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This document is comprised of a collection of updated preliminary parameters for the key parts of the muon collider. The updated preliminary parameters follow on from the October 2023 Tentative Parameters Report. Particular attention has been given to regions of the facility that are believed to hold greater technical uncertainty in their design and that have a strong impact on the cost and power consumption of the facility. The data is collected from a collaborative spreadsheet and transferred to overleaf.

We present the results of Phase I of an ongoing review of Monte Carlo tools relevant for low-energy hadronic cross sections. This includes a detailed comparison of Monte Carlo codes for electron-positron scattering into a muon pair, pion pair, and electron pair, for scan and radiative-return experiments. After discussing the various approaches that are used and effects that are included, we show differential cross sections obtained with AfkQed, BabaYaga@NLO, KKMC, MCGPJ, McMule, Phokhara, and Sherpa, for scenarios that are inspired by experiments providing input for the dispersive evaluation of the hadronic vacuum polarisation., Comment: RadioMonteCarLow 2 Working Group report Phase I, 67 pages, 34 figures

The Cluster HEritage project with XMM-Newton - Mass Assembly and Thermodynamics at the Endpoint of structure formation (CHEX-MATE) is a programme to study a minimally biased sample of 118 galaxy clusters detected by Planck through the Sunyaev-Zeldovich effect. Accurate and precise mass measurements are required to exploit CHEX-MATE as an astrophysical laboratory and a calibration sample for cosmological probes in the era of large surveys. We measured masses based on the galaxy dynamics, which are highly complementary to weak-lensing or X-ray estimates. We analysed the sample with a uniform pipeline that is stable both for poorly sampled or rich clusters - using spectroscopic redshifts from public (NED, SDSS, and DESI) or private archives - and dedicated observational programmes. We modelled the halo mass density and the anisotropy profile. Membership is confirmed with a cleaning procedure in phase space. We derived masses from measured velocity dispersions under the assumed model. We measured dynamical masses for 101 CHEX-MATE clusters with at least ten confirmed members within the virial radius r_200c. Estimated redshifts and velocity dispersions agree with literature values when available. Validation with weak-lensing masses shows agreement within 8+-16(stat.)+-5(sys.)%, and confirms dynamical masses as an unbiased proxy. Comparison with {\it Planck} masses shows them to be biased low by 34+-3(stat.)+-5(sys.)%. A follow-up spectroscopic campaign is underway to cover the full CHEX-MATE sample., Comment: 18 pages, 12 figures. In press on A&A

We design a distributed feedback optimization strategy, embedded into a modular ROS 2 control architecture, which allows a team of heterogeneous robots to cooperatively monitor and encircle a target while patrolling points of interest. Relying on the aggregative feedback optimization framework, we handle multi-robot dynamics while minimizing a global performance index depending on both microscopic (e.g., the location of single robots) and macroscopic variables (e.g., the spatial distribution of the team). The proposed distributed policy allows the robots to cooperatively address the global problem by employing only local measurements and neighboring data exchanges. These exchanges are performed through an asynchronous communication protocol ruled by locally-verifiable triggering conditions. We formally prove that our strategy steers the robots to a set of configurations representing stationary points of the considered optimization problem. The effectiveness and scalability of the overall strategy are tested via Monte Carlo campaigns of realistic Webots ROS 2 virtual experiments. Finally, the applicability of our solution is shown with real experiments on ground and aerial robots.

The BICEP3 and BICEP Array polarimeters are small-aperture refracting telescopes located at the South Pole designed to measure primordial gravitational wave signatures in the Cosmic Microwave Background (CMB) polarization, predicted by inflation. Constraining the inflationary signal requires not only excellent sensitivity, but also careful control of instrumental systematics. Both instruments use antenna-coupled orthogonally polarized detector pairs, and the polarized sky signal is reconstructed by taking the difference in each detector pair. As a result, the differential response between detectors within a pair becomes an important systematic effect we must control. Additionally, mapping the intensity and polarization response in regions away from the main beam can inform how sidelobe levels affect CMB measurements. Extensive calibration measurements are taken in situ every austral summer for control of instrumental systematics and instrument characterisation. In this work, we detail the set of beam calibration measurements that we conduct on the BICEP receivers, from deep measurements of main beam response to polarized beam response and sidelobe mapping. We discuss the impact of these measurements for instrumental systematics studies and design choices for future CMB receivers., Comment: 13 pages, 7 figures, 1 table, Proceedings paper SPIE 2024

The Continuous-Variable Firing Rate (CVFR) model, widely used in neuroscience to describe the intertangled dynamics of excitatory biological neurons, is here trained and tested as a veritable dynamically assisted classifier. To this end the model is supplied with a set of planted attractors which are self-consistently embedded in the inter-nodes coupling matrix, via its spectral decomposition. Learning to classify amounts to sculp the basin of attraction of the imposed equilibria, directing different items towards the corresponding destination target, which reflects the class of respective pertinence. A stochastic variant of the CVFR model is also studied and found to be robust to aversarial random attacks, which corrupt the items to be classified. This remarkable finding is one of the very many surprising effects which arise when noise and dynamical attributes are made to mutually resonate.

This work presents a novel rehabilitation framework designed for a therapist, wearing an inertial measurement unit (IMU) suit, to virtually interact with a lower-limb exoskeleton worn by a patient with motor impairments. This framework aims to harmonize the skills and knowledge of the therapist with the capabilities of the exoskeleton. The therapist can guide the patient's movements by moving their own joints and making real-time adjustments to meet the patient's needs, while reducing the physical effort of the therapist. This eliminates the need for a predefined trajectory for the patient to follow, as in conventional robotic gait training. For the virtual interaction medium between the therapist and patient, we propose an impedance profile that is stiff at low frequencies and less stiff at high frequencies, that can be tailored to individual patient needs and different stages of rehabilitation. The desired interaction torque from this medium is commanded to a whole-exoskeleton closed-loop compensation controller. The proposed virtual interaction framework was evaluated with a pair of unimpaired individuals in different teacher-student gait training exercises. Results show the proposed interaction control effectively transmits haptic cues, informing future applications in rehabilitation scenarios.

Despite the recent advances in computer vision research, estimating the 3D human pose from single RGB images remains a challenging task, as multiple 3D poses can correspond to the same 2D projection on the image. In this context, depth data could help to disambiguate the 2D information by providing additional constraints about the distance between objects in the scene and the camera. Unfortunately, the acquisition of accurate depth data is limited to indoor spaces and usually is tied to specific depth technologies and devices, thus limiting generalization capabilities. In this paper, we propose a method able to leverage the benefits of depth information without compromising its broader applicability and adaptability in a predominantly RGB-camera-centric landscape. Our approach consists of a heatmap-based 3D pose estimator that, leveraging the paradigm of Privileged Information, is able to hallucinate depth information from the RGB frames given at inference time. More precisely, depth information is used exclusively during training by enforcing our RGB-based hallucination network to learn similar features to a backbone pre-trained only on depth data. This approach proves to be effective even when dealing with limited and small datasets. Experimental results reveal that the paradigm of Privileged Information significantly enhances the model's performance, enabling efficient extraction of depth information by using only RGB images., Comment: ECCV 2024 Workshop T-CAP: TOWARDS A COMPLETE ANALYSIS OF PEOPLE: FINE-GRAINED UNDERSTANDING FOR REAL-WORLD APPLICATIONS

Deep Neural Networks have significantly impacted many computer vision tasks. However, their effectiveness diminishes when test data distribution (target domain) deviates from the one of training data (source domain). In situations where target labels are unavailable and the access to the labeled source domain is restricted due to data privacy or memory constraints, Source-Free Unsupervised Domain Adaptation (SF-UDA) has emerged as a valuable tool. Recognizing the key role of SF-UDA under these constraints, we introduce a novel approach marked by two key contributions: Few Trusted Samples Pseudo-labeling (FTSP) and Temperature Scaled Adaptive Loss (TSAL). FTSP employs a limited subset of trusted samples from the target data to construct a classifier to infer pseudo-labels for the entire domain, showing simplicity and improved accuracy. Simultaneously, TSAL, designed with a unique dual temperature scheduling, adeptly balance diversity, discriminability, and the incorporation of pseudo-labels in the unsupervised adaptation objective. Our methodology, that we name Trust And Balance (TAB) adaptation, is rigorously evaluated on standard datasets like Office31 and Office-Home, and on less common benchmarks such as ImageCLEF-DA and Adaptiope, employing both ResNet50 and ViT-Large architectures. Our results compare favorably with, and in most cases surpass, contemporary state-of-the-art techniques, underscoring the effectiveness of our methodology in the SF-UDA landscape.

We introduce a nonstabilizerness monotone which we name basis-minimised stabilizerness asymmetry (BMSA). It is based on the notion of $G$-asymmetry, a measure of how much a certain state deviates from being symmetric with respect to a symmetry group $G$. For pure states, we show that the BMSA is a strong monotone for magic-state resource theory, while it can be extended to mixed states via the convex roof construction. We discuss its relation with other magic monotones, first showing that the BMSA coincides with the recently introduced basis-minimized measurement entropy, thereby establishing the strong monotonicity of the latter. Next, we provide inequalities between the BMSA and other nonstabilizerness measures known in the literature. Finally, we present numerical methods to compute the BMSA, highlighting its advantages and drawbacks compared to other nonstabilizerness measures in the context of pure many-body quantum states. We also discuss the importance of additivity and strong monotonicity for measures of nonstabilizerness in many-body physics, motivating the search for additional computable nonstabilizerness monotones., Comment: 19 pages, 3 figures

This letter investigates target position estimation in integrated sensing and communications (ISAC) networks composed of multiple cooperating monostatic base stations (BSs). Each BS employs a MIMO-orthogonal time-frequency space (OTFS) scheme, enabling the coexistence of communication and sensing. A general cooperative maximum likelihood (ML) framework is derived, directly estimating the target position in a common reference system rather than relying on local range and angle estimates at each BS. Positioning accuracy is evaluated in single-target scenarios by varying the number of collaborating BSs, using root mean square error (RMSE), and comparing against the Cram\'er-Rao lower bound. Numerical results demonstrate that the ML framework significantly reduces the position RMSE as the number of cooperating BSs increases., Comment: 5 pages

In this paper, we address the large-scale shepherding control problem using a continuification-based strategy. We consider a scenario in which a large group of follower agents (targets) must be confined within a designated goal region through indirect interactions with a controllable set of leader agents (herders). Our approach transforms the microscopic agent-based dynamics into a macroscopic continuum model via partial differential equations (PDEs). This formulation enables efficient, scalable control design for the herders' behavior, with guarantees of global convergence. Numerical and experimental validations in a mixed-reality swarm robotics framework demonstrate the method's effectiveness.

This paper presents a novel distributed vehicle platooning control and coordination strategy. We propose a distributed predecessor-follower CACC scheme that allows to choose an arbitrarily small inter-vehicle distance while guaranteeing no rear-end collisions occur, even in the presence of undetected cyber-attacks on the communication channels such as false data injection. The safety guarantees of the CACC policy are derived by combing a sensor-based ACC policy that explicitly accounts for actuator saturation, and a communication-based predictive term that has state-dependent limits on its control authority, thus containing the effects of an unreliable communication channel. An undetected attack may still however be able to degrade platooning performance. To mitigate it, we propose a tailored Kalman observer-based attack detection algorithm that initially triggers a switch from the CACC policy to the ACC policy. Subsequently, by relying on a high-level coordinator, our strategy allows to isolate a compromised vehicle from the platoon formation by reconfiguring the platoon topology itself. The coordinator can also handle merging and splitting requests. We compare our algorithm in simulation against a state of the art distributed MPC scheme and we extensively test our full method in practice on a real system, a team of scaled-down car-like robots. Furthermore, we share the code to run both the simulations and robotic experiments.

Three decades ago, Stanley and Brenti initiated the study of the Kazhdan--Lusztig--Stanley (KLS) functions, putting on common ground several polynomials appearing in algebraic combinatorics, discrete geometry, and representation theory. In the present paper we develop a theory that parallels the KLS theory. To each kernel in a given poset, we associate a polynomial function that we call the \emph{Chow function}. The Chow function often exhibits remarkable properties, and sometimes encodes the graded dimensions of a cohomology or Chow ring. The framework of Chow functions provides natural polynomial analogs of graded module decompositions that appear in algebraic geometry, but that work for arbitrary posets, even when no graded module decomposition is known to exist. In this general framework, we prove a number of unimodality and positivity results without relying on versions of the Hard Lefschetz theorem. Our framework shows that there is an unexpected relation between positivity and real-rootedness conjectures about chains on face lattices of polytopes by Brenti and Welker, Hilbert--Poincar\'e series of matroid Chow rings by Ferroni and Schr\"oter, and flag enumerations on Bruhat intervals of Coxeter groups by Billera and Brenti., Comment: 48 pages

In today's online environments users experience harm and abuse on a daily basis. Therefore, content moderation is crucial to ensure their safety and well-being. However, the effectiveness of many moderation interventions is still uncertain. We evaluate the effectiveness of The Great Ban, one of the largest deplatforming interventions carried out by Reddit that affected almost 2,000 communities. We analyze 53M comments shared by nearly 34K users, providing in-depth results on both the intended and unintended consequences of this ban. We found that 15.6% of the moderated users abandoned the platform while the remaining ones decreased their overall toxicity by 4.1%. Nonetheless, a subset of those users increased their toxicity by 70% after the intervention. In any case, increases in toxicity did not lead to marked increases in activity or engagement, meaning that the most toxic users had overall a limited impact. Our findings bring to light new insights on the effectiveness of deplatforming. Furthermore, they also contribute to informing future content moderation strategies., Comment: arXiv admin note: text overlap with arXiv:2401.11254 This work is an extension of this conference paper: Cima, L., Trujillo, A., Avvenuti, M., & Cresci, S. (2024, May). The Great Ban: Efficacy and Unintended Consequences of a Massive Deplatforming Operation on Reddit. In Companion Publication of the 16th ACM Web Science Conference (pp. 85-93)

We present ALMA observations on the high-redshift galaxy GHZ2 and report a successful detection of the rest-frame 88um atomic transition from doubly-ionized Oxygen at z=12.3327+/-0.0005. Based on these observations, combined with additional constraints on the [OIII] 52um line luminosity and previous JWST data, we argue that GHZ2 is likely powered by compact and young star formation, and show that it follows well-established relationships found for giant HII regions and metal-poor star-forming dwarf galaxies that are known to host bright super star clusters. Additionally, these observations provide new constraints on the Oxygen electron density (100 < n_e[cm^-3] < 4,000) and dynamical mass (M_dyn=3-8x10^8M_sun). The existence of these massive starburst systems 13.3Gyr ago might explain the origin of today's globular clusters, a long-standing question in astronomy. To test this, we present observational probes to investigate whether sources like GHZ2 are linked to the formation of today's globular clusters or other more massive compact stellar systems., Comment: Accepted for publication in The Astrophysical Journal Letters

We study the evolution of eccentric, equatorial extreme-mass-ratio inspirals (EMRIs) immersed in the accretion disks of active galactic nuclei. We find that single gravitational-wave observations from these systems could provide measurements with ~ 10 % relative precision of, simultaneously, the disk viscosity and mass accretion rate of the central supermassive black hole. This is possible when the EMRI transitions, within the observation time, from supersonic to subsonic motion relative to the disk gas, for eccentricities e > ~ 0.025-0.1. The estimate of the accretion rate would assist in the identification of the EMRI's host galaxy, or the observation of a direct electromagnetic counterpart, improving the chances of using these sources as cosmological sirens. Our work highlights the rich phenomenology of binary evolution in astrophysical environments and the need to improve the modelling and analysis of these systems for future gravitational-wave astronomy., Comment: 12 pages + 3 pages in Appendix, 8 figures

In many research fields, researchers aim to identify significant associations between a set of explanatory variables and a response while controlling the false discovery rate (FDR). To this aim, we develop a fully Bayesian generalization of the classical model-X knockoff filter. Knockoff filter introduces controlled noise in the model in the form of cleverly constructed copies of the predictors as auxiliary variables. In our approach we consider the joint model of the covariates and the response and incorporate the conditional independence structure of the covariates into the prior distribution of the auxiliary knockoff variables. We further incorporate the estimation of a graphical model among the covariates, which in turn aids knockoffs generation and improves the estimation of the covariate effects on the response. We use a modified spike-and-slab prior on the regression coefficients, which avoids the increase of the model dimension as typical in the classical knockoff filter. Our model performs variable selection using an upper bound on the posterior probability of non-inclusion. We show how our model construction leads to valid model-X knockoffs and demonstrate that the proposed characterization is sufficient for controlling the BFDR at an arbitrary level, in finite samples. We also show that the model selection is robust to the estimation of the precision matrix. We use simulated data to demonstrate that our proposal increases the stability of the selection with respect to classical knockoff methods, as it relies on the entire posterior distribution of the knockoff variables instead of a single sample. With respect to Bayesian variable selection methods, we show that our selection procedure achieves comparable or better performances, while maintaining control over the FDR. Finally, we show the usefulness of the proposed model with an application to real data.

We establish fully-discrete a priori and semi-discrete in time a posteriori error estimates for a discontinuous-continuous Galerkin discretization of the wave equation in second order formulation; the resulting method is a Petrov-Galerkin scheme based on piecewise and piecewise continuous polynomial in time test and trial spaces, respectively. Crucial tools in the a priori analysis for the fully-discrete formulation are the design of suitable projection and interpolation operators extending those used in the parabolic setting, and stability estimates based on a nonstandard choice of the test function; a priori estimates are shown, which are measured in $L^\infty$-type norms in time. For the semi-discrete in time formulation, we exhibit constant-free, reliable a posteriori error estimates for the error measured in the $L^\infty(L^2)$ norm; to this aim, we design a reconstruction operator into $\mathcal C^1$ piecewise polynomials over the time grid with optimal approximation properties in terms of the polynomial degree distribution and the time steps. Numerical examples illustrate the theoretical findings.

In this study we address whether the age--metallicity relation (AMR) deviates from the expected trend of metallicity increasing smoothly with age. We also show the presence (or absence) of two populations, as recently claimed using a relatively small dataset. Moreover, we studied the Milky Way thin disk's chemical evolution using solar twins, including the effect of radial migration and accretion events. In particular, we exploited high-resolution spectroscopy of a large sample of solar twins in tandem with an accurate age determination to investigate the Milky Way thin disk age--metallicity relationship. Additionally, we derived the stars' birth radius and studied the chemical evolution of the thin disk. We discovered that statistical and selection biases can lead to a misinterpretation of the observational data. An accurate accounting of all the uncertainties led us to detect no separation in the AMR into different populations for solar twins around the Sun (-0.3 < [Fe/H] < 0.3 dex). This lead us to the conclusion that the thin disk was formed relatively smoothly. For the main scenario of the Milky Way thin disk formation, we suggest that the main mechanism for reaching today's chemical composition around the Sun is radial migration with the possible contribution of well-known accretion events such as Gaia-Enceladus/Sausage (GES) and Sagittarius (Sgr).

Scaling large language models (LLMs) demands extensive data and computing resources, which are traditionally constrained to data centers by the high-bandwidth requirements of distributed training. Low-bandwidth methods like federated learning (FL) could enable collaborative training of larger models across weakly-connected GPUs if they can effectively be used for pre-training. To achieve this, we introduce Photon, the first complete system for federated end-to-end LLM training, leveraging cross-silo FL for global-scale training with minimal communication overheads. Using Photon, we train the first federated family of decoder-only LLMs from scratch. We show that: (1) Photon can train model sizes up to 7B in a federated fashion while reaching an even better perplexity than centralized pre-training; (2) Photon model training time decreases with available compute, achieving a similar compute-time trade-off to centralized; and (3) Photon outperforms the wall-time of baseline distributed training methods by 35% via communicating 64x-512xless. Our proposal is robust to data heterogeneity and converges twice as fast as previous methods like DiLoCo. This surprising data efficiency stems from a unique approach combining small client batch sizes with extremely high learning rates, enabled by federated averaging's robustness to hyperparameters. Photon thus represents the first economical system for global internet-wide LLM pre-training., Comment: 13 pages, 9 appendix pages, 10 figures, 3 algorithms, 8 tables

Berezin and Weyl quantizations are renown procedures for mapping classical, commutative Poisson algebras of observables to their non-commutative, quantum counterparts. The latter map is famous for its use on Weyl algebras, while the former is more appropriate for continuous functions decaying at infinity. In this work we define a variant of Berezin quantization map, which operates on classical Weyl algebras $\mathcal{W}(E,0)$ and constitutes a positive \textit{strict deformation quantization}. We use this map to compare classical and quantum thermal equilibrium states for a boson gas and to compute its rigorous classical limit. For this scope, we first define a purely algebraic notion of KMS states for the classical Weyl algebra and verify that in the finite volume setting there is only one possible KMS state, which can be interpreted as the Fourier transform of a Gibbs measure on some Hilbert space. Then, we show how the classical KMS states have thermodynamic limits which can manifest condensation in the zero mode, similarly to what happens in the standard Bose-Einstein condensation. Lastly, we prove that there exist sequences of quantum KMS states for the infinite volume Bose gas, that converge weakly$^*$ to classical KMS states. Moreover, since the different thermal phases are preserved by this limit, it is shown that a quantum condensate is mapped to a classical one., Comment: 46 pages

Machine learning (ML) has the potential to become an essential tool in supporting clinical decision-making processes, offering enhanced diagnostic capabilities and personalized treatment plans. However, outsourcing medical records to train ML models using patient data raises legal, privacy, and security concerns. Federated learning has emerged as a promising paradigm for collaborative ML, meeting healthcare institutions' requirements for robust models without sharing sensitive data and compromising patient privacy. This study proposes a novel method that combines federated learning (FL) and Graph Neural Networks (GNNs) to predict stroke severity using electroencephalography (EEG) signals across multiple medical institutions. Our approach enables multiple hospitals to jointly train a shared GNN model on their local EEG data without exchanging patient information. Specifically, we address a regression problem by predicting the National Institutes of Health Stroke Scale (NIHSS), a key indicator of stroke severity. The proposed model leverages a masked self-attention mechanism to capture salient brain connectivity patterns and employs EdgeSHAP to provide post-hoc explanations of the neurological states after a stroke. We evaluated our method on EEG recordings from four institutions, achieving a mean absolute error (MAE) of 3.23 in predicting NIHSS, close to the average error made by human experts (MAE $\approx$ 3.0). This demonstrates the method's effectiveness in providing accurate and explainable predictions while maintaining data privacy., Comment: 13 pages, 5 figures, Proceedings of the II edition of the Workshop on Unifying Representations in Neural Models (UniReps 2024)

In a full 3D context, we study a projectile subject to linear drag, a non-uniform gravitational field, time-dependent wind, and parameterized atmospheric thinning. In this general context, we provide integral solutions, exact to $\mathcal{ O }( \varepsilon )$, for the position and velocity of the projectile, where $\varepsilon$ is a small perturbation parameter; in the special case of constant wind, we provide closed-form solutions, exact to $\mathcal{ O }( \varepsilon )$. Under the constant-wind assumption, we provide closed-form solutions of $\mathcal{ O }( 1 )$ for the time of tangency, times of flight, and extreme values of the radius achieved by the projectile. We provide physical interpretations throughout, including a physical interpretation of the branches $W_0$ and $W_{ -1 }$ of the Lambert W function in the context of flight time. We also provide parameterized, error-controlled algorithms to compute trajectories, complete with a full Matlab implementation that we make freely available. We compare the results of our implementation to a general-purpose, stiff ODE solver., Comment: 32 pages, 6 figures

The symbiotic X-ray binary GX 1+4 possesses a number of peculiar properties that have been studied since the early 1970s. In particular, the orbital period has been a point of debate for many years, until radial velocity measurements were able to settle the debate. These radial velocity findings have so far not been confirmed using X-ray data, even though multiple factors would cause a periodic variation on the same timescale as the orbital period at these energies. Because the orbit of GX 1+4 is eccentric and not seen face-on, changes in the accretion rate and column density along the line of sight could cause a periodic variation in the spin-frequency measurements, X-ray light curves, and hardness ratios of the source. Furthermore, for a high inclination of the orbital plane, the neutron star could be eclipsed by the companion, which would lead to periodic decreases in brightness. We used data from a number of different X-ray telescopes to search directly for periodicity by applying the Lomb-Scargle and epoch-folding approaches to long-term light-curve and spin-frequency measurement data of the source. We support our findings using folded light curves, hardness ratios, and images. We find that our results agree with the radial velocity findings, and we form a self-consistent model that is supported by folded hardness-ratios and light curves. We find that the source is clearly detected in X-rays during the predicted eclipse. Motivated by this absence of an eclipse in the system, we constrain the inclination of the system to $\sim 76^\circ-84^\circ$ and the mass of the neutron star in the system to $\sim1.23M_\odot - 1.45M_\odot$ using the constraints on the red giant mass and surface gravity provided in the literature. Furthermore, we constrain the radius of the red giant to $\sim 60R_\odot - 150R_\odot$., Comment: 8 pages, 8 figures, to be published in A&A

Given an integral domain $D$ with quotient field $\mathcal{Q}(D)$, the reciprocal complement of $D$ is the subring $R(D)$ of $\mathcal{Q}(D)$ whose elements are all the sums $\frac{1}{d_1}+\ldots+\frac{1}{d_n} $ for $d_1, \ldots, d_n$ nonzero elements of $D$. In this article we study problems related with prime ideals, localizations and Krull dimension of rings of the form $R(D)$ and we describe the reciprocal complements of classes of domains, including semigroup algebras and $ D+ \mathfrak{m} $ constructions. We also characterize when $R(D)$ is a DVR., Comment: 24 pages, comments are welcome

In the context of Chameleon gravity, we present a semi-analytical solution of the chameleon field profile in accurately modelled galaxy cluster's mass components, namely: the stellar mass of the Brightest Cluster Galaxy (BCG), the baryonic mass in galaxies (other than the BCG), the mass of the Intra-Cluster Medium (ICM) and the diffuse cold dark matter (CDM). The obtained semi-analytic profile is validated against the numerical solution of the chameleon field equation and implemented in the \textsc{MG-MAMPOSSt} code for kinematic analyses of galaxy clusters in modified gravity scenarios. By means of mock halos, simulated both in GR and in modified gravity, we show that the combination of velocities and positions of cluster member galaxies, along with data of the stellar velocity dispersion profile of the BCG, can impose constraints on the parameter space of the Chameleon model; for a cluster generated in GR, these constraints are at the same level as a joint lensing+kinematics analysis of a cluster modelled with a single mass profile, without the BCG data., Comment: 22 pages, 10 figures

This paper investigates the solutions to the two-phase Serrin's problem, an overdetermined boundary value problem motivated by shape optimization. Specifically, we study the torsional rigidity of composite beams, where two distinct materials interact, and examine the properties of the optimal configurations (critical shapes) under volume constraints. We first show that such a shape optimization problem admits no local minimizers. Then, using the method of moving planes, we show that the solutions exhibit no extended or narrow branches ("tentacles") away from the core. We then show that the outer boundary of a solution cannot exhibit flat parts and that the only configuration whose outer boundary contains a portion of a sphere is the one given by concentric balls. Finally, we establish that concentric balls are the only admissible configurations that solve the two-phase Serrin's problem for two distinct sets of conductivity values., Comment: 12 pages, 1 figure

When examined through the lens of their residual streams, a puzzling property emerges in transformer networks: residual contributions (e.g., attention heads) sometimes specialize in specific tasks or input attributes. In this paper, we analyze this phenomenon in vision transformers, focusing on the spectral geometry of residuals, and explore its implications for modality alignment in vision-language models. First, we link it to the intrinsically low-dimensional structure of visual head representations, zooming into their principal components and showing that they encode specialized roles across a wide variety of input data distributions. Then, we analyze the effect of head specialization in multimodal models, focusing on how improved alignment between text and specialized heads impacts zero-shot classification performance. This specialization-performance link consistently holds across diverse pre-training data, network sizes, and objectives, demonstrating a powerful new mechanism for boosting zero-shot classification through targeted alignment. Ultimately, we translate these insights into actionable terms by introducing ResiDual, a technique for spectral alignment of the residual stream. Much like panning for gold, it lets the noise from irrelevant unit principal components (i.e., attributes) wash away to amplify task-relevant ones. Remarkably, this dual perspective on modality alignment yields fine-tuning level performances on different data distributions while modeling an extremely interpretable and parameter-efficient transformation, as we extensively show on more than 50 (pre-trained network, dataset) pairs.

In this contribution we extend the concept of a Petri net morphism to Elementary Object Systems (EOS). EOS are a nets-within-nets formalism, i.e. we allow the tokens of a Petri net to be Petri nets again. This nested structure has the consequence that even systems defined by very small Petri nets have a quite huge reachability graph. In this contribution we use automorphism to describe symmetries of the Petri net topology. Since these symmetries carry over to markings as well this leads to a condensed state space, too.

We show that a certain conjecture by Atiyah and Sutcliffe implies the existence of an $ E_3 $-algebra (respectively $ E_2 $-algebra) structure on the disjoint union of all complex (respectively real) full flag manifolds modulo symmetric groups. Moreover, we show that these structures are liftings of exotic $ E_3 $ (respectively $ E_2 $) structures on the free $ E_\infty $-algebras on $ BU(1)+ $ (respectively $ BO(1)+ $), that do not extend to $ E_4 $ (respectively $ E_3 $) structures. We also provide some (co)homological calculations supporting the conjecture., Comment: 26 pages, 1 figure v2: correction of minimal misprints

T2K is a long baseline neutrino experiment, entering Phase II with a Near Detector upgrade. The T2K near detector (ND280) upgrade consists of the installation of three new detector systems: a plastic scintillator neutrino active target (Super-FGD), two time projection chambers (HA-TPC) and a time of flight detector (TOF). The Super-FGD is composed of 2-million 1 cm-cube scintillating cubes read by almost 60 thousand wavelength-shifting (WLS) fibers coupled to an MPPC on one end. Given the large number of channels, the limited space inside magnetic environment, and the limited time from production to installation, the development and testing of the Front-end electronics boards (FEB) for the read-out of the Super-FGD channels represented a challenging task for the success of the upgrade. This work presents the performance tests confirming that the FEB aligns with detector requirements, and the hardware qualification of 240 FEBs through a custom QC test bench designed to detect and locate hardware failures to speed up the repairing process. Installation of the electronics in the detector took place in March 2024, one year after the beginning of the FEB mass production, and the first successful neutrino beam run took place in June of the same year., Comment: Topical Workshop on Electronics for Particle Physics - TWEPP 2024 - 30 September - 4 October, 2024 - Glasgow, Scotland

Petri Nets (PN) are extensively used as a robust formalism to model concurrent and distributed systems; however, they encounter difficulties in accurately modeling adaptive systems. To address this issue, we defined rewritable PT nets (RwPT) using Maude, a declarative language that ensures consistent rewriting logic semantics. Recently, we proposed a modular approach that employs algebraic operators to build extensive RwPT models. This methodology uses composite node labeling to maintain hierarchical organization through net rewrites and has been shown to be effective. Once stochastic parameters are integrated into the formalism, we introduce an automated procedure to derive a lumped CTMC from the quotient graph generated by a modular RwPT model. To demonstrate the effectiveness of our method, we present a fault-tolerant manufacturing system as a case study., Comment: In Proceedings FROM 2024, arXiv:2410.23020

The INTEGRAL satellite has collected a large amount of data on magnetars in our Galaxy, spanning more than 20 years starting from 2003. The large data set obtained with the IBIS/ISGRI instrument at energies above 20 keV allows us to study both the properties and long-term evolution of their persistent hard X-ray emission and the population characteristics of the short bursts emitted during active periods. We are carrying out a comprehensive analysis of the observed magnetars, exploiting the most recent calibrations and analysis software. Here we report on the long term evolution of the hard X-ray flux of the magnetars detected with ISGRI and the results of a sensitive search for short bursts in SGR J1935+2154., Comment: 6 pages, 5 figures. Accepted for publication in Astronomische Nachrichten, Proceedings of the XMM-Newton 2024 Science Workshop

One-proton emission from the $^{102}$Sb nucleus is discussed, assuming an inert $^{100}$Sn core and the valence proton and neutron. There are experimentally measured bound states in the $^{100}$Sn-neutron system, whereas no particle-bound $^{100}$Sn-proton state has been observed. With time-dependent three-body calculations, the $1^+$ ground state of $^{102}$Sb is suggested as a possible proton emitter. This conclusion is reached by assuming a weakening effect on the proton-neutron ($pn$) interaction with respect to a bare deuteron. An analogous phenomenon is necessary to reproduce the empirical binding energies of $^{42}$Sc and $^{18}$F. Continuous shift from the unbound to bound regions by changing the $pn$-interaction strength is demonstrated. The lower limit of lifetime is evaluated as $\tau \gtrsim 4.4 \times 10^{-18}$ seconds in the no-$pn$-interaction limit. However, the actual lifetime is expected as longer with a finite $pn$ interaction. Observation of a resonant state in $^{102}$Sb and its decay would provide a benchmark of the $pn$-pairing correlation., Comment: 6 pages, 6 figures, 4 tables

A Heffter array over an additive group $G$ is any partially filled array $A$ satisfying that: (1) each one of its rows and columns sum to zero in $G$, and (2) if $i\in G\setminus\{0\}$, then either $i$ or $-i$ appears exactly once in $A$. In this paper, this notion is naturally generalized to that of $\mathcal{B}$-Heffter array over a partial loop, where $\mathcal{B}$ is a set of block-sum polynomials over an affine $1$-design on the set of entries in $A$.

In this paper, we present the Federated Upper Confidence Bound Value Iteration algorithm ($\texttt{Fed-UCBVI}$), a novel extension of the $\texttt{UCBVI}$ algorithm (Azar et al., 2017) tailored for the federated learning framework. We prove that the regret of $\texttt{Fed-UCBVI}$ scales as $\tilde{\mathcal{O}}(\sqrt{H^3 |\mathcal{S}| |\mathcal{A}| T / M})$, with a small additional term due to heterogeneity, where $|\mathcal{S}|$ is the number of states, $|\mathcal{A}|$ is the number of actions, $H$ is the episode length, $M$ is the number of agents, and $T$ is the number of episodes. Notably, in the single-agent setting, this upper bound matches the minimax lower bound up to polylogarithmic factors, while in the multi-agent scenario, $\texttt{Fed-UCBVI}$ has linear speed-up. To conduct our analysis, we introduce a new measure of heterogeneity, which may hold independent theoretical interest. Furthermore, we show that, unlike existing federated reinforcement learning approaches, $\texttt{Fed-UCBVI}$'s communication complexity only marginally increases with the number of agents.

The definition of generalized random processes in Gel'fand sense allows to extend well-known stochastic models, such as the fractional Brownian motion, and study the related fractional pde's, as well as stochastic differential equations in distributional sense. By analogy with the construction (in the infinite-dimensional white-noise space) of the latter, we introduce two processes defined by means of Hadamard-type fractional operators. When used to replace the time derivative in the governing p.d.e.'s, the Hadamard-type derivatives are usually associated with ultra-slow diffusions. On the other hand, in our construction, they directly determine the memory properties of the so-called Hadamard fractional Brownian motion (H-fBm) and its long-time behaviour. Still, for any finite time horizon, the H-fBm displays a standard diffusing feature. We then extend the definition of the H-fBm from the white noise space to an infinite dimensional grey-noise space built on the Le Roy measure, so that our model represents an alternative to the generalized grey Brownian motion. In this case, we prove that the one-dimensional distribution of the process satisfies a heat equation with non-constant coefficients and fractional Hadamard time-derivative. Finally, once proved the existence of the distributional derivative of the above defined processes and derived an integral formula for it, we construct an Ornstein-Uhlenbeck type process and evaluate its distribution., Comment: 30 pages

We propose novel numerical schemes based on the Boris method in curved spacetime, incorporating both hadronic and radiative interactions for the first time. Once the proton has lost significant energy due to radiative and hadronic losses, and its gyroradius has decreased below typical scales on which the electromagnetic field varies, we apply a guiding center approximation (GCA). We fundamentally simulate collision processes either with a Monte-Carlo method or, where applicable, as a continuous energy loss, contingent on the local optical depth. To test our algorithm for the first time combining the effects of electromagnetic, gravitational, and radiation fields including hadronic interactions, we simulate highly relativistic protons traveling through various electromagnetic fields and proton backgrounds. We provide unit tests in various spatially dependent electromagnetic and gravitational fields and background photon and proton distributions, comparing the trajectory against analytic results. We propose that our method can be used to analyze hadronic interactions in black hole accretion disks, jets, and coronae to study the neutrino abundance from active galactic nuclei., Comment: 15 pages, 9 figures, submitted to Physical Review D

Face analysis has been studied from different angles to infer emotion, poses, shapes, and landmarks. Traditionally RGB cameras are used, yet for fine-grained tasks standard sensors might not be up to the task due to their latency, making it impossible to record and detect micro-movements that carry a highly informative signal, which is necessary for inferring the true emotions of a subject. Event cameras have been increasingly gaining interest as a possible solution to this and similar high-frame rate tasks. We propose a novel spatiotemporal Vision Transformer model that uses Shifted Patch Tokenization (SPT) and Locality Self-Attention (LSA) to enhance the accuracy of Action Unit classification from event streams. We also address the lack of labeled event data in the literature, which can be considered one of the main causes of an existing gap between the maturity of RGB and neuromorphic vision models. Gathering data is harder in the event domain since it cannot be crawled from the web and labeling frames should take into account event aggregation rates and the fact that static parts might not be visible in certain frames. To this end, we present FACEMORPHIC, a temporally synchronized multimodal face dataset composed of RGB videos and event streams. The dataset is annotated at a video level with facial Action Units and contains streams collected with various possible applications, ranging from 3D shape estimation to lip-reading. We then show how temporal synchronization can allow effective neuromorphic face analysis without the need to manually annotate videos: we instead leverage cross-modal supervision bridging the domain gap by representing face shapes in a 3D space. Our proposed model outperforms baseline methods by effectively capturing spatial and temporal information, crucial for recognizing subtle facial micro-expressions., Comment: Under review at CVIU. arXiv admin note: substantial text overlap with arXiv:2409.10213

We report a time-resolved analysis of the accreting X-ray pulsar Cen X-3 using observations carried out by NuSTAR, which cover approximately two binary orbits in different intensity states. The pulse profile is relatively stable over the orbital phase and shows energy dependence. It has an obvious double-peaked shape in the energy band below 15 keV -- with the second pulse peak decreasing as energy increases -- and is gradually dominated by a single peak in higher energy bands. We find that the pulse profile in the energy band of 3-5 keV at high-intensity states shows a subtle triple-peaked shape, with the main peak divided into two subpeaks. We also find a positive correlation between the pulse fraction and both energy and flux. Our spectral analysis reveals that the spectra can be well described by the continuum of Fermi-Dirac cutoff and NPEX models, and the cyclotron line is detected with the centroid energies varying from 26 keV to 29 keV, along with the iron emission line around 6.4 keV. We investigated the dependence between the cyclotron resonant scattering feature (CRSF) centroid energy and luminosity and discuss the theoretical critical luminosity. Although the variation of $E_{\rm cyc}- L_X$ is not distinct, there is a possibility that the critical luminosity lies within the range of $\sim (0.5-4)\times 10^{37}$ erg s$^{-1}$ in the band of $4-78$ keV. The photon index shows a strong positive correlation with luminosity. Our orbital-phase analysis reveals that the spectral parameters show orbital variability, and the highly variable photoelectric absorption may indicate the existence of clumpy stellar winds., Comment: 10 pages, 10 figures

We present a cooperative protocol to charge quantum spin networks up to the highest-energy configuration, in terms of the network's magnetization. The charging protocol leverages spin-spin interactions and the crossing of a phase transition's critical point. Exploiting collective dynamics of the spin network, the cooperative protocol guarantees a precision advantage over any local charging protocol and leads to fluctuations (standard deviation) of the magnetization that scale as $1/N$, with $N$ being the number of spins in the network, i.e., the size of the spin battery. These findings mirror the Heisenberg limit for precision for parameter estimation in quantum metrology. We test our protocol on the D-Wave's Advantage quantum processing unit by charging sub-lattices with sizes ranging from $40$ to $5\,612$ spins, achieving the maximum magnetization and reaching a scalable charging precision beyond the standard quantum limit of $1/\sqrt{N}$., Comment: 13 pages, 10 figures

We present the results of the "Fast Calorimeter Simulation Challenge 2022" - the CaloChallenge. We study state-of-the-art generative models on four calorimeter shower datasets of increasing dimensionality, ranging from a few hundred voxels to a few tens of thousand voxels. The 31 individual submissions span a wide range of current popular generative architectures, including Variational AutoEncoders (VAEs), Generative Adversarial Networks (GANs), Normalizing Flows, Diffusion models, and models based on Conditional Flow Matching. We compare all submissions in terms of quality of generated calorimeter showers, as well as shower generation time and model size. To assess the quality we use a broad range of different metrics including differences in 1-dimensional histograms of observables, KPD/FPD scores, AUCs of binary classifiers, and the log-posterior of a multiclass classifier. The results of the CaloChallenge provide the most complete and comprehensive survey of cutting-edge approaches to calorimeter fast simulation to date. In addition, our work provides a uniquely detailed perspective on the important problem of how to evaluate generative models. As such, the results presented here should be applicable for other domains that use generative AI and require fast and faithful generation of samples in a large phase space., Comment: 204 pages, 100+ figures, 30+ tables

People increasingly use digital platforms to exchange resources in accordance to some policies stating what resources users offer and what they require in return. In this paper, we propose a formal model of these environments, focussing on how users' policies are defined and enforced, so ensuring that malicious users cannot take advantage of honest ones. To that end, we introduce the declarative policy language MuAC and equip it with a formal semantics. To determine if a resource exchange is fair, i.e., if it respects the MuAC policies in force, we introduce the non-standard logic MuACL that combines non-linear, linear and contractual aspects, and prove it decidable. Notably, the operator for contractual implication of MuACL is not expressible in linear logic. We define a semantics preserving compilation of MuAC policies into MuACL, thus establishing that exchange fairness is reduced to finding a proof in MuACL. Finally, we show how this approach can be put to work on a blockchain to exchange non-fungible tokens.

It is shown that $S(G) = O\left(m/\log_2 m + d\right)$ pebbles are sufficient to pebble any DAG $G=(V,E)$, with $m$ edges and maximum in-degree $d$. It was previously known that $S(G) = O\left(d n/\log n\right)$. The result builds on two novel ideas. The first is the notion of $B-budget\ decomposition$ of a DAG $G$, an efficiently computable partition of $G$ into at most $2^{\lfloor \frac{m}{B} \rfloor}$ sub-DAGs, whose cumulative space requirement is at most $B$. The second is the challenging vertices technique, which constructs a pebbling schedule for $G$ from a pebbling schedule for a simplified DAG $G'$, obtained by removing from $G$ a selected set of vertices $W$ and their incident edges. This technique also yields improved pebbling upper bounds for DAGs with bounded genus and for DAGs with bounded topological depth.

We exhibit new minimal 2-spheres in hyperk\"ahler 4-manifolds arising from the Gibbons--Hawking ansatz and in the K3 manifold endowed with a hyperk\"ahler metric. These minimal surfaces are obtained via a gluing construction using the Scherk surface in flat space and the holomorphic cigar in the Taub-NUT space as building blocks. As for the stable minimal 2-sphere in the Atiyah--Hitchin manifold, the minimal surfaces we construct are not holomorphic with respect to any complex structure compatible with the metric, have degree-1 positive Gauss lift so they can be parametrised by a harmonic map that satisfies a first-order Fueter-type PDE, and yet are unstable. This shows that there is no characterisation of stable minimal surfaces in hyperk\"ahler 4-manifolds in terms of topological data., Comment: 27 pages, 1 figure

Asymptotically tight lower bounds are derived for the Input/Output (I/O) complexity of a class of dynamic programming algorithms including matrix chain multiplication, optimal polygon triangulation, and the construction of optimal binary search trees. Assuming no recomputation of intermediate values, we establish an $\Omega\left(\frac{n^3}{\sqrt{M}B}\right)$ I/O lower bound, where $n$ denotes the size of the input and $M$ denotes the size of the available fast memory (cache). When recomputation is allowed, we show the same bound holds for $M < cn$, where $c$ is a positive constant. In the case where $M \ge 2n$, we show an $\Omega\left(n/B\right)$ I/O lower bound. We also discuss algorithms for which the number of executed I/O operations matches asymptotically each of the presented lower bounds, which are thus asymptotically tight. Additionally, we refine our general method to obtain a lower bound for the I/O complexity of the Cocke-Younger-Kasami algorithm, where the size of the grammar impacts the I/O complexity. An upper bound with asymptotically matching performance in many cases is also provided.

Chaos characterized by its irregularity and high sensitivity to initial conditions finds various applications in secure optical communications, random number generations, light detection and ranging systems, etc. Semiconductor lasers serve as ideal light platforms for chaos generations owing to the advantages in on-chip integration and complex nonlinear effects. In near-infrared wavelengths, semiconductor laser based chaotic light sources have been extensively studied and experimentally demonstrated. However, in the terahertz (THz) spectral range, due to the lack of effective THz light sources and high-speed detectors, chaos generation in THz semiconductor lasers, e.g., quantum cascade lasers (QCLs), is particularly challenging. Due to the fast intersubband carrier transitions, single mode THz QCLs resemble Class A lasers, where chaos can be hardly excited, even with external perturbations. In this work, we experimentally show a THz chaos source based on a sole multimode THz QCL without any external perturbations. Such a dynamical regime is characterized by the largest Lyapunov exponent associated to the temporal traces of the measured radio frequency (intermode beatnote) signal of the laser. The experimental results and chaos validation are confirmed by simulations of our model based on effective semiconductor Maxwell-Bloch Equations. To further understand the physical mechanism of the chaos generation in THz QCLs, a reduced model based on two coupled complex Ginzburg-Landau equations is derived from the full model cited above to systematically investigate the effects of the linewidth enhancement factor and group velocity dispersion on the chaotic regime. This model allows us to show that the chaos generation in the THz QCL can be ascribed to the system attaining the defect mediated turbulence regime., Comment: 30 pages, 6 figures

Refracted Gravity (RG) is a a classical theory of gravity where a gravitational permittivity $ a monotonically-increasing function of the local density rho , is introduced in the Poisson equation to mimic the effect of dark matter at astrophysical scales. We use high precision spectroscopic data of two massive galaxy clusters, MACS J1206.2-0847 at redshift z=0.44, and Abell S1063 (RXC J2248.7-4431) at z=0.35, to determine the total gravitational potential in the context of RG and to constrain the three, supposedly universal, free parameters of this model. Using an upgraded version of the MG-MAMPOSSt algorithm, we perform a kinematic analysis which combines the velocity distribution of the cluster galaxies and the velocity dispersion profile of the stars within the Brightest Cluster Galaxy (BCG). The unprecedented dataset used has been obtained by an extensive spectroscopic campaign carried out with the VIMOS and MUSE spectrographs at the ESO VLT. We found that RG describes the kinematics of these two clusters as well as Newtonian gravity, although the latter is slightly preferred. However, (i) each cluster requires a different set of the three free RG parameters, and (ii) the two sets are inconsistent with other results in the literature at different scales. We discuss the limitation of the method used to constrain the RG parameters as well as possible systematic effects which can give rise to the observed tension, notably deviations from the spherical symmetry and from the dynamical equilibrium of the clusters., Comment: 10 pages, 6 figures. Submitted to A&A

We present a study on the possibility of observing a hypothetical particle known as the Flavon $H_F$, which is predicted in an extension of the standard model that includes the so-called Froggatt-Nielsen mechanism. The proposed decay channel is through a $b\bar{b}h$ final state, where the Higgs boson $(h)$ decays to a pair of photons or a pair of $b$ quarks $(h\to \gamma\gamma,\,b\bar{b})$. We found that, under special scenarios of the model parameter space, the processes analyzed could provide evidence for the existence of the Flavon in the next stage of the LHC: the High Luminosity LHC. Specifically, we predict a \textit{signal significance} of $5\sigma$ ($2\sigma$) in the $h\to b\bar{b}$ ($h\to\gamma\gamma$) channel for a Flavon mass of $800$ ($900$) GeV and an integrated luminosity of $2500$ ($3000$) fb$^{-1}$., Comment: arXiv admin note: text overlap with arXiv:2205.12641