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Motivated by a vaccination coverage problem, we consider here a zero-sum differential game governed by a differential system consisting of a hyperbolic partial differential equation (PDE) and an ordinary differential equation (ODE). Two players act through their respective controls to influence the evolution of the system with the aim of minimizing their objective functionals $\mathcal F_1$ and $\mathcal F_2$, under the assumption that $\mathcal F_1 +\mathcal F_2 = 0$. First we prove a well posedness and a stability result for the differential system, once the control functions are fixed. Then we introduce the concept of non-anticipating strategies for both players and we consider the associated value functions, which solve two infinite-dimensional Hamilton-Jacobi-Isaacs equations in the viscosity sense.

We report on the nonlinear temporal post-compression of 7 mJ sub-40 fs pulses from a commercial kHz Ti:Sapphire laser down to a record 4 fs duration (1.5 optical cycle) in a compact single-stage gas-filled multipass cell, with 60% overall compression efficiency.

We present two multilingual LLMs designed to embrace Europe's linguistic diversity by supporting all 24 official languages of the European Union. Trained on a dataset comprising around 60% non-English data and utilizing a custom multilingual tokenizer, our models address the limitations of existing LLMs that predominantly focus on English or a few high-resource languages. We detail the models' development principles, i.e., data composition, tokenizer optimization, and training methodologies. The models demonstrate competitive performance across multilingual benchmarks, as evidenced by their performance on European versions of ARC, HellaSwag, MMLU, and TruthfulQA.

Citizen science offers an opportunity for ordinary people, known as citizen scientists or citizen astronomers in the context of astronomy, to contribute to scientific research. The Pan-African Citizen Science e-Lab (PACS e-Lab) was founded to promote and engage the African public in citizen science and soft astronomy research to advance space research and exploration and enhance space education and outreach. PACS e-Lab, in collaboration with several international astronomy research, education, and outreach organizations, currently runs several projects including but not limited to asteroid search, exoplanet photometry, research writing for peer-reviewed publications, astrophoto visual development, and Amateur Radio contact with astronauts aboard the International Space Station (ARISS). Despite several challenges, the group has engaged over 600 Africans from more than 40 countries and is working towards covering the entire continent in the future. PACS e-Lab's development efforts resonate with seven United Nations Sustainable Development Goals (UN-SDGs)., Comment: 32 pages,17 figures, 2 Tables

Asteroid search is a global effort for planetary defense. The International Astronomical Search Collaboration (IASC) is the leading global educational outreach program that provides high-quality astronomical datasets to citizen scientists to discover asteroids. Since December 4, 2020, the Pan-African Citizen Science e-Lab (PACS e-Lab) has been IASC's biggest partner on the continent in recruiting and training citizen scientists in asteroid search endeavors. Over 30 asteroids have been discovered by 60 citizen scientists. About 595 citizen scientists from over 40 countries have been engaged in the project up to the time of composing this literature. The group is set to expand its endeavors to the rest of the continent and aims to engage thousands of citizen scientists., Comment: 16 pages, 10 figures, 5 Tables

We propose a mathematical framework to the study of scalar conservation laws with moving interfaces. This framework is developed on a LWR model with constraint on the flux along these moving interfaces. Existence is proved by means of a finite volume scheme. The originality lies in the local modification of the mesh and in the treatment of the crossing points of the trajectories.

We build a finite volume scheme for the scalar conservation law $\partial_t u + \partial_x (H(x, u)) = 0$ with bounded initial condition for a wide class of flux function $H$, convex with respect to the second variable. The main idea for the construction of the scheme is to use the theory of discontinuous flux. We prove that the resulting approximating sequence converges boundedly almost everywhere on $\mathopen]0, +\infty\mathclose[$ to the entropy solution.

In this paper, we propose a macroscopic model that describes the influence of a slow moving large vehicle on road traffic. The model consists of a scalar conservation law with a non-local constraint on the flux. The constraint level depends on the trajectory of the slower vehicle which is given by an ODE depending on the downstream traffic density. After proving well-posedness, we first build a finite volume scheme and prove its convergence, and then investigate numerically this model by performing a series of tests. In particular, the link with the limit local problem of [M. L. Delle Monache and P. Goatin, J. Differ. Equ. 257 (2014), 4015--4029] is explored numerically.

Multi-pass cell (MPC) compressors have proven to be the method of choice for compression of high average power long-pulse Yb lasers. Yet, generating sub-30 fs pulses at high pulse energy with compact and simple components remains a challenge. This work demonstrates an efficient and cost-effective approach for nonlinear pulse compression at high pulse energy using a hybrid air-bulk MPC. By carefully balancing the relative nonlinear contributions of ambient air and fused silica, we achieve strong spectral broadening without dispersion engineering or pressure-control inside the cell at 400 uJ pulse energy. In this way, we compress pulses from 220 fs to 27 fs at 40.3 W of average power (100 kHz repetition rate), enhancing the peak power from 1.6 GW to 10.2 GW while maintaining 78% of the energy within the main pulse. Our approach combines the strengths of gas-filled and bulk compression schemes and exhibits excellent overall optical transmission (91%) and spectral uniformity. Moreover, we utilize the INSIGHT technique to investigate spatio-temporal couplings and geometrical aberrations of the compressed pulse. Our results demonstrate remarkable temporal homogeneity, with an average Strehl ratio of 0.97 consistently observed throughout the entire spectral profile. Additionally, all spectrally-integrated Zernike coefficients for geometrical aberrations maintain values below 0.02{\lambda}.

We present a non-reactive force field for molecular dynamics simulations of interfaces between passivated amorphous surfaces and their interaction with water. The force field enables large-scale dynamic simulations of dry and lubricated tribological contacts and is tailored to surfaces with hydrogen, hydroxyl and aromatic surface passivation. To favour its compatibility with existing force-field parameterizations for liquids and allow a straightforward extension to other types of surface passivation species, we adopt the commonly used OPLS functional form. The optimisation of the force-field parameters is systematic and follows a protocol that can be reused for other surface-molecule combinations. Reference data are calculated with gradient- and dispersion-corrected density functional theory and include the bonding structure and elastic deformation of bulk and surface structures as well as surface adhesion and water adsorption energy landscapes. The conventions adopted to define the different force-field atom types are based on the hybridisation of carbon orbitals and enable a simple and efficient parameter optimisation strategy based on quantum-mechanical calculations performed only on crystalline reference structures. Transferability tests on amorphous interfaces demonstrate the effectiveness of this approach. After testing the force field, we present two examples of application to tribological problems. Namely, we investigate relationships between dry friction and the corrugation of the contact potential energy surface and the dependency of friction on the thickness of interface water films. We finally discuss the limitations of the force field and propose strategies for its improvement and extension.

Recently, results regarding the Inverse Design problem for Conservation Laws and Hamilton-Jacobi equations with space-dependent convex fluxes were obtaine. More precisely, characterizations of attainable sets and the set of initialdata evolving at a prescribed time into a prescribed profile were obtained. Here, wepresent an explicit example that underlines deep diff erences between the space-dependentand space-independent cases. Moreover, we add a detailed analysis of the time asymptoticsolution of this example, again underlining diff erences with the space-independent case., Comment: arXiv admin note: text overlap with arXiv:2304.05092

This white paper was written by the members of the Work Group focusing on design practices of the COST Action 18230 - Interactive Narrative Design for Complexity Representation (INDCOR, WG1). It presents an overview of Interactive Digital Narratives (IDNs) design for complexity representations through IDN workflows and methodologies, IDN authoring tools and applications. It provides definitions of the central elements of the IDN alongside its best practices, designs and methods. Finally, it describes complexity as a feature of IDN, with related examples. In summary, this white paper serves as an orienting map for the field of IDN design, understanding where we are in the contemporary panorama while charting the grounds of their promising futures., Comment: 11 pages, This whitepaper was produced by members of the COST Action 18230 - Interactive Narrative Design for Complexity Representation (INDCOR - https://indcor.eu)

Consider a Conservation Law and a Hamilton-Jacobi equation with a ux/Hamiltonian depending also on the space variable. We characterize rst the attainable set of the two equations and, second, the set of initial data evolving at a prescribed time into a prescribed prole. An explicit example then shows the deep dierences between the cases of x-independent and x-dependent uxes/Hamiltonians.