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We study the generation of gravitational waves (GWs) during a first-order cosmological phase transition (PT) using the recently introduced Higgsless approach to numerically evaluate the fluid motion induced by the PT. We present for the first time spectra from strong first-order PTs ($\alpha = 0.5$), alongside weak ($\alpha = 0.0046$) and intermediate ($\alpha = 0.05$) transitions previously considered in the literature. We test the regime of applicability of the stationary source assumption, characteristic of the sound-shell model, and show that it agrees with our numerical results when the kinetic energy, sourcing GWs, does not decay with time. However, we find in general that for intermediate and strong PTs, the kinetic energy in our simulations decays following a power law in time, and provide a theoretical framework that extends the stationary assumption to one that allows to include the time evolution of the source. This decay of the kinetic energy, potentially determined by non-linear dynamics and hence, related to the production of vorticity, modifies the usually assumed linear growth with the source duration to an integral over time of the kinetic energy fraction, effectively reducing the growth rate. We validate the novel theoretical model with the results of our simulations covering a broad range of wall velocities. We provide templates for the GW amplitude and spectral shape for a broad range of PT parameters., Comment: 55 pages, 15 figures

The optical manipulation of magnetism enabled by rare earth-transition metal ferrimagnets holds the promise of ultrafast, energy efficient spintronic technologies. This work investigates laser-induced picosecond spin currents generated by ferrimagnetic GdCo via terahertz emission spectroscopy. A suppression of the THz emission and spin current is observed at magnetization compensation when varying the temperature or alloy composition in the presence of a magnetic field. It is demonstrated that this is due to the formation of domains in the GdCo equilibrium magnetic configuration. Without an applied magnetic field, the picosecond spin current persists at the compensation point. The experimental findings support the model for THz spin current generation based on transport of hot spin-polarized electrons, which is dominated by the Co sublattice at room temperature. Only at low temperature a comparable contribution from Gd is detected but with slower dynamics. Finally, spectral analysis reveals a blueshift of the THz emission related to the formation of magnetic domains close to magnetization compensation.

Detecting monotonic changes in heart rate (HR) is crucial for early identification of cardiac conditions and health management. This is particularly important for dementia patients, where HR trends can signal stress or agitation. Developing wearable technologies that can perform always-on monitoring of HRs is essential to effectively detect slow changes over extended periods of time. However, designing compact electronic circuits that can monitor and process bio-signals continuously, and that can operate in a low-power regime to ensure long-lasting performance, is still an open challenge. Neuromorphic technology offers an energy-efficient solution for real-time health monitoring. We propose a neuromorphic implementation of a Neural State Machine (NSM) network to encode different health states and switch between them based on the input stimuli. Our focus is on detecting monotonic state switches in electrocardiogram data to identify progressive HR increases. This innovative approach promises significant advancements in continuous health monitoring and management.

The self-organization of active particles on a two-dimensional single-occupancy lattice is investigated, with an emphasis on the effects of boundary confinement and the influence of an external mean fluid flow. The study examines collective behaviors, particularly the transition from a disordered phase to the formation of orientationally ordered patterns, and their impact on particle transport and flux. In the absence of fluid flow, confinement causes particles to accumulate near the walls, leading to clogs or obstructions that hinder movement, or to the formation of bands aligned with the channel. Although these bands limit the particles ability to freely self-propel, they still result in a net flux along the channel. The introduction of an external Poiseuille fluid flow induces vorticity, shifts the phase transition to higher alignment sensitivities, and promotes particle clustering at the channel center, significantly enhancing overall flux.

Background and Objective: Diabetes presents a significant challenge to healthcare due to the negative impact of poor blood sugar control on health and associated complications. Computer simulation platforms, notably exemplified by the UVA/Padova Type 1 Diabetes simulator, has emerged as a promising tool for advancing diabetes treatments by simulating patient responses in a virtual environment. The UVA Virtual Lab (UVLab) is a new simulation platform to mimic the metabolic behavior of people with Type 2 diabetes (T2D) with a large population of 6062 virtual subjects. Methods: The work introduces the Distribution-Based Population Selection (DSPS) method, a systematic approach to identifying virtual subsets that mimic the clinical behavior observed in real trials. The method transforms the sub-population selection task into a Linear Programing problem, enabling the identification of the largest representative virtual cohort. This selection process centers on key clinical outcomes in diabetes research, such as HbA1c and Fasting plasma Glucose (FPG), ensuring that the statistical properties (moments) of the selected virtual sub-population closely resemble those observed in real-word clinical trial. Results: DSPS method was applied to the insulin degludec (IDeg) arm of a phase 3 clinical trial. This method was used to select a sub-population of virtual subjects that closely mirrored the clinical trial data across multiple key metrics, including glycemic efficacy, insulin dosages, and cumulative hypoglycemia events over a 26-week period. Conclusion: The DSPS algorithm is able to select virtual sub-population within UVLab to reproduce and predict the outcomes of a clinical trial. This statistical method can bridge the gap between large population simulation platforms and previously conducted clinical trials.

Robotic-assisted surgery (RAS) relies on accurate depth estimation for 3D reconstruction and visualization. While foundation models like Depth Anything Models (DAM) show promise, directly applying them to surgery often yields suboptimal results. Fully fine-tuning on limited surgical data can cause overfitting and catastrophic forgetting, compromising model robustness and generalization. Although Low-Rank Adaptation (LoRA) addresses some adaptation issues, its uniform parameter distribution neglects the inherent feature hierarchy, where earlier layers, learning more general features, require more parameters than later ones. To tackle this issue, we introduce Depth Anything in Robotic Endoscopic Surgery (DARES), a novel approach that employs a new adaptation technique, Vector Low-Rank Adaptation (Vector-LoRA) on the DAM V2 to perform self-supervised monocular depth estimation in RAS scenes. To enhance learning efficiency, we introduce Vector-LoRA by integrating more parameters in earlier layers and gradually decreasing parameters in later layers. We also design a reprojection loss based on the multi-scale SSIM error to enhance depth perception by better tailoring the foundation model to the specific requirements of the surgical environment. The proposed method is validated on the SCARED dataset and demonstrates superior performance over recent state-of-the-art self-supervised monocular depth estimation techniques, achieving an improvement of 13.3% in the absolute relative error metric. The code and pre-trained weights are available at https://github.com/mobarakol/DARES., Comment: 11 pages

Three-dimensional (3D) reconstruction from two-dimensional images is an active research field in computer vision, with applications ranging from navigation and object tracking to segmentation and three-dimensional modeling. Traditionally, parametric techniques have been employed for this task. However, recent advancements have seen a shift towards learning-based methods. Given the rapid pace of research and the frequent introduction of new image matching methods, it is essential to evaluate them. In this paper, we present a comprehensive evaluation of various image matching methods using a structure-from-motion pipeline. We assess the performance of these methods on both in-domain and out-of-domain datasets, identifying key limitations in both the methods and benchmarks. We also investigate the impact of edge detection as a pre-processing step. Our analysis reveals that image matching for 3D reconstruction remains an open challenge, necessitating careful selection and tuning of models for specific scenarios, while also highlighting mismatches in how metrics currently represent method performance., Comment: 19 pages, 5 figures

We examine three non-conservative interacting particle systems in one dimension modeling epidemic spreading: the diffusive contact process (DCP), a model that we introduce and call generalized diffusive contact process (GDCP), and the susceptible-infectious-recovered (SIR) model. For each system, we establish duality relations through an analytical approach. As an application, we provide a new expression of the correlation functions for the steady state of the finite volume DCP and GDCP in contact with boundary reservoirs. We explicitly compute the one point correlation function of the steady state of a small sized DCP, and for arbitrary size in a particular setting of the GDCP. For the infinite SIR model, the duality relation obtained yields an explicit expression of the time evolution of some specific correlation functions, describing the time decay of the sizes of chains of susceptible individuals.

We consider the solution of an additive fractional stochastic differential equation (SDE) and, leveraging continuous observations of the process, introduce a methodology for estimating its stationary density $\pi$. Initially, employing a tailored martingale decomposition specifically designed for the statistical challenge at hand, we establish convergence rates surpassing those found in existing literature. Subsequently, we refine the attained rate for the case where $H < \frac{1}{2}$ by incorporating bounds on the density of the semi-group. This enhancement outperforms previous rates. Finally, our results weaken the usual convexity assumptions on the drift component, allowing to consider settings where strong convexity only holds outside a compact set.

We introduce 2D-Malafide, a novel and lightweight adversarial attack designed to deceive face deepfake detection systems. Building upon the concept of 1D convolutional perturbations explored in the speech domain, our method leverages 2D convolutional filters to craft perturbations which significantly degrade the performance of state-of-the-art face deepfake detectors. Unlike traditional additive noise approaches, 2D-Malafide optimises a small number of filter coefficients to generate robust adversarial perturbations which are transferable across different face images. Experiments, conducted using the FaceForensics++ dataset, demonstrate that 2D-Malafide substantially degrades detection performance in both white-box and black-box settings, with larger filter sizes having the greatest impact. Additionally, we report an explainability analysis using GradCAM which illustrates how 2D-Malafide misleads detection systems by altering the image areas used most for classification. Our findings highlight the vulnerability of current deepfake detection systems to convolutional adversarial attacks as well as the need for future work to enhance detection robustness through improved image fidelity constraints., Comment: Accepted at BIOSIG 2024

We present millimeter observations of the host galaxy of the most distant blazar known, VLASSJ041009.05-013919.88 (hereafter J0410-0139) at z=7, using ALMA and NOEMA observations. The ALMA data reveal a 2e42 erg/s [CII] 158um emission line at z=6.9964 with a [CII]-inferred star-formation rate of 58 Msun/yr. We estimate a dynamical mass of 4.6e9 Msun, implying a black hole mass to host a dynamical mass ratio of 0.15. The 238 GHz continuum (rest-frame IR) decreased by ~33% from the NOEMA to the ALMA observations taken ~10 months apart. The VLA 3-10 GHz radio flux densities showed a ~37% decrease in a similar time frame, suggesting a causal connection. At face value, J0410-0139 would have the lowest [CII]-to-IR luminosity ratio of a z>5.7 quasar reported to date (~1e-4). However, if only <20% of the measured IR luminosity were due to thermal emission from dust, the [CII]-to-IR luminosity ratio would be typical of (U)LIRGS, and the star formation rates derived from [CII] and IR luminosities would be consistent. These results provide further evidence that synchrotron emission significantly contributes to the observed rest-frame IR emission of J0410-0139, similar to what has been reported in some radio-loud AGN at z<1., Comment: Version after addressing referee report. See also companion paper: arXiv:2407.07236

The forthcoming generation of radio telescope arrays promises significant advancements in sensitivity and resolution, enabling the identification and characterization of many new faint and diffuse radio sources. Conventional manual cataloging methodologies are anticipated to be insufficient to exploit the capabilities of new radio surveys. Radio interferometric images of diffuse sources present a challenge for image segmentation tasks due to noise, artifacts, and embedded radio sources. In response to these challenges, we introduce Radio U-Net, a fully convolutional neural network based on the U-Net architecture. Radio U-Net is designed to detect faint and extended sources in radio surveys, such as radio halos, relics, and cosmic web filaments. Radio U-Net was trained on synthetic radio observations built upon cosmological simulations and then tested on a sample of galaxy clusters, where the detection of cluster diffuse radio sources relied on customized data reduction and visual inspection of LOFAR Two Metre Sky Survey (LoTSS) data. The 83% of clusters exhibiting diffuse radio emission were accurately identified, and the segmentation successfully recovered the morphology of the sources even in low-quality images. In a test sample comprising 246 galaxy clusters, we achieved a 73% accuracy rate in distinguishing between clusters with and without diffuse radio emission. Our results establish the applicability of Radio U-Net to extensive radio survey datasets, probing its efficiency on cutting-edge high-performance computing systems. This approach represents an advancement in optimizing the exploitation of forthcoming large radio surveys for scientific exploration., Comment: Accepted by MNRAS, 16 pages, 9 figures, 2 tables

The NANOGrav 15-year data provides compelling evidence for a stochastic gravitational-wave (GW) background at nanohertz frequencies. The simplest model-independent approach to characterizing the frequency spectrum of this signal consists in a simple power-law fit involving two parameters: an amplitude A and a spectral index \gamma. In this paper, we consider the next logical step beyond this minimal spectral model, allowing for a running (i.e., logarithmic frequency dependence) of the spectral index, \gamma_run(f) = \gamma + \beta \ln(f/f_ref). We fit this running-power-law (RPL) model to the NANOGrav 15-year data and perform a Bayesian model comparison with the minimal constant-power-law (CPL) model, which results in a 95% credible interval for the parameter \beta consistent with no running, \beta \in [-0.80,2.96], and an inconclusive Bayes factor, B(RPL vs. CPL) = 0.69 +- 0.01. We thus conclude that, at present, the minimal CPL model still suffices to adequately describe the NANOGrav signal; however, future data sets may well lead to a measurement of nonzero \beta. Finally, we interpret the RPL model as a description of primordial GWs generated during cosmic inflation, which allows us to combine our results with upper limits from big-bang nucleosynthesis, the cosmic microwave background, and LIGO-Virgo-KAGRA., Comment: 17 pages, 4 figures, 2 tables

In this paper, we address high-dimensional parametric estimation of the drift function in diffusion models, specifically focusing on a $d$-dimensional ergodic diffusion process observed at discrete time points. Assuming sparsity of the parameter vector, we examine the statistical behavior of the Lasso estimator for the unknown parameter. Our primary contribution is the proof of an oracle inequality for the Lasso estimator, which holds on the intersection of three specific sets defined for our analysis. We carefully control the probability of these sets, tackling the central challenge of our study. This approach allows us to derive error bounds for the $l_1$ and $l_2$ norms, assessing the performance of the proposed Lasso estimator. Our results demonstrate that, under certain conditions, the discretization error becomes negligible, enabling us to achieve the same optimal rate of convergence as if the continuous trajectory of the process were observed. We validate our theoretical findings through numerical experiments, which show that the Lasso estimator significantly outperforms the maximum likelihood estimator (MLE) in terms of support recovery.

Manipulating the dispersive characteristics of vibrational waves is beneficial for many applications, e.g., high-precision instruments. architected hierarchical phononic materials have sparked promise tunability of elastodynamic waves and vibrations over multiple frequency ranges. In this article, hierarchical unit-cells are obtained, where features at each length scale result in a band gap within a targeted frequency range. Our novel approach, the ``hierarchical unit-cell template method,'' is an interpretable machine-learning approach that uncovers global unit-cell shape/topology patterns corresponding to predefined band-gap objectives. A scale-separation effect is observed where the coarse-scale band-gap objective is mostly unaffected by the fine-scale features despite the closeness of their length scales, thus enabling an efficient hierarchical algorithm. Moreover, the hierarchical patterns revealed are not predefined or self-similar hierarchies as common in current hierarchical phononic materials. Thus, our approach offers a flexible and efficient method for the exploration of new regions in the hierarchical design space, extracting minimal effective patterns for inverse design in applications targeting multiple frequency ranges.

Confronted with the challenge of identifying the most suitable metric to validate the merits of newly proposed models, the decision-making process is anything but straightforward. Given that comparing rankings introduces its own set of formidable challenges and the likely absence of a universal metric applicable to all scenarios, the scenario does not get any better. Furthermore, metrics designed for specific contexts, such as for Recommender Systems, sometimes extend to other domains without a comprehensive grasp of their underlying mechanisms, resulting in unforeseen outcomes and potential misuses. Complicating matters further, distinct metrics may emphasize different aspects of rankings, frequently leading to seemingly contradictory comparisons of model results and hindering the trustworthiness of evaluations. We unveil these aspects in the domain of ranking evaluation metrics. Firstly, we show instances resulting in inconsistent evaluations, sources of potential mistrust in commonly used metrics; by quantifying the frequency of such disagreements, we prove that these are common in rankings. Afterward, we conceptualize rankings using the mathematical formalism of symmetric groups detaching from possible domains where the metrics have been created; through this approach, we can rigorously and formally establish essential mathematical properties for ranking evaluation metrics, essential for a deeper comprehension of the source of inconsistent evaluations. We conclude with a discussion, connecting our theoretical analysis to the practical applications, highlighting which properties are important in each domain where rankings are commonly evaluated. In conclusion, our analysis sheds light on ranking evaluation metrics, highlighting that inconsistent evaluations should not be seen as a source of mistrust but as the need to carefully choose how to evaluate our models in the future.

Data in the healthcare domain arise from a variety of sources and modalities, such as x-ray images, continuous measurements, and clinical notes. Medical practitioners integrate these diverse data types daily to make informed and accurate decisions. With recent advancements in language models capable of handling multimodal data, it is a logical progression to apply these models to the healthcare sector. In this work, we introduce a framework that connects small language models to multiple data sources, aiming to predict the risk of various diseases simultaneously. Our experiments encompass 12 different tasks within a multitask learning setup. Although our approach does not surpass state-of-the-art methods specialized for single tasks, it demonstrates competitive performance and underscores the potential of small language models for multimodal reasoning in healthcare., Comment: 6 pages, submitted to ICMLA

Proximally-sensed laser scanning offers significant potential for automated forest data capture, but challenges remain in automatically identifying tree species without additional ground data. Deep learning (DL) shows promise for automation, yet progress is slowed by the lack of large, diverse, openly available labeled datasets of single tree point clouds. This has impacted the robustness of DL models and the ability to establish best practices for species classification. To overcome these challenges, the FOR-species20K benchmark dataset was created, comprising over 20,000 tree point clouds from 33 species, captured using terrestrial (TLS), mobile (MLS), and drone laser scanning (ULS) across various European forests, with some data from other regions. This dataset enables the benchmarking of DL models for tree species classification, including both point cloud-based (PointNet++, MinkNet, MLP-Mixer, DGCNNs) and multi-view image-based methods (SimpleView, DetailView, YOLOv5). 2D image-based models generally performed better (average OA = 0.77) than 3D point cloud-based models (average OA = 0.72), with consistent results across different scanning platforms and sensors. The top model, DetailView, was particularly robust, handling data imbalances well and generalizing effectively across tree sizes. The FOR-species20K dataset, available at https://zenodo.org/records/13255198, is a key resource for developing and benchmarking DL models for tree species classification using laser scanning data, providing a foundation for future advancements in the field.

The MiG-V was designed for high-security applications and is the first commercially available logic-locked RISC-V processor on the market. In this context logic locking was used to protect the RISC-V processor design during the untrusted manufacturing process by using key-driven logic gates to obfuscate the original design. Although this method defends against malicious modifications, such as hardware Trojans, logic locking's impact on the RISC-V processor's data confidentiality during runtime has not been thoroughly examined. In this study, we evaluate the impact of logic locking on data confidentiality. By altering the logic locking key of the MiG-V while running SSL cryptographic algorithms, we identify data leakages resulting from the exploitation of the logic locking hardware. We show that changing a single bit of the logic locking key can expose 100% of the cryptographic encryption key. This research reveals a critical security flaw in logic locking, highlighting the need for comprehensive security assessments beyond logic locking key-recovery attacks., Comment: preprint accepted at the Philosophical Transactions of the Royal Society A, 13 pages

Recent outcomes by the DESI Collaboration have shed light on a possible slightly evolving dark energy, challenging the standard $\Lambda$CDM paradigm. To better understand dark energy nature, high-redshift observations like gamma-ray burst data become essential for mapping the universe expansion history, provided they are calibrated with other probes. To this aim, we calibrate the $E_p-E_{iso}$ (or Amati) correlation through model-independent B\'ezier interpolations of the updated Hubble rate and the novel DESI data sets. More precisely, we provide two B\'ezier calibrations: i) handling the entire DESI sample, and ii) excluding the point at $z_{eff}=0.51$, criticized by the recent literature. In both the two options, we let the comoving sound horizon at the drag epoch, $r_d$, vary in the range $r_d \in [138, 156]$ Mpc. The Planck value is also explored for comparison. By means of the so-calibrated gamma-ray bursts, we thus constrain three dark energy frameworks, namely the standard $\Lambda$CDM, the $\omega_0$CDM and the $\omega_0\omega_1$CDM models, in both spatially flat and non-flat universes. To do so, we worked out Monte Carlo Markov chain analyses, making use of the Metropolis-Hastings algorithm. Further, we adopt model selection criteria to check the statistically preferred cosmological model finding a preference towards the concordance paradigm only whether the spatial curvature is zero. Conversely, and quite interestingly, the flat $\omega_0$CDM and both the cases, flat/non-flat, $\omega_0\omega_1$CDM model, leave evidently open the chance that dark energy evolves at higher redshifts., Comment: 15 pages, 7 figures, 8 tables

Underground gas storage is a versatile tool for managing energy resources and addressing pressing environmental concerns. While natural gas is stored in geological formations since the beginning of the 20th century, hydrogen has recently been considered as a potential candidate toward a more flexible and sustainable energy infrastructure. Furthermore, these formations can also be used to sequester environmentally harmful gases such as CO2. When such operations are implemented in faulted basins, however, safety concerns may arise due to the possible reactivation of pre-existing faults, which could result in (micro)-seismicity events. In the Netherlands, it has been recently noted that fault reactivation can occur "unexpectedly" during the life of an underground gas storage (UGS) site, even when stress conditions are not expected to cause a failure. The present two-part work aims to develop a modeling framework to investigate the physical mechanisms causing such occurrences and define a safe operational bandwidth for pore pressure variation for UGS operations in the faulted reservoirs of the Rotliegend formation, the Netherlands. In this follow-up paper, we investigate in detail the mechanisms and crucial factors that result in fault reactivation at various stages of a UGS. The mathematical and numerical model described in Part I is used, also accounting for the effect of geochemical dissolution on reservoir and caprock weakening. TThe study investigates the risks of fault activation caused by the storage of different fluids for various purposes, such as long-term CO2 sequestration, CH4 and N2 injection and extraction cycles, and N2 permanent storage. The results show how geomechanical properties and reservoir operating conditions may increase the risk of fault reactivation at various UGS stages. Finally, operational guidelines for improving secure storage operations are presented., Comment: 31 pages, 24 figures, 4 tables

In a porous medium featuring heterogeneous permeabilities, a wide range of fluid velocities may be recorded, so that significant inertial and frictional effects may arise in high-speed regions. In such parts, the link between pressure gradient and velocity is typically made via Darcy's law, which may fail to account for these effects; instead, the Darcy Forchheimer law, which introduces a nonlinear term, may be more adequate. Applying the Darcy Forchheimer law globally in the domain is very costly numerically and, rather, should only be done where strictly necessary. The question of finding a prori the subdomain where to restrict the use of the Darcy Forchheimer law was recently answered in FP23 by using an adaptive model: given a threshold on the flow velocity, the model locally selects the more appropriate law as it is being solved. At the end of the resolution, each mesh cell is flagged as being in the Darcy or Darcy Forchheimer subdomain. Still, this model is nonlinear itself and thus relatively expensive to run. In this paper, to accelerate the subdivision of the domain into low and high speed regions, we instead exploit the adaptive model from FP23 to generate partitioning data given an array of different input parameters, such as boundary conditions and inertial coefficients, and then train neural networks on these data classifying each mesh cell as Darcy or not. Two test cases are studied to illustrate the results, where cost functions, parity plots, precision-recall plots and receiver operating characteristic curves are analyzed.

Trefftz schemes are high-order Galerkin methods whose discrete spaces are made of elementwise exact solutions of the underlying PDE. Trefftz basis functions can be easily computed for many PDEs that are linear, homogeneous, and have piecewise-constant coefficients. However, if the equation has variable coefficients, exact solutions are generally unavailable. Quasi-Trefftz methods overcome this limitation relying on elementwise "approximate solutions" of the PDE, in the sense of Taylor polynomials. We define polynomial quasi-Trefftz spaces for general linear PDEs with smooth coefficients and source term, describe their approximation properties and, under a non-degeneracy condition, provide a simple algorithm to compute a basis. We then focus on a quasi-Trefftz DG method for variable-coefficient elliptic diffusion-advection-reaction problems, showing stability and high-order convergence of the scheme. The main advantage over standard DG schemes is the higher accuracy for comparable numbers of degrees of freedom. For non-homogeneous problems with piecewise-smooth source term we propose to construct a local quasi-Trefftz particular solution and then solve for the difference. Numerical experiments in 2 and 3 space dimensions show the excellent properties of the method both in diffusion-dominated and advection-dominated problems., Comment: 26 pages, 6 figures, 2 tables, added some remarks and one figure

Ultrafast all-optical logic devices based on nonlinear light-matter interactions hold the promise to overcome the speed limitations of conventional electronic devices. Strong coupling of excitons and photons inside an optical resonator enhances such interactions and generates new polariton states which give access to unique nonlinear phenomena, such as Bose-Einstein condensation, used for all-optical ultrafast polariton transistors. However, the pulse energies required to pump such devices range from tens to hundreds of pJ, making them not competitive with electronic transistors. Here we introduce a new paradigm for all-optical switching based on the ultrafast transition from the strong to the weak coupling regime in microcavities embedding atomically thin transition metal dichalcogenides. Employing single and double stacks of hBN-encapsulated MoS$_2$ homobilayers with high optical nonlinearities and fast exciton relaxation times, we observe a collapse of the 55-meV polariton gap and its revival in less than one picosecond, lowering the threshold for optical switching below 4 pJ per pulse, while retaining ultrahigh switching frequencies. As an additional degree of freedom, the switching can be triggered pumping either the intra- or the interlayer excitons of the bilayers at different wavelengths, speeding up the polariton dynamics, owing to unique interspecies excitonic interactions. Our approach will enable the development of compact ultrafast all-optical logical circuits and neural networks, showcasing a new platform for polaritonic information processing based on manipulating the light-matter coupling.

We prove sharp upper and lower estimates for the parabolic kernel of the singular elliptic operator \begin{align*} \mathcal L&=\mbox{Tr }\left(AD^2\right)+\frac{\left(v,\nabla\right)}y, \end{align*} in the half-space $\mathbb{R}^{N+1}_+=\{(x,y): x \in \mathbb{R}^N, y>0\}$ under Neumann or oblique derivative boundary conditions at $y=0$.

In the past, high-z AGNs were given a minor role as possible drivers of reionization, despite initial evidences in favor of their large space densities at low luminosities by Chandra and HST. Recent observations from JWST are finding relatively large numbers of faint AGNs at z>4, convincingly confirming these early results. We present a sample of z~5 AGNs (both from wide, shallow ground-based surveys and from deep, pencil-beam observations from JWST), allowing to estimate their space densities with unprecedented accuracy. The bright end (M1450<-26) of the z~5 AGN luminosity function is well constrained, with a rather steep slope. The faint end (M1450>-22) indicates a high space density, the scatter is significant and the knee (M1450~-24) is mostly undetermined. Comparisons with state-of-the-art models find reasonable agreement with the observed AGN luminosity function at z=5, while the predicted space density evolution at higher redshifts appears to be too fast with respect to observational constraints. Given the large variance at the faint end, we consider different options in fitting the luminosity functions and deriving the ionizing emissivity. Even in the most conservative scenario, the photo-ionization rate produced by z~5 AGNs is consistent with the UV background measurements. A slow evolution of the space density of faint AGNs is observed, indicating that active SMBHs are probably producing large amounts of ionizing photons at z>6, well into the epoch of reionization. This is an important indication that high-z AGNs could be the major contributors to the reionization of the Universe., Comment: Accepted for publication on ApJ, 20 pages, 9 figures, 3 tables

Pulsar-timing-array experiments have reported evidence for a stochastic background of nanohertz gravitational waves consistent with the signal expected from a population of supermassive--black-hole binaries. Those analyses assume power-law spectra for intrinsic pulsar noise and for the background, as well as a Hellings--Downs cross-correlation pattern among the gravitational-wave--induced residuals across pulsars. These assumptions are idealizations that may not be realized in actuality. We test them in the NANOGrav 15 yr data set using Bayesian posterior predictive checks: after fitting our fiducial model to real data, we generate a population of simulated data-set replications, and use them to assess whether the optimal-statistic significance, inter-pulsar correlations, and spectral coefficients assume extreme values for the real data when compared to the replications. We confirm that the NANOGrav 15 yr data set is consistent with power-law and Hellings--Downs assumptions. We also evaluate the evidence for the stochastic background using posterior-predictive versions of the frequentist optimal statistic and of Bayesian model comparison, and find comparable significance (3.2\ $\sigma$ and 3\ $\sigma$ respectively) to what was previously reported for the standard statistics. We conclude with novel visualizations of the reconstructed gravitational waveforms that enter the residuals for each pulsar. Our analysis strengthens confidence in the identification and characterization of the gravitational-wave background as reported by NANOGrav., Comment: 20 pages, 14 Figures

Designing anisotropic structured materials by reducing symmetry results in unique behaviors, such as shearing under uniaxial compression or tension. This direction-dependent coupled mechanical phenomenon is crucial for applications such as energy redirection. While rank-deficient materials such as hierarchical laminates have been shown to exhibit extreme elastic anisotropy, there is limited knowledge about the fully anisotropic elasticity tensors achievable with single-scale fabrication techniques. No established upper and lower bounds on anisotropic moduli achieving extreme elastic anisotropy exist, similar to Hashin-Shtrikman bounds in isotropic composites. In this paper, we estimate the range of anisotropic stiffness tensors achieved by single-scale two-dimensional structured materials. To achieve this, we first develop a database of periodic anisotropic single-scale unit cell geometries using linear combinations of periodic cosine functions. The database covers a wide range of anisotropic elasticity tensors, which are then compared with the elasticity tensors of hierarchical laminates. Through this comparison, we identify the regions in the property space where hierarchical design is necessary to achieve extremal properties. We demonstrate a method to construct various 2D functionally graded structures using this cosine function representation for the unit cells. These graded structures seamlessly interpolate between unit cells with distinct patterns, allowing for independent control of several functional gradients, such as porosity, anisotropic moduli, and symmetry. The graded structures exhibit unique mechanical behaviors when designed with unit cells positioned at extreme parts of the property space. Specific graded designs are numerically studied to observe behaviors such as selective strain energy localization, compressive strains under tension, and localized rotations.

The Terracini locus $\mathbb{T}(n, d; x)$ is the locus of all finite subsets $S \subset \mathbb{P}^n$ of cardinality $x$ such that $\langle S \rangle = \mathbb{P}^n$, $h^0(\mathcal{I}_{2S}(d)) > 0$, and $h^1(\mathcal{I}_{2S}(d)) > 0$. The celebrated Alexander-Hirschowitz Theorem classifies the triples $(n,d,x)$ for which $\dim\mathbb{T}(n, d; x)=xn$. Here we fully characterize the next step in the case $n=2$, namely, we prove that $\mathbb{T}(2,d;x)$ has at least one irreducible component of dimension $2x-1$ if and only if either $(d,x)=(6,10)$ or $(d,x)=(4,4)$ or $d\equiv 1,2 \pmod{3}$ and $x=(d+2)(d+1)/6$., Comment: 9 pages, comments are welcome

In the context of the CERN EP R&D on monolithic sensors and the ALICE ITS3 upgrade, the Tower Partners Semiconductor Co (TPSCo) 65 nm process has been qualified for use in high energy physics, and adopted for the ALICE ITS3 upgrade. An Analog Pixel Test Structure (APTS) featuring fast per pixel operational-amplifier-based buffering for a small matrix of four by four pixels, with a sensor with a small collection electrode and a very non-uniform electric field, was designed to allow detailed characterization of the pixel performance in this technology. Several variants of this chip with different pixel designs have been characterized with a (120 GeV/$c$) positive hadron beam. This result indicates that the APTS-OA prototype variants with the best performance achieve a time resolution of 63 ps with a detection efficiency exceeding 99% and a spatial resolution of 2 $\mu$m, highlighting the potential of TPSCo 65nm CMOS imaging technology for high-energy physics and other fields requiring precise time measurement, high detection efficiency, and excellent spatial resolution.

Particle sedimentation through porous media is limited by the inability of passive material to overcome surface interactions and a tortuous network of pores. This limits transport, delivery, and effectiveness of chemicals used as reactants, nutrients, pesticides, or for waste remediation. This work develops magnetically responsive microrollers that navigate the complex interstitial network of porous matter. Rather than arresting on the upward facing surfaces of the pores, particles can roll and fall further, increasing transport by orders of magnitude. This work directly investigates Janus microrollers, activated by a rotating magnetic field, rolling and sedimenting though an index-matched porous medium. The mechanism of enhanced transport is determined, and the material flux is primarily a function of microroller concentration, rotation rate, and magnetic field strength. This mechanism is most efficient using a minimum number of rotations spaced out periodically in time to reduce the required energy input to greatly enhance transport. This general mechanism of transport enhancement can be broadly applied in numerous applications because the particles delivered within the porous matrix may be comprised of a wide variety of functional materials.

Low-luminosity AGNs with low-mass black holes (BHs) in the early universe are fundamental to understanding the BH growth and their co-evolution with the host galaxies. Utilizing JWST NIRCam Wide Field Slitless Spectroscopy (WFSS), we perform a systematic search for broad-line ${\rm H\alpha}$ emitters (BHAEs) at $z\approx 4-5$ in 25 fields of the ASPIRE (A SPectroscopic survey of biased halos In the Reionization Era) project, covering a total area of 275 arcmin$^2$. We identify 16 BHAEs with FWHM of the broad components spanning from $\sim$ 1000 km s$^{-1}$ to 3000 km s$^{-1}$. Assuming the broad linewidths arise due to Doppler broadening around BHs, the implied BH masses range from $10^7$ to $10^{8}~M_\odot$, with broad ${\rm H\alpha}$-converted bolometric luminosity of $10^{44.5}-10^{45.5}$ erg s$^{-1}$ and Eddington ratios of $0.07-0.47$. The spatially extended structure of the F200W stacked image may trace the stellar light from the host galaxies. The ${\rm H\alpha}$ luminosity function indicates an increasing AGN fraction towards the higher ${\rm H\alpha}$ luminosities. We find possible evidence for clustering of BHAEs: two sources are at the same redshift with a projected separation of 519 kpc; one BHAE appears as a composite system residing in an overdense region with three close companion ${\rm H\alpha}$ emitters. Three BHAEs exhibit blueshifted absorption troughs indicative of the presence of high-column-density gas. We find the broad-line and photometrically selected BHAE samples exhibit different distributions in the optical continuum slopes, which can be attributed to their different selection methods. The ASPIRE broad-line ${\rm H\alpha}$ sample provides a good database for future studies of faint AGN populations at high redshift., Comment: 19 pages, 13 figures, 4 tables. Accepted by the ApJ

Recent research has challenged the widespread belief that gender inequities in academia would disappear simply by increasing the number of women. More complex causes might be at play, embodied in the networked structure of scientific collaborations. Here, we aim to understand the structural inequality between male and female scholars in the dissemination of scientific knowledge. We use a large-scale dataset of academic publications from the American Physical Society (APS) to build a time-varying network of collaborations from 1970 to 2020. We model knowledge dissemination as a contagion process in which scientists become informed based on the propagation of knowledge through their collaborators. We quantify the fairness of the system in terms of how women acquire and diffuse knowledge compared to men. Our results indicate that knowledge acquisition and diffusion are slower for women than expected. We find that the main determinant of women's disadvantage is the gap in the cumulative number of collaborators, highlighting how time creates structural disadvantages that contribute to marginalize women in physics. Our work sheds light on how the dynamics of scientific collaborations shape gender disparities in knowledge dissemination and calls for a deeper understanding on how to intervene to improve fairness and diversity in the scientific community.

We prove Rellich-Kondrachov type theorems and weighted Poincar\'e inequalities on the half-space $\mathbb{R}^{N+1}_+=\{z=(x,y): x \in \mathbb{R}^N, y>0\}$ endowed with the weighted Gaussian measure $\mu :=y^ce^{-a|z|^2}dz$ where $c+1>0$ and $a>0$. We prove that for some positive constant $C>0$ one has \begin{align*} \left\|u-\overline u\right\|_{L^2_\mu(\mathbb{R}^{N+1}_+)}\leq C \|\nabla u\|_{L^2_\mu (\mathbb{R}^{N+1}_+)},\qquad \forall u\in H^1_\mu(\mathbb{R}^{N+1}_+) \end{align*} where $\overline u=\frac 1{\mu(\mathbb{R}^{N+1}_+)}\int_{\mathbb{R}^{N+1}_+} u\,d\mu(z)$. Besides this we also consider the local case of bounded domains of $\mathbb{R}^{N+1}_+$ where the measure $\mu$ is $y^cdz$.

We study Hegselmann-Krause type opinion formation models with non-universal interaction and time-delayed coupling. We assume the presence of a common influencer between two different agents. Moreover, we explore two cases in which such an assumption does not hold but leaders with independent opinion are present. By using careful estimates on the system's trajectories, we are able to prove asymptotic convergence to consensus estimates. Some numerical tests illustrate the theoretical results.

We characterize, using time-frequency analysis, the continuity and compactness of the Weyl operator in global classes of ultradifferentiable functions $\mathcal{S}_\omega$, for weight functions $\omega$ in the sense of Braun, Meise and Taylor. As a consequence, we give results about the compactness of the localization operator in $\mathcal{S}_\omega$, in relation with the spaces of $\omega$-multipliers and $\omega$-convolutors of $\mathcal{S}_\omega$. Moreover, we provide several examples that complement our investigation.

Recent experiments have searched for evidence of the impact of non-inertial motion on the entanglement of particles. The success of these endeavours has been hindered by the fact that such tests were performed within spatial scales that were only "local" when compared to the spatial scales over which the non-inertial motion was taking place. We propose a Sagnac-like interferometer that, by challenging such bottlenecks, is able to achieve entangled states through a mechanism induced by the mechanical rotation of a photonic interferometer. The resulting states violate the Bell-Clauser-Horne-Shimony-Holt (CHSH) inequality all the way up to the Tsirelson bound, thus signaling strong quantum nonlocality. Our results demonstrate that mechanical rotation can be thought of as resource for controlling quantum non-locality with implications also for recent proposals for experiments that can probe the quantum nature of curved spacetimes and non-inertial motion., Comment: 6 pages, 1 figure

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 prove that operators of the form $A=-a(x)^2\Delta^{2}$, with suitable growth conditions on the coefficient $a(x)$, generate analytic semigroups in $L^1(\mathbb{R}^N)$. In particular, we deduce generation results for the operator $A :=- (1+|x|^2)^{\alpha} \Delta^{2}$, $0\leq\alpha\leq2$. Moreover, we characterise the maximal domain of $A$ in $L^1(\mathbb{R}^N)$., Comment: arXiv admin note: text overlap with arXiv:2401.14187

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 discovery of pulsations in (at least) six ultraluminous X-ray sources (ULXs) has shown that neutron stars can accrete at (highly) super-Eddington rates, challenging the standard accretion theories. M51 ULX-7, with a spin signal of $P\simeq2.8$ s, is the pulsating ULX (PULX) with the shortest known orbital period ($P_\mathrm{orb}\simeq2$ d) and has been observed multiple times by XMM-Newton, Chandra, and NuSTAR. We report on the timing and spectral analyses of three XMM-Newton observations of M51 ULX-7 performed between the end of 2021 and the beginning of 2022, together with a timing re-analysis of XMM-Newton, Chandra, and NuSTAR archival observations. We investigated the spin signal by applying accelerated search techniques and studied the power spectrum through the fast Fourier transform, looking for (a)periodic variability in the source flux. We analysed the energy spectra of the 2021-2022 observations and compared them to the older ones. We report the discovery of a recurrent, significant ($>$3$\sigma$) broad complex at mHz frequencies in the power spectra of M51 ULX-7. We did not detect the spin signal, setting a 3$\sigma$ upper limit on the pulsed fraction of $\lesssim10\%$ for the single observation. The complex is significantly detected also in five Chandra observations performed in 2012. M51 ULX-7 represents the second PULX for which we have a significant detection of mHz-QPOs at super-Eddington luminosities. These findings suggest that one should avoid using the observed QPO frequency to infer the mass of the accretor in a ULX. The absence of spin pulsations when the broad complex is detected suggests that the mechanism responsible for the aperiodic modulation also dampens the spin signal's pulsed fraction. If true, this represents an additional obstacle in the detection of new PULXs, suggesting an even larger occurrence of PULXs among ULXs., Comment: 14 pages (12 main text + Appendix), 5 figures. Accepted for publication on A&A

We give a partial negative answer to a question left open in a previous work by Brasco and the first and third-named authors concerning the sharp constant in the fractional Hardy inequality on convex sets. Our approach has a geometrical flavor and equivalently reformulates the sharp constant in the limit case $p=1$ as the Cheeger constant for the fractional perimeter and the Lebesgue measure with a suitable weight. As a by-product, we obtain new lower bounds on the sharp constant in the $1$-dimensional case, even for non-convex sets, some of which optimal in the case $p=1$., Comment: 25 pages

Infrared subtraction algorithms beyond next-to-leading order necessitate the analysis of multiple infrared limits of scattering amplitudes, where several particles sequentially become soft or collinear. In this contribution, we report on the study performed in arXiv:2403.11975, which investigates these limits from the perspective of infrared factorisation, offering general definitions for strongly-ordered soft and collinear kernels, expressed in terms of gauge-invariant operator matrix elements. These definitions facilitate the identification of local subtraction counterterms for strongly-ordered configurations, whose integrals are designed to cancel the IR poles of real-virtual counterterms. This framework is validated at tree level for multiple emissions, and at one loop for single and double emissions., Comment: 10 pages. Contribution to the Proceedings of the Loops and Legs in Quantum Field Theory conference (LL2024)

In this paper, we deal with first and second-order alignment models with non-universal interaction, time delay and possible lack of connection between the agents. More precisely, we analyze the situation in which the system's agents do not transmit information to all the other agents and also agents that are linked to each other can suspend their interaction at certain times. Moreover, we take into account of possible time lags in the interactions. To deal with the considered "non-universal" connection, a graph topology over the structure of the model has to be considered. Under a so-called Persistence Excitation Condition, we establish the exponential convergence to consensus for both models whenever the digraph that describes the interaction between the agents is strongly connected.

Relativistic jets are thought to play a crucial role in the formation of massive galaxies and supermassive black holes. Here we report multi-wavelength and multi-epoch observations of the quasar VLASSJ0410-0139 at redshift z=7, powered by a 7e8 solar-mass black hole. Its radio variability, X-ray properties, and compact radio emission on parsec scales reveal that J0410-0139 is a blazar with a relativistic jet aligned with our line of sight. This blazar's existence implies that many more similar (unaligned) jetted sources must exist at z=7. One scenario is that we observe an intrinsically low-power radio jet, but we see it at high luminosity due to relativistic beaming effects. In this case, a large fraction (>80%) of the UV bright quasars must have a similar jet to match the number density expected from the UV quasar luminosity function. These jets can enhance the growth of supermassive black holes and substantially affect their host galaxies. However, the implications would be even more severe if the quasar belongs to the top 10% radio luminous quasars, as measured if the beaming enhancement is less than a factor of 10-15. In this scenario, there should be hundreds to thousands of radio-quiet quasars at z=7 with intrinsic properties similar to J0410-0139 -- in strong tension with the number density of bright quasars derived from their UV luminosity function. To reconcile these results, most black hole growth at z=7 must happen in an obscured phase, as some models predict. The existence of supermassive black holes in the epoch of reionization is facilitated by significant jet-enhanced or obscured super-Eddington accretion., Comment: Submitted

A distinct feature of pancreatic ductal adenocarcinoma (PDAC) is a prominent tumor microenvironment (TME) with remarkable cellular and spatial heterogeneity that meaningfully impacts disease biology and treatment resistance. The dynamic crosstalk between cancer cells and the dense stromal compartment leads to spatially and temporally heterogeneous metabolic alterations, such as acidic pH that contributes to drug resistance in PDAC. Thus, monitoring the extracellular pH metabolic fluctuations within the TME is crucial to predict and to quantify anticancer drug efficacy. Here, a simple and reliable alginate-based 3D PDAC model embedding ratiometric optical pH sensors and cocultures of tumor (AsPC-1) and stromal cells for simultaneously monitoring metabolic pH variations and quantify drug response is presented. By means of time-lapse confocal laser scanning microscopy (CLSM) coupled with a fully automated computational analysis, the extracellular pH metabolic variations are monitored and quantified over time during drug testing with gemcitabine, folfirinox, and paclitaxel, commonly used in PDAC therapy. In particular, the extracellular acidification is more pronounced after drugs treatment, resulting in increased antitumor effect correlated with apoptotic cell death. These findings highlight the importance of studying the influence of cellular metabolic mechanisms on tumor response to therapy in 3D tumor models, this being crucial for the development of personalized medicine approaches.

This study comprehensively investigates the gamma-ray dim population of Fanaroff-Riley Type 0 (FR0) radio galaxies as potentially significant sources of ultra-high-energy cosmic rays (UHECRs, E $>$ 10$^{18}$ eV) detected on Earth. While individual FR0 luminosities are relatively low compared to the more powerful Fanaroff-Riley Type 1 and Type 2 galaxies, FR0s are substantially more prevalent in the local universe, outnumbering the more energetic galaxies by a factor of $\sim$5 within a redshift of z $\leq$ 0.05. Employing CRPropa3 simulations, we estimate the mass composition and energy spectra of UHECRs originating from FR0 galaxies for energies above 10$^{18.6}$ eV. This estimation fits data from the Pierre Auger Observatory (Auger) using three extensive air shower models; both constant and energy-dependent observed elemental fractions are considered. The simulation integrates an isotropic distribution of FR0 galaxies, extrapolated from observed characteristics, with UHECR propagation in the intergalactic medium, incorporating various plausible configurations of extragalactic magnetic fields, both random and structured. We then compare the resulting emission spectral indices, rigidity cutoffs, and elemental fractions with recent Auger results. In total, 25 combined energy spectrum and mass composition fits are considered. Beyond the cosmic ray fluxes emitted by FR0 galaxies, this study predicts the secondary photon and neutrino fluxes from UHECR interactions with intergalactic cosmic photon backgrounds. The multi-messenger approach, encompassing observational data and theoretical models, helps elucidate the contribution of low luminosity FR0 radio galaxies to the total cosmic ray energy density., Comment: To be submitted to The Astrophysical Journal. 22 pages, 16 figures, 6 tables

Linear causal disentanglement is a recent method in causal representation learning to describe a collection of observed variables via latent variables with causal dependencies between them. It can be viewed as a generalization of both independent component analysis and linear structural equation models. We study the identifiability of linear causal disentanglement, assuming access to data under multiple contexts, each given by an intervention on a latent variable. We show that one perfect intervention on each latent variable is sufficient and in the worst case necessary to recover parameters under perfect interventions, generalizing previous work to allow more latent than observed variables. We give a constructive proof that computes parameters via a coupled tensor decomposition. For soft interventions, we find the equivalence class of latent graphs and parameters that are consistent with observed data, via the study of a system of polynomial equations. Our results hold assuming the existence of non-zero higher-order cumulants, which implies non-Gaussianity of variables.

Moduli of vector bundles on stacky curves behave similarly to moduli of vector bundles on curves, except there are additional numerical invariants giving many different notions of stability. We apply the existence criterion for good moduli spaces of stacks to show that the moduli stack of semistable vector bundles on a stacky curve has a proper good moduli space. We moduli-theoretically prove that a natural determinantal line bundle on this moduli space is ample, thus proving this moduli space is projective. Our methods give effective bounds for when a power of this line bundle is basepoint-free. As a special case, we obtain new and effective constructions of moduli spaces of parabolic bundles.

Transition Metal Dichalcogenides (TMD) are layered materials obtained by stacking two-dimensional sheets weakly bonded by van der Waals interactions. In bulk TMD, band dispersions are observed in the direction normal to the sheet plane (z-direction) due to the hybridization of out-of-plane orbitals but no kz-dispersion is expected at the single-layer limit. Using angle-resolved photoemission spectroscopy, we precisely address the two-dimensional to three-dimensional crossover of the electronic band structure of epitaxial WSe$_2$ thin films. Increasing number of discrete electronic states appears in given kz-ranges while increasing the number of layers. The continuous bulk dispersion is nearly retrieved for 6-sheet films. These results are reproduced by calculations going from a relatively simple tight-binding model to a sophisticated KKR-Green's function calculation. This two-dimensional system is hence used as a benchmark to compare different theoretical approaches.