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The structure and kinematics of the Milky Way disk are largely inferred from the solar vicinity. To gain a comprehensive understanding, it is essential to find reliable tracers in less-explored regions like the bulge and the far side of the disk. Mira variables, which are well-studied and bright standard candles, offer an excellent opportunity to trace intermediate and old populations in these complex regions. We aim to isolate a clean sample of Miras in the Vista Variables in the V\'ia L\'actea survey using Gaussian process algorithms. This sample will be used to study intermediate and old age populations in the Galactic bulge and far disk. Near- and mid-infrared time-series photometry were processed using Gaussian Process algorithms to identify Mira variables and model their light curves. We calibrated selection criteria with a visually inspected sample to create a high-purity sample of Miras, integrating multi-band photometry and kinematic data from proper motions. We present a catalog of 3602 Mira variables. By analyzing photometry, we classify them by O-rich or C-rich surface chemistry and derive selective-to-total extinction ratios of $A_{K_{s}}/E(J - K_{s}) = 0.471 \pm 0.01$ and $A_{K_{s}}/E(H - K_{s}) = 1.320 \pm 0.020$. Using the Mira period-age relation, we find evidence supporting the inside-out formation of the Milky Way disk. The distribution of proper motions and distances aligns with the Galactic rotation curve and disk kinematics. We extend the rotation curve up to R$_{\rm GC} \sim 17 \ \rm{kpc}$ and find no strong evidence of the nuclear stellar disk in our Mira sample. This study constitutes the largest catalog of variable stars on the far side of the Galactic disk to date., Comment: 20 pages, 19 figures, Accepted in A&A

We present interferometric observations at 1 and 3\,mm with the Atacama Large Millimeter Array (ALMA) of the free-free continuum and mm-wavelength recombination line (mRRL) emission of the ionized core (within $\lsim$130\,au) of the young Planetary Nebula (PN) candidate M\,2-9.These inner regions are concealed in the vast majority of similar objects. A spectral index for the mm-to-cm continuum of $\sim$0.9 indicates predominantly free-free emission from an ionized wind, with a minor contribution from warm dust. The mm-continuum emission in M\,2-9 reveals an elongated structure along the main symmetry axis of the large-scale bipolar nebula with a C-shaped curvature surrounded by a broad-waisted component. This structure is consistent with an ionized bent jet and a perpendicular compact dusty disk. The presence of a compact equatorial disk (of radius $\sim$50\,au) is also supported by red-shifted CO and \trecem\ absorption profiles observed from the base of the receding north lobe against the compact background continuum. The redshift observed in the CO absorption profiles likely signifies gas infall movements from the disk toward a central source. The mRRLs exhibit velocity gradients along the axis, implying systematic expansion in the C-shaped bipolar outflow. The highest expansion velocities ($\sim$80\,\kms) are found in two diagonally opposed compact regions along the axis, referred to as the high-velocity spots/shells (HVS), indicating either rapid wind acceleration or shocks at radial distances of $\sim$0\farc02-0\farc04 ($\sim$15-25\,au) from the center. A subtle velocity gradient perpendicular to the lobes is also found, suggestive of rotation. Our ALMA observations detect increased brightness and broadness in the mRRLs... (abridged)., Comment: 28 pages. Accepted for publication in A&A

We study a flaring activity of the HSP Mrk421 that was characterized from radio to very-high-energy (VHE; E $>0.1$TeV) gamma rays with MAGIC, Fermi-LAT, Swift, XMM-Newton and several optical and radio telescopes. These observations included, for the first time for a gamma-ray flare of a blazar, simultaneous X-ray polarization measurements with IXPE. We find substantial variability in both X-rays and VHE gamma rays throughout the campaign, with the highest VHE flux above 0.2 TeV occurring during the IXPE observing window, and exceeding twice the flux of the Crab Nebula. However, the VHE and X-ray spectra are on average softer, and the correlation between these two bands weaker that those reported in previous flares of Mrk421. IXPE reveals an X-ray polarization degree significantly higher than that at radio and optical frequencies. The X-ray polarization angle varies by $\sim$100$^\circ$ on timescales of days, and the polarization degree changes by more than a factor 4. The highest X-ray polarization degree reaches 26%, around which a X-ray counter-clockwise hysteresis loop is measured with XMM-Newton. It suggests that the X-ray emission comes from particles close to the high-energy cutoff, hence possibly probing an extreme case of the Turbulent Extreme Multi-Zone model. We model the broadband emission with a simplified stratified jet model throughout the flare. The polarization measurements imply an electron distribution in the X-ray emitting region with a very high minimum Lorentz factor, which is expected in electron-ion plasma, as well as a variation of the emitting region size up to a factor of three during the flaring activity. We find no correlation between the fluxes and the evolution of the model parameters, which indicates a stochastic nature of the underlying physical mechanism. Such behaviour would be expected in a highly turbulent electron-ion plasma crossing a shock front., Comment: Submitted to Astronomy and Astrophysics. Corresponding authors: Axel Arbet-Engels, Lea Heckmann, David Paneque

OT 081 is a well-known, luminous blazar that is remarkably variable in many energy bands. We present the first broadband study of the source which includes very-high-energy (VHE, $E>$100\,GeV) $\gamma$-ray data taken by the MAGIC and H.E.S.S. imaging Cherenkov telescopes. The discovery of VHE $\gamma$-ray emission happened during a high state of $\gamma$-ray activity in July 2016, observed by many instruments from radio to VHE $\gamma$-rays. We identify four states of activity of the source, one of which includes VHE $\gamma$-ray emission. Variability in the VHE domain is found on daily timescales. The intrinsic VHE spectrum can be described by a power-law with index $3.27\pm0.44_{\rm stat}\pm0.15_{\rm sys}$ (MAGIC) and $3.39\pm0.58_{\rm stat}\pm0.64_{\rm sys}$ (H.E.S.S.) in the energy range of 55--300\,GeV and 120--500\,GeV, respectively. The broadband emission cannot be sucessfully reproduced by a simple one-zone synchrotron self-Compton model. Instead, an additional external Compton component is required. We test a lepto-hadronic model that reproduces the dataset well and a proton-synchrotron dominated model that requires an extreme proton luminosity. Emission models that are able to successfully represent the data place the emitting region well outside of the Broad Line Region (BLR) to a location at which the radiative environment is dominated by the infrared thermal radiation field of the dusty torus. In the scenario described by this flaring activity, the source appears to be an FSRQ, in contrast with past categorizations. This suggests that the source can be considered to be a transitional blazar, intermediate between BL~Lac and FSRQ objects., Comment: Accepted on MNRAS Corresponding authors: M. Manganaro, J. Becerra Gonz\'alez, M. Seglar-Arroyo, D. A. Sanchez

We present optical and IR observations from maximum light until around 600 d of SN 2022jli, a peculiar SE SN showing two maxima, each one with a peak luminosity of about 3 x 10^{42} erg/s and separated by 50 d. The second maximum is followed by periodic undulations with a period of P ~ 12.5 days. The spectra and the photometric evolution of the first maximum are consistent with the behaviour of a standard SE SN with an ejecta mass of 1.5 +/- 0.4 Msun, and a nickel mass of 0.12 +/- 0.01 Msun. The optical spectra after 400 d correspond to a standard SN Ic event, and at late times SN 2022jli exhibits a significant drop in the optical luminosity implying that the physical phenomena that produced the secondary maximum has ceased to power the SN light curve. One possibility is that the second maximum is powered by a magnetar with an initial spin period of P=48.5 ms and a magnetic field of B = 8.5x10^{14} G, while the light curve periodic undulations could be produced by accretion of material from a companion star onto the neutron star in a binary system. The near-IR spectra shows clear 1st CO overtone emission from about 190 d after the first maximum, and it becomes undetected at 400 d. A significant near-IR excess from hot dust emission is detected at 238 d produced by either newly formed dust in the SN ejecta or due to a strong near-IR dust echo. Depending on the assumptions of the dust composition, the estimated dust mass is 2-16 x 10^{-4} Msun. The magnetar power of the second maximum can fit in a more general picture where magnetars are the power source of super-luminous SNe, could produce their frequent bumps and undulations, and where pulsars could produce the late time excess observed in some SE SNe. The detection of CO and the potential detection of dust formed in the ejecta of SN2022jli are important to understand the formation molecules and dust in the ejecta of SE SNe., Comment: Submitted to A&A (27 pages and 22 figures)

The stellar stripping of satellites in cluster haloes is understood to play an important role in the production of intracluster light. Increasingly, cosmological simulations have been utilised to investigate its origin and assembly. However, such simulations typically model individual galaxies at relatively coarse resolutions, raising concerns about their accuracy. Although there is a growing literature on the importance of numerical resolution for the accurate recovery of the mass loss rates of dark matter (DM) haloes, there has been no comparable investigation into the numerical resolution required to accurately recover stellar mass loss rates in galaxy clusters. Using N-body simulations of satellite galaxies orbiting in a cluster halo represented by a static external potential, we conduct a set of convergence tests in order to explore the role of numerical resolution and force softening length on stellar stripping efficiency. We consider a number of orbital configurations, satellite masses and satellite morphologies. We find that stellar mass resolution is of minor importance relative to DM resolution. Resolving the central regions of satellite DM halos is critical to accurately recover stellar mass loss rates. Poorly resolved DM haloes develop cored inner profiles and, if this core is of comparable size to the stellar component of the satellite galaxy, this leads to significant over-stripping. To prevent this, relatively high DM mass resolutions of around $m_{\rm DM}\sim10^{6}$ M$_{\odot}$, better than those achieved by many contemporary cosmological simulations, are necessary., Comment: Accepted for publication in MNRAS. 19 pages, 13 figures

The large-scale linear halo bias encodes the relation between the clustering of dark-matter (DM) halos and that of the underlying matter density field. Although the primary dependence of bias on halo mass is well understood in the context of structure formation, the physical origins of the multiple additional relations at fixed halo mass, commonly known as secondary halo bias, have not been fully elucidated. Of particular relevance is the secondary dependence on halo assembly history, known as halo assembly bias. Our goal is to determine whether the properties of the initial regions from which $z=0$ halos originate produce any secondary bias at $z=0$. By analyzing these initial dependencies in connection with halo assembly bias, we intend to provide insight on the physical origins of the effect. To this end, we select halos at $z=0$ in the IllustrisTNG DM-only simulation and trace back the positions and velocities of their DM particles to $z=12$. The resulting initial regions are characterized according to several shape-related and kinematic properties. The secondary bias signal produced by these properties at $z=0$ is measured using an object-by-object bias estimator, which offers significant analytical advantages. We show that, when split by the properties of their initial DM clouds, $z=0$ halos display significant secondary bias, clearly exceeding the amplitude of the well-known halo assembly bias signal produced by concentration and age. The maximum bias segregation is measured for cloud velocity dispersion and radial velocity, followed by cloud concentration, sphericity, ellipticity and triaxiality. We further show that both velocity dispersion and radial velocity are also the properties of the initial clouds that most strongly correlate with halo age and concentration at fixed halo mass. Our results highlight the importance of linear effects in shaping halo assembly bias., Comment: 9 pages, 5 figures. Submitted to A&A, comments welcome

Mobile systems will have to support multiple AI-based applications, each leveraging heterogeneous data sources through DNN architectures collaboratively executed within the network. To minimize the cost of the AI inference task subject to requirements on latency, quality, and - crucially - reliability of the inference process, it is vital to optimize (i) the set of sensors/data sources and (ii) the DNN architecture, (iii) the network nodes executing sections of the DNN, and (iv) the resources to use. To this end, we leverage dynamic gated neural networks with branches, and propose a novel algorithmic strategy called Quantile-constrained Inference (QIC), based upon quantile-Constrained policy optimization. QIC makes joint, high-quality, swift decisions on all the above aspects of the system, with the aim to minimize inference energy cost. We remark that this is the first contribution connecting gated dynamic DNNs with infrastructure-level decision making. We evaluate QIC using a dynamic gated DNN with stems and branches for optimal sensor fusion and inference, trained on the RADIATE dataset offering Radar, LiDAR, and Camera data, and real-world wireless measurements. Our results confirm that QIC matches the optimum and outperforms its alternatives by over 80%.

Delirium is an acute confusional state that has been shown to affect up to 31% of patients in the intensive care unit (ICU). Early detection of this condition could lead to more timely interventions and improved health outcomes. While artificial intelligence (AI) models have shown great potential for ICU delirium prediction using structured electronic health records (EHR), most of them have not explored the use of state-of-the-art AI models, have been limited to single hospitals, or have been developed and validated on small cohorts. The use of large language models (LLM), models with hundreds of millions to billions of parameters, with structured EHR data could potentially lead to improved predictive performance. In this study, we propose DeLLiriuM, a novel LLM-based delirium prediction model using EHR data available in the first 24 hours of ICU admission to predict the probability of a patient developing delirium during the rest of their ICU admission. We develop and validate DeLLiriuM on ICU admissions from 104,303 patients pertaining to 195 hospitals across three large databases: the eICU Collaborative Research Database, the Medical Information Mart for Intensive Care (MIMIC)-IV, and the University of Florida Health's Integrated Data Repository. The performance measured by the area under the receiver operating characteristic curve (AUROC) showed that DeLLiriuM outperformed all baselines in two external validation sets, with 0.77 (95% confidence interval 0.76-0.78) and 0.84 (95% confidence interval 0.83-0.85) across 77,543 patients spanning 194 hospitals. To the best of our knowledge, DeLLiriuM is the first LLM-based delirium prediction tool for the ICU based on structured EHR data, outperforming deep learning baselines which employ structured features and can provide helpful information to clinicians for timely interventions.

Imaging atmospheric Cherenkov telescopes (IACTs) are used to observe very high-energy photons from the ground. Gamma rays are indirectly detected through the Cherenkov light emitted by the air showers they induce. The new generation of experiments, in particular the Cherenkov Telescope Array Observatory (CTAO), sets ambitious goals for discoveries of new gamma-ray sources and precise measurements of the already discovered ones. To achieve these goals, both hardware and data analysis must employ cutting-edge techniques. This also applies to the LST-1, the first IACT built for the CTAO, which is currently taking data on the Canary island of La Palma. This paper introduces a new event reconstruction technique for IACT data, aiming to improve the image reconstruction quality and the discrimination between the signal and the background from misidentified hadrons and electrons. The technique models the development of the extensive air shower signal, recorded as a waveform per pixel, seen by CTAO telescopes' cameras. Model parameters are subsequently passed to random forest regressors and classifiers to extract information on the primary particle. The new reconstruction was applied to simulated data and to data from observations of the Crab Nebula performed by the LST-1. The event reconstruction method presented here shows promising performance improvements. The angular and energy resolution, and the sensitivity, are improved by 10 to 20% over most of the energy range. At low energy, improvements reach up to 22%, 47%, and 50%, respectively. A future extension of the method to stereoscopic analysis for telescope arrays will be the next important step., Comment: Accepted in A&A

We present a proof of the folklore result that any length metric on $\mathbb R^d$ can be approximated by conformally flat Riemannian distance functions in the uniform distance. This result is used to study Liouville quantum gravity in another paper by the same authors., Comment: arXiv admin note: substantial text overlap with arXiv:2305.15588

For the incompressible Navier--Stokes system with variable density and viscosity, we propose and analyse an IMEX framework treating the convective and diffusive terms semi-implicitly. This extends to variable density and second order in time some methods previously analysed for variable viscosity and constant density. We present three new schemes, both monolithic and fractional-step. All of them share the methodological novelty that the viscous term is treated in an implicit-explicit (IMEX) fashion, which allows decoupling the velocity components. Unconditional temporal stability is proved for all three variants. Furthermore, the system to solve at each time step is linear, thus avoiding the costly solution of nonlinear problems even if the viscosity follows a non-Newtonian rheological law. Our presentation is restricted to the semi-discrete case, only considering the time discretisation. In this way, the results herein can be applied to any spatial discretisation. We validate our theory through numerical experiments considering finite element methods in space. The tests range from simple manufactured solutions to complex two-phase viscoplastic flows., Comment: 23 pages

In this work, we propose a machine learning approach to address one aspect of the quantum marginal problem: finding a global density matrix compatible with a given set of quantum marginals. Our method involves combining a quantum marginal imposition technique with convolutional denoising autoencoders. The loss function ensures that the output density matrix satisfies essential properties such as hermiticity, positivity, and normalization. Through extensive numerical simulations, we demonstrate the effectiveness of our approach, achieving a high success rate and accuracy. Our model can serve as an initial guess generator for solving semidefinite programs (SDPs) associated with the quantum marginal problem, potentially accelerating convergence and improving accuracy. This work highlights the potential of machine learning techniques to address complex problems in quantum mechanics.

Let $M$ be a simply connected Riemannian manifold in $\mathscr{M}_{k,v}^D(n)$, the space of closed Riemannian manifolds of dimension $n$ with sectional curvature bounded below by $k$, volume bounded below by $v$, and diameter bounded above by $D$. Let $c$ be the smallest positive real number such that any closed curve of length at most $2d$ can be contracted to a point over curves of length at most $cd$, where $d$ is the diameter of $M$. In this paper, we show that under these hypotheses there exists a computable rational function, $G(n,k,v,D)$, such that any continuous map of $S^l$ to $\Omega_{p,q}M$, the space of piecewise differentiable curves on $M$ connecting $p$ and $q$, is homotopic to a map whose image consists of curves of length at most $\exp(c\exp(G(n,k,v,D))$. In particular, for any points $p,q \in M$ and any integer $m>0$ there exist at least $m$ geodesics connecting $p$ and $q$ of length at most $m\exp(c\exp(G(n,k,v,D))$., Comment: 22 pages, 10 figures

In this paper we study the relationship between the strict locally minimizing orbits for time dependent lagrangian systems and hyperbolicity properties of the corresponding lagrangian flow.

Type II supernovae (SNeII) mark the endpoint in the lives of hydrogen-rich massive stars. Their large explosion energies and luminosities allow us to measure distances, metallicities, and star formation rates into the distant Universe. To fully exploit their use in answering different astrophysical problems, high-quality low-redshift data sets are required. Such samples are vital to understand the physics of SNeII, but also to serve as calibrators for distinct - and often lower-quality - samples. We present uBgVri optical and YJH near-infrared (NIR) photometry for 94 low-redshift SNeII observed by the Carnegie Supernova Project (CSP). A total of 9817 optical and 1872 NIR photometric data points are released, leading to a sample of high-quality SNII light curves during the first ~150 days post explosion on a well-calibrated photometric system. The sample is presented and its properties are analysed and discussed through comparison to literature events. We also focus on individual SNeII as examples of classically defined subtypes and outlier objects. Making a cut in the plateau decline rate of our sample (s2), a new subsample of fast-declining SNeII is presented. The sample has a median redshift of 0.015, with the nearest event at 0.001 and the most distant at 0.07. At optical wavelengths (V), the sample has a median cadence of 4.7 days over the course of a median coverage of 80 days. In the NIR (J), the median cadence is 7.2 days over the course of 59 days. The fast-declining subsample is more luminous than the full sample and shows shorter plateau phases. Of the non-standard SNeII highlighted, SN2009A particularly stands out with a steeply declining then rising light curve, together with what appears to be two superimposed P-Cygni profiles of H-alpha in its spectra. We outline the significant utility of these data, and finally provide an outlook of future SNII science., Comment: Accepted for publication in A&A. Photometric data will be uploaded to the CDS and the CSP website, and can also be requested from the first author

Dark photons serve as a portal to connect the dark and standard model sectors. Here, we propose photon-induced exclusive diffractive processes as a new tool to study the production of dark photons in current and future colliders. These processes join the strength of the strong force, yielding large cross sections, with the cleanliness of diffractive photoproduction, providing a clean experimental environment. Although the measurement would be extremely difficult, we identified a currently unexplored region around dark photon masses of 1 GeV/$c^2$ and coupling suppression $\varepsilon$ values around $10^{-4}$ where dark photons could be potentially found at the LHC., Comment: 6 pages, 5 figures

Instruments for gamma-ray astronomy at Very High Energies ($E>100\,{\rm GeV}$) have traditionally derived their scientific results through proprietary data and software. Data standardisation has become a prominent issue in this field both as a requirement for the dissemination of data from the next generation of gamma-ray observatories and as an effective solution to realise public data legacies of current-generation instruments. Specifications for a standardised gamma-ray data format have been proposed as a community effort and have already been successfully adopted by several instruments. We present the first production of standardised data from the Major Atmospheric Gamma-ray Imaging Cherenkov (MAGIC) telescopes. We converted $166\,{\rm h}$ of observations from different sources and validated their analysis with the open-source software Gammapy. We consider six data sets representing different scientific and technical analysis cases and compare the results obtained analysing the standardised data with open-source software against those produced with the MAGIC proprietary data and software. Aiming at a systematic production of MAGIC data in this standardised format, we also present the implementation of a database-driven pipeline automatically performing the MAGIC data reduction from the calibrated down to the standardised data level. In all the cases selected for the validation, we obtain results compatible with the MAGIC proprietary software, both for the manual and for the automatic data productions. Part of the validation data set is also made publicly available, thus representing the first large public release of MAGIC data. This effort and this first data release represent a technical milestone toward the realisation of a public MAGIC data legacy., Comment: Accepted for publication in the Journal of High Energy Astrophysics

In this paper, as a continuation of [Contreras-Astorga A., Escobar-Ruiz A. M. and Linares R., \textit{Phys. Scr.} {\bf99} 025223 (2024)] the one-dimensional quasi-exactly solvable (QES) sextic potential $V^{\rm(qes)}(x) = \frac{1}{2}(\nu\, x^{6} + 2\, \nu\, \mu\,x^{4} + \left[\mu^2-(4N+3)\nu \right]\, x^{2})$ is considered. In the cases $N=0,\frac{1}{4},\,\frac{1}{2},\,\frac{7}{10}$ the WKB correction $\gamma=\gamma(N,n)$ is calculated for the first lowest 50 states $n\in [0,\,50]$ using highly accurate data obtained by the Lagrange Mesh Method. Closed analytical approximations for both $\gamma$ and the energy $E=E(N,n)$ of the system are constructed. They provide a reasonably relative accuracy $|\Delta|$ with upper bound $\lesssim 10^{-3}$ for all the values of $(N,n)$ studied. Also, it is shown that the QES Morse potential is shape invariant characterized by a hidden $\mathfrak{sl}_2(\mathbb{R})$ Lie algebra and vanishing WKB correction $\gamma=0$., Comment: 12 pages, 12 figures

Near-sun sky twilight observations allow for the detection of asteroid interior to the orbit of Venus (Aylos), the Earth (Atiras), and comets. We present the results of observations with the Palomar 48-inch telescope (P48)/Zwicky Transient Facility (ZTF) camera in 30 s r-band exposures taken during evening astronomical twilight from 2019 Sep 20 to 2022 March 7 and during morning astronomical twilight sky from 2019 Sep 21 to 2022 Sep 29. More than 46,000 exposures were taken in evening and morning astronomical twilight within 31 to 66 degrees from the Sun with an r-band limiting magnitude between 18.1 and 20.9. The twilight pointings show a slight seasonal dependence in limiting magnitude and ability to point closer towards the Sun, with limiting magnitude slightly improving during summer. In total, the one Aylo, (594913) 'Ayl\'o'chaxnim, and 4 Atiras, 2020 OV1, 2021 BS1, 2021 PB2, and 2021 VR3, were discovered in evening and morning twilight observations. Additional twilight survey discoveries also include 6 long-period comets: C/2020 T2, C/2020 V2, C/2021 D2, C/2021 E3, C/2022 E3, and C/2022 P3, and two short-period comets: P/2021 N1 and P/2022 P2 using deep learning comet detection pipelines. The P48/ZTF twilight survey also recovered 11 known Atiras, one Aylo, three short-period comes, two long-period comets, and one interstellar object. Lastly, the Vera Rubin Observatory will conduct a twilight survey starting in its first year of operations and will cover the sky within 45 degrees of the Sun. Twilight surveys such as those by ZTF and future surveys will provide opportunities for discovering asteroids inside the orbits of Earth and Venus., Comment: 26 pages, 13 figures, 4 tables, accepted for publication in Icarus

Reinforcement Learning (RL) has been shown to be effective and convenient for a number of tasks in robotics. However, it requires the exploration of a sufficiently large number of state-action pairs, many of which may be unsafe or unimportant. For instance, online model-free learning can be hazardous and inefficient in the absence of guarantees that a certain set of desired states will be reached during an episode. An increasingly common approach to address safety involves the addition of a shielding system that constrains the RL actions to a safe set of actions. In turn, a difficulty for such frameworks is how to effectively couple RL with the shielding system to make sure the exploration is not excessively restricted. This work presents a novel safe model-free RL agent called Critic As Lyapunov Function (CALF) and showcases how CALF can be used to improve upon control baselines in robotics in an efficient and convenient fashion while ensuring guarantees of stable goal reaching. The latter is a crucial part of safety, as seen generally. With CALF all state-action pairs remain explorable and yet reaching of desired goal states is formally guaranteed. Formal analysis is provided that shows the goal stabilization-ensuring properties of CALF and a set of real-world and numerical experiments with a non-holonomic wheeled mobile robot (WMR) TurtleBot3 Burger confirmed the superiority of CALF over such a well-established RL agent as proximal policy optimization (PPO), and a modified version of SARSA in a few-episode setting in terms of attained total cost.

The observation of a massive galaxy with an extremely low dark matter content (i.e. NGC 1277) has posed questions about how such objects form and evolve in a hierarchical universe. We here report on the finding of several massive, dark matter-deficient galaxies in a set of 324 galaxy clusters theoretically modelled by means of full-physics hydrodynamical simulations. We first focus on two example galaxies selected amongst the most massive and dark matter-deficient ones. By tracing the evolution of these galaxies, we find that their lack of dark matter is a result of multiple pericentre passages. While orbiting their host halo, tidal interactions gradually strip away dark matter while preserving the stellar component. A statistical analysis of all massive satellite galaxies in the simulated clusters shows that the stellar-to-total mass ratio today is strongly influenced by the number of orbits and the distance at pericentres. Galaxies with more orbits and closer pericentres are more dark matter-deficient. Additionally, we find that massive, dark matter-deficient galaxies at the present day are either the remnants of very massive galaxies at infall or former central galaxies of infalling groups. We conclude that such massive yet dark matter-deficient galaxies exist and are natural by-products of typical cluster galaxy evolution, with no specific requirement for an exotic formation scenario., Comment: 12 pages, 11 figures. Accepted for publication in Astronomy & Astrophysics

We demonstrate the use of [2-($\textit{9H}$-carbazol-9-yl)ethyl]phosphonic acid (2PACz) and [2-(3,6-di-$\textit{tert}$-butyl-$\textit{9H}$-carbazol-9-yl)ethyl]phosphonic acid (t-Bu-2PACz) as anode modification layers in metal-halide perovskite quantum dot light-emitting diodes (QLEDs). Compared to conventional QLED structures with PEDOT:PSS (poly(3,4-ethylenedioxythiophene) polystyrene sulfonate)/PVK (poly(9-vinylcarbazole)) hole-transport layers, QLEDs made with phosphonic acid (PA)-modified indium tin oxide (ITO) anodes show an over 7-fold increase in brightness, achieving a brightness of 373,000 cd m$^{-2}$, one of the highest brightnesses reported to date for colloidal perovskite QLEDs. Importantly, the onset of efficiency roll-off, or efficiency droop, occurs at ~1000-fold higher current density for QLEDs made with PA-modified anodes compared to control QLEDs made with conventional PEDOT:PSS/PVK hole transport layers, allowing the devices to sustain significantly higher levels of external quantum efficiency at a brightness of >10$^{5}$ cd m$^{-2}$. Steady-state and time-resolved photoluminescence measurements indicate these improvements are due to a combination of multiple factors, including reducing quenching of photoluminescence at the PEDOT:PSS interface and reducing photoluminescence efficiency loss at high levels of current density.

Galaxy cluster mergers are believed to generate large-scale shock waves that are ideal sites for electron acceleration. We compute radio emission light curves for galaxy group and cluster mergers simulated in a cosmological context to study the dependence of radio luminosity on cluster mass, redshift, and impact parameter. We used model galaxy clusters from The Three Hundred project to identify cluster mergers characterised by the two main merging structures and follow their evolution throughout the simulated cosmic history. We found that the median non-thermal radio relic luminosity light curve produced in galaxy cluster mergers can be described by a skewed Gaussian function abruptly rising after core-passage of the secondary cluster that peaks after $\sim0.1-0.8\,$Gyr as a function of $M_{200,1}$, the mass of the primary, displaying a mass-dependent luminosity output increase of $\lesssim10$ to about $\gtrsim10-50$ times relative to the radio emission measured at core-passage for galaxy groups and clusters, respectively. In general, most merger orbits are fairly radial with a median opening angle of $\sim20^{\circ}$ before the collision. We also found that, independent of the cluster mass, less radial mergers tend to last longer, although the trend is weak. Finally, we found that the peak radio luminosity shows a significant correlation with mass, $P_{1.4}\propto M_{200,1}^{2.05}$, demonstrating that this relation holds all the way up from galaxy group scales to the most massive galaxy clusters. We conclude that cluster mass is the primary driver for radio `gischt' median luminosity, although there are significant variations for a given cluster mass. Our simulations suggest that the shock-driven, non-thermal radio emission observed on cluster outskirts are the result of massive galaxy cluster mergers at $z\lesssim1$, peaking at $z\sim0-0.5$., Comment: 15 pages, 10 figures. Accepted for publication in A&A

As mass-losing asymptotic giant branch (AGB) stars evolve to planetary nebulae (PNe), the mass outflow geometries transform from nearly spherical to extreme aspherical. The physical mechanisms governing this transformation are widely believed to be linked to binarity and the associated production of disks and fast jets during transitional (post-AGB) evolutionary stages. We are carrying out a systematic ALMA survey ($P$re-planet$A$ry $N$ebulae high-angular-res$O$lution su$R$vey with $A$L$MA$ or PANORAMA) of a representative sample of bipolar and multipolar post-AGB objects. We have obtained high angular-resolution (0".1-0".4) observations of the CO(3--2) and/or 6--5 emission in order to probe the spatio-kinematic structure of the collimated outflows and the central disk/torii. The results are remarkable, generally showing the presence of bipolar or multipolar high-velocity outflows, dense toroidal waists, and in one case, a geometrically-thin circular ring around the central bipolar nebula. A high degree of point-symmetry characterizes the morphology of the mass ejecta. In this contribution, we present these and other highlights from our survey. We aim to use 2D/3D radiative transfer modeling in order to derive accurate outflow momenta, masses and mass-loss rates for our sample, and build hydrodynamical models that can explain the observed spatio-kinematic structures. These results will then be used to distinguish between different classes of PN-shaping binary interaction models.

After shipment to the Daresbury Lab and return to Fermilab, the prototype HB650 cryomodule underwent another phase of 2K RF testing to ascertain any performance issues that may have arisen from the transport of the cryomodule. While measurements taken at room temperature after the conclusion of shipment indicated that there were no negative impacts on cavity alignment, beamline vacuum, or cavity frequency, testing at 2K was required to validate other aspects such as tuner operation, cavity coupling, cryogenic system integrity, and cavity performance. Results of this latest round of limited 2K testing will be presented., Comment: 32nd Linear Accelerator Conference (LINAC 2024)

The ESO public survey VISTA Variables in the V\'ia L\'actea (VVV) surveyed the inner Galactic bulge and the adjacent southern Galactic disk from $2009-2015$. Upon its conclusion, the complementary VVV eXtended (VVVX) survey has expanded both the temporal as well as spatial coverage of the original VVV area, widening it from $562$ to $1700$ sq. deg., as well as providing additional epochs in $JHK_{\rm s}$ filters from $2016-2023$. With the completion of VVVX observations during the first semester of 2023, we present here the observing strategy, a description of data quality and access, and the legacy of VVVX. VVVX took $\sim 2000$ hours, covering about 4% of the sky in the bulge and southern disk. VVVX covered most of the gaps left between the VVV and the VISTA Hemisphere Survey (VHS) areas and extended the VVV time baseline in the obscured regions affected by high extinction and hence hidden from optical observations. VVVX provides a deep $JHK_{\rm s}$ catalogue of $\gtrsim 1.5\times10^9$ point sources, as well as a $K_{\rm s}$ band catalogue of $\sim 10^7$ variable sources. Within the existing VVV area, we produced a $5D$ map of the surveyed region by combining positions, distances, and proper motions of well-understood distance indicators such as red clump stars, RR Lyrae, and Cepheid variables. In March 2023 we successfully finished the VVVX survey observations that started in 2016, an accomplishment for ESO Paranal Observatory upon 4200 hours of observations for VVV+VVVX. The VVV+VVVX catalogues complement those from the Gaia mission at low Galactic latitudes and provide spectroscopic targets for the forthcoming ESO high-multiplex spectrographs MOONS and 4MOST., Comment: 17 pages, 11 figures (+ appendix). Accepted for publication in Astronomy and Astrophysics in section 14: Catalogs and data

This paper presents a mini-review of the current state of research in mobile manipulators with variable levels of autonomy, emphasizing their associated challenges and application environments. The need for mobile manipulators in different environments is evident due to the unique challenges and risks each presents. Many systems deployed in these environments are not fully autonomous, requiring human-robot teaming to ensure safe and reliable operations under uncertainties. Through this analysis, we identify gaps and challenges in the literature on Variable Autonomy, including cognitive workload and communication delays, and propose future directions, including whole-body Variable Autonomy for mobile manipulators, virtual reality frameworks, and large language models to reduce operators' complexity and cognitive load in some challenging and uncertain scenarios., Comment: Presented at Variable Autonomy for Human-Robot Teaming (VAT) at IEEE RO-MAN 2024 Workshop

We prove that in the $C^k$ topology generic hyperbolic Ma\~n\'e sets have zero topological entropy., Comment: arXiv admin note: text overlap with arXiv:2408.01009

We prove that $C^2$ generic hyperbolic Ma\~n\'e sets contain a periodic periodic orbit. In dimension 2, adding a result by Contreras, Figalli, Rifford, which states that $C^2$ generic Ma\~n\'e sets are hyperbolic; we obtain Ma\~n\'e's Conjecture for surfaces in the $C^2$ topology: Given a Tonelli Lagrangian $L$ on a compact surface $M$ there is a $C^2$ open and dense set of functions $f:M\to\mathbb{R}$ such that the Ma\~n\'e set of the Lagrangian $L+f$ is a hyperbolic periodic orbit.

- Aims: We intended to quantify the impact of stellar multiplicity on the presence and properties of exoplanets. - Methods: We investigated all exoplanet host stars at less than 100 pc using the latest astrometric data from Gaia DR3 and advanced statistical methodologies. We complemented our search for common proper motion and parallax companions with data from the Washington Double Star catalogue and the literature. After excluding a number of systems based on radial velocity data, and membership in clusters and open associations, or with resolved ultracool companions, we kept 215 exoplanet host stars in 212 multiple-star systems. - Results: We found 17 new companions in the systems of 15 known exoplanet host stars, measured precise angular and projected physical separations and position angles for 236 pairs of stars, compiled key parameters for 276 planets in multiple systems, and established a comparison sample comprising 687 single stars with exoplanets. With all of this, we statistically analysed a series of hypothesis regarding planets in multiple stellar systems. Although they are only statistically significant at a 2{\sigma} level, our analysis pointed to several interesting results on the comparison in the mean number of planets in multiple versus single stellar systems and the tendency of high mass planets to be located in closer orbits in multiple systems. We confirm that planets in multiple systems tend to have orbits with larger eccentricities than those in single systems. In particular, we found a significant (> 4{\sigma}) preference for planets to exhibit high orbital eccentricities at small ratios between star-star projected physical separations and star-planet semi-major axes., Comment: Accepted in A&A. 47 Pages, 14 figures and 9 tables (4 tables online)

We present the abundances of magnesium (Mg) and silicon (Si) for 314 dwarf stars with spectral types in the interval K7.0-M5.5 (Teff range ~4200-3050 K) observed with the CARMENES high-resolution spectrograph at the 3.5 m telescope at the Calar Alto Observatory. Our analysis employs the BT-Settl model atmospheres, the radiative transfer code Turbospectrum, and a state-of-the-art selection of atomic and molecular data. These Mg and Si abundances are critical for understanding both the chemical evolution and assembly of the Milky Way and the formation and composition of rocky planets. Our chemical abundances show a line-to-line scatter at the level of 0.1 dex for all studied spectral types. The typical error bar of our chemical abundance measurements is +- 0.11 dex (Mg) and +- 0.16 dex (Si) for all spectral types based on the comparison of the results obtained for stellar components of multiple systems. The derived abundances are consistent with the galactic evolution trends and observed chemical abundance distribution of earlier FGK-type stars in the solar neighbourhood. Besides, our analysis provides compatible abundances for stars in multiple systems. In addition, we studied the abundances of different galactic stellar populations. In this paper, we also explore the relation of the Mg and Si abundances of stars with and without known planets., Comment: 11 Pages, 5 figures. Accepted for publication in A&A

Context. Mock galaxy catalogues are essential for correctly interpreting current and future generations of galaxy surveys. Despite their significance in galaxy formation and cosmology, little to no work has been done to validate the predictions of these mocks for high-order clustering statistics. Aims. We compare the predicting power of the latest generation of empirical models used in the creation of mock galaxy catalogues: a 13-parameter Halo Occupation Distribution (HOD) and an extension of the SubHalo Abundance Matching technique (SHAMe). Methods. We build GalaxyEmu-Planck, an emulator that makes precise predictions for the two-point correlation function, galaxy-galaxy lensing (restricted to distances greater than 1 $h^{-1} {\rm Mpc}$ to avoid baryonic effects), and other high-order statistics resulting from the evaluation of SHAMe and HOD models. Results. We evaluate the precision of GalaxyEmu-Planck using two galaxy samples extracted from the FLAMINGO hydrodynamical simulation that mimic the properties of DESI-BGS and BOSS galaxies, finding that the emulator reproduces all the predicted statistics precisely. The HOD showed comparable performance when fitting galaxy clustering and galaxy-galaxy lensing. In contrast, the SHAMe model showed better predictions for higher-order statistics, especially regarding the galaxy assembly bias. We also tested the performance of the models after removing some of their extensions, finding that we can withdraw two of the HOD parameters without a loss of performance. Conclusions. The results of this paper validate the current generation of empirical models as a way to reproduce galaxy clustering, galaxy-galaxy lensing and other high-order statistics. The excellent performance of the SHAMe model with a small number of free parameters suggests that it is a valid method to extract cosmological constraints from galaxy clustering., Comment: 22 pages, 12 figures, submitted to A&A. Comments welcomed!

NGC 6357, a star-forming complex at $\sim 1.7$ kpc from the Sun, contains giant molecular clouds and three prominent star clusters alongside with HII regions, very massive stars and thousands of young stellar objects in different evolutionary stages. We present a combined infrared kinematic and time domain study of the line of sight towards this region enabled by the VVVX survey. In terms of kinematics, a novel discovery emerges: an asymmetrical distribution in the vector point diagram. Some stars in the sample exhibit spatial proximity to dusty regions, with their proper motions aligned with filament projections, hinting at a younger population linked to triggered star formation. However, this distribution could also stem from an asymmetric stellar expansion event within NGC 6357, warranting further investigation. Comparing this data with Gaia revealed inconsistencies likely due to high extinction levels in the region. Additionally, owing to accretion episodes and surface cool spots, young stars display high variability. Using the $K_s$-band time series data, we overcome the extreme levels of extinction towards the region, and compile a catalogue of $774$ infrared light curves of young stars. Each light curve has been characterized in terms of asymmetry and periodicity, to infer the dominant underlying physical mechanism. These findings are then correlated with evolutionary stages, aiming to uncover potential age disparities among the observed stars. This study contributes to our understanding the intricate dynamics and evolutionary processes within NGC 6357, offering valuable insights into the formation and development of stellar populations within such complex environments., Comment: Version resubmitted to MNRAS with minor revisions requested by the referee

Context. Observational evidence has accumulated in the past years, showing that the Galactic bulge includes two populations, a metal poor and a metal rich one that, in addition to a different metallicity, show different alpha over iron abundances, spatial distribution, and kinematics. While the metal rich, barred component has been fairly well characterized, the metal poor, spheroidal component has been more elusive and harder to describe. RR Lyrae variables are clean tracers of the old bulge component, and they are, on average, more metal poor than red clump stars. Aims. In the present paper, we provide a new catalog of 16488 ab type RR Lyrae variables in the bulge region within -10

The stability and reproducibility issues related to metal halide Perovskite Solar Cells (PSCs) have prevented so far from exploiting this highly efficient photovoltaic technology under rainy or even moisture conditions and in combination with drop triboelectric nanogenerators (D-TENGs). Protecting the PSCs with a waterproof encapsulator could overcome such a disadvantage. Herein, we propose the implementation of fluorinated carbon (CFx) coatings produced by PECVD, enabling waterproof capability for the PSC and working as an energy harvesting surface for D-TENGs. These 100 nm - films present optimal optical transmittance, fully preserving the photovoltaic parameters of the cell. The improved long-term stability of the water-resistant PSCs prevents degradation under illumination in outdoor or simulated adverse environments with high humidity, high temperature, water immersion, or rain. As a remarkable result, the 50% Power Conversion Efficiency (PCE) has been retained after ten days of illumination under 100% relative humidity at 50 degrees Celsius. Also, the CFx coatings were successfully tested as a promoter agent to integrate commercial UV-curable sealants compatible with Spiro-OMeTAD, enhancing the performance stability of up to 80 % of PCE after 100 hours under illumination in a humid environment. This PSC was tested in a top-bottom electrode configuration for harvesting kinetic energy from droplets. Devices were compatible with simultaneously working as D-TENG and photovoltaic cells, yielding voltage outputs up to 12 V with maximum peak power density reaching 2.75 uW/cm2 defined by the D-TENG and PCE of 11.5 % and 8.46 mA/cm2 of short circuit current determined by the PSC under dripping and for an illumination angle of 45 degrees. The durability of the multisource device was tested under constant illumination and periodical drop impacting for more than 5 hours.

We prove that, on any closed manifold of dimension at least two with non-trivial first Betti number, a $C^\infty$ generic Riemannian metric has infinitely many closed geodesics, and indeed closed geodesics of arbitrarily large length. We derive this existence result combining a theorem of Ma\~n\'e together with the following new theorem of independent interest: the existence of minimal closed geodesics, in the sense of Aubry-Mather theory, implies the existence of a transverse homoclinic, and thus of a horseshoe, for the geodesic flow of a suitable $C^\infty$-close Riemannian metric., Comment: 19 pages

We present a comprehensive analysis of young stellar object (YSO) variability within the M17 Southwest Extension (M17 SWex), using 3.5 years of monitoring data from the JCMT Transient Survey at sub-millimeter (sub-mm) and 9 years from the NEOWISE mission at mid-infrared (mid-IR). Our study encompasses observations of 147 bright sub-mm peaks identified within our deep JCMT co-added map as well as 156 YSOs in NEOWISE W1 and 179 in W2 that were previously identified in Spitzer surveys. We find three robust sub-mm variables: two are candidate YSOs and one is a likely extragalactic source. At mid-IR wavelengths, our analysis reveals secular and stochastic variability in 47 YSOs, with the highest fraction of secular variability occurring at the earliest evolutionary stage. This is similar to what has previously been observed for low-mass YSO variability within the Gould Belt. However, we observe less overall variability in M17SWex at both the sub-mm and mid-IR. We suspect that this lower fraction is due to the greater distance to M17 SWex. Our findings showcase the utility of multi-wavelength observations to better capture the complex variability phenomena inherent to star formation processes and demonstrate the importance of years-long monitoring of a diverse selection of star-forming environments., Comment: Accepted for Publication in The Astronomical Journal

Context: There are currently three pulsars firmly detected by imaging atmospheric Cherenkov telescopes (IACTs), two of them reaching TeV energies, challenging models of very-high-energy (VHE) emission in pulsars. More precise observations are needed to better characterize pulsar emission at these energies. The LST-1 is the prototype of the Large-Sized Telescope, that will be part of the Cherenkov Telescope Array Observatory (CTAO). Its improved performance over previous IACTs makes it well suited for studying pulsars. Aims: To study the Crab pulsar emission with the LST-1, improving and complementing the results from other telescopes. These observations can also be used to characterize the potential of the LST-1 to study other pulsars and detect new ones. Methods: We analyzed a total of $\sim$103 hours of gamma-ray observations of the Crab pulsar conducted with the LST-1 in the period from September 2020 to January 2023. The observations were carried out at zenith angles less than 50 degrees. A new analysis of the Fermi-LAT data was also performed, including $\sim$14 years of observations. Results: The Crab pulsar phaseogram, long-term light-curve, and phase-resolved spectra are reconstructed with the LST-1 from 20 GeV to 450 GeV for P1 and up to 700 GeV for P2. The pulsed emission is detected with a significance of 15.2$\sigma$. The two characteristic emission peaks of the Crab pulsar are clearly detected (>10$\sigma$), as well as the so-called bridge emission (5.7$\sigma$). We find that both peaks are well described by power laws, with spectral indices of $\sim$3.44 and $\sim$3.03 respectively. The joint analysis of Fermi-LAT and LST-1 data shows a good agreement between both instruments in the overlapping energy range. The detailed results obtained in the first observations of the Crab pulsar with LST-1 show the potential that CTAO will have to study this type of sources., Comment: Accepted by A&A

Numerous metrics exist to quantify the dynamical state of galaxy clusters, both observationally and within simulations. Many of these correlate strongly with one another, but it is not clear whether all of these measures probe the same intrinsic properties. In this work, we use two different statistical approaches -- principal component analysis (PCA) and uniform manifold approximation and projection (UMAP) -- to investigate which dynamical properties of a cluster are in fact the best descriptors of its dynamical state. We use measurements taken directly from The Three Hundred suite of galaxy cluster simulations, as well as morphological properties calculated using mock X-ray and SZ maps of the same simulated clusters. We find that four descriptions of dynamical state naturally arise, and although correlations exist between these, a given cluster can be "dynamically relaxed" according to all, none, or some of these four descriptions. These results demonstrate that it is highly important for future observational and theoretical studies to consider in which sense clusters are dynamically relaxed. Cluster dynamical states are complex and multi-dimensional, and so it is not meaningful to classify them simply as "relaxed" and "unrelaxed" based on a single linear scale., Comment: 18 pages, 7 figures, 3 tables, accepted for publication in MNRAS

With the rise of a new generation of applications (e.g., virtual and augmented reality, artificial intelligence, etc) demanding stringent performance requirements, the need for networking solutions and architectures that can enable a higher Quality of Experience (QoE) is becoming increasingly important. While jointly optimizing application and network may increase the applications' QoE and simultaneously improve the utilization of network resources, such a paradigm has had limited success in real production networks. However, with the combination of revolutionary trends in (1) compute processing demands, (2) networking capabilities, and (3) sustainable business models, it is high time the community explores the full potential of deeper integration between application and network. In this paper, recent trends observed over the past few years are systematically reviewed. These include the paradigm shift in modern communication services towards computing-driven applications, such as on-site AI training, advances in programmable network technologies like Software Defined Networking (SDN), and new business models incentivizing collaboration and cooperation between parties. Following this, successful scenarios that benefit from various forms of deeper network-application integration are reported, highlighting their considerable potential. A unified framework is then introduced, providing an overview of possible architecture paradigms for network-application integration and bringing awareness to existing abstractions, mechanisms, tools, and their potential combinations. The paper concludes with a discussion of several remaining challenges in building practical network-application integrated systems.

In this paper we continue to develop the homotopy method for solving of the non linear evolution equation for the diffractive production in deep inelastic scattering(DIS). We introduce part of the nonlinear corrections as a first step of this approach. This simplified nonlinear evolution equation is solved analytically taking into account the initial and boundary conditions for the process. At the second step of our approach we demonstrated that the perturbative procedure can be used for the remaining parts of the non-linear corrections. It turns out that these corrections are small and can be estimated in the regular iterative procedure., Comment: 22 pages, 16 figures in pdf files

Rapport is known as a conversational aspect focusing on relationship building, which influences outcomes in collaborative tasks. This study aims to establish human-agent rapport through small talk by using a rapport-building strategy. We implemented this strategy for the virtual agents based on dialogue strategies by prompting a large language model (LLM). In particular, we utilized two dialogue strategies-predefined sequence and free-form-to guide the dialogue generation framework. We conducted analyses based on human evaluations, examining correlations between total turn, utterance characters, rapport score, and user experience variables: naturalness, satisfaction, interest, engagement, and usability. We investigated correlations between rapport score and naturalness, satisfaction, engagement, and conversation flow. Our experimental results also indicated that using free-form to prompt the rapport-building strategy performed the best in subjective scores., Comment: will be presented at INTERSPEECH 2024

We investigate the notion of curvature in the context of Liouville quantum gravity (LQG) surfaces. We define the Gaussian curvature for LQG, which we conjecture is the scaling limit of discrete curvature on random planar maps. Motivated by this, we study asymptotics for the discrete curvature of $\epsilon$-mated CRT maps. More precisely, we prove that the discrete curvature integrated against a $C_c^2$ test function is of order $\epsilon^{o(1)},$ which is consistent with our scaling limit conjecture. On the other hand, we prove the total discrete curvature on a fixed space-filling SLE segment scaled by $\epsilon^{\frac{1}{4}}$ converges in distribution to an explicit random variable.

The slope problem in holomorphic dynamics in the unit disk goes back to Wolff in 1929. However, there have been several contributions to this problem in the last decade. In this article the problem is revisited, comparing the discrete and continuous cases. Some advances are derived in the discrete parabolic case of zero hyperbolic step, showing that the set of slopes has to be a closed interval which is independent of the initial point. The continuous setting is used to show that any such interval is a possible example. In addition, the set of slopes of a family of parabolic function is discussed, leading to examples of functions with some regularity whose set of slopes is non-trivial.

The Lorentz Invariance Violation (LIV), a proposed consequence of certain quantum gravity (QG) scenarios, could instigate an energy-dependent group velocity for ultra-relativistic particles. This energy dependence, although suppressed by the massive QG energy scale $E_\mathrm{QG}$, expected to be on the level of the Planck energy $1.22 \times 10^{19}$ GeV, is potentially detectable in astrophysical observations. In this scenario, the cosmological distances traversed by photons act as an amplifier for this effect. By leveraging the observation of a remarkable flare from the blazar Mrk\,421, recorded at energies above 100 GeV by the MAGIC telescopes on the night of April 25 to 26, 2014, we look for time delays scaling linearly and quadratically with the photon energies. Using for the first time in LIV studies a binned-likelihood approach we set constraints on the QG energy scale. For the linear scenario, we set $95\%$ lower limits $E_\mathrm{QG}>2.7\times10^{17}$ GeV for the subluminal case and $E_\mathrm{QG}> 3.6 \times10^{17}$ GeV for the superluminal case. For the quadratic scenario, the $95\%$ lower limits for the subluminal and superluminal cases are $E_\mathrm{QG}>2.6 \times10^{10}$ GeV and $E_\mathrm{QG}>2.5\times10^{10}$ GeV, respectively.