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In this paper we study the mixed Poincar\'e polynomial of generic parabolic $\mathrm{PGL}_2(\mathbb{C})$-character varieties with coefficients in some local systems arising from the conjugacy class of $\mathrm{PGL}_2(\mathbb{C})$ which has a non-connected stabiliser. We give a conjectural formula that we prove to be true under the Euler specialisation. We then prove that this conjectured formula interpolates the structure coefficients of the two based rings$ \left(\mathcal{C}(\mathrm{PGL}_2(\mathbb{F}_q)),Loc(\mathrm{PGL}_2),*\right)$ and $\left(\mathcal{C}(\mathrm{SL}_2(\mathbb{F}_q)), CS(\mathrm{SL}_2),\cdot\right) $ where for a group $H$, $\mathcal{C}(H)$ denotes the space of complex valued class functions on $H$, $Loc(\mathrm{PGL}_2)$ denotes the basis of characteristic functions of intermediate extensions of equivariant local systems on conjugacy classes of $\mathrm{PGL}_2$ and $CS(\mathrm{SL}_2)$ the basis of characteristic functions of Lusztig's character-sheaves on $\mathrm{SL}_2$. Our result reminds us of a non-abelian Fourier transform., Comment: All comments and questions are welcome!

Coherent quantum emitters are a central resource for advanced quantum technologies. Hexagonal boron nitride (hBN) hosts a range of quantum emitters that can be engineered using techniques such as high-temperature annealing, optical doping, and irradiation with electrons or ions. Here, we demonstrate that such processes can degrade the coherence, and hence the functionality, of quantum emitters in hBN. Specifically, we show that hBN annealing and doping methods that are used routinely in hBN nanofabrication protocols give rise to decoherence of B-center quantum emitters. The decoherence is characterized in detail, and attributed to defects that act as charge traps which fluctuate electrostatically during SPE excitation and induce spectral diffusion. The decoherence is minimal when the emitters are engineered by electron beam irradiation of as-grown, pristine flakes of hBN, where B-center linewidths approach the lifetime limit needed for quantum applications involving interference and entanglement. Our work highlights the critical importance of crystal lattice quality to achieving coherent quantum emitters in hBN, despite the common perception that the hBN lattice and hBN SPEs are highly-stable and resilient against chemical and thermal degradation. It underscores the need for nanofabrication techniques that are minimally invasive and avoid crystal damage when engineering hBN SPEs and devices for quantum-coherent technologies.

Inspired by the large success of Transformers in Large Language Models, these architectures are increasingly applied to tabular data. This is achieved by embedding tabular data into low-dimensional Euclidean spaces resulting in similar structures as time-series data. We introduce a novel credibility mechanism to this Transformer architecture. This credibility mechanism is based on a special token that should be seen as an encoder that consists of a credibility weighted average of prior information and observation based information. We demonstrate that this novel credibility mechanism is very beneficial to stabilize training, and our Credibility Transformer leads to predictive models that are superior to state-of-the-art deep learning models., Comment: 30 pages

Relic galaxies, the oldest ultra-compact massive galaxies (UCMGs), contain almost exclusively "pristine" stars formed during an intense star formation (SF) burst at high redshift. As such, they allow us to study in detail the early mechanism of galaxy assembly in the Universe. Using the largest catalogue of spectroscopically confirmed UCMGs for which a degree of relicness (DoR) had been estimated, the INSPIRE catalogue, we investigate whether or not relics prefer dense environments. The objective of this study is to determine if the DoR, which measures how extreme the SF history was, and the surrounding environment are correlated. In order to achieve this goal, we employ the AMICO galaxy cluster catalogue to compute the probability for a galaxy to be a member of a cluster, and measure the local density around each UCMG using machine learning-based photometric redshifts. We find that UCMGs can reside both in clusters and in the field, but objects with very low DoR (< 0.3, i.e., a relatively extended SF history) prefer under-dense environments. We additionally report a correlation between the DoR and the distance from the cluster centre: more extreme relics, when located in clusters, tend to occupy the more central regions of them. We finally outline potential evolution scenarios for UCMGs at different DoR to reconcile their presence in both clusters and field environments, Comment: Accepted for publication on MNRAS, 11 pages, 8 figure, 1 table

The integration of van der Waals (vdW) materials into photonic devices has laid out a foundation for many new quantum and optoelectronic applications. Despite tremendous progress in the nanofabrication of photonic building blocks from vdW crystals, there are still limitations, specifically with large-area devices and masking. Here, we focus on hexagonal boron nitride (hBN) as a vdW material and present a double etch method that overcomes problems associated with methods that employ metallic films and resist-based films for masking. Efficacy of the developed protocol is demonstrated by designing and fabricating a set of functional photonic components including waveguides, ring resonators and photonic crystal cavities. The functionality of the fabricated structures is demonstrated through optical characterization over several key spectral ranges. These include the near-infrared and blue ranges, where the hBN boron vacancy (VB-) spin defects and the coherent B center quantum emitters emit, respectively. The double etch method enables fabrication of high-quality factor optical cavities and constitutes a promising pathway toward on-chip integration of vdW materials., Comment: 10 pages, 4 figures

The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015-2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14,000 deg^2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance., Comment: Accepted for publication in the A&A special issue`Euclid on Sky'

The ultrafast relaxation dynamics of tetracene following UV excitation to a bright singlet state S6 has been studied with time-resolved photoelectron spectroscopy. With the help of high-level ab-initio multireference perturbation theory calculations, we assign photoelectron signals to intermediate dark electronic states S3, S4 and S5 as well as a to a low-lying electronic state S2. The energetic structure of these dark states has not been determined experimentally previously. The time-dependent photoelectron yields assigned to the states S6, S5 and S4 have been analyzed and reveal the depopulation of S6 within 50 fs, while S5 and S4 are populated with delays of about 50 and 80 fs. The dynamics of the lower-lying states S3 and S2 seem to agree with a delayed population coinciding with the depopulation of the higher-lying states S4-S6, but could not be elucidated in full detail due to the low signal levels of the corresponding two-photon ionization probe processes., Comment: The following article has been accepted by The Journal of Chemical Physics. After it is published, it will be found at https://doi.org/10.1063/5.0214006

Hexagonal boron nitride (hBN) has recently gained attention as a solid state host of quantum emitters. However, hBN emitters reported to date lack the properties needed for their deployment in scalable quantum technologies. Here we employ spectral hole burning spectroscopy and resonant polarization measurements to observe nearly-coherent hBN quantum emitters, both as singles and in ensembles, with three discrete polarization axes indicative of a C2v symmetry defect. Our results constitute an important milestone towards the implementation of hBN quantum emitters in integrated quantum photonics., Comment: 10 pages, 4 figures

This manuscript introduces deep learning models that simultaneously describe the dynamics of several yield curves. We aim to learn the dependence structure among the different yield curves induced by the globalization of financial markets and exploit it to produce more accurate forecasts. By combining the self-attention mechanism and nonparametric quantile regression, our model generates both point and interval forecasts of future yields. The architecture is designed to avoid quantile crossing issues affecting multiple quantile regression models. Numerical experiments conducted on two different datasets confirm the effectiveness of our approach. Finally, we explore potential extensions and enhancements by incorporating deep ensemble methods and transfer learning mechanisms.

The INSPIRE project has built the largest sample of ultra-compact massive galaxies (UCMGs) at 0.12, and the other stellar population parameters.We use the Full-Index-Fitting method to fit the INSPIRE spectra to single stellar population (SSP) models. This allows us to measure, for the first time, the low-mass end slope of the IMF, as well as stellar metallicity [M/H], [Mg/Fe], [Ti/Fe] and [Na/Fe] ratios, and study correlations between them and the DoR. Similarly to normal-sized galaxies, UCMGs with larger stellar masses have overall higher metallicities. We found a correlation between the low-mass end of the IMF slope and the DoR, that, however, breaks down for systems with a more extended SFH. An even stronger dependency is found between the IMF and the fraction of mass formed at high-z. At equal velocity dispersion and metallicity, galaxies with a higher DoR have a dwarf-richer IMF than that of low-DoR counterparts. This might indicate that the cosmic epoch and formation mechanisms influence the fragmentation of the star formation cloud and hence might be the explanation for IMF variations detected in massive ETGs., Comment: 16 pages, 11 figures, submitted to MNRAS

With their high angular resolutions of 30--100 mas, large fields of view, and complex optical systems, imagers on next-generation optical/near-infrared space observatories, such as the Near-Infrared Camera (NIRCam) on the James Webb Space Telescope (JWST), present both new opportunities for science and also new challenges for empirical point spread function (PSF) characterization. In this context, we introduce ShOpt, a new PSF fitting tool developed in Julia and designed to bridge the advanced features of PIFF (PSFs in the Full Field of View) with the computational efficiency of PSFEx (PSF Extractor). Along with ShOpt, we propose a suite of non-parametric statistics suitable for evaluating PSF fit quality in space-based imaging. Our study benchmarks ShOpt against the established PSF fitters PSFEx and PIFF using real and simulated COSMOS-Web Survey imaging. We assess their respective PSF model fidelity with our proposed diagnostic statistics and investigate their computational efficiencies, focusing on their processing speed relative to the complexity and size of the PSF models. We find that ShOpt can already achieve PSF model fidelity comparable to PSFEx and PIFF while maintaining competitive processing speeds, constructing PSF models for large NIRCam mosaics within minutes., Comment: 53 pages, 27 figures, submitted to Astronomical Journal. Same as v2 with a corrected typo, which contained revisions from v1

Quantum communication has been at the forefront of modern research for decades, however it is severely hampered in underwater applications, where the properties of water absorb nearly all useful optical wavelengths and prevent them from propagating more than, in most cases, a few metres. This research reports on-demand quantum light sources, suitable for underwater optical communication. The single photon emitters, which can be engineered using an electron beam, are based on impurities in hexagonal boron nitride. They have a zero phonon line at ~ 436 nm, near the minimum value of water absorption and are shown to suffer negligible transmission and purity loss when travelling through water channels. These emitters are also shown to possess exceptional underwater transmission properties compared to emitters at other optical wavelengths and are utilised in a proof of principle underwater communication link with rates of several kbits/s.

During the early stages of galaxy evolution, a significant fraction of galaxies undergo a transitional phase between the ``blue nugget" systems, which arise from the compaction of large, active star-forming disks, and the ``red nuggets", which are red and passive compact galaxies. These objects are typically only observable with space telescopes, and detailed studies of their size, mass, and stellar population parameters have been conducted on relatively small samples. Strong gravitational lensing can offer a new opportunity to study them in detail, even with ground-based observations. In this study, we present the first 6 \textit{bona fide} sample of strongly lensed post-blue nugget (pBN) galaxies, which were discovered in the Kilo Degree Survey. By using the lensing-magnified luminosity from optical and near-infrared bands, we have derived robust structural and stellar population properties of the multiple images of the background sources. \rui{The pBN galaxies have very small sizes of $\rm R_{eff}<1.3$ kpc, high mass density inside 1 kpc of $ \rm \log (\Sigma_1/M_{\odot} \mathrm{kpc}^{-2})>9.3$, and low specific star formation rates of $\log (\mathrm{sSFR/Gyr})\lesssim0$, The size-mass and $\Sigma_1$-mass relations of this sample are consistent with those of the red nuggets, while their sSFR is close to the lower end of compact star-forming blue nugget systems at the same redshift, suggesting a clear evolutionary link between them., Comment: Accepted for publication in APJ

We study (compactly supported) cohomology of character stacks of punctured Riemann surfaces with prescribed semisimple local monodromies at punctures. In the case of generic local monodromies, the cohomology of these character stacks has already been studied by Hausel, Letellier and Rodriguez-Villegas and by Mellit. In this paper, we extend the results of Hausel, Letellier and Rodriguez-Villegas to the non-generic case. In particular, we compute the E-series and we give a conjectural formula for the mixed Poincar\'e series. Moreover, we verify our conjecture in the case of the projective line with 4 punctures and a certain choice of a non-generic quadruple., Comment: Corrected typos and mistakes in the exposition+added some infos about multiplicative quiver stacks. All comments are welcome!

This paper presents the third data release of the INvestigating Stellar Population In RElics (INSPIRE) project, comprising 52 ultra-compact massive galaxies (UCMGs) observed with the X-Shooter spectrograph. We measure integrated stellar velocity dispersion, [Mg/Fe] abundances, ages, and metallicities for all the INSPIRE objects. We thus infer star formation histories and confirm the existence of a degree of relicness (DoR), defined in terms of the fraction of stellar mass formed by $z=2$, the time at which a galaxy has assembled 75\% of its mass, and the final assembly time. Objects with a high DoR assembled their stellar mass at early epochs, while low-DoR objects show a non-negligible fraction of later-formed populations and hence a spread in ages and metallicities. A higher DoR correlates with larger [Mg/Fe], super-solar metallicity, and larger velocity dispersion values. The 52 UMCGs span a large range of DoR from 0.83 to 0.06, with 38 of them having formed more than 75\% of their mass by $z=2$. Of these, nine are extreme relics (DoR$>0.7$), since they formed the totality ($>99\%$) of their stellar mass by redshift $z=2$. The remaining 14 UCMGs cannot be considered relics, as they are characterised by more extended star formation histories. With INSPIRE, we built the first sizeable sample of relics outside the local Universe, up to $z\sim0.4$, increasing the number of confirmed relics by a factor of $>10$, and opening up an important window to explain the mass assembly of massive galaxies in the high-z Universe., Comment: accepted for publication on MNRAS, 20 pages, 15 figures, 3 tables

We study the multiplicities of semisimple split characters in tensor product of semisimple split characters of $GL_n(\mathbb{F}_q)$. We prove that these multiplicities are polynomial in q with non-negative integer coefficients and we obtain a criterion for their non-vanishing. We give moreover an interpretation of these polynomials in terms of the counting of the representations of star-shaped quivers, generalizing a previous result of Hausel, Letellier and Rodriguez-Villegas, who linked multiplicities for generic $k$-tuples of semisimple split characters and Kac polynomials., Comment: Corrected minor typos in the exposition. All comments are welcome!

Negatively charged boron vacancies ($\small{V_B^-}$) in hexagonal boron nitride (hBN) have recently gained interest as spin defects for quantum information processing and quantum sensing by a layered material. However, the boron vacancy can exist in a number of charge states in the hBN lattice, but only the -1 state has spin-dependent photoluminescence and acts as a spin-photon interface. Here, we investigate charge state switching of $\small{V_B}$ defects under laser and electron beam excitation. We demonstrate deterministic, reversible switching between the -1 and 0 states ($\small{V_B^- \rightleftharpoons V_B^0 + e^-}$), occurring at rates controlled by excess electrons or holes injected into hBN by a layered heterostructure device. Our work provides a means to monitor and manipulate the $\small{V_B}$ charge state, and to stabilize the -1 state which is a prerequisite for optical spin manipulation and readout of the defect.

In the last decade, growing evidence has emerged supporting a non-universal stellar Initial Mass Function (IMF) in massive galaxies, with a larger number of dwarf stars with respect to the Milky-Way (bottom-heavy IMF). However, a consensus about the mechanisms that cause IMF variations is yet to be reached. Recently, it has been suggested that stars formed early-on in cosmic time, via a star formation burst, could be characterised by a bottom-heavy IMF. A promising way to confirm this is to use relics, ultra-compact massive galaxies, almost entirely composed by these "pristine" stars. The INSPIRE Project aims at assembling a large sample of confirmed relics, that can serve as laboratory to investigate on the conditions of star formation in the first 1-3 Gyr of the Universe. In this third INSPIRE paper, we build a high signal-to-noise spectrum from five relics and one from five galaxies with similar sizes, masses, and kinematical properties, but characterised by a more extended star formation history (non-relics). Our detailed stellar population analysis suggests a systematically bottom-heavier IMF slope for relics than for non-relics, adding new observational evidence for the non-universality of the IMF at various redshifts and further supporting the above proposed physical scenario., Comment: Accepted for publication in MNRAS. 8 pages, 5 figures

This is the second data release (DR2) of the INvestigating Stellar Population In RElics (INSPIRE) project, comprising 21 new systems with observations completed before March 2022. For each system, we release four one-dimensional (1D) spectra to the ESO Science Archive, one spectrum for each arm of the X-Shooter spectrograph. In this paper, we focus on the line-of-sight velocity distribution, measuring integrated stellar velocity dispersions from the spectra, and assessing their robustness and the associated uncertainties. For each of the 21 new systems, we systematically investigated the effect of the parameters and set-ups of the full spectral fitting on the stellar velocity dispersion ($\sigma$) measurements. In particular, we tested how $\sigma$ changes when several parameters of the fit as well as the resolution and spectral coverage of the input spectra are varied. We found that the effect that causes the largest systematic uncertainties on $\sigma$ is the wavelength range used for the fit, especially for spectra with a lower signal-to-noise ratio (S/N $\leq$ 30). When using blue wavelengths (UVB arm) one generally underestimates the velocity dispersion (by $\sim$15 km/s). The values obtained from the near-IR (NIR) arm present a larger scatter because the quality of the spectra is lower. We finally compared our results with those in literature, finding a very good agreement overall. Joining results obtained in DR1 with those presented here, INSPIRE contains 40 ultra-compact massive galaxies, corresponding to 75% of the whole survey. By plotting these systems in a stellar mass-velocity dispersion diagram, we identify at least four highly reliable relic candidates among the new systems. Their velocity dispersion is larger than that of normal-sized galaxies of similar stellar mass., Comment: Accepted for publication, and in press on A&A

We give a counterexample to a formula suggested by the work of Letellier and Rodriguez-Villegas (arXiv:2008.13435) for the mixed Poincar\'e series of character stacks for non-orientable surfaces. The counterexample is obtained by an explicit description of these character stacks for (real) elliptic curves., Comment: 15 pages. All comments are welcome! V2: Minor changes in the exposition and the title, corrected some typos

We present the survey design, implementation, and outlook for COSMOS-Web, a 255 hour treasury program conducted by the James Webb Space Telescope in its first cycle of observations. COSMOS-Web is a contiguous 0.54 deg$^2$ NIRCam imaging survey in four filters (F115W, F150W, F277W, and F444W) that will reach 5$\sigma$ point source depths ranging $\sim$27.5-28.2 magnitudes. In parallel, we will obtain 0.19 deg$^2$ of MIRI imaging in one filter (F770W) reaching 5$\sigma$ point source depths of $\sim$25.3-26.0 magnitudes. COSMOS-Web will build on the rich heritage of multiwavelength observations and data products available in the COSMOS field. The design of COSMOS-Web is motivated by three primary science goals: (1) to discover thousands of galaxies in the Epoch of Reionization ($64$ and place constraints on the formation of the Universe's most massive galaxies ($M_\star>10^{10}$\,M$_\odot$), and (3) directly measure the evolution of the stellar mass to halo mass relation using weak gravitational lensing out to $z\sim2.5$ and measure its variance with galaxies' star formation histories and morphologies. In addition, we anticipate COSMOS-Web's legacy value to reach far beyond these scientific goals, touching many other areas of astrophysics, such as the identification of the first direct collapse black hole candidates, ultracool sub-dwarf stars in the Galactic halo, and possibly the identification of $z>10$ pair-instability supernovae. In this paper we provide an overview of the survey's key measurements, specifications, goals, and prospects for new discovery., Comment: 46 pages, 16 figures, ApJ accepted

Aims. With the next generation of large surveys coming to the stage of observational cosmology soon, it is important to explore their potential synergies and to maximise their scientific outcomes. In this study, we aim to investigate the complementarity of the two upcoming space missions Euclid and the China Space Station Telescope (CSST), focusing on weak lensing (WL) cosmology. In particular, we analyse the photometric redshifts (photo-zs) and the galaxy blending effects. For Euclid, WL measurements suffer from chromatic PSF effects. For this, CSST can provide valuable information for Euclid to obtain more accurate PSF, and to calibrate the color and color-gradient biases for WL measurements. Methods. We create image simulations for different surveys, and quantify the photo-z performance. For blending analyses, we employ high-resolution HST/CANDELS data to mock Euclid, CSST, and an LSST-like survey. We analyse the blending fraction for different cases, and the blending effects on galaxy photometry. Furthermore, we demonstrate that CSST can provide a large enough number of high SNR multi-band galaxy images to calibrate the color-gradient biases for Euclid. Results. The sky coverage of Euclid lies entirely within the CSST footprint. The combination of Euclid with CSST data can be done more uniformly than with the various ground-based data. Our studies show that by combining Euclid and CSST, we can reach a photo-z precision of $\sigma_{\rm NMAD} \approx 0.04$, and an outlier fraction of $\eta\approx 2.4\%$. Because of the similarly high resolutions, the data combination of Euclid and CSST can be relatively straightforward for photometry. To include ground-based data, however, sophisticated deblending utilizing priors from high-resolution space data is demanded. The color-gradient biases for Euclid can be well calibrated to the level of 0.1% using galaxies from CSST deep survey., Comment: 18 pages, 19 figures and 2 tables. Accepted for publication in A&A

We present a Hubble Space Telescope (HST) weak gravitational lensing study of nine distant and massive galaxy clusters with redshifts $1.0 \lesssim z \lesssim 1.7$ ($z_\mathrm{median} = 1.4$) and Sunyaev Zel'dovich (SZ) detection significance $\xi > 6.0$ from the South Pole Telescope Sunyaev Zel'dovich (SPT-SZ) survey. We measured weak lensing galaxy shapes in HST/ACS F606W and F814W images and used additional observations from HST/WFC3 in F110W and VLT/FORS2 in $U_\mathrm{HIGH}$ to preferentially select background galaxies at $z\gtrsim 1.8$, achieving a high purity. We combined recent redshift estimates from the CANDELS/3D-HST and HUDF fields to infer an improved estimate of the source redshift distribution. We measured weak lensing masses by fitting the tangential reduced shear profiles with spherical Navarro-Frenk-White (NFW) models. We obtained the largest lensing mass in our sample for the cluster SPT-CLJ2040$-$4451, thereby confirming earlier results that suggest a high lensing mass of this cluster compared to X-ray and SZ mass measurements. Combining our weak lensing mass constraints with results obtained by previous studies for lower redshift clusters, we extended the calibration of the scaling relation between the unbiased SZ detection significance $\zeta$ and the cluster mass for the SPT-SZ survey out to higher redshifts. We found that the mass scale inferred from our highest redshift bin ($1.2 < z < 1.7$) is consistent with an extrapolation of constraints derived from lower redshifts, albeit with large statistical uncertainties. Thus, our results show a similar tendency as found in previous studies, where the cluster mass scale derived from the weak lensing data is lower than the mass scale expected in a Planck $\nu\Lambda$CDM (i.e. $\nu$ $\Lambda$ Cold Dark Matter) cosmology given the SPT-SZ cluster number counts., Comment: 23 pages, 10 figures + appendix (9 pages, 9 figures); accepted for publication in A&A

Bone pain typically occurs immediately following skeletal damage with mechanical distortion or rupture of nociceptive fibres. The pain mechanism is also associated with chronic pain conditions where the healing process is impaired. Any load impacting on the area of the fractured bone will increase the intraosseous pressure, consequently stimulating the nociceptive response, necessitating rapid clinical intervention to relieve pain associated with the bone damage and appropriate mitigation of any processes involved with the loss of bone mass, muscle, mobility and, to prevent death. The following review has examined the mechanisms of pain associated with trauma or cancer-related skeletal damage focusing on new approaches for the development of innovative therapeutic interventions. In particular, the current review highlights tissue engineering approaches that offer considerable promise in the application of functional biomimetic fabrication of bone and nerve tissues, resembling the pathological micro-environment. The strategic combination of bone and nerve tissue engineered models provides significant potential to develop a new class of in vitro platforms, capable of replacing in vivo models and testing the safety and efficacy of novel drug treatments aimed at the resolution of bone-associated pain. To date, the field of bone pain research has centred on animal models, with accompanying disparity within models often noted and a paucity of data correlating to the human physiological response. This review explores the evident gap in pain drug development research and suggests a step change in approach to harness tissue engineering technologies to recapitulate the complex pathophysiological environment of the damaged bone tissue enabling evaluation of the associated pain-mimicking mechanism with, ultimately, significant therapeutic potential therein for improved patient quality of life., Comment: Submitted to In Vitro Models journal