Search

Language models have proven successful across a wide range of software engineering tasks, but their significant computational costs often hinder their practical adoption. To address this challenge, researchers have begun applying various compression strategies to improve the efficiency of language models for code. These strategies aim to optimize inference latency and memory usage, though often at the cost of reduced model effectiveness. However, there is still a significant gap in understanding how these strategies influence the efficiency and effectiveness of language models for code. Here, we empirically investigate the impact of three well-known compression strategies -- knowledge distillation, quantization, and pruning -- across three different classes of software engineering tasks: vulnerability detection, code summarization, and code search. Our findings reveal that the impact of these strategies varies greatly depending on the task and the specific compression method employed. Practitioners and researchers can use these insights to make informed decisions when selecting the most appropriate compression strategy, balancing both efficiency and effectiveness based on their specific needs.

Transitional millisecond pulsars (tMSPs) bridge the evolutionary gap between accreting neutron stars in low-mass X-ray binaries and millisecond radio pulsars. These systems exhibit a unique subluminous X-ray state characterized by the presence of an accretion disk and rapid switches between high and low X-ray emission modes. The high mode features coherent millisecond pulsations spanning from the X-ray to the optical band. We present multiwavelength polarimetric observations of the tMSP PSR J1023+0038 aimed at conclusively identifying the physical mechanism powering its emission in the subluminous X-ray state. During the high mode, we detect polarized emission in the 2-6 keV energy range, with a polarization degree of 12% +/- 3% and a polarization angle of -2deg +/- 9deg (1sigma) measured counterclockwise from the North celestial pole towards East. At optical wavelengths, we find a polarization degree of 1.41% +/- 0.04% and a polarization angle aligned with that in the soft X-rays, suggesting a common physical mechanism operating across these bands. Remarkably, the polarized flux spectrum matches the pulsed emission spectrum from optical to X-rays. The polarization properties differ markedly from those observed in other accreting neutron stars and isolated rotation-powered pulsars and are also inconsistent with an origin in a compact jet. Our results provide direct evidence that the polarized and pulsed emissions both originate from synchrotron radiation at the shock formed where the pulsar wind interacts with the inner regions of the accretion disk., Comment: Submitted

While the effect of intrinsic defects on the electronic properties of half-Heusler compounds has been extensively discussed in literature, their effect on the lattice vibrations has received much less attention, due to the prohibitive computational demands. This may lead to an erroneous description of the lattice thermal conductivity, which plays a crucial role in the thermoelectric efficiency, and for which there exists a significant discrepancy between ideal theoretical values and available experimental measurements. In this article, we employ a combination of density-functional theory (DFT) and machine-learning interatomic potentials (MLIPs) to investigate how intrinsic defects affect the phonon spectra and lattice thermal conductivity of TaFeSb, alongside its electronic structure. The calculation of the formation energies of various defects identifies Fe interstitial atoms sitting at the vacant side of the HH crystal structure as the most likely to form, immediately followed by Sb substitution at Ta sites and by other antisite configurations. Phonon calculations illustrate that both defects generate localized phonon modes that significantly lower the lattice thermal conductivity, especially around room temperature. This reduction aligns the calculated values with available measurements, underscoring the critical role of intrinsic defects in reconciling the existing discrepancies between theory and experiment. Our findings also reveal that these defects introduce localized electronic states, effectively reducing the theoretical electronic band gap and bringing it closer to the experimentally observed values. Finally, our analysis demonstrates the efficiency and effectiveness of machine-learning-based approaches to investigate defect-induced properties in complex materials for thermoelectric applications., Comment: 11 pages, 5 figures

We study an inflation model with nonminimal derivative coupling that features a coupling between the derivative of the inflaton field and the Einstein tensor. This model naturally amplifies curvature perturbations at small scales via gravitationally enhanced friction, a mechanism critical for the formation of primordial black holes and the associated production of potentially detectable scalar-induced gravitational waves. We derive analytical expressions for the primordial power spectrum, enabling efficient exploration of the model parameter space without requiring computationally intensive numerical solutions of the Mukhanov-Sasaki equation. Using the third data release of the Parkes Pulsar Timing Array (PPTA DR3), we constrain the model parameters characterizing the coupling function: $\phi_c = 3.7^{+0.3}_{-0.5} M_\mathrm{P}$, $\log_{10} \omega_L = 7.1^{+0.6}_{-0.3}$, and $\log_{10} \sigma = -8.3^{+0.3}_{-0.6}$ at 90\% confidence level. Our results demonstrate the growing capability of pulsar timing arrays to probe early Universe physics, complementing traditional cosmic microwave background observations by providing unique constraints on inflationary dynamics at small scales., Comment: 14 pages, 5figures

The abundance of information on social media has reshaped public discussions, shifting attention to the mechanisms that drive online discourse. This study analyzes large-scale Twitter (now X) data from three global debates -- Climate Change, COVID-19, and the Russo-Ukrainian War -- to investigate the structural dynamics of engagement. Our findings reveal that discussions are not primarily shaped by specific categories of actors, such as media or activists, but by shared ideological alignment. Users consistently form polarized communities, where their ideological stance in one debate predicts their positions in others. This polarization transcends individual topics, reflecting a broader pattern of ideological divides. Furthermore, the influence of individual actors within these communities appears secondary to the reinforcing effects of selective exposure and shared narratives. Overall, our results underscore that ideological alignment, rather than actor prominence, plays a central role in structuring online discourse and shaping the spread of information in polarized environments.

The X-ray polarization observations made possible with the Imaging X-ray Polarimetry Explorer (IXPE) offer new ways of probing high-energy emission processes in astrophysical jets from blazars. Here we report on the first X-ray polarization observation of the blazar S4 0954+65 in a high optical and X-ray state. During our multi-wavelength campaign on the source, we detected an optical flare whose peak coincided with the peak of an X-ray flare. This optical-X-ray flare most likely took place in a feature moving along the parsec-scale jet, imaged at 43 GHz by the Very Long Baseline Array. The 43 GHz polarization angle of the moving component underwent a rotation near the time of the flare. In the optical band, prior to the IXPE observation, we measured the polarization angle to be aligned with the jet axis. In contrast, during the optical flare the optical polarization angle was perpendicular to the jet axis; after the flare, it reverted to being parallel to the jet axis. Due to the smooth behavior of the optical polarization angle during the flare, we favor shocks as the main acceleration mechanism. We also infer that the ambient magnetic field lines in the jet were parallel to the jet position angle. The average degree of optical polarization during the IXPE observation was (14.3$\pm$4.1)%. Despite the flare, we only detected an upper limit of 14% (at 3$\sigma$ level) on the X-ray polarization degree; although a reasonable assumption on the X-ray polarization angle results in an upper limit of 8.8% ($3\sigma$). We model the spectral energy distribution (SED) and spectral polarization distribution (SPD) of S4 0954+65 with leptonic (synchrotron self-Compton) and hadronic (proton and pair synchrotron) models. The constraints we obtain with our combined multi-wavelength polarization observations and SED modeling tentatively disfavor hadronic models for the X-ray emission in S4 0954+65., Comment: Submitted to A&A, 16 pages, 5 figures, and 7 tables

Synchrotron X-ray emission has been detected from nearly a dozen young supernova remnants (SNRs). X-rays of synchrotron origin exhibit linear polarization in a regular, non-randomly oriented magnetic field. The significant polarized X-ray emission from four such SNRs has already been reported on the basis of observations with the Imaging X-ray Polarimetry Explorer (IXPE). The magnetic-field structure as derived from IXPE observations is radial for Cassiopeia A, Tycho's SNR, and SN 1006, and tangential for RX J1713.7-3946. The latter together with the recent detection of a tangential magnetic field in SNR 1E 0102.2-7219 by the Australia Telescope Compact Array in the radio band shows that tangential magnetic fields can also be present in young SNRs. Thus, the dichotomy in polarization between young and middle-aged SNRs (radial magnetic fields in young SNRs, but tangential magnetic fields in middle-aged SNRs), previously noticed in the radio band, deserves additional attention. The present analysis of IXPE observations determines, for the first time, a magnetic-field structure in the northwestern rim of Vela Jr, also known as RX J0852.0-4622, and provides a new example of a young SNR with a tangential magnetic field., Comment: Accepted for publication in Astronomy and Astrophysics

X-ray polarization is a unique new probe of the particle acceleration in astrophysical jets made possible through the Imaging X-ray Polarimetry Explorer. Here we report on the first dense X-ray polarization monitoring campaign on the blazar Mrk 421. Our observations were accompanied by an even denser radio and optical polarization campaign. We find significant short-timescale variability in both X-ray polarization degree and angle, including a $\sim90^\circ$ angle rotation about the jet axis. We attribute this to random variations of the magnetic field, consistent with the presence of turbulence but also unlikely to be explained by turbulence alone. At the same time, the degree of lower-energy polarization is significantly lower and shows no more than mild variability. Our campaign provides further evidence for a scenario in which energy-stratified shock-acceleration of relativistic electrons, combined with a turbulent magnetic field, is responsible for optical to X-ray synchrotron emission in blazar jets., Comment: 23 pages, including 8 pages of appendices. 12 figures, 3 tables. Submitted to ApJ

This study aims to enrich and leverage data from the Informatics Europe Higher Education (IEHE) data portal to extract and analyze trends in female participation in Informatics across Europe. The research examines the proportion of female students, first-year enrollments, and degrees awarded to women in the field. The issue of low female participation in Informatics has long been recognized as a persistent challenge and remains a critical area of scholarly inquiry. Furthermore, existing literature indicates that socio-economic factors can unpredictably influence female participation, complicating efforts to address the gender gap. The analysis focuses on participation data from research universities at various academic levels, including Bachelors, Masters, and PhD programs, and seeks to uncover potential correlations between female participation and geographical or economic zones. The dataset was first enriched by integrating additional information, such as each country's GDP and relevant geographical data, sourced from various online repositories. Subsequently, the data was cleaned to ensure consistency and eliminate incomplete time series. A final set of complete time series was selected for further analysis. We then used the data collected from the internet to assign countries to different clusters. Specifically, we employed Economic Zone, Geographical Area, and GDP quartile to cluster countries and compare their temporal trends both within and between clusters. We analyze the results for each classification and derive conclusions based on the available data.

Polarization measurements provide insight into the magnetic field, a critical aspect of the dynamics and emission properties around the compact object. In this paper, we present the polarized magnetic field of the Crab outer torus and the Vela arc utilizing Imaging X-ray Polarimetry Explorer observation data. The polarization angle (PA) measured for the Crab outer torus exhibits two monotonic evolutions along the azimuth angle, which are consistent with the normal line of the elliptical ring. There is a slight increase in PA along the azimuth angle for both the inner arc and the outer arc of the Vela nebula. The polarized magnetic vector along the outer torus of the Crab nebula shows the polarized magnetic field aligns with Crab outer torus structure. The PA variation along the Crab outer torus suggests a bulk flow speed of 0.8c. Meanwhile, the Vela nebula polarized magnetic field does not exactly align with the Vela arc structure. We noted that the Crab nebula possesses a polarized toroidal magnetic field, where as the Vela nebula exhibits an incomplete toroidal magnetic field., Comment: 8 pages, 5 figures

We prove a Stepanov differentiability type theorem for intrinsic graphs in sub-Riemannian Heisenberg groups., Comment: 17 pages

We report the first detection of X-ray polarization in the horizontal branch for GX 340+0 as obtained by Imaging X-ray Polarimetry Explorer (IXPE). A polarization degree of 4.3%$\pm$0.3% is obtained. This value is in agreement with the previous polarization measurements of Z-sources in the horizontal branch. Spectro-polarimetric analysis, performed using a broad-band spectral model obtained by NICER and NuSTAR quasi-simultaneous observations, allowed us to constrain the polarization for the soft and hard spectral components typical to these sources. The polarization angle for the two components differs by ${\sim}40{\deg}$. This result could be explained by a misalignment of the NS rotations axis with respect to the accretion disk axis. We provide a comparison of the results with polarization expected in different models. Theoretical expectations for the polarization of the disk and the Comptonization components favor an orbital inclination for GX 340+0 higher than 60{\deg}, as expected for Cyg-like sources, in contrast with results we report for the reflection component using broad-band spectrum., Comment: A&A 691, A253 (2024)

While neutrinos are often treated as a background for many dark matter experiments, these particles offer a new avenue for physics: the detection of core-collapse supernovae. Supernovae are extremely energetic, violent and complex events that mark the death of massive stars. During their collapse stars emit a large number of neutrinos in a short burst. These neutrinos carry 99\% of the emitted energy which makes their detection fundamental in understanding supernovae. This paper illustrates how COSINUS (Cryogenic Observatory for SIgnatures seen in Next-generation Underground Searches), a sodium iodide (NaI) based dark matter search, will be sensitive to the next galactic core-collapse supernova. The experiment is composed of two separate detectors which will be sensitive to far and nearby supernovae. The inner core of the experiment will consist of NaI crystals operating as scintillating calorimeters, mainly sensitive to the Coherent Elastic Scattering of Neutrinos (CE$\nu$NS) against the Na and I nuclei. The low mass of the cryogenic detectors gives the experiment a sensitivity to close supernovae below 1kpc without pileup. They will see up to hundreds of CE$\nu$NS events from a supernova happening at 200pc. The crystals reside at the center of a cylindrical 230T water tank, instrumented with 30 photomultipliers. This tank acts as a passive and active shield able to detect the Cherenkov radiation induced by impinging charged particles from ambient and cosmogenic radioactivity. A supernova near the Milky Way Center (10kpc) will be easily detected inducing $\sim$60 measurable events, and the water tank will have a 3$\sigma$ sensitivity to supernovae up to 22kpc, seeing $\sim$10 events. This paper shows how, even without dedicated optimization, modern dark matter experiments will also play their part in the multi-messenger effort to detect the next galactic core-collapse supernova.

Low-mass X-ray binaries hosting weakly magnetized neutron stars (NS-LMXBs) are among the brightest sources in the X-ray sky. Since 2021, the Imaging X-ray Polarimetry Explorer (IXPE) has provided new measurements of the X-ray polarization of these sources. IXPE observations have revealed that most NS-LMXBs are significantly polarized in the X-rays, providing unprecedented insight into the geometry of their accretion flow. In this review paper, we summarize the first results obtained by IXPE on NS-LMXBs, the emerging trends within each class of sources (atoll/Z), and possible physical interpretations., Comment: 8 pages, 3 figures, invited review for the Special Issue X-ray Polarization: A New Era Begins

In the last few years the literature has witnessed a remarkable surge of interest for chaotic maps implemented by discrete-time (DT) memristor circuits. This paper investigates on the reasons underlying this type of chaotic behavior. To this end, the papers considers the map implemented by the simplest memristor circuit given by a capacitor and an ideal flux-controlled memristor or an inductor and an ideal charge-controlled memristor. In particular, the manuscript uses the DT flux-charge analysis method (FCAM) introduced in a recent paper to ensure that the first integrals and foliation in invariant manifolds of continuous-time (CT) memristor circuits are preserved exactly in the discretization for any step size. DT-FCAM yields a two-dimensional map in the voltage-current domain (VCD) and a manifold-dependent one-dimensional map in the flux-charge domain (FCD), i.e., a one-dimensional map on each invariant manifold. One main result is that, for suitable choices of the circuit parameters and memristor nonlinearities, both DT circuits can exactly embed two classic chaotic maps, i.e., the logistic map and the tent map. Moreover, due to the property of extreme multistability, the DT circuits can simultaneously embed in the manifolds all the dynamics displayed by varying one parameter in the logistic and tent map. The paper then considers a DT memristor Murali-Lakshmanan-Chua circuit and its dual. Via DT-FCAM these circuits implement a three-dimensional map in the VCD and a two-dimensional map on each invariant manifold in the FCD. It is shown that both circuits can simultaneously embed in the manifolds all the dynamics displayed by two other classic chaotic maps, i.e., the Henon map and the Lozi map, when varying one parameter in such maps. In essence, these results provide an explanation of why it is not surprising to observe complex dynamics even in simple DT memristor circuits.

Recent gamma-ray observations have detected photons up to energies of a few PeV. These highly energetic gamma rays are emitted by the most powerful sources in the Galaxy. Propagating over astrophysical distances, gamma rays might interact with background photons producing electron-positron pairs, then deflected by astrophysical magnetic fields. In turn, these charged particles might scatter through inverse Compton galactic radiation fields, triggering electromagnetic cascades. In this scenario, the characterisation of astrophysical environment in which gamma rays travel, specifically background photons and magnetic fields, is crucial. We explore the impact of propagation effects on observables at Earth by simulating galactic sources emitting gamma rays with energy between $100 \; \text{GeV}$ and $100 \; \text{PeV}$. We analyse the imprint of the galactic environment on observed energy spectra and arrival direction maps, revealing gamma-ray absorption features in the former and ``deflection" of gamma rays in the latter. Specifically, owing to interstellar radiation field spatial distribution and the galactic magnetic field structure, propagation effects on observables are found to be related to the specific gamma-ray source position and to the prompt emission model. Detailed investigations of the propagation effect on galactic gamma rays will improve the robustness of both current and future gamma-ray detections and indirect dark matter searches., Comment: 26 pages, 24 figures and 1 table. Fixed typos and figures. Submitted to JCAP. Comments welcome!

In this review, a pedagogical introduction to the concepts of slow-roll inflationary Universe and number of $e$-folds is provided. In particular, the differences between the basic notion of number of $e$-folds ($N_e$), total number of $e$-folds ($N_T$) and number of $e$-folds before the end of inflation ($N$), are outlined. The proper application of the number of $e$-folds before the end of inflation is discussed both as a time-like variable for the scalar field evolution and as a key parameter for computing inflationary predictions., Comment: 23 pages, Review for the Special Issue Universe: Feature Papers 2024 - 'Cosmology'

We report on the discovery of polarized X-ray emission from an accreting millisecond pulsar. During a 10-day-long coverage of the February 2024 outburst of SRGA J144459.2-604207, the Imaging X-ray Polarimetry Explorer (IXPE) detected an average polarization degree of the 2-8 keV emission of 2.3% +/- 0.4% at an angle of 59{\deg} +/- 6{\deg} (East of North; uncertainties quoted at the 1${\sigma}$ confidence level). The polarized signal shows a significant energy dependence with a degree of 4.0% +/- 0.5% between 3 and 6 keV and < 1.5% (90% c.l.) in the 2-3 keV range. We used NICER, XMM-Newton, and NuSTAR observations to obtain an accurate pulse timing solution and perform a phase-resolved polarimetric analysis of IXPE data. We did not detect any significant variability of the Stokes parameters Q and U with the spin and the orbital phases. We used the relativistic rotating vector model to show that a moderately fan-beam emission from two point-like spots at a small magnetic obliquity ($\simeq$ 10{\deg}) is compatible with the observed pulse profile and polarization properties. IXPE also detected 52 type-I X-ray bursts, with a recurrence time $\Delta t_{rec}$ increasing from 2 to 8 h as a function of the observed count rate $C$ as as $\Delta t_{rec} \simeq C^{-0.8}$ We stacked the emission observed during all the bursts and obtained an upper limit on the polarization degree of 8.5% (90% c.l.)., Comment: 10 pages, 10 figures, accepted for publication by A&A

This study examines Facebook and YouTube content from over a thousand news outlets in four European languages from 2018 to 2023, using a Bayesian structural time-series model to evaluate the impact of viral posts. Our results show that most viral events do not significantly increase engagement and rarely lead to sustained growth. The virality effect usually depends on the engagement trend preceding the viral post, typically reversing it. When news emerges unexpectedly, viral events enhances users' engagement, reactivating the collective response process. In contrast, when virality manifests after a sustained growth phase, it represents the final burst of that growth process, followed by a decline in attention. Moreover, quick viral effects fade faster, while slower processes lead to more persistent growth. These findings highlight the transient effect of viral events and underscore the importance of consistent, steady attention-building strategies to establish a solid connection with the user base rather than relying on sudden visibility spikes.

We present Crab X-ray polarization measurements using IXPE data with a total exposure of 300ks, three times more than the initial 2022 discovery paper. Polarization is detected in three times more pulsar phase bins, revealing an S-shaped $+40^\circ$ polarization angle sweep in the main pulse and ${>}1\sigma$ departures from the OPTIMA optical polarization in both pulses, suggesting different radiation mechanisms or sites for the polarized emission at the two wavebands. Our polarization map of the inner nebula reveals a toroidal magnetic field, as seen in prior IXPE analyses. Along the southern jet, the magnetic field orientation relative to the jet axis changes from perpendicular to parallel and the polarization degree decreases by ${\sim}6\%$. These observations may be explained by kink instabilities along the jet or a collision with a dense, jet-deflecting medium at the tip. Using spectropolarimetric analysis, we find asymmetric polarization in the four quadrants of the inner nebula, as expected for a toroidal field geometry, and a spatial correlation between polarization degree and photon index., Comment: 14 pages, 7 figures, 3 tables. Accepted by The Astrophysical Journal

We present multiwavelength polarization measurements of the luminous blazar Mrk~501 over a 14-month period. The 2--8 keV X-ray polarization was measured with the Imaging X-ray Polarimetry Explorer (IXPE) with six 100-ks observations spanning from 2022 March to 2023 April. Each IXPE observation was accompanied by simultaneous X-ray data from NuSTAR, Swift/XRT, and/or XMM-Newton. Complementary optical-infrared polarization measurements were also available in the B, V, R, I, and J bands, as were radio polarization measurements from 4.85 GHz to 225.5 GHz. Among the first five IXPE observations, we did not find significant variability in the X-ray polarization degree and angle with IXPE. However, the most recent sixth observation found an elevated polarization degree at $>3\sigma$ above the average of the other five observations. The optical and radio measurements show no apparent correlations with the X-ray polarization properties. Throughout the six IXPE observations, the X-ray polarization degree remained higher than, or similar to, the R-band optical polarization degree, which remained higher than the radio value. This is consistent with the energy-stratified shock scenario proposed to explain the first two IXPE observations, in which the polarized X-ray, optical, and radio emission arises from different regions., Comment: Accepted for publication in ApJ

The CUbesat Solar Polarimeter (CUSP) project is a future CubeSat mission orbiting the Earth aimed to measure the linear polarization of solar flares in the hard X-ray band, by means of a Compton scattering polarimeter. CUSP will allow us to study the magnetic reconnection and particle acceleration in the flaring magnetic structures of our star. The project is in the framework of the Italian Space Agency Alcor Program, which aims to develop new CubeSat missions. CUSP is approved for a Phase B study that will last for 12 months, starting in mid-2024. We report on the current status of the CUSP mission project as the outcome of the Phase A., Comment: Proceeding of SPIE Conference "Astronomical Telescopes+ Instrumentation", Yokohama (Japan), 16-21 June 2024. arXiv admin note: substantial text overlap with arXiv:2208.06211

X-ray polarimetry of solar flares is still a not well established field of observation of our star. Past polarimeters were not able to measure with a high significance the polarization in X-rays from solar flares. Moreover, they had no imaging capabilities and measured only the polarization by integrating on all the image of the source. We propose a mission concept based on a gas photoelectric polarimeter, coupled with multilayer lobster-eye optics, to perform imaging-spectro-polarimetry of solar flares while monitoring the entire solar disc., Comment: Proceeding of SPIE Conference "Astronomical Telescopes+ Instrumentation", Yokohama (Japan), 16-21 June 2024

The CUbesat Solar Polarimeter (CUSP) project is a CubeSat mission orbiting the Earth aimed to measure the linear polarization of solar flares in the hard X-ray band by means of a Compton scattering polarimeter. CUSP will allow the study of the magnetic reconnection and particle acceleration in the flaring magnetic structures of our star. CUSP is a project in the framework of the Alcor Program of the Italian Space Agency aimed at developing new CubeSat missions. It is approved for a Phase B study. In this work, we report on the characterization of the Avalanche Photodiodes (APDs) that will be used as readout sensors of the absorption stage of the Compton polarimeter. We assessed the APDs gain and energy resolution as a function of temperature by irradiating the sensor with a \textsuperscript{55}Fe radioactive source. Moreover, the APDs were also characterized as being coupled to a GAGG scintillator., Comment: Proceeding of SPIE Conference "Astronomical Telescopes+ Instrumentation", Yokohama (Japan), 16-21 June 2024

The CUbesat Solar Polarimeter (CUSP) project aims to develop a constellation of two CubeSats orbiting the Earth to measure the linear polarization of solar flares in the hard X-ray band by means of a Compton scattering polarimeter on board of each satellite. CUSP will allow to study the magnetic reconnection and particle acceleration in the flaring magnetic structures. CUSP is a project approved for a Phase B study by the Italian Space Agency in the framework of the Alcor program aimed to develop CubeSat technologies and missions. In this paper we describe the a method for a multi-physical simulation analysis while analyzing some possible design optimization of the payload design solutions adopted. In particular, we report the mechanical design for each structural component, the results of static and dynamic finite element analysis, the preliminary thermo-mechanical analysis for two specific thermal cases (hot and cold orbit) and a topological optimization of the interface between the platform and the payload., Comment: Proceeding of SPIE Conference "Astronomical Telescopes+ Instrumentation", Yokohama (Japan), 16-21 June 2024

The CUbesat Solar Polarimeter (CUSP) project is a CubeSat mission orbiting the Earth aimed to measure the linear polarization of solar flares in the hard X-ray band by means of a Compton scattering polarimeter. CUSP will allow to study the magnetic reconnection and particle acceleration in the flaring magnetic structures of our star. CUSP is a project in the framework of the Alcor Program of the Italian Space Agency aimed to develop new CubeSat missions. It is approved for a Phase B study. In this work, we report on the accurate simulation of the detector's response to evaluate the scientific performance. A GEANT4 Monte Carlo simulation is used to assess the physical interactions of the source photons with the detector and the passive materials. Using this approach, we implemented a detailed CUSP Mass Model. In this work, we report on the evaluation of the detector's effective area as a function of the beam energy., Comment: Proceeding of SPIE Conference "Astronomical Telescopes+ Instrumentation", Yokohama (Japan), 16-21 June 2024

Social media platforms significantly influence ideological divisions by enabling users to select information that aligns with their beliefs and avoid opposing viewpoints. Analyzing approximately 47 million Facebook posts, this study investigates the interactions of around 170 million users with news pages, revealing distinct patterns based on political orientations. While users generally prefer content that reflects their political biases, the extent of engagement varies even among individuals with similar ideological leanings. Specifically, political biases heavily influence commenting behaviors, particularly among users leaning towards the center-left and the right. Conversely, the 'likes' from center-left and centrist users are more indicative of their political affiliations. This research illuminates the complex relationship between social media behavior and political polarization, offering new insights into the manifestation of ideological divisions online.

Cygnus X-3 is an enigmatic X-ray binary, that is both an exceptional accreting system and a cornerstone for the population synthesis studies. Prominent X-ray and radio properties follow a well-defined pattern, yet the physical reasons for the state changes observed in this system are not known. Recently, the presence of an optically thick envelope around the central source in the hard state was revealed using the X-ray polarization data obtained with Imaging X-ray Polarimetry Explorer (IXPE). In this work, we analyse IXPE data obtained in the ultrasoft (radio quenched) state of the source. The average polarization degree (PD) of $11.9\pm0.5\%$ at a polarization angle (PA) of $94^{\circ}\pm1^{\circ}$ is inconsistent with the simple geometry of the accretion disc viewed at an intermediate inclination. The high PD, the blackbody-like spectrum, and the weakness of fluorescent iron line imply that the central source is hidden behind the optically thick outflow and its beamed radiation is scattered towards our line of sight. In this picture the observed PD is directly related to the source inclination, which we conservatively determine to lie in the range $26^{\circ}

Understanding the impact of digital platforms on user behavior presents foundational challenges, including issues related to polarization, misinformation dynamics, and variation in news consumption. Comparative analyses across platforms and over different years can provide critical insights into these phenomena. This study investigates the linguistic characteristics of user comments over 34 years, focusing on their complexity and temporal shifts. Utilizing a dataset of approximately 300 million English comments from eight diverse platforms and topics, we examine the vocabulary size and linguistic richness of user communications and their evolution over time. Our findings reveal consistent patterns of complexity across social media platforms and topics, characterized by a nearly universal reduction in text length, diminished lexical richness, but decreased repetitiveness. Despite these trends, users consistently introduce new words into their comments at a nearly constant rate. This analysis underscores that platforms only partially influence the complexity of user comments. Instead, it reflects a broader, universal pattern of human behaviour, suggesting intrinsic linguistic tendencies of users when interacting online.

We present the first X-ray spectropolarimetric results for Cygnus X-1 in its soft state from a campaign of five IXPE observations conducted during 2023 May-June. Companion multiwavelength data during the campaign are likewise shown. The 2-8 keV X-rays exhibit a net polarization degree PD=1.99%+/-0.13% (68% confidence). The polarization signal is found to increase with energy across IXPE's 2-8 keV bandpass. The polarized X-rays exhibit an energy-independent polarization angle of PA=-25.7+/-1.8 deg. East of North (68% confidence). This is consistent with being aligned to Cyg X-1's AU-scale compact radio jet and its pc-scale radio lobes. In comparison to earlier hard-state observations, the soft state exhibits a factor of 2 lower polarization degree, but a similar trend with energy and a similar (also energy-independent) position angle. When scaling by the natural unit of the disk temperature, we find the appearance of a consistent trendline in the polarization degree between soft and hard states. Our favored polarimetric model indicates Cyg X-1's spin is likely high (a* above ~0.96). The substantial X-ray polarization in Cyg X-1's soft state is most readily explained as resulting from a large portion of X-rays emitted from the disk returning and reflecting off the disk surface, generating a high polarization degree and a polarization direction parallel to the black hole spin axis and radio jet. In IXPE's bandpass, the polarization signal is dominated by the returning reflection emission. This constitutes polarimetric evidence for strong gravitational lensing of X-rays close to the black hole., Comment: 20 pages, accepted for publication in ApJL

Recent observations of X-ray pulsars (XRPs) performed by the Imaging X-ray Polarimetry Explorer (IXPE) have made it possible to investigate the intricate details of these objects in a new way, thanks to the added value of X-ray polarimetry. Here we present the results of the IXPE observations of SMC X-1, a member of the small group of XRPs displaying super-orbital variability. SMC X-1 was observed by IXPE three separate times during the high state of its super-orbital period. The observed luminosity in the 2-8 keV energy band of $L=2\times10^{38}$ erg/s makes SMC X-1 the brightest XRP ever observed by IXPE. We detect significant polarization in all three observations, with values of the phase-averaged polarization degree (PD) and polarization angle (PA) of $3.2\pm0.8$% and $97\deg\pm8\deg$ for Observation 1, $3.0\pm0.9$% and $90\deg\pm8\deg$ for Observation 2, and $5.5\pm1.1$% and $80\deg\pm6\deg$ for Observation 3, for the spectro-polarimetric analysis. The observed PD shows an increase over time with decreasing luminosity, while the PA decreases in decrements of 10\deg. The phase-resolved spectro-polarimetric analysis reveals significant detection of polarization in three out of seven phase bins, with the PD ranging between 2% and 10%, and a corresponding range in the PA from $\sim$70\deg\ to $\sim$100\deg. The pulse-phase resolved PD displays an apparent anti-correlation with the flux. Using the rotating vector model, we obtain constraints on the pulsar's geometrical properties for the individual observations. The position angle of the pulsar displays an evolution over time supporting the idea that we observe changes related to different super-orbital phases. Scattering in the wind of the precessing accretion disk may be responsible for the behavior of the polarimetric properties observed during the high-state of SMC X-1's super-orbital period., Comment: 11 pages, 11 figures, submitted to A&A

The CYGNO experiment aims to build a large ($\mathcal{O}(10)$ m$^3$) directional detector for rare event searches, such as nuclear recoils (NRs) induced by dark matter (DM), such as weakly interactive massive particles (WIMPs). The detector concept comprises a time projection chamber (TPC), filled with a He:CF$_4$ 60/40 scintillating gas mixture at room temperature and atmospheric pressure, equipped with an amplification stage made of a stack of three gas electron multipliers (GEMs) which are coupled to an optical readout. The latter consists in scientific CMOS (sCMOS) cameras and photomultipliers tubes (PMTs). The maximisation of the light yield of the amplification stage plays a major role in the determination of the energy threshold of the experiment. In this paper, we simulate the effect of the addition of a strong electric field below the last GEM plane on the GEM field structure and we experimentally test it by means of a 10$\times$10 cm$^2$ readout area prototype. The experimental measurements analyse stacks of different GEMs and helium concentrations in the gas mixture combined with this extra electric field, studying their performances in terms of light yield, energy resolution and intrinsic diffusion. It is found that the use of this additional electric field permits large light yield increases without degrading intrinsic characteristics of the amplification stage with respect to the regular use of GEMs., Comment: Correction of typos in Section 2 and 6. Improved quality of plots with some modifications to clarify the content

In 2024, half of the global population is expected to participate in elections, offering researchers a unique opportunity to study online information diffusion and user behavior. This study investigates the media landscape on social media by analyzing Facebook posts from national political parties and major news agencies across Europe, Mexico, and India. Our methodology identifies key topics and evaluates public interaction, reflecting broader trends in political engagement. Using Principal Component Analysis, we distil these topics to uncover patterns of correlation and differentiation. This approach reveals dominant themes that engage global audiences, providing critical insights into the interplay between public opinion and digital narratives during a major electoral cycle. Our findings highlight how different topics resonate across political spectrums, shaping political debate and offering a comprehensive view of the interaction between media content, political ideology, and audience engagement.

We report the X-ray polarization properties of the high-synchrotron-peaked (HSP) blazar PKS 2155$-$304 based on observations with the Imaging X-ray Polarimetry Explorer (IXPE). We observed the source between Oct 27 and Nov 7, 2023. We also conducted an extensive contemporaneous multiwavelength (MW) campaign. We find that during the first half ($T_1$) of the IXPE pointing, the source exhibited the highest X-ray polarization degree detected for an HSP blazar thus far, (30.7$\pm$2.0)%, which dropped to (15.3$\pm$2.1)% during the second half ($T_2$). The X-ray polarization angle remained stable during the IXPE pointing at 129.4$^\circ$$\pm$1.8$^\circ$ and 125.4$^\circ$$\pm$3.9$^\circ$ during $T_1$ and $T_2$, respectively. Meanwhile, the optical polarization degree remained stable during the IXPE pointing, with average host-galaxy-corrected values of (4.3$\pm$0.7)% and (3.8$\pm$0.9)% during the $T_1$ and $T_2$, respectively. During the IXPE pointing, the optical polarization angle changed achromatically from $\sim$140$^\circ$ to $\sim$90$^\circ$ and back to $\sim$130$^\circ$. Despite several attempts, we only detected (99.7% conf.) the radio polarization once (during $T_2$, at 225.5 GHz): with degree (1.7$\pm$0.4)% and angle 112.5$^\circ$$\pm$5.5$^\circ$. The direction of the broad pc-scale jet is rather ambiguous and has been found to point to the east and south at different epochs; however, on larger scales (> 1.5 pc) the jet points toward the southeast ($\sim$135$^\circ$), similar to all of the MW polarization angles. Moreover, the X-ray to optical polarization degree ratios of $\sim$7 and $\sim$4 during $T_1$ and $T_2$, respectively, are similar to previous IXPE results for several HSP blazars. These findings, combined with the lack of correlation of temporal variability between the MW polarization properties, agree with an energy-stratified shock-acceleration scenario in HSP blazars., Comment: 17 pages, 10 figures, 4 tables, Accepted for publication in A&A

The CYGNO collaboration is developing next generation directional Dark Matter (DM) detection experiments, using gaseous Time Projection Chambers (TPCs), as a robust method for identifying Weakly Interacting Massive Particles (WIMPs) below the Neutrino Fog. SF6 is potentially ideal for this since it provides a high fluorine content, enhancing sensitivity to spin-dependent interactions and, as a Negative Ion Drift (NID) gas, reduces charge diffusion leading to improved positional resolution. CF4, although not a NID gas, has also been identified as a favourable gas target as it provides a scintillation signal which can be used for a complimentary light/charge readout approach. These gases can operate at low pressures to elongate Nuclear Recoil (NR) tracks and facilitate directional measurements. In principle, He could be added to low pressure SF6/CF4 without significant detriment to the length of 16S, 12C, and 19F recoils. This would improve the target mass, sensitivity to lower WIMP masses, and offer the possibility of atmospheric operation; potentially reducing the cost of a containment vessel. In this article, we present gas gain and energy resolution measurements, taken with a Multi-Mesh Thick Gaseous Electron Multiplier (MMThGEM), in low pressure SF6 and CF4:SF6 mixtures following the addition of He. We find that the CF4:SF6:He mixtures tested were able to produce gas gains on the order of 10^4 up to a total pressure of 100 Torr. These results demonstrate an order of magnitude improvement in charge amplification in NID gas mixtures with a He component., Comment: Corresponding Author: A.G. McLean

A search for full energy depositions from bosonic keV-scale dark matter candidates of masses between 65 keV and 1021 keV has been performed with data collected during Phase II of the GERmanium Detector Array (GERDA) experiment. Our analysis includes direct dark matter absorption as well as dark Compton scattering. With a total exposure of 105.5 kg yr, no evidence for a signal above the background has been observed. The resulting exclusion limits deduced with either Bayesian or Frequentist statistics are the most stringent direct constraints in the major part of the 140-1021 keV mass range. As an example, at a mass of 150 keV the dimensionless coupling of dark photons and axion-like particles to electrons has been constrained to $\alpha$'/$\alpha$ < 8.7x10$^{-24}$ and g$_{ae}$ < 3.3x10$^{-12}$ at 90% credible interval (CI), respectively. Additionally, a search for peak-like signals from beyond the Standard Model decays of nucleons and electrons is performed. We find for the inclusive decay of a single neutron in $^{76}$Ge a lower lifetime limit of $\tau_n$ > 1.5x10$^{24}$ yr and for a proton $\tau_p$ > 1.3x10$^{24}$ yr at 90% CI. For the electron decay e$^-\rightarrow\nu_e\gamma$ a lower limit of $\tau_e$ > 5.4x10$^{25}$ yr at 90% CI has been determined., Comment: 20 pages, 12 figures, 7 tables

Discovery of pulsations from a number of ULXs proved that accretion onto neutron stars can produce luminosities exceeding the Eddington limit by several orders of magnitude. The conditions necessary to achieve such high luminosities as well as the exact geometry of the accretion flow in the neutron star vicinity are, however, a matter of debate. The pulse phase-resolved polarization measurements that became possible with the launch of the Imaging X-ray Polarimetry Explorer (IXPE) can be used to determine the pulsar geometry and its orientation relative to the orbital plane. They provide an avenue to test different theoretical models of ULX pulsars. In this paper we present the results of three IXPE observations of the first Galactic ULX pulsar Swift J0243.6+6124 during its 2023 outburst. We find strong variations in the polarization characteristics with the pulsar phase. The average polarization degree increases from about 5% to 15% as the flux dropped by a factor of three in the course of the outburst. The polarization angle (PA) as a function of the pulsar phase shows two peaks in the first two observations, but changes to a characteristic sawtooth pattern in the remaining data set. This is not consistent with a simple rotating vector model. Assuming the existence of an additional constant polarized component, we were able to fit the three observations with a common rotating vector model and obtain constraints on the pulsar geometry. In particular, we find the pulsar angular momentum inclination with respect to the line of sight of 15-40 deg, the magnetic obliquity of 60-80 deg, and the pulsar spin position angle of -50 deg, which significantly differs from the constant component PA of about 10 deg. Combining these X-ray measurements with the optical PA, we find evidence for at least a 30 deg misalignment between the pulsar angular momentum and the binary orbital axis., Comment: 13 pages, 10 figures, version published in A&A

Supernova remnants (SNRs) provide insights into cosmic-ray acceleration and magnetic field dynamics at shock fronts. Recent X-ray polarimetric measurements by the Imaging X-ray Polarimetry Explorer (IXPE) have revealed radial magnetic fields near particle acceleration sites in young SNRs, including Cassiopeia A, Tycho, and SN 1006. We present here the spatially-resolved IXPE X-ray polarimetric observation of the northwestern rim of SNR RX J1713.7-3946. For the first time, our analysis shows that the magnetic field in particle acceleration sites of this SNR is oriented tangentially with respect to the shock front. Because of the lack of precise Faraday-rotation measurements in the radio band, this was not possible before. The average measured polarization degree (PD) of the synchtrotron emission is 12.5 {\pm} 3.3%, lower than the one measured by IXPE in SN 1006, comparable to the Tycho one, but notably higher than the one in Cassiopeia A. On sub-parsec scales, localized patches within RX J1713.7-3946 display PD up to 41.5 {\pm} 9.5%. These results are compatible with a shock-compressed magnetic field. However, in order to explain the observed PD, either the presence of a radial net magnetic field upstream of the shock, or partial reisotropization of the turbulence downstream by radial magneto-hydrodynamical instabilities, can be invoked. From comparison of PD and magnetic field distribution with {\gamma}-rays and 12 CO data, our results provide new inputs in favor of a leptonic origin of the {\gamma}-ray emission., Comment: 18 pages, 6 figures, 2 tables, published in ApJ Letters

The design and optimization of Reconfigurable Intelligent Surfaces (RISs) are key challenges for future wireless communication systems. RISs are devices that can manipulate electromagnetic (EM) waves in a programmable way, thus enhancing the performance and efficiency of wireless links. To achieve this goal, it is essential to have reliable EM models that can capture the behavior of RISs in different scenarios. This work demonstrates that the Partial Elements Equivalent Circuit (PEEC) method is a powerful tool for EM analysis of RIS-aided wireless links. It might also be integrated with optimization algorithms in order to optimize wireless communication networks.

Reconfigurable Intelligent Surface (RIS) modeling and optimization are a crucial steps in developing the next generation of wireless communications. To this aim, the availability of accurate electromagnetic (EM) models is of paramount important for the design of RIS-assisted communication links. In this work, we validate a widely-used analytical multiport network for RISs by means of a well-established full-wave numerical method based on the Partial Elements Equivalent Circuit (PEEC) approach. Numerical results show good agreement between the two methods, thus demonstrating i) the considered multiport network model being effective and ii) the PEEC method being appropriate for EM modeling of RIS-assisted wireless links.

COSINUS is a dark matter (DM) direct search experiment that uses sodium iodide (NaI) crystals as cryogenic calorimeters. Thanks to the low nuclear recoil energy threshold and event-by-event discrimination capability, COSINUS will address the long-standing DM claim made by the DAMA/LIBRA collaboration. The experiment is currently under construction at the Laboratori Nazionali del Gran Sasso, Italy, and employs a large cylindrical water tank as a passive shield to meet the required background rate. However, muon-induced neutrons can mimic a DM signal therefore requiring an active veto system, which is achieved by instrumenting the water tank with an array of photomultiplier tubes (PMTs). This study optimizes the number, arrangement, and trigger conditions of the PMTs as well as the size of an optically invisible region. The objective was to maximize the muon veto efficiency while minimizing the accidental trigger rate due to the ambient and instrumental background. The final configuration predicts a veto efficiency of 99.63 $\pm$ 0.16 $\%$ and 44.4 $\pm$ $5.6\%$ in the tagging of muon events and showers of secondary particles, respectively. The active veto will reduce the cosmogenic neutron background rate to 0.11 $\pm$ 0.02 cts$\cdot$kg$^{-1}$$\cdot$year$^{-1}$, corresponding to less than one background event in the region of interest for the whole COSINUS-1$\pi$ exposure of 1000 kg$\cdot$days.

In this paper, we present the first measurement of a Gallium Arsenide crystal working as low-temperature calorimeter for direct Dark Matter (DM) searches within the DAREDEVIL (DARk-mattEr DEVIces for Low energy detection) project. In the quest for direct dark matter detection, innovative approaches to lower the detection thershold and explore the sub-GeV mass DM range, have gained high relevance in the last decade. This study presents the pioneering use of Gallium Arsenide (GaAs) as a low-temperature calorimeter for probing the dark matter-electron interaction channel. Our experimental setup features a GaAs crystal at ultralow temperature of 15 mK, coupled with a Neutron Transmutation Doped (NTD) thermal sensor for precise energy estimation. This configuration is the first step towards the detection of single electrons scattered by dark matter particles within the GaAs crystal, to significantly improve the sensitivity to low-mass dark matter candidates.

Analysis of microservices' performance is a considerably challenging task due to the multifaceted nature of these systems. Each request to a microservices system might raise several Remote Procedure Calls (RPCs) to services deployed on different servers and/or containers. Existing distributed tracing tools leverage swimlane visualizations as the primary means to support performance analysis of microservices. These visualizations are particularly effective when it is needed to investigate individual end-to-end requests' performance behaviors. Still, they are substantially limited when more complex analyses are required, as when understanding the system-wide performance trends is needed. To overcome this limitation, we introduce vamp, an innovative visual analytics tool that enables, at once, the performance analysis of multiple end-to-end requests of a microservices system. Vamp was built around the idea that having a wide set of interactive visualizations facilitates the analyses of the recurrent characteristics of requests and their relation w.r.t. the end-to-end performance behavior. Through an evaluation of 33 datasets from an established open-source microservices system, we demonstrate how vamp aids in identifying RPC execution time deviations with significant impact on end-to-end performance. Additionally, we show that vamp can support in pinpointing meaningful structural patterns in end-to-end requests and their relationship with microservice performance behaviors., Comment: Accepted for publication in The 39th ACM/SIGAPP Symposium on Applied Computing (SAC '24)

Fairness is a critical concept in ethics and social domains, but it is also a challenging property to engineer in software systems. With the increasing use of machine learning in software systems, researchers have been developing techniques to automatically assess the fairness of software systems. Nonetheless, a significant proportion of these techniques rely upon pre-established fairness definitions, metrics, and criteria, which may fail to encompass the wide-ranging needs and preferences of users and stakeholders. To overcome this limitation, we propose a novel approach, called MODNESS, that enables users to customize and define their fairness concepts using a dedicated modeling environment. Our approach guides the user through the definition of new fairness concepts also in emerging domains, and the specification and composition of metrics for its evaluation. Ultimately, MODNESS generates the source code to implement fair assessment based on these custom definitions. In addition, we elucidate the process we followed to collect and analyze relevant literature on fairness assessment in software engineering (SE). We compare MODNESS with the selected approaches and evaluate how they support the distinguishing features identified by our study. Our findings reveal that i) most of the current approaches do not support user-defined fairness concepts; ii) our approach can cover two additional application domains not addressed by currently available tools, i.e., mitigating bias in recommender systems for software engineering and Arduino software component recommendations; iii) MODNESS demonstrates the capability to overcome the limitations of the only two other Model-Driven Engineering-based approaches for fairness assessment.

It has become increasingly useful to answer questions in gravitational-wave astronomy using transdimensional models where the number of free parameters can be varied depending on the complexity required to fit the data. Given the growing interest in transdimensional inference, we introduce a new package for the Bayesian inference Library (Bilby) called tBilby. The tBilby package allows users to set up transdimensional inference calculations using the existing Bilby architecture with off-the-shelf nested samplers and/or Markov Chain Monte Carlo algorithms. Transdimensional models are particularly helpful when we seek to test theoretically uncertain predictions described by phenomenological models. For example, bursts of gravitational waves can be modelled using a superposition of N wavelets where N is itself a free parameter. Short pulses are modelled with small values of N whereas longer, more complicated signals are represented with a large number of wavelets stitched together. Other transdimensional models have found use describing instrumental noise and the population properties of gravitational-wave sources. We provide a few demonstrations of tBilby, including fitting the gravitational-wave signal GW150914 with a superposition of N sine-Gaussian wavelets. We outline our plans to further develop the tbilby code suite for a broader range of transdimensional problems., Comment: 12 pages, 7 figures

Weakly magnetized neutron stars (WMNS) are complicated sources with challenging phenomenology. For decades, they have been studied via spectrometry and timing. It has been established that the spectrum of WMNSs consists of several components traditionally associated with the accretion disk, the boundary or spreading layer, and the wind and their interactions with each other. Since 2022, WMNSs have been actively observed with the Imaging X-ray Polarimetry Explorer (IXPE). Polarimetric studies provided new information about the behavior and geometry of these sources. One of the most enigmatic sources of the class, galactic X-ray burster GX 13+1 was first observed with IXPE in October 2023. A strongly variable polarization at the level 2-5$\%$ was detected with the source showing a rotation of the polarization angle (PA) that hinted towards the misalignment within the system. The second observation was performed in February 2024 with a complementary observation by Swift/XRT. IXPE measured an overall polarization degree (PD) of 2.5$\%$ and the PA of 24 degrees, and the Swift/XRT data helped us evaluate the galactic absorption and fit the continuum. Here we study the similarities and differences between the polarimetric properties of the source during the two observations. We confirm the expectation of the misalignment in the system and the assignment of the harder component to the boundary layer. We emphasize the importance of the wind in the system. We note the difference in the variation of polarimetric properties with energy and with time., Comment: 8 pages, 7 figures

We employ ab-initio electronic structure calculations to investigate the charge-density waves and periodic lattice distortions in bilayer 2H-NbSe$_2$. We demonstrate that the vertical stacking can give rise to a variety of patterns that may lower the symmetry of the charge-density waves exhibited separately by the two composing 1H-NbSe$_2$ monolayers. The general tendency to a spontaneous symmetry breaking observed in the ground state and the first excited states is shown to originate from a non-negligible inter-layer coupling. Simulated images for scanning tunnelling microscopy (STM) as well as diffraction/scattering patterns show signatures of the different stacking orders. This may not only be useful to reinterpret past experiments on surfaces and thin films, but may also be exploited to devise ad-hoc experiments for the investigation of the stacking order in 2H-NbSe$_2$. We anticipate that our analysis does not only apply to the 2H-NbSe$_2$ bilayer, but is also relevant for thin films and bulk, whose smallest centro-symmetric component is indeed the bilayer. Finally, our results illustrate clearly that the vertical stacking is not only important for 1T structures, as exemplified by the metal-to-insulator transition observed in 1T-TaS$_2$, but seems to be a general feature of metallic layered transition metal dichalcogenides as well., Comment: 15 pages, 9 figures