On the one side, the formalism of Global Transformations comes with the claim of capturing any transformation of space that is local, synchronous and deterministic. The claim has been proven for different classes of models such as mesh refinements from computer graphics, Lindenmayer systems from morphogenesis modeling and cellular automata from biological, physical and parallel computation modeling. The Global Transformation formalism achieves this by using category theory for its genericity, and more precisely the notion of Kan extension to determine the global behaviors based on the local ones. On the other side, Causal Graph Dynamics describe the transformation of port graphs in a synchronous and deterministic way and has not yet being tackled. In this paper, we show the precise sense in which the claim of Global Transformations holds for them as well. This is done by showing different ways in which they can be expressed as Kan extensions, each of them highlighting different features of Causal Graph Dynamics. Along the way, this work uncovers the interesting class of Monotonic Causal Graph Dynamics and their universality among General Causal Graph Dynamics.

This white paper explores the potential for strategic synergies between the JWST and the Ariel telescopes, two flagship observatories poised to revolutionise the study of exoplanet atmospheres. Both telescopes have the potential to address common fundamental questions about exoplanets-especially concerning their nature and origins-and serve a growing scientific community. With their operations now anticipated to overlap, starting from 2030, there is a unique opportunity to enhance the scientific outputs of both observatories through coordinated efforts. In this report, authored by the Ariel-JWST Synergy Working Group, part of the Ariel Consortium Science Team, we summarise the capabilities of JWST and Ariel; we highlight their key differences, similarities, synergies, and distinctive strengths. Ariel is designed to conduct a broad survey of exoplanet atmospheres but remains highly flexible, allowing the mission to integrate insights from JWST's discoveries. Findings from JWST, including data from initiatives shaped by NASA's decadal survey priorities and community-driven research themes, will inform the development of Ariel's core survey strategy. Conversely, Ariel's ability to perform broad-wavelength coverage observations for bright targets provides complementary avenues for exoplanet researchers, particularly those interested in time-domain observations and large-scale atmospheric studies. This paper identifies key pathways for fostering JWST-Ariel synergies, many of which can be initiated even before Ariel's launch. Leveraging their complementary designs and scopes, JWST and Ariel can jointly address fundamental questions about the nature, formation, and evolution of exoplanets. Such strategic collaboration has the potential to maximise the scientific returns of both observatories and lay the foundation for future facilities in the roadmap to exoplanet exploration.

The Commission Femmes et Astronomie of the French Astronomical Society, has conducted a statistical study aimed at mapping the current presence of women in French professional astronomy and establishing a baseline for tracking its evolution over time. This study follows an initial survey carried out in 2021, which covered eight astronomy and astrophysics institutes (1,060 employees). This year, the scope was expanded to 11 institutes, bringing together a total of 1,525 employees, including PhD students, postdoctoral researchers, academics, as well as technical and administrative staff, representing about 57% of the whole French community. We examined how the proportion of women varies according to career stage, level of responsibility, job security, and income. The results are compared to the 2021-2022 survey and appear to illustrate the well-known "leaky pipeline", with one of the main bottlenecks being access to permanent positions. The study shows that the proportion of women consistently declines with increasing job security, career seniority, qualification level, and salary.

In the mathematical tradition, reversibility requires that the evolution of a dynamical system be a bijective function. In the context of graph rewriting, however, the evolution is not even a function, because it is not even deterministic -- as the rewrite rules get applied at non-deterministically chosen locations. Physics, by contrast, suggests a more flexible understanding of reversibility in space-time, whereby any two closeby snapshots (aka `space-like cuts'), must mutually determine each other. We build upon the recently developed framework of space-time deterministic graph rewriting, in order to formalise this notion of space-time reversibility, and henceforth study reversible graph rewriting. We establish sufficient, local conditions on the rewrite rules so that they be space-time reversible. We provide an example featuring time dilation, in the spirit of general relativity.

The notion of Laplacian of a graph can be generalized to simplicial complexes and hypergraphs, and contains information on the topology of these structures. Even for a graph, the consideration of associated simplicial complexes is interesting to understand its shape. Whereas the Laplacian of a graph has a simple probabilistic interpretation as the generator of a continuous time Markov chain on the graph, things are not so direct when considering simplicial complexes. We define here new Markov chains on simplicial complexes. For a given order~$k$, the state space is the set of $k$-cycles that are chains of $k$-simplexes with null boundary. This new framework is a natural generalization of the canonical Markov chains on graphs. We show that the generator of our Markov chain is the upper Laplacian defined in the context of algebraic topology for discrete structure. We establish several key properties of this new process: in particular, when the number of vertices is finite, the Markov chain is positive recurrent. This result is not trivial, since the cycles can loop over themselves an unbounded number of times. We study the diffusive limits when the simplicial complexes under scrutiny are a sequence of ever refining triangulations of the flat torus. Using the analogy between singular and Hodge homologies, we express this limit as valued in the set of currents. The proof of tightness and the identification of the limiting martingale problem make use of the flat norm and carefully controls of the error terms in the convergence of the generator. Uniqueness of the solution to the martingale problem is left open. An application to hole detection is carried.

In this paper, we propose an approach for Facial Expressions Recognition (FER) based on a deep multi-facial patches aggregation network. Deep features are learned from facial patches using deep sub-networks and aggregated within one deep architecture for expression classification . Several problems may affect the performance of deep-learning based FER approaches, in particular, the small size of existing FER datasets which might not be sufficient to train large deep learning networks. Moreover, it is extremely time-consuming to collect and annotate a large number of facial images. To account for this, we propose two data augmentation techniques for facial expression generation to expand FER labeled training datasets. We evaluate the proposed framework on three FER datasets. Results show that the proposed approach achieves state-of-art FER deep learning approaches performance when the model is trained and tested on images from the same dataset. Moreover, the proposed data augmentation techniques improve the expression recognition rate, and thus can be a solution for training deep learning FER models using small datasets. The accuracy degrades significantly when testing for dataset bias.

Activated Random Walks, on $\mathbb{Z}^d$ for any $d\geqslant 1$, is an interacting particle system, where particles can be in either of two states: active or frozen. Each active particle performs a continuous-time simple random walk during an exponential time of parameter $\lambda$, after which it stays still in the frozen state, until another active particle shares its location, and turns it instantaneously back into activity. This model is known to have a phase transition, and we show that the critical density, controlling the phase transition, is less than one in any dimension and for any value of the sleep rate $\lambda$. We provide upper bounds for the critical density in both the small $\lambda$ and large $\lambda$ regimes.

We consider a pure-jump stable Cox-Ingersoll-Ross ($\alpha$-stable CIR) process driven by a non-symmetric stable L{\'e}vy process with jump activity $\alpha$ $\in$ (1, 2) and we address the joint estimation of drift, scaling and jump activity parameters from high-frequency observations of the process on a fixed time period. We first prove the existence of a consistent, rate optimal and asymptotically conditionally gaussian estimator based on an approximation of the likelihood function. Moreover, uniqueness of the drift estimators is established assuming that the scaling coefficient and the jump activity are known or consistently estimated. Next we propose easy-toimplement preliminary estimators of all parameters and we improve them by a one-step procedure.

The goal of this white paper is to provide a snapshot of the data availability and data needs primarily for the Ariel space mission, but also for related atmospheric studies of exoplanets and brown dwarfs. It covers the following data-related topics: molecular and atomic line lists, line profiles, computed cross-sections and opacities, collision-induced absorption and other continuum data, optical properties of aerosols and surfaces, atmospheric chemistry, UV photodissociation and photoabsorption cross-sections, and standards in the description and format of such data. These data aspects are discussed by addressing the following questions for each topic, based on the experience of the "data-provider" and "data-user" communities: (1) what are the types and sources of currently available data, (2) what work is currently in progress, and (3) what are the current and anticipated data needs. We present a GitHub platform for Ariel-related data, with the goal to provide a go-to place for both data-users and data-providers, for the users to make requests for their data needs and for the data-providers to link to their available data. Our aim throughout the paper is to provide practical information on existing sources of data whether in databases, theoretical, or literature sources.

Constraining the chemical structure of exoplanetary atmospheres is pivotal for interpreting spectroscopic data and understanding planetary evolution. Traditional retrieval methods often assume thermochemical equilibrium or free profiles, which may fail to capture disequilibrium processes like photodissociation and vertical mixing. This study leverages the TauREx 3.1 retrieval framework coupled with FRECKLL, a disequilibrium chemistry model, to address these challenges. The study aims to (1) assess the impact of disequilibrium chemistry on constraining metallicity and C/O ratios; (2) evaluate the role of refractory species (TiO and VO) in spectral retrievals; (3) explore consistency between transit and eclipse observations for temperature and chemical profiles; and (4) determine the effects of retrieval priors and data reduction methods. Ten hot-Jupiter atmospheres were reanalyzed using Hubble Space Telescope (HST) WFC3 data in eclipse and transit. The TauREx-FRECKLL model incorporated disequilibrium chemistry calculations with a Bayesian framework to infer atmospheric properties. The disequilibrium approach significantly altered retrieved metallicity and C/O ratios compared to equilibrium models, impacting planet formation insights. Retrievals reconciled transit and eclipse temperature profiles in deeper atmospheric layers but not in upper layers. Results were highly dependent on spectral resolution and retrieval priors, emphasizing limitations of HST data and the need for broader spectral coverage from instruments like JWST. This study demonstrates the feasibility and importance of incorporating disequilibrium chemistry in atmospheric retrievals, highlighting its potential for advancing our understanding of exoplanetary atmospheres with next-generation telescopes.

A three-stage metal hydride hydrogen compressor (MHHC) system based in AB2-type alloys has been set-up. Every stage can be considered as a Sieverts-type apparatus. The MHHC system can work in the pressure and temperature ranges comprised from vacuum to 250 bar and from RT to 200C, respectively. An efficient thermal management system was set up for the operational ranges of temperature designed. It dumps temperature shifts due to hydrogen expansion during stage coupling and hydrogen absorption/desorption in the alloys. Each reactor consists of a single and thin stainless-steel tube to maximize heat transfer. They are filled with similar amount of AB2 alloy. The MHHC system was able to produce a compression ratio (CR) as high as of 84.7 for inlet and outlet hydrogen pressures of 1.44 and 122 bar for a temperature span of 23 to 120C.

The current energy transition imposes a rapid implementation of energy storage systems with high energy density and eminent regeneration and cycling efficiency. Metal hydrides are potential candidates for generalized energy storage, when coupled with fuel cell units and/or batteries. An overview of ongoing research is reported and discussed in this review work on the light of application as hydrogen and heat storage matrices, as well as thin films for hydrogen optical sensors. These include a selection of single-metal hydrides, Ti-V(Fe) based intermetallics, multi-principal element alloys (high-entropy alloys), and a series of novel synthetically accessible metal borohydrides. Metal hydride materials can be as well of important usefulness for MH-based electrodes with high capacity (e.g. MgH2 ~ 2000 mAh g-1) and solid-state electrolytes displaying high ionic conductivity suitable, respectively, for Li-ion and Li/Mg battery technologies. To boost further research and development directions some characterization techniques dedicated to the study of M-H interactions, their equilibrium reactions, and additional quantification of hydrogen concentration in thin film and bulk hydrides are presented at the end of this manuscript.

Exoplanet atmospheric modeling is advancing from chemically diverse one-dimensional (1D) models to three-dimensional (3D) global circulation models (GCMs), which are crucial for interpreting observations from facilities like the James Webb Space Telescope (JWST) and Extremely Large Telescope (ELT). However, maintaining chemical diversity in models, especially in GCMs, is computationally expensive, limiting their complexity. Optimizing the number of reactions and species can address this tradeoff, but transparent and efficient methods for such optimization are lacking in current exoplanet literature. We aim to develop a systematic approach for reducing chemical networks in exoplanetary atmospheres while balancing accuracy and computational efficiency. Our data-driven method selects optimal reduced chemical networks based on accuracy and computational efficiency metrics. This approach can optimize networks for similar planets simultaneously, assign weights to prioritize accuracy or efficiency, and is applicable when including photochemistry. We base our method on sensitivity analysis of a typical 1D chemical kinetics model, applying principal component analysis to the sensitivities. To achieve fast and reliable network reduction, we utilize a genetic algorithm, a machine-learning optimization method that mimics natural selection. We present three schemes tailored for different priorities (accuracy, computational efficiency, and adaptability to photochemistry) that demonstrate improved performance and reduced computational costs. Our genetic algorithm-based method, the first to reduce a chemical network including photochemistry in exoplanet research, offers a versatile and efficient approach to enhance both accuracy and computational efficiency.

Cyanogen ($C_2N_2$) was among the many molecules identified in the coma of 67P/Churyumov-Gerasimenko during the Rosetta mission. As a potential parent species of the CN radical, its abundance relative to other species such as HCN should be generalized to comets observed from ground-based facilities. To investigate its presence from infrared spectra in other comets, we developed a new fluorescence model for the $\nu_3$ fundamental band. From new high-resolution infrared spectra of cyanogen, we analyzed the region of the $\nu_3$ band of $C_2N_2$, centered around 4.63 $\mu$m 2158 cm$^{-1}$). In addition to line positions and intensities, ground and excited molecular parameters were obtained. The spectroscopic analysis allowed us to develop a new fluorescence model for cyanogen. Excitation rates of the $\nu_3$ band of cyanogen are presented. An attempt to detect cyanogen in a high-resolution spectrum of comet C/2022 E3 (ZTF) is discussed.

We introduce a new Python 1D chemical kinetic code FRECKLL (Full and Reduced Exoplanet Chemical Kinetics distiLLed) to evolve large chemical networks efficiently. FRECKLL employs `distillation' in computing the reaction rates, which minimizes the error bounds to the minimum allowed by double precision values ($\epsilon \leq 10^{-15}$). Compared to summation of rates with traditional algorithms like pairwise summation, distillation provides a tenfold reduction in solver time for both full and reduced networks. Both the full and reduced Venot2020 networks are packaged in FRECKLL as well as a TauREx 3.1 plugin for usage in forward modelling and retrievals of exoplanet atmospheres. We present TauREx retrievals performed on a simulated HD189733 JWST spectra using the full and reduced Venot2020 chemical networks and demonstrate the viability of total disequilibrium chemistry retrievals and the ability for JWST to detect disequilibrium processes.

We consider the synthesis problem on timed automata with B\"uchi objectives, where delay choices made by a controller are subjected to small perturbations. Usually, the controller needs to avoid punctual guards, such as testing the equality of a clock to a constant. In this work, we generalize to a robustness setting that allows for punctual transitions in the automaton to be taken by controller with no perturbation. In order to characterize cycles that resist perturbations in our setting, we introduce a new structural requirement on the reachability relation along an accepting cycle of the automaton. This property is formulated on the region abstraction, and generalizes the existing characterization of winning cycles in the absence of punctual guards. We show that the problem remains within PSPACE despite the presence of punctual guards.

Studying chemistry and chemical composition is fundamental to go back to formation history of planetary systems. We propose here to have another look at five targets to better determine their composition and the chemical mechanisms that take place in their atmospheres. We present a re-analysis of five Hot Jupiters, combining multiple instruments and using Bayesian retrieval methods. We compare different combinations of molecules present in the simulated atmosphere, different chemistry types as well as different clouds parametrization. As a consequence of recent studies questioning the detection of Na and K in the atmosphere of HD 209458b as being potentially contaminated by stellar lines when present, we study the impact on other retrieval parameters of misinterpreting the presence of these alkali species. We use spatially scanned observations from the grisms G102 and G141 of the WFC3 on HST, with a wavelength coverage of $\sim$0.8 to $\sim$1.7 microns. We analyse these data with the publicly available Iraclis pipeline. We added to our datasets STIS observations to increase our wavelength coverage from $\sim$0.4 to $\sim$1.7 microns. We then performed a Bayesian retrieval analysis with the open-source TauREx using a nested sampling algorithm. We explore the influence of including Na and K on the retrieval of the molecules from the atmosphere. Our data re-analysis and Bayesian retrieval are consistent with previous studies but we find small differences in the retrieved parameters. After all, Na and K has no significant impact on the properties of the planet atmospheres. Therefore, we present here our new best-fit models, taking into account molecular abundances varying freely and equilibrium chemistry. This work is a preparation for a future addition of more sophisticated representation of chemistry taking into account disequilibrium effects such as vertical mixing and photochemistry.

Variations with oxygen concentration of titanium lattice parameters are obtained by means of ab initio calculations, considering the impact of oxygen ordering. The quasiharmonic approximation is used to take into account the thermal expansion at finite temperature. Results show that lattice parameters depend mainly on oxygen concentration and, to a lesser extent, on the ordering state. Knowing these theoretical variations, one can get insights into the composition of ordered compounds existing in Ti-O binary alloys from their lattice mismatch measured experimentally by x-ray diffraction. The approach is used in a binary alloy containing 6000 ppm in weight of oxygen. It is concluded that the ordered compounds, which are observed after a recrystallization heat treatment, do not have the expected Ti6O stoichiometry but have a composition close to the nominal concentration. Oxygen ordering proceeds, therefore, before oxygen partitioning in titanium.

We prove the following type of discrete entropy monotonicity for sums of isotropic, log-concave, independent and identically distributed random vectors $X_1,\dots,X_{n+1}$ on $\mathbb{Z}^d$: $$H(X_1+\cdots+X_{n+1}) \geq H(X_1+\cdots+X_{n}) + \frac{d}{2}\log{\Bigl(\frac{n+1}{n}\Bigr)} +o(1),$$ where $o(1)$ vanishes as $H(X_1) \to \infty$. Moreover, for the $o(1)$-term, we obtain a rate of convergence $O\Bigl({H(X_1)}{e^{-\frac{1}{d}H(X_1)}}\Bigr)$, where the implied constants depend on $d$ and $n$. This generalizes to $\mathbb{Z}^d$ the one-dimensional result of the second named author (2023). As in dimension one, our strategy is to establish that the discrete entropy $H(X_1+\cdots+X_{n})$ is close to the differential (continuous) entropy $h(X_1+U_1+\cdots+X_{n}+U_{n})$, where $U_1,\dots, U_n$ are independent and identically distributed uniform random vectors on $[0,1]^d$ and to apply the theorem of Artstein, Ball, Barthe and Naor (2004) on the monotonicity of differential entropy. In fact, we show this result under more general assumptions than log-concavity, which are preserved up to constants under convolution. In order to show that log-concave distributions satisfy our assumptions in dimension $d\ge2$, more involved tools from convex geometry are needed because a suitable position is required. We show that, for a log-concave function on $\mathbb{R}^d$ in isotropic position, its integral, barycenter and covariance matrix are close to their discrete counterparts. Moreover, in the log-concave case, we weaken the isotropicity assumption to what we call almost isotropicity. One of our technical tools is a discrete analogue to the upper bound on the isotropic constant of a log-concave function, which extends to dimensions $d\ge1$ a result of Bobkov, Marsiglietti and Melbourne (2022).

For an integer $k\ge 2$, let $S^{(1)}, S^{(2)}, \dots, S^{(k)}$ be $k$ independent simple symmetric random walks on $\mathbb{Z}$. A pair $(n,z)$ is called a collision event if there are at least two distinct random walks, namely, $S^{(i)},S^{(j)}$ satisfying $S^{(i)}_n= S^{(j)}_n=z$. We show that under the same scaling as in Donsker's theorem, the sequence of random measures representing these collision events converges to a non-trivial random measure on $[0,1]\times \mathbb{R}$. Moreover, the limit random measure can be characterized using Wiener chaos. The proof is inspired by methods from statistical mechanics, especially, by a partition function that has been developed for the study of directed polymers in random environments.