_x$ of the solution is positive or negative, respectively. We study here the stable case where $f(u)

We consider a hydrodynamic model of flocking-type with all-to-all interaction kernel in a periodic domain in one-space dimension with linear pressure term. The main result is the global existence of periodic entropy weak solutions, for periodic initial data having finite total variation and initial density bounded away from zero.

Atmospheric characterization is key to understanding exoplanetary systems, offering insights into the planets current and past conditions. By analyzing key lines like H alpha and the He I triplet, we can trace the evolution of planets through atmospheric photo-evaporation. While ultra-hot Jupiters have been the focus for years, attention is shifting toward smaller, colder planets, which are more challenging to study due to weaker signals, requiring more precise techniques. This study aims to characterize the atmosphere of TOI-5398 b, a warm Saturn with a 10.59-day orbit around a young (650 Myr) G-type star. The system also hosts a smaller inner planet, TOI-5398 c, with a 4.77-day orbit. Both planets are ideal for atmospheric studies due to their proximity to the host star, which drives strong photo-evaporation, especially in planet b, whose high transmission spectroscopy metric (288) makes it a prime target. We analyzed data from a transit observed with the HARPS-N and GIANO-B high-resolution spectrographs, using cross-correlation and single-line analysis to search for atomic species. During this observation, planet c was also transiting, so we investigated the source of the signals. Based on photo-evaporation models, we attribute the signal mainly to planet b, which is expected to lose more mass. We detected H alpha and He I triplets, key markers of photo-evaporation, corresponding to atmospheric heights of 2.33 Rp and 1.65 Rp, respectively. The ATES models supported our observations, predicting a similar He I absorption for planet b and suggesting an He/H ratio of 1/99. Additionally, we detected an Na I doublet via single-line analysis, though cross-correlation did not reveal other atomic species., Comment: Accepted to A&A

Game development is a long process that involves many stages before a product is ready for the market. Human play testing is among the most time consuming, as testers are required to repeatedly perform tasks in the search for errors in the code. Therefore, automated testing is seen as a key technology for the gaming industry, as it would dramatically improve development costs and efficiency. Toward this end, we propose EVOLUTE, a novel imitation learning-based architecture that combines behavioural cloning (BC) with energy based models (EBMs). EVOLUTE is a two-stream ensemble model that splits the action space of autonomous agents into continuous and discrete tasks. The EBM stream handles the continuous tasks, to have a more refined and adaptive control, while the BC stream handles discrete actions, to ease training. We evaluate the performance of EVOLUTE in a shooting-and-driving game, where the agent is required to navigate and continuously identify targets to attack. The proposed model has higher generalisation capabilities than standard BC approaches, showing a wider range of behaviours and higher performances. Also, EVOLUTE is easier to train than a pure end-to-end EBM model, as discrete tasks can be quite sparse in the dataset and cause model training to explore a much wider set of possible actions while training.

This paper describes methods for training autonomous agents to play the game "Doom 2" through Imitation Learning (IL) using only pixel data as input. We also explore how Reinforcement Learning (RL) compares to IL for humanness by comparing camera movement and trajectory data. Through behavioural cloning, we examine the ability of individual models to learn varying behavioural traits. We attempt to mimic the behaviour of real players with different play styles, and find we can train agents that behave aggressively, passively, or simply more human-like than traditional AIs. We propose these methods of introducing more depth and human-like behaviour to agents in video games. The trained IL agents perform on par with the average players in our dataset, whilst outperforming the worst players. While performance was not as strong as common RL approaches, it provides much stronger human-like behavioural traits to the agent., Comment: 13 pages

We consider a hydrodynamic model of flocking-type with all-to-all interaction kernel in one-space dimension and establish that the global entropy weak solutions, constructed in [2] to the Cauchy problem for any $BV$ initial data that has finite total mass confined in a bounded interval and initial density uniformly positive therein, admit unconditional time-asymptotic flocking without any further assumptions on the initial data. In addition, we show that the convergence to a flocking profile occurs exponentially fast., Comment: 31 pages, 2 figures

We provide an overview of the results on Hughes' model for pedestrian movements available in the literature. After the first successful approaches to solving a regularised version of the model, researchers focused on the structure of the Riemann problem, which led to local-in-time existence results for Riemann-type data and paved the way for a WFT (Wave-Front Tracking) approach to the solution semigroup. In parallel, a DPA (Deterministic Particles Approximation) approach was developed in the spirit of follow-the-leader approximation results for scalar conservation laws. Beyond having proved to be powerful analytical tools, the WFT and the DPA approaches also led to interesting numerical results. However, only existence theorems on very specific classes of initial data (essentially ruling out non-classical shocks) have been available until very recently. A proper existence result using a DPA approach was proven not long ago in the case of a linear coupling with the density in the eikonal equation. Shortly after, a similar result was proven via a fixed point approach. We provide a detailed statement of the aforementioned results and sketch the main proofs. We also provide a brief overview of results that are related to Hughes' model, such as the derivation of a dynamic version of the model via a mean-field game strategy, an alternative optimal control approach, and a localized version of the model. We also present the main numerical results within the WFT and DPA frameworks.

Ear EEG based driver fatigue monitoring systems have the potential to provide a seamless, efficient, and feasibly deployable alternative to existing scalp EEG based systems, which are often cumbersome and impractical. However, the feasibility of detecting the relevant delta, theta, alpha, and beta band EEG activity through the ear EEG is yet to be investigated. Through measurements of scalp and ear EEG on ten subjects during a simulated, monotonous driving experiment, this study provides statistical analysis of characteristic ear EEG changes that are associated with the transition from alert to mentally fatigued states, and subsequent testing of a machine learning based automatic fatigue detection model. Novel numerical evidence is provided to support the feasibility of detection of mental fatigue with ear EEG that is in agreement with widely reported scalp EEG findings. This study paves the way for the development of ultra-wearable and readily deployable hearables based driver fatigue monitoring systems.

Wearable technologies are envisaged to provide critical support to future healthcare systems. Hearables - devices worn in the ear - are of particular interest due to their ability to provide health monitoring in an efficient, reliable and unobtrusive way. Despite the considerable potential of these devices, the ECG signal that can be acquired through a hearable device worn on a single ear is still relatively unexplored. Biophysics modelling of ECG volume conduction was used to establish principles behind the single ear ECG signal, and measurements of cardiac rhythms from 10 subjects were found to be in good correspondence with simulated equivalents. Additionally, the viability of the single ear ECG in real-world environments was determined through one hour duration measurements during a simulated driving task on 5 subjects. Results demonstrated that the single ear ECG resembles the Lead I signal, the most widely used ECG signal in the identification of heart conditions such as myocardial infarction and atrial fibrillation, and was robust against real-world measurement noise, even after prolonged measurements. This study conclusively demonstrates that hearables can enable continuous monitoring of vital signs in an unobtrusive and seamless way, with the potential for reliable identification and management of heart conditions such as myocardial infarction and atrial fibrillation.

The detection of lines in emission in planetary atmospheres provides direct evidence of temperature inversion. We confirm the trend of ultra-hot Jupiters orbiting A-type stars showing temperature inversions on their daysides, by detecting metals emission lines in the dayside of KELT-20b. We first detect the planetary emission by using the G2 stellar mask of the HARPS-N pipeline, which is mainly composed of neutral iron lines, as a template. Using neutral iron templates, we perform a retrieval of the atmospheric temperature-pressure profile of the planet, confirming a thermal inversion. Then we create models of planetary emission of different species using the retrieved inverted temperature-pressure profile. By using the cross-correlation technique, we detect FeI, FeII and CrI at signal-to-noise ratio levels of 7.1, 3.9 and 3.6, respectively. The latter is detected for the first time in emission in the atmosphere of an exoplanet. Contrary to FeI, FeII and CrI are detected only after the occultation and not before, hinting for different atmospheric properties in view on the pre- and post- occultation orbital phases. A further retrieval of the temperature-pressure profile performed independently on the pre- and post- occultation phases, while not highly significant, points to a steeper thermal inversion in the post-occultation., Comment: Accepted for publication in A&A. Submitted 27 Nov. 2021