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In this paper we study the $L^p$ boundedness of the centred and the uncentred Hardy--Littlewood maximal operators on certain Riemannian manifolds with bounded geometry. Our results complement those of various authors. We show that, under mild assumptions, $L^p$ estimates for the centred operator are ``stable'' under conformal changes of the metric, and prove sharp~$L^p$ estimates for the centred operator on Riemannian models with pinched negative scalar curvature. Furthermore, we prove that the centred operator is of weak type $(1,1)$ on the connected sum of two space forms with negative curvature, whereas the uncentred operator is, perhaps surprisingly, bounded only on $L^\infty$. We also prove that if two locally doubling geodesic metric measure spaces enjoying the uniform ball size condition are strictly quasi-isometric, then they share the same boundedness properties for both the centred and the uncentred maximal operator. Finally, we discuss some $L^p$ mapping properties for the centred operator on a specific Riemannian surface introduced by Str\"omberg, providing new interesting results., Comment: 38 pages, 1 figure

The Athena mission entered a redefinition phase in July 2022, driven by the imperative to reduce the mission cost at completion for the European Space Agency below an acceptable target, while maintaining the flagship nature of its science return. This notably called for a complete redesign of the X-ray Integral Field Unit (X-IFU) cryogenic architecture towards a simpler active cooling chain. Passive cooling via successive radiative panels at spacecraft level is now used to provide a 50 K thermal environment to an X-IFU owned cryostat. 4.5 K cooling is achieved via a single remote active cryocooler unit, while a multi-stage Adiabatic Demagnetization Refrigerator ensures heat lift down to the 50 mK required by the detectors. Amidst these changes, the core concept of the readout chain remains robust, employing Transition Edge Sensor microcalorimeters and a SQUID-based Time-Division Multiplexing scheme. Noteworthy is the introduction of a slower pixel. This enables an increase in the multiplexing factor (from 34 to 48) without compromising the instrument energy resolution, hence keeping significant system margins to the new 4 eV resolution requirement. This allows reducing the number of channels by more than a factor two, and thus the resource demands on the system, while keeping a 4' field of view (compared to 5' before). In this article, we will give an overview of this new architecture, before detailing its anticipated performances. Finally, we will present the new X-IFU schedule, with its short term focus on demonstration activities towards a mission adoption in early 2027., Comment: 44 pages, 14 figures, accepted for publication in Experimental Astronomy

This paper aims to describe the Pointing Reconstruction Model (PRM) and the prototype Star Tracker, which will be mounted on LSPE-Strip, a microwave Q- and W-band CMB telescope planned for installation at the "Observatorio del Teide" in Tenerife. The PRM integrates information on the instantaneous attitude provided by the telescope control system to determine the actual pointing direction and focal plane orientation of the telescope. It accounts for various non-idealities in the telescope setup, represented by eight configuration angles, which will be calibrated using the Star Tracker. Following the derivation of the PRM formalism and its implementation, we investigate the pointing errors caused by incorrect calibration of these configuration angles to validate the required 1 arcminute maximum systematic pointing error for the LSPE-Strip survey. This paper also describes the main structure and operations of the Star Tracker and presents the results of a campaign of actual sky observations conducted with a prototype. The results demonstrate a Star Tracker RMS accuracy of approximately 3 arcseconds, while systematic errors remain below 10 arcseconds. Based on these results, we analyzed the problem of reconstructing the PRM configuration angles. Two methods for intercalibrating the Star Tracker's pointing direction with respect to the focal plane's pointing direction were examined: (1) observations of planets and (2) observations of a drone carrying both an optical beacon and a radio beacon. In the first case, an intercalibration accuracy between 1/3 arcminute and 1 arcminute is achievable. In the second case, the expected intercalibration accuracy ranges from 0.25 arcminute to 1 arcminute., Comment: 37 pages; 16 figures; 5 tables; the limited length of the arXiv abstract required shortening the original abstract, which is presented in its full length in the PDF; paper accepted for pubblication 2025 jan 06 in the Journal of Instrumentation (JINST)

Machine Learning (ML) is driving a revolution in the way scientists design, develop, and deploy data-intensive software. However, the adoption of ML presents new challenges for the computing infrastructure, particularly in terms of provisioning and orchestrating access to hardware accelerators for development, testing, and production. The INFN-funded project AI_INFN ("Artificial Intelligence at INFN") aims at fostering the adoption of ML techniques within INFN use cases by providing support on multiple aspects, including the provision of AI-tailored computing resources. It leverages cloud-native solutions in the context of INFN Cloud, to share hardware accelerators as effectively as possible, ensuring the diversity of the Institute's research activities is not compromised. In this contribution, we provide an update on the commissioning of a Kubernetes platform designed to ease the development of GPU-powered data analysis workflows and their scalability on heterogeneous, distributed computing resources, possibly federated as Virtual Kubelets with the interLink provider., Comment: Under review in EPJ Web of Conferences (CHEP 2024)

Dust is a fundamental component of the interstellar medium (ISM) within galaxies, as dust grains are highly efficient absorbers of UV and optical photons. Accurately quantifying this obscuration is crucial for interpreting galaxy spectral energy distributions (SEDs). The extinction curves in the Milky Way (MW) and Large Magellanic Cloud (LMC) exhibit a strong feature known as the 2175A UV bump, most often attributed to small carbonaceous dust grains. This feature was recently detected in faint galaxies out to z~7 suggesting rapid formation channels. Here we report the detection of a strong UV bump in a luminous Lyman-break galaxy at z = 7.11235, GNWY-7379420231, through observations taken as part of the NIRSpec Wide GTO survey. We fit a dust attenuation curve that is consistent with the MW extinction curve within 1{\sigma}, in a galaxy just ~700 Myr after the Big Bang. From the integrated spectrum, we infer a young mass-weighted age (t* ~ 22-59 Myr) for this galaxy, however spatially resolved SED fitting unveils the presence of an older stellar population (t* ~ 252 Myr). Furthermore, morphological analysis provides evidence for a potential merger. The underlying older stellar population suggests the merging system could be pre-enriched, with the dust illuminated by a merger-induced starburst. Moreover, turbulence driven by stellar feedback in this bursty region may be driving PAH formation through top-down shattering. The presence of a UV bump in GNWY-7379420231 solidifies growing evidence for the rapid evolution of dust properties within the first billion years of cosmic time., Comment: Submitted to MNRAS

COCOA (COmpact COmpton cAmera) is a next-generation, cost-effective gamma-ray telescope designed for astrophysical observations in the MeV energy range. The detector comprises a scatterer volume employing the LiquidO detection technology and an array of scintillating crystals acting as absorber. Surrounding plastic scintillator panels serve as a veto system for charged particles. The detector's compact, scalable design enables flexible deployment on microsatellites or high-altitude balloons. Gamma rays at MeV energies have not been well explored historically (the so-called "MeV gap") and COCOA has the potential to improve the sensitivity in this energy band by up to two orders of magnitude., Comment: 12 pages, 16 figures

We study soliton and black hole solutions with scalar hair in AdS$_3$ in a theory with a Maxwell field and a charged scalar field with double trace boundary conditions, which can trigger the dual boundary theory to become a superconductor. We investigate the phase diagram as a function of the temperature $T$ and of the double trace coupling $\kappa$ and we find a rich pattern of phase transitions, which can be of the Hawking-Page kind or can be due to the condensation of the order parameter. We also find a transition between vortex solutions and the zero temperature limit of the black hole for a critical value of the double trace coupling $\kappa$. The Little-Park periodicity is realized for the dual of the black hole solution with hair as a shift in the winding number and in the gauge field., Comment: 34 pages, 18 figures

In physics, all dynamical equations that describe fundamental interactions are second order ordinary differential equations in the time derivatives. In the literature, this property is traced back to a result obtained by Ostrogradski in the mid 19th century, which is the technical basis of a 'no-go' theorem for higher order theories. In this work, we review the connection of symmetry properties with the order of dynamical equations, before reconsidering Ostrogradski's result. Then, we show how Ostrogradski's conclusion is reached by applying to higher order theories concepts and method that have been specifically developed for second order theories. We discuss a potential lack of consistency in this approach, to support the claim that Ostrogradski's result applies to a class of higher order theories that is nowhere representative of generic ones: we support this claim by giving an example of a higher-order Lagrangian that is asymptotically stable, but that would be unstable under Ostrogradski's criterion. We also conclude that, when considering higher order theories as fundamental, we may need to reconsider and extend the conceptual framework on which our standard treatment of second order theories is based., Comment: Submitted to Philosophical Transactions of the Royal Society A

Having everything interconnected through the Internet, including vehicle onboard systems, is making security a primary concern in the automotive domain as well. Although Ethernet and CAN XL provide link-level security based on symmetric cryptography, they do not support origin authentication for multicast transmissions. Asymmetric cryptography is unsuitable for networked embedded control systems with real-time constraints and limited computational resources. In these cases, solutions derived from the TESLA broadcast authentication protocol may constitute a more suitable option. In this paper, some such strategies are presented and analyzed that allow for multicast origin authentication, also improving robustness to frame losses by means of interleaved keychains. A flexible authentication mechanism that relies on a unified receiver is then proposed, which enables transmitters to select strategies at runtime, to achieve the best compromise among security, reliability, and resource consumption., Comment: 11 pages, 2025

The study of many-body quantum systems out of equilibrium remains a significant challenge with complexity barriers arising in both state and operator-based representations. In this work, we review recent approaches based on finding better contraction strategies for the full spatio-temporal tensor networks that encode the path integral of the dynamics, as well as the conceptual integration of influence functionals, process tensors, and transfer matrices within the tensor network formalism. We discuss recent algorithmic developments, highlight the complexity of influence functionals in various dynamical regimes and present consistent results of different communities, showing how ergodic dynamics render these functionals exponentially difficult to compress. Finally, we provide an outlook on strategies to encode complementary influence functional overlaps, paving the way for accurate descriptions of open and closed quantum systems with tensor networks., Comment: 17 pages, 10 figures. Invited mini-review, comments welcome

Quantum computer emulators model the behavior and error rates of specific quantum processors. Without accurate noise models in these emulators, it is challenging for users to optimize and debug executable quantum programs prior to running them on the quantum device, as device-specific noise is not properly accounted for. To overcome this challenge, we introduce a general protocol to approximate device-specific emulators without requiring pulse-level control. By applying machine learning to data obtained from gate set tomography, we construct a device-specific emulator by predicting the noise model input parameters that best match the target device. We demonstrate the effectiveness of our protocol's emulator in estimating the unitary coupled cluster energy of the H$_2$ molecule and compare the results with those from actual quantum hardware. Remarkably, our noise model captures device noise with high accuracy, achieving a mean absolute difference of just 0.3\% in expectation value relative to the state-vector simulation., Comment: 12 pages, 5 figures

This paper introduces the SOAR framework for imitation learning. SOAR is an algorithmic template that learns a policy from expert demonstrations with a primal dual style algorithm that alternates cost and policy updates. Within the policy updates, the SOAR framework uses an actor critic method with multiple critics to estimate the critic uncertainty and build an optimistic critic fundamental to drive exploration. When instantiated in the tabular setting, we get a provable algorithm with guarantees that matches the best known results in $\epsilon$. Practically, the SOAR template is shown to boost consistently the performance of imitation learning algorithms based on Soft Actor Critic such as f-IRL, ML-IRL and CSIL in several MuJoCo environments. Overall, thanks to SOAR, the required number of episodes to achieve the same performance is reduced by half.

Graphene on SiC intercalated with two-dimensional metal layers, such as Pt, offers a versatile platform for applications in spintronics, catalysis, and beyond. Recent studies have demonstrated that Pt atoms can intercalate at the heterointerface between SiC(0001) and the C-rich $(6\sqrt{3}\times6\sqrt{3})$R30{\deg} reconstructed surface (hereafter referred as the buffer layer). However, key aspects such as intercalated phase structure and intercalation mechanisms remain unclear. In this work, we investigate changes in morphology, chemistry, and electronic structure for both buffer layer and monolayer graphene grown on SiC(0001) following Pt deposition and annealing cycles, which eventually led to Pt intercalation at temperatures above 500{\deg}C. Atomic-resolution imaging of the buffer layer reveals a single intercalated Pt layer that removes the periodic corrugation of the buffer layer, arising from partial bonding of C-atoms with Si-atoms of the substrate. In monolayer graphene, the Pt-intercalated regions exhibit a two-level structure: the first level corresponds to a Pt layer intercalated below the buffer layer, while the second level contains a second Pt layer, giving rise to a $(12\times12)$ superstructure relative to graphene. Upon intercalation, Pt atoms appear as silicides, indicating a reaction with Si atoms from the substrate. Additionally, charge neutral $\pi$-bands corresponding to quasi-free-standing monolayer and bilayer graphene emerge. Analysis of multiple samples, coupled with a temperature-dependent study of the intercalation rate, demonstrates the pivotal role of buffer layer regions in facilitating the Pt intercalation in monolayer graphene. These findings provide valuable insight into Pt intercalation, advancing the potential for applications.

Effective personalization of LLMs is critical for a broad range of user-interfacing applications such as virtual assistants and content curation. Inspired by the strong in-context learning capabilities of LLMs, we propose Few-Shot Preference Optimization (FSPO), which reframes reward modeling as a meta-learning problem. Under this framework, an LLM learns to quickly adapt to a user via a few labeled preferences from that user, constructing a personalized reward function for them. Additionally, since real-world preference data is scarce and challenging to collect at scale, we propose careful design choices to construct synthetic preference datasets for personalization, generating over 1M synthetic personalized preferences using publicly available LLMs. In particular, to successfully transfer from synthetic data to real users, we find it crucial for the data to exhibit both high diversity and coherent, self-consistent structure. We evaluate FSPO on personalized open-ended generation for up to 1,500 synthetic users across across three domains: movie reviews, pedagogical adaptation based on educational background, and general question answering, along with a controlled human study. Overall, FSPO achieves an 87% Alpaca Eval winrate on average in generating responses that are personalized to synthetic users and a 72% winrate with real human users in open-ended question answering., Comment: Website: https://fewshot-preference-optimization.github.io/

Among the biogenic macroelements, phosphorus is the one bringing the most fascinating and unsolved mysteries for what concern its prebiotic history. It possibly landed on Earth as a metal phosphide (Schreibersite, (Fe,Ni)3P), throughout the Heavy Meteor Bombardment during the Archean Era. Its subsequent corrosion by water led to P-oxygenated compounds, which is the subject of this kinetic computational study, thus complementing our previous thermodynamic characterization. The reaction was studied at periodic DFT level, simulating the water corrosion reaction on the reactive Fe2NiP Schreibersite (001)2 surface. Results show that the timescale of the reaction at 350 K is of few hours., Comment: 18 pages, 2 Figures, 1 TOC

We introduce the use of Gaussian Processes (GPs) for the probabilistic forecasting of intermittent time series. The model is trained in a Bayesian framework that accounts for the uncertainty about the latent function and marginalizes it out when making predictions. We couple the latent GP variable with two types of forecast distributions: the negative binomial (NegBinGP) and the Tweedie distribution (TweedieGP). While the negative binomial has already been used in forecasting intermittent time series, this is the first time in which a fully parameterized Tweedie density is used for intermittent time series. We properly evaluate the Tweedie density, which is both zero-inflated and heavy tailed, avoiding simplifying assumptions made in existing models. We test our models on thousands of intermittent count time series. Results show that our models provide consistently better probabilistic forecasts than the competitors. In particular, TweedieGP obtains the best estimates of the highest quantiles, thus showing that it is more flexible than NegBinGP., Comment: Under review

Knowledge Graphs (KGs) are widely used in data-driven applications and downstream tasks, such as virtual assistants, recommendation systems, and semantic search. The accuracy of KGs directly impacts the reliability of the inferred knowledge and outcomes. Therefore, assessing the accuracy of a KG is essential for ensuring the quality of facts used in these tasks. However, the large size of real-world KGs makes manual triple-by-triple annotation impractical, thereby requiring sampling strategies to provide accuracy estimates with statistical guarantees. The current state-of-the-art approaches rely on Confidence Intervals (CIs), derived from frequentist statistics. While efficient, CIs have notable limitations and can lead to interpretation fallacies. In this paper, we propose to overcome the limitations of CIs by using \emph{Credible Intervals} (CrIs), which are grounded in Bayesian statistics. These intervals are more suitable for reliable post-data inference, particularly in KG accuracy evaluation. We prove that CrIs offer greater reliability and stronger guarantees than frequentist approaches in this context. Additionally, we introduce \emph{a}HPD, an adaptive algorithm that is more efficient for real-world KGs and statistically robust, addressing the interpretive challenges of CIs., Comment: 26 pages

A strong first-order phase transition in a dark sector may produce all or part of the low-frequency gravitational wave signal recently reported by the NANOGrav Collaboration and other pulsar timing arrays. Here we point out, with a simple toy model, that even if the amplitude of the gravitational wave background from the dark phase transition is insufficient to match the NANOGrav signal, a modified expansion rate at early times may considerably enhance the gravitational wave signal. In particular, a faster-than-standard expansion rate, triggered, for instance, by the presence of one or more additional sources of energy density redshifting with higher powers of temperatures than radiation, boosts upper limits on the gravitational wave signal from first-order cosmological phase transitions, enlarging the slate of possible dark sector scenarios matching the NANOGrav signal., Comment: 21 pages, 3 figures; comments welcome!

Antimonene, the two-dimensional phase of antimony, appears in two distinct allotropes when epitaxially grown on Bi2Se3: the puckered asymmetric washboard ({\alpha}) and buckled honeycomb ({\beta}) bilayer structures. As-deposited antimony films exhibit varying proportions of single {\alpha} and {\beta} structures. We identify the conditions necessary for ordered, pure-phase growth of single to triple {\beta}-antimonene bilayers. Additionally, we determine their electronic structure, work function, and characteristic core-level binding energies, offering an explanation for the relatively large chemical shifts observed among the different phases. This study not only establishes a protocol for achieving a single {\beta} phase of antimonene but also provides key signatures for distinguishing between the different allotropes using standard spectroscopic and microscopic techniques., Comment: 9 pages, 4 figures, 77 references

Providing Large Language Models with relevant contextual knowledge at inference time has been shown to greatly improve the quality of their generations. This is often achieved by prepending informative passages of text, or 'contexts', retrieved from external knowledge bases to their input. However, processing additional contexts online incurs significant computation costs that scale with their length. State Space Models (SSMs) offer a promising solution by allowing a database of contexts to be mapped onto fixed-dimensional states from which to start the generation. A key challenge arises when attempting to leverage information present across multiple contexts, since there is no straightforward way to condition generation on multiple independent states in existing SSMs. To address this, we leverage a simple mathematical relation derived from SSM dynamics to compose multiple states into one that efficiently approximates the effect of concatenating textual contexts. Since the temporal ordering of contexts can often be uninformative, we enforce permutation-invariance by efficiently averaging states obtained via our composition algorithm across all possible context orderings. We evaluate our resulting method on WikiText and MSMARCO in both zero-shot and fine-tuned settings, and show that we can match the strongest performing baseline while enjoying on average 5.4x speedup., Comment: Published in The Thirteenth International Conference on Learning Representations, ICLR 2025

Surface contamination on electrical grid insulators leads to an increase in leakage current until an electrical discharge occurs, which can result in a power system shutdown. To mitigate the possibility of disruptive faults resulting in a power outage, monitoring contamination and leakage current can help predict the progression of faults. Given this need, this paper proposes a hybrid deep learning (DL) model for predicting the increase in leakage current in high-voltage insulators. The hybrid structure considers a multi-criteria optimization using tree-structured Parzen estimation, an input stage filter for signal noise attenuation combined with a large language model (LLM) applied for time series forecasting. The proposed optimized LLM outperforms state-of-the-art DL models with a root-mean-square error equal to 2.24$\times10^{-4}$ for a short-term horizon and 1.21$\times10^{-3}$ for a medium-term horizon.

We prove the global existence of weak solutions of the one-dimensional Navier-Stokes-Korteweg (NSK) equations when the viscosity and the capillarity coefficients are power functions of the density, which may be zero on a set with positive measure. The proofs are based on a truncation argument combined with the Energy estimate and BD Entropy. Notably, we do not require any upper bound on the exponent of the power of the viscosity coefficient. In particular, we are able to consider very degenerate viscosity coefficient and to substantially improve previous results.

Most vaccines require multiple doses, the first to induce recognition and antibody production and subsequent doses to boost the primary response and achieve optimal protection. We show that properly prioritizing the administration of first and second doses can shift the epidemic threshold, separating the disease-free from the endemic state and potentially preventing widespread outbreaks. Assuming homogeneous mixing, we prove that at a low vaccination rate, the best strategy is to give absolute priority to first doses. In contrast, for high vaccination rates, we propose a scheduling that outperforms a first-come first-served approach. We identify the threshold that separates these two scenarios and derive the optimal prioritization scheme and inter-dose interval. Agent-based simulations on real and synthetic contact networks validate our findings. We provide specific guidelines for effective resource allocation, showing that adjusting the timing between primer and booster significantly impacts epidemic outcomes and can determine whether the disease persists or disappears., Comment: 5 pages, 5 figures

We explore a novel mechanism for dark matter production through the formation of light black holes from the collapse of dark baryons in confining SU(N) gauge theories in the large $N$ limit. While glueballs and mesons cannot form black holes under physically reasonable conditions, we prove that for appropriate ranges of the confinement scale, quark masses, number of colors $N$, and dark sector temperature, dark baryons can produce Planck-scale black hole relics in the early universe. Assuming the relics are stable, the abundance of both the dark baryon black hole population directly arising at confinement and that frozen in from dark glueball and meson pair annihilation are exponentially suppressed in $N$, leading to an upper limit $N\lesssim 100$ and of a few hundreds Planck units in mass for models where the black hole relics are the entirety of the dark matter. We present a detailed numerical study of the parameter space where this scenario is realized., Comment: 23 pages, 4 figures; comments, thoughts, and feedback warmly welcome!

Assuming that (1) the universe underwent a post-inflationary accelerated expansion phase driven by a fluid with equation of state $P=w\rho$ and $-1

We study the convergence of a linear atomic cluster expansion (ACE) potential with respect to its basis functions, in terms of the effective two-body interactions of elemental Carbon systems. We build ACE potentials with descriptor sets truncated at body-orders $K=2,3,4$ trained on pure dimers, or on large datasets of different diversities but without any dimers. Potentials trained on a more diverse dataset fare better in validation and result in a nontrivial dimer curve, but still very far from the theoretical two-body interaction calculated by DFT. Moreover, dimer curves between descriptor sets clipped at different $K$ do not seem to converge to a universal function for a given dataset. We conclude that machine learning potentials employing atomic cluster expansions optimize losses at low $K$ but fail to generalize and converge properties described by two-body interactions.

We investigate the dynamics of the ground state entanglement entropy for a discretized scalar field propagating within the Oppenheimer-Snyder collapse metric. Starting from a well-controlled initial configuration, we follow the system as it evolves toward the formation of a horizon and, eventually, a singularity. Our approach employs an Ermakov-like equation to determine the time-dependent ground state of the field and calculates the resulting entanglement entropy by tracing out the degrees of freedom inside a spherical region within the matter sphere. We find that the entanglement entropy exhibits nontrivial scaling and time dependence during collapse. Close to the horizon, the entropy can deviate from the simple area law, reflecting the rapid changes in geometry and field configuration. Although the model is idealized, these results provide insights into the generation and scaling of entanglement in the presence of realistic, dynamically evolving gravitational fields., Comment: 18 pages, 6 figures, 1 table

We propose a novel method for model-based time super-sampling of turbulent flow fields. The key enabler is the identification of an empirical Galerkin model from the projection of the Navier-Stokes equations on a data-tailored basis. The basis is obtained from a Proper Orthogonal Decomposition (POD) of the measured fields. Time super-sampling is thus achieved by a time-marching integration of the identified dynamical system, taking the original snapshots as initial conditions. Temporal continuity of the reconstructed velocity fields is achieved through a forward-backwards integration between consecutive measured Particle Image Velocimetry measurements of a turbulent jet flow. The results are compared with the interpolation of the POD temporal coefficients and the low-order reconstruction of data measured at a higher sampling rate. In both cases, the results obtained show the ability of the method to reconstruct the dynamics of the flow with small errors during several flow characteristic times.

In this paper we prove that if $1\tau$, and it is of weak type $(\tau,\tau)$, where $\tau := \log_ab$. A key step in the proof is a new structural theorem for Gromov hyperbolic spaces with $(a,b)$-pinched exponential growth at infinity, consisting in a discretisation of $X$ by means of certain graphs, introduced in this paper and called spider's webs, with ``good connectivity properties". Our result applies to trees with bounded geometry, and Cartan--Hadamard manifolds of pinched negative curvature, providing new boundedness results in these settings. The index $\tau$ is optimal in the sense that if $p<\tau$, then there exists $X$ satisfying the assumptions above such that $\mathcal M$ is not of weak type $(p,p)$. Furthermore, if $b>a^2$, then there are examples of spaces $X$ satisfying the assumptions above such that $\mathcal M$ bounded on $L^p(X)$ if and only if $p=\infty$.

We present the discovery of the radio afterglow of the most distant ultra-long gamma-ray burst (GRB) detected to date, GRB~220627A at redshift $z=3.084$. Its prompt gamma-ray light curve shows a double-pulse profile, with the pulses separated by a period of quiescence lasting ${\sim} 15\,$min, leading to early speculation it could be a strongly gravitationally lensed GRB. However, our analysis of the $\textit{Fermi}$/GBM spectra taken during the time intervals of both pulses show clear differences in their spectral energy distributions, disfavouring the lensing scenario. We observed the radio afterglow from $7$ to $456\,$d post-burst: an initial, steep decay ($F_{\nu} \propto t^{-2}$) is followed by a shallower decline ($F_{\nu} \propto t^{-1/2}$) after ${\sim} 20\,$d. Our afterglow modelling shows that these radio properties can be explained by the presence of a slow, wide ejecta component in addition to a fast, narrow ejecta component, consistent with the picture of a highly-collimated jet and its thermal cocoon decelerating into the ambient medium. The properties of the cocoon point toward a progenitor with a large stellar radius, supporting the blue supergiant scenario proposed for ultra-long GRBs. We also conducted an independent test of the lensing hypothesis via Very Long Baseline Interferometry (VLBI) observations at ${\sim} 12\,$d post-burst by searching, for the first time, for multiple images of the candidate lensed GRB afterglow. Our experiment highlighted the growing need for developments in real-time correlation capabilities for time-critical VLBI experiments, particularly as we advance towards the SKA and ngVLA era of radio astronomy., Comment: 19 pages, 7 figures; submitted to ApJ, comments are welcome

Variational inequalities play a pivotal role in a wide array of scientific and engineering applications. This project presents two techniques for adaptive mesh refinement (AMR) in the context of variational inequalities, with a specific focus on the classical obstacle problem. We propose two distinct AMR strategies: Variable Coefficient Elliptic Smoothing (VCES) and Unstructured Dilation Operator (UDO). VCES uses a nodal active set indicator function as the initial iterate to a time-dependent heat equation problem. Solving a single step of this problem has the effect of smoothing the indicator about the free boundary. We threshold this smoothed indicator function to identify elements near the free boundary. Key parameters such as timestep and threshold values significantly influence the efficacy of this method. The second strategy, UDO, focuses on the discrete identification of elements adjacent to the free boundary, employing a graph-based approach to mark neighboring elements for refinement. This technique resembles the dilation morphological operation in image processing, but tailored for unstructured meshes. We also examine the theory of variational inequalities, the convergence behavior of finite element solutions, and implementation in the Firedrake finite element library. Convergence analysis reveals that accurate free boundary estimation is pivotal for solver performance. Numerical experiments demonstrate the effectiveness of the proposed methods in dynamically enhancing mesh resolution around free boundaries, thereby improving the convergence rates and computational efficiency of variational inequality solvers. Our approach integrates seamlessly with existing Firedrake numerical solvers, and it is promising for solving more complex free boundary problems., Comment: 60 pages, 26 figures, 1 table

We introduce a subproduct system of finite-dimensional Hilbert spaces using the Motzkin planar algebra and its Jones-Wenzl idempotents, which generalizes the Temperley-Lieb subproduct system of Habbestad and Neshveyev. We provide a description of the corresponding Toeplitz C$^*$-algebra as a universal C$^*$-algebra, defined in terms of generators and relations, and we highlight properties of its representation theory.

Each year, the European Space Agency (ESA) organizes challenges for university students, from BSc to PhD levels. The ESA Concurrent Engineering Challange 2024 was hosted by four Concurrent Design Facilites (CDF) across Europe: ESEC Galazia, ISAE SUPAERO, the University of Athens, and the University of Portsmouth. A total of 102 students participated in the event. Over five days, students worked on a feasibility study for a space mission, simulating ESA's design session at ESTEC, the ESA headquarters. Students were divided into specializes groups based on their backgrounds, reflecting ESA's concurrent engineering teams. This paper discusses the design of subsystems by students, their trade-off results, and the outcomes of the CDF study. It highlights the effectiveness of concurrent engineering, which enabled rapid and efficient results even from non-esxpert teams. The future development roadmap and lessons learned are also presented. The students used CDP4-Comet software within the replicated ESA CDF, resulting in the PEDRO-V mission proposal: Planetary Exploration Deployment and Research Operation - Venus. The teams collaboratively defined the Concept of Operations, identified actors, worst-case scenarios, use cases, and activities. Their output included a list of requirements, a draft product breakdown structure, and key subsystems information. The concurrent engineering process led to continuous improvement and convergence of key parameters. This approach proved to be effective by aligning different teams' solutions and comparing them to similar missions. The PEDRO-V mission feasibility was confirmed, demonstrating the potential of concurrent engineering in accademic settings for space missions. (summarized with AI), Comment: ESA SECESA 2024 Conference, Strasbourg (France), 8 pages

In the last decade of Active Galactic Nuclei (AGN) monitoring programs, the Mets\"ahovi Radio Observatory detected multiple times seven powerful flaring narrow-line Seyfert 1 (NLS1) galaxies at 37 GHz. Several hypotheses have been proposed, but the understanding of this unique phenomenon is still far. To look at the case from a different point of view, we performed an emission line analysis of the optical spectra, with the aim of identifying similarities among the sources, that can be in turn possibly tied with the radio behavior. Our data were obtained with the Gran Telescopio Canarias. The results we obtained show that six out of seven sources have typical properties for the NLS1 class, and one of them is an intermediate Seyfert galaxy. We found on average black hole masses above the median value for the class (> 10$^7$ M$_\odot$), and a strong Fe II emission, which could be a proxy for an intense ongoing accretion activity. Although interesting, the characteristics we found are not unusual for these kind of AGN: the optical spectra of our sources do not related with their unique radio properties. Therefore, further multi-wavelength studies will be necessary to narrow the field of hypotheses for this peculiar phenomenon., Comment: 22 pages with appendix, 6 figures and 4 tables in the main text. Accepted for publication in A&A

The rampdown in tokamak operations is a difficult to simulate phase during which the plasma is often pushed towards multiple instability limits. To address this challenge, and reduce the risk of disrupting operations, we leverage recent advances in Scientific Machine Learning (SciML) to develop a neural state-space model (NSSM) that predicts plasma dynamics during Tokamak \`a Configuration Variable (TCV) rampdowns. By integrating simple physics structure and data-driven models, the NSSM efficiently learns plasma dynamics during the rampdown from a modest dataset of 311 pulses with only five pulses in the reactor relevant high performance regime. The NSSM is parallelized across uncertainties, and reinforcement learning (RL) is applied to design trajectories that avoid multiple instability limits with high probability. Experiments at TCV ramping down high performance plasmas show statistically significant improvements in current and energy at plasma termination, with improvements in speed through continuous re-training. A predict-first experiment, increasing plasma current by 20\% from baseline, demonstrates the NSSM's ability to make small extrapolations with sufficient accuracy to design trajectories that successfully terminate the pulse. The developed approach paves the way for designing tokamak controls with robustness to considerable uncertainty, and demonstrates the relevance of the SciML approach to learning plasma dynamics for rapidly developing robust trajectories and controls during the incremental campaigns of upcoming burning plasma tokamaks.

Transmission loss represents a major obstacle for the demonstration of quantum Bell nonlocality over long distances and applications that rely on it, such as Device-Independent Quantum Key Distribution. In this work, we investigate the recently proposed concept of routed Bell experiments, in which one party can perform measurements either near or far from the source. We prove that routed Bell tests can certify quantum correlations for arbitrary loss on the channel to the distant device, using only entangled qubits. This is achieved by applying the concepts of self-testing and quantum steering to routed Bell tests. Finally, we present a DIQKD protocol for the routed Bell scenario that can operate over arbitrary distances., Comment: 5+15 pages, 2 figures

This paper explores the possibility of learning custom tokens for representing new concepts in Vision-Language Models (VLMs). Our aim is to learn tokens that can be effective for both discriminative and generative tasks while composing well with words to form new input queries. The targeted concept is specified in terms of a small set of images and a parent concept described using text. We operate on CLIP text features and propose to use a combination of a textual inversion loss and a classification loss to ensure that text features of the learned token are aligned with image features of the concept in the CLIP embedding space. We restrict the learned token to a low-dimensional subspace spanned by tokens for attributes that are appropriate for the given super-class. These modifications improve the quality of compositions of the learned token with natural language for generating new scenes. Further, we show that learned custom tokens can be used to form queries for text-to-image retrieval task, and also have the important benefit that composite queries can be visualized to ensure that the desired concept is faithfully encoded. Based on this, we introduce the method of Generation Aided Image Retrieval, where the query is modified at inference time to better suit the search intent. On the DeepFashion2 dataset, our method improves Mean Reciprocal Retrieval (MRR) over relevant baselines by 7%.

The unexpectedly high nitrogen-to-oxygen (N/O) ratios observed in high-redshift (z) galaxies have challenged our understanding of early star formation. Notably, many of these nitrogen-rich galaxies show signatures of active galactic nuclei (AGNs), suggesting a possible connection between black hole formation and nitrogen enrichment. To explore this connection, we analyse stacked spectra of z=4-7 broad-line and narrow-line AGNs using deep NIRSpec data from the JADES survey. We identify a significant Niii] quintuplet and a high electron density ($\sim10^{4}\,\mathrm{cm^{-3}}$) only in the broad-line AGN stack, indicating nitrogen-rich ($\log(\mathrm{N/C})\simeq0.5$, $\log(\mathrm{N/O})>-0.6$) and dense gas similar to the high-z nitrogen-rich galaxies. Our findings suggest that dense nuclear star formation may trap nitrogen-rich gas in proto-globular clusters, in line with the high N/O observed in local globular clusters; associated runaway stellar collisions could produce intermediate-mass black hole seeds, as predicted by some models and simulations, whose accretion results into AGN signatures. These findings support scenarios connecting the early black hole seeding and growth to merging processes within and between proto-globular clusters in primeval galaxies., Comment: Submitted to MNRAS Letter

Open-vocabulary semantic segmentation enables models to identify novel object categories beyond their training data. While this flexibility represents a significant advancement, current approaches still rely on manually specified class names as input, creating an inherent bottleneck in real-world applications. This work proposes a Vocabulary-Free Semantic Segmentation pipeline, eliminating the need for predefined class vocabularies. Specifically, we address the chicken-and-egg problem where users need knowledge of all potential objects within a scene to identify them, yet the purpose of segmentation is often to discover these objects. The proposed approach leverages Vision-Language Models to automatically recognize objects and generate appropriate class names, aiming to solve the challenge of class specification and naming quality. Through extensive experiments on several public datasets, we highlight the crucial role of the text encoder in model performance, particularly when the image text classes are paired with generated descriptions. Despite the challenges introduced by the sensitivity of the segmentation text encoder to false negatives within the class tagging process, which adds complexity to the task, we demonstrate that our fully automated pipeline significantly enhances vocabulary-free segmentation accuracy across diverse real-world scenarios., Comment: Submitted to: Pattern Recognition Letters, Klara Reichard and Giulia Rizzoli equally contributed to this work

Chord recognition serves as a critical task in music information retrieval due to the abstract and descriptive nature of chords in music analysis. While audio chord recognition systems have achieved significant accuracy for small vocabularies (e.g., major/minor chords), large-vocabulary chord recognition remains a challenging problem. This complexity also arises from the inherent long-tail distribution of chords, where rare chord types are underrepresented in most datasets, leading to insufficient training samples. Effective chord recognition requires leveraging contextual information from audio sequences, yet existing models, such as combinations of convolutional neural networks, bidirectional long short-term memory networks, and bidirectional transformers, face limitations in capturing long-term dependencies and exhibit suboptimal performance on large-vocabulary chord recognition tasks. This work proposes ChordFormer, a novel conformer-based architecture designed to tackle structural chord recognition (e.g., triads, bass, sevenths) for large vocabularies. ChordFormer leverages conformer blocks that integrate convolutional neural networks with transformers, thus enabling the model to capture both local patterns and global dependencies effectively. By addressing challenges such as class imbalance through a reweighted loss function and structured chord representations, ChordFormer outperforms state-of-the-art models, achieving a 2% improvement in frame-wise accuracy and a 6% increase in class-wise accuracy on large-vocabulary chord datasets. Furthermore, ChordFormer excels in handling class imbalance, providing robust and balanced recognition across chord types. This approach bridges the gap between theoretical music knowledge and practical applications, advancing the field of large-vocabulary chord recognition., Comment: 13 pages, 4 figures

Concept-based Models are neural networks that learn a concept extractor to map inputs to high-level concepts and an inference layer to translate these into predictions. Ensuring these modules produce interpretable concepts and behave reliably in out-of-distribution is crucial, yet the conditions for achieving this remain unclear. We study this problem by establishing a novel connection between Concept-based Models and reasoning shortcuts (RSs), a common issue where models achieve high accuracy by learning low-quality concepts, even when the inference layer is fixed and provided upfront. Specifically, we first extend RSs to the more complex setting of Concept-based Models and then derive theoretical conditions for identifying both the concepts and the inference layer. Our empirical results highlight the impact of reasoning shortcuts and show that existing methods, even when combined with multiple natural mitigation strategies, often fail to meet these conditions in practice.

Quantum computing promises to revolutionize our understanding of the limits of computation, and its implications in cryptography have long been evident. Today, cryptographers are actively devising post-quantum solutions to counter the threats posed by quantum-enabled adversaries. Meanwhile, quantum scientists are innovating quantum protocols to empower defenders. However, the broader impact of quantum computing and quantum machine learning (QML) on other cybersecurity domains still needs to be explored. In this work, we investigate the potential impact of QML on cybersecurity applications of traditional ML. First, we explore the potential advantages of quantum computing in machine learning problems specifically related to cybersecurity. Then, we describe a methodology to quantify the future impact of fault-tolerant QML algorithms on real-world problems. As a case study, we apply our approach to standard methods and datasets in network intrusion detection, one of the most studied applications of machine learning in cybersecurity. Our results provide insight into the conditions for obtaining a quantum advantage and the need for future quantum hardware and software advancements., Comment: Computers & Security (2025): 104341

We conducted precise measurements of Active Galactic Nuclei (AGNs) clustering at $z\sim1$ and $z\sim2$ by measuring the two-point cross-correlation function (CCF) between galaxies and X-ray-selected AGNs, and the two-point auto-correlation function (ACF) of galaxies in the COSMOS field to interpret the CCF results. The galaxy sample was selected from the COSMOS2015 catalog, while the AGN sample was chosen from the {\sl Chandra} COSMOS-Legacy survey catalog. For the AGN samples at $z\sim1$ and $z\sim2$, we calculated AGN bias values of $b=1.16\ (1.16;1.31)$ and $b=2.95\ (2.30;3.55)$, respectively. These values correspond to typical host dark matter halo (DMH) masses of log$(M_{\rm typ}/M_{\odot})=11.82\ (11.82;12.12)$ and log$(M_{\rm typ}/M_{\odot})=12.80\ (12.38;13.06)$, respectively. Subsequently, we performed Halo Occupation Distribution (HOD) modeling of X-ray-selected AGNs using the CCF and ACF of galaxies. We have found a significant satellite AGN population at $z\sim 1$ all over the DMH mass ($M_{\rm DMH}$) range occupied by AGNs. While $z\sim 2$ AGNs in our sample are associated with higher mass DMHs and smaller satellite fractions. The HOD analysis suggests a marginal tendency of increasing satellite slope with redshift, but larger samples are needed to confirm this with sufficient statistical significance. We find that the best-fit values of satellite slope in both redshift bins are greater than 0, suggesting tendencies of increasing satellite AGN number with $M_{\rm DMH}$., Comment: 20 pages, 13 figures, accepted for publication in ApJ

The Integrated Sensing and Communications (ISAC) paradigm is anticipated to be a cornerstone of the upcoming 6G networks. In order to optimize the use of wireless resources, 6G ISAC systems need to harness the communication data payload signals, which are inherently random, for both sensing and communication (S&C) purposes. This tutorial paper provides a comprehensive technical overview of the fundamental theory and signal processing methodologies for ISAC transmission with random communication signals. We begin by introducing the deterministic-random tradeoff (DRT) between S&C from an information-theoretic perspective, emphasizing the need for specialized signal processing techniques tailored to random ISAC signals. Building on this foundation, we review the core signal models and processing pipelines for communication-centric ISAC systems, and analyze the average squared auto-correlation function (ACF) of random ISAC signals, which serves as a fundamental performance metric for multi-target ranging tasks. Drawing insights from these theoretical results, we outline the design principles for the three key components of communication-centric ISAC systems: modulation schemes, constellation design, and pulse shaping filters. The goal is to either enhance sensing performance without compromising communication efficiency or to establish a scalable tradeoff between the two. We then extend our analysis from a single-antenna ISAC system to its multi-antenna counterpart, discussing recent advancements in multi-input multi-output (MIMO) precoding techniques specifically designed for random ISAC signals. We conclude by highlighting several open challenges and future research directions in the field of sensing with communication signals., Comment: 25 pages, 13 figures, submitted to IEEE for possible publication

Gravitational lensing is a universal phenomenon: it affects both gravitational waves (GWs) and electromagnetic signals travelling through the gravitational field of a massive object. In this work, we explore the prospects of observing lensed GW signals from the mergers of massive black holes, lensed by dark matter halos composed of Fuzzy Dark Matter (FDM), which form dense cores known as solitons. We focus on wave optics phenomena, where frequency-dependent signatures can be observed in the weak lensing regime (i.e. single-image). Our results show that lensing diffraction signatures differ for low-mass halos in FDM, and can reveal the presence of a solitonic core. Furthermore, we demonstrate that FDM and cold dark matter profiles can be distinguished in GW signals from binary massive black hole mergers, which will be observed by the Laser Interferometer Space Antenna (LISA) mission. However, the dense solitonic core does not substantially enhance the detectability of FDM halos at large source-lens offsets, relative to standard cold dark matter. Our analysis confirms FDM halos as a promising signature of dark matter on GW observations, Comment: 22 pages, 7 figures

The ultraviolet/optical telescope (UVOT) onboard the Neil Gehrels Swift Observatory is capable of imaging with 7 lenticular filters and of taking slitless spectra with 2 grisms. Both image and grism data have been widely used to study gamma-ray bursts, supernovae and other ultraviolet/optical transients, and proved UVOT is a powerful instrument in time-domain astronomy. However, the second order contamination, for blue sources, strongly limits the red end of ultraviolet (UV) grism spectra. This, in turn, reduces the valid wavelength range to only about 33% of the total. However, to explore the broadband spectral energy distribution of GRBs at the early stage, a larger valid wavelength range is required. Hence based on the uvotpy package, we propose a method to remove the second order contamination from UV grism spectra (nominal mode) up to about 4000\AA, i.e., about 70% of the full wavelength range. The 1-sigma systematic uncertainty of this method is about 11.2%. In addition, if a source is red enough, the red end of the valid range could reach about 5000\AA. The source code is available on GitHub., Comment: 14 pages, 8 figures, 3 tables. Accepted by the ApJS. Updated the DOI & acknowledgments in V2

We obtained five new infinite families of linear near-MDS codes uniformly packed in the wide sense (UPWS); these codes are also almost perfect multiple coverings of the deep holes or farthest-off points (APMCF), i.e.\ the vectors lying at distance $R$ (covering radius) from the code. The families are constructed by $m$-lifting when one takes a starting code $C$ over the ground Galois field $F_q$ with a parity check matrix $H(C)$ and then considers the codes $C_m$ over $F_{q^m}$, $m\ge2$, with the same parity check matrix $H(C)$. As starting codes we used the ternary perfect Golay code and codes obtained by its extension and puncturing. To prove the needed combinatorial properties (UPWS and APMCF) we used the $m$-lifting of the dual codes and features of near-MDS codes. A general theorem on infinite families of UPWS near-MDS codes is proved., Comment: 27 pages