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Recently, multimodal deep learning, which integrates histopathology slides and molecular biomarkers, has achieved a promising performance in glioma grading. Despite great progress, due to the intra-modality complexity and inter-modality heterogeneity, existing studies suffer from inadequate histopathology representation learning and inefficient molecular-pathology knowledge alignment. These two issues hinder existing methods to precisely interpret diagnostic molecular-pathology features, thereby limiting their grading performance. Moreover, the real-world applicability of existing multimodal approaches is significantly restricted as molecular biomarkers are not always available during clinical deployment. To address these problems, we introduce a novel Focus on Focus (FoF) framework with paired pathology-genomic training and applicable pathology-only inference, enhancing molecular-pathology representation effectively. Specifically, we propose a Focus-oriented Representation Learning (FRL) module to encourage the model to identify regions positively or negatively related to glioma grading and guide it to focus on the diagnostic areas with a consistency constraint. To effectively link the molecular biomarkers to morphological features, we propose a Multi-view Cross-modal Alignment (MCA) module that projects histopathology representations into molecular subspaces, aligning morphological features with corresponding molecular biomarker status by supervised contrastive learning. Experiments on the TCGA GBM-LGG dataset demonstrate that our FoF framework significantly improves the glioma grading. Remarkably, our FoF achieves superior performance using only histopathology slides compared to existing multimodal methods. The source code is available at https://github.com/peterlipan/FoF.

The properties of the warm-hot intergalactic medium (WHIM) in cosmic filaments are among the least quantified units in modern astrophysics. The Spectrum Roentgen Gamma/eROSITA All Sky Survey ((SRG/eRASS) provides a unique opportunity to study the X-ray emission of the WHIM. We applied both imaging and spectroscopic stacking techniques to the data of the first four eRASS scans to inspect the X-ray emissions from 7817 cosmic filaments identified from Sloan Digital Sky Survey (SDSS) optical galaxy samples. We obtained a $9\sigma$ significant detection of the total X-ray signal from filaments in the 0.3--1.2~keV band. Here, we introduce a novel method to estimate the contamination fraction from unmasked X-ray halos, active galactic nuclei, and X-ray binaries associated with filament galaxies. We found an approximately 40\% contamination fraction for these unmasked sources, suggesting that the remaining 60\% of the signal could be coming from the WHIM and a $5.4\sigma$ detection significance of the WHIM. Moreover, we modeled the temperature and baryon density contrast of the detected WHIM by fitting the stacked spectrum and surface brightness profile. The best-fit temperature $\log(T/\mathrm{K})=6.84\pm0.07$, obtained by using a single temperature model, is marginally higher than in the simulation results. This could be due to the fitting of a single temperature model on a multi-temperature spectrum. Assuming a 0.2 solar abundance, the best-fit baryon density contrast $\log\Delta_\mathrm{b}=1.88\pm0.18$ is in general agreement with the X-ray emitting phases in the IllustrisTNG simulation. This result suggests that the broadband X-ray emission traces the high end of the temperature and density values that characterize the entire WHIM population., Comment: 15+8 pages, 11+7 figures, accepted for publication in A&A

Methods. We utilized the combined five SRG/eROSITA All-Sky Survey data (eRASS:5) to perform X-ray imaging and spectral analyses of the Centaurus cluster in various directions to large radii. Surface brightness (SB) profiles out to $2R_{200}$ were constructed. We acquired gas temperature, metallicity, and normalization per area profiles out to $R_{200}$. We compared our results with previous Centaurus studies, cluster outskirts measurements, and simulations. Comprehensive sky background analysis was done across the FoV, in particular, to assess the variation of the eROSITA Bubble emission that partially contaminates the field. Results. The processed X-ray images show the known sloshing-induced structures in the core. The core ($r\leq11~\mathrm{kpc}$) is better described with a 2T model than a 1T model. Here, we measured lower T from the cooler component (~1.0 keV) and higher Z ($\sim\!1.6Z_\odot$), signifying an iron bias. In the intermediate radial range, we observed prominent SB and normalization per area excesses in the eastern sector (Cen 45 location), reaching out to $R_{500}$. Temperature enhancements near the location of Cen 45 imply that the gas is shock-heated due to the interaction with Cen 30, the significant excess behind Cen 45 center might be the tail/ram-pressure-stripped gas. We found good agreement between the outskirt temperatures with the profile from simulations and fit from Suzaku outskirts measurements. We detected significant SB emission to the sky background level out to $R_{200}$ with a $3.5\sigma$ and followed by $2.9\sigma$ at $1.1R_{200}$. The metallicity at $R_{500}-R_{200}$ is low but within the ranges of other outskirts studies. Conclusions. We present the first measurement of ICM morphology and properties of Centaurus cluster sampling the whole azimuth beyond $30'$, increasing the probed volume by a factor of almost 30., Comment: Submitted to the Astronomy & Astrophysics journal: 19 pages, 10 figures (main text), 2 figure (appendix)

[abridged] Hot plasma plays a crucial role in regulating the baryon cycle within the Milky Way, flowing from the energetic sources in the Galactic center and disc, to the corona and the halo. This hot plasma represents an important fraction of the Galactic baryons, plays a key role in galactic outflows and is an important ingredient in galaxy evolution models. Taking advantage of the Spectrum-Roentgen-Gamma (SRG))/eROSITA first all-sky survey (eRASS1), in this work, we aim to provide a panoramic view of the hot circumgalactic medium (CGM) of the Milky Way. Here we present the eROSITA eRASS1 half sky maps in narrow energy bands corresponding to the most prominent soft X-ray lines: OVII and OVIII, which allow us to constrain the distribution of the hot plasma within and surrounding the Milky Way. We corrected the maps by removing the expected contribution associated with the cosmic X-ray background, the time-variable solar wind charge exchange, and the local hot bubble. We applied corrections to mitigate the effect of absorption, therefore highlighting the emission from the CGM of the Milky Way. We use the line ratio of the oxygen lines as a proxy to constrain the temperature of the warm-hot CGM, and we define a pseudo-temperature $\mathcal{T}$ map. The map highlights how different regions are dominated by different thermal components. Towards the outer halo, the temperature distribution of the CGM on angular scales of 2-20 deg is consistent with being constant $\Delta \mathcal{T} / \langle \mathcal{T}\rangle \leq 4\%$, with a marginal detection of $\Delta \mathcal{T} / \langle \mathcal{T}\rangle = 2.7 \% \pm 0.2\%$ (statistical) $\pm 0.6\%$ (systematic) in the southern hemisphere. Instead, significant variations $\sim 12\%$ are observed on many tens of degrees scales when comparing the northern and southern hemispheres., Comment: 15 pages, 14 figures, 1 table, A&A in press

Understanding how the properties of galaxies relate to the properties of the hot circum-galactic medium (CGM) around them can constrain galaxy evolution models. We measured the X-ray luminosity of the hot CGM based on the surface brightness profiles of central galaxy samples measured from Spectrum Roentgen Gamma (SRG)/eROSITA all-sky survey data. We related the X-ray luminosity to the galaxies' stellar and halo mass, and we compared the observed relations to the self-similar model and intrinsic (i.e., not forward-modeled) output of the IllustrisTNG, EAGLE, and SIMBA simulations. The average hot CGM X-ray luminosity ($L_{\rm X,CGM}$) correlates with the galaxy's stellar mass ($M_*$). It increases from $(1.6 \pm 2.1)\times10^{39} \rm erg\,s^{-1}$ to $(3.4 \pm 0.3)\times10^{41} \rm erg\,s^{-1}$, when $\log(M_*)$ increases from 10.0 to 11.5. A power law describes the correlation as $\log(L_{\rm X,CGM})= (2.4\pm 0.1)\times \log(M_*)+(14.6\pm1.5)$. The hot CGM X-ray luminosity as a function of halo mass is measured within $\log(M_{\rm 500c})=11.3-13.7$, extending our knowledge of the scaling relation by more than two orders of magnitude. $L_{\rm X,CGM}$ increases with $M_{\rm 500c}$ from $(3.0 \pm 1.6)\times10^{39}\ \rm erg\,s^{-1}$ at $\log(M_{\rm 500c})=11.3$ to $(1.3 \pm 0.1)\times10^{42}\ \rm erg\,s^{-1}$ at $\log(M_{\rm 500c})=13.7$. The relation follows a power law of $\log(L_{\rm X,CGM})= (1.32\pm 0.05)\times \log(M_{\rm 500c})+(24.1\pm0.7)$. Our observations highlight the necessity of non-gravitational processes at the galaxy group scale while suggesting these processes are sub-dominant at the galaxy scale. We show that the outputs of current cosmological galaxy simulations generally align with the observational results uncovered here but with possibly important deviations in selected mass ranges., Comment: Abstract abridged for arXiv submission, accepted by A&A

The circumgalactic medium (CGM) provides the material needed for galaxy formation and influences galaxy evolution. The hot ($T>10^6K$) CGM is poorly detected around galaxies with stellar masses ($M_*$) lower than $3\times10^{11}M_\odot$ due to the low surface brightness. We used the X-ray data from the first four SRG/eROSITA All-Sky Surveys (eRASS:4). Based on the SDSS spectroscopic survey and halo-based group finder algorithm, we selected central galaxies with spectroscopic redshifts of $z_{\rm spec}<0.2$ and stellar masses of $10.0<\log(M_*/M_\odot)<11.5$ (85,222 galaxies) -- or halo masses of $11.5<\log(M_{\rm 200m}/M_\odot)<14.0$ (125,512 galaxies). By stacking the X-ray emission around galaxies, masking the detected X-ray point sources and carefully modeling the X-ray emission from the unresolved active galactic nuclei (AGN) and X-ray binaries (XRB), we obtain the X-ray emission from the hot CGM. We detected the X-ray emission around MW-mass and more massive central galaxies extending up to the virial radius ($R_{\rm vir}$). We used a $\beta$ model to describe the X-ray surface brightness profile and found $\beta =0.43^{+0.10}_{-0.06}\,(0.37^{+0.04}_{-0.02})$ for MW-mass (M31-mass) galaxies.We estimated the baryon budget of the hot CGM and obtained a value that is lower than the prediction of $\Lambda$CDM cosmology, indicating significant gas depletion in these halos. We extrapolated the hot CGM profile measured within $R_{\rm vir}$ to larger radii and found that within $\approx 3 R_{\rm vir}$, the baryon budget is close to the $\Lambda$CDM cosmology prediction. Our results set a firm footing for the presence of the hot CGM around such galaxies. These measurements constitute a new benchmark for galaxy evolution models and possible implementations of feedback processes therein., Comment: Abstract abridged for arXiv submission, accepted by A&A

Context: Environmental soft protons have affected the performance of the X-ray detectors on board Chandra and XMM-Newton, and they pose a threat for future high energy astrophysics missions with larger aperture, such as ATHENA. Aims: We aim at estimating soft proton fluxes at the ATHENA detectors independently of any modelisation of the external fluxes in the space environment.We analysed the background data measured by eROSITA on board SRG, and with the help of simulations we defined a range of values for the potential count-rate of quiet-time soft protons focused through the mirror shells. We used it to derive an estimate of soft proton fluxes at the ATHENA detectors, assuming ATHENA in the same L2-orbit as SRG. Results: The scaling, based on the computed proton transmission yields of the optics and optical/thermal filters of eROSITA and ATHENA, indicates that the soft proton induced WFI and X-IFU backgrounds could be expected close to the requirement. Conclusions: No soft proton fluxes detrimental to the observations have been suffered by eROSITA during its all-sky survey in orbit around L2. Regardless of where ATHENA will be placed (L1 or L2), our analysis suggests that increasing somewhat the thickness of the WFI optical blocking filter, e.g. by 30%, would help to reduce the soft proton flux onto the detector, in case the planned magnetic diverters perform worse than expected due to soft proton neutralisation at the mirror level.

The eROSITA telescope array aboard the Spektrum Roentgen Gamma (SRG) satellite began surveying the sky in December 2019, with the aim of producing all-sky X-ray source lists and sky maps of an unprecedented depth. Here we present catalogues of both point-like and extended sources using the data acquired in the first six months of survey operations (eRASS1; completed June 2020) over the half sky whose proprietary data rights lie with the German eROSITA Consortium. We describe the observation process, the data analysis pipelines, and the characteristics of the X-ray sources. With nearly 930000 entries detected in the most sensitive 0.2-2.3 keV energy range, the eRASS1 main catalogue presented here increases the number of known X-ray sources in the published literature by more than 60%, and provides a comprehensive inventory of all classes of X-ray celestial objects, covering a wide range of physical processes. A smaller catalogue of 5466 sources detected in the less sensitive but harder 2.3-5 keV band is the result of the first true imaging survey of the entire sky above 2 keV. We show that the number counts of X-ray sources in eRASS1 are consistent with those derived over narrower fields by past X-ray surveys of a similar depth, and we explore the number counts variation as a function of the location in the sky. Adopting a uniform all-sky flux limit (at 50% completeness) of F_{0.5-2 keV} > 5 \times 10^{-14}$ erg\,s$^{-1}$\,cm$^{-2}$, we estimate that the eROSITA all-sky survey resolves into individual sources about 20% of the cosmic X-ray background in the 1-2 keV range. The catalogues presented here form part of the first data release (DR1) of the SRG/eROSITA all-sky survey. Beyond the X-ray catalogues, DR1 contains all detected and calibrated event files, source products (light curves and spectra), and all-sky maps. Illustrative examples of these are provided., Comment: 39 pages, 23 figures. Accepted for publication in A&A. Accompanying eROSITA-DE Data Release 1

An adaptive algorithm for spectral proper orthogonal decomposition (SPOD) of mixed broadband-tonal turbulent flows is developed. Sharp peak resolution at tonal frequencies is achieved by locally minimizing the bias of the spectrum. Smooth spectrum estimates of broadband regions are achieved by locally reducing the variance of the spectrum. The method utilizes multitaper estimation with sine tapers. An iterative criterion based on modal convergence is introduced to enable the SPOD to adapt to spectral features. For tonal flows, the adaptivity is controlled by a single user input; for broadband flows, a constant number of sine tapers is recommended without adaptivity. The discrete version of Parseval's theorem for SPOD is stated. Proper normalization of the tapers ensures that Parseval's theorem is satisfied in expectation. Drastic savings in computational complexity and memory usage are facilitated by two aspects: (i) sine tapers, which permit post hoc windowing of a single Fourier transform; and (ii) time-domain lossless compression using a QR or eigenvalue decomposition. Sine-taper SPOD is demonstrated on time-resolved particle image velocimetry (TR-PIV) data from an open cavity flow and high-fidelity large-eddy simulation (LES) data from a round jet, with and without adaptivity. For the tonal cavity flow, the adaptive algorithm outperforms Slepian-based multitaper SPOD in terms of variance and local bias of the spectrum, mode convergence, and memory usage.

The first all-sky maps of the diffuse emission of high ionization lines observed in X-rays by SRG/eROSITA, provide an excellent probe for the study of the warm-hot phase (T~10^6 K) of the circumgalactic medium (CGM) of the Milky Way (MW). In this work we analyse the O VIII line detected in the first eROSITA All-Sky Survey data (eRASS1). We fit a sky map made in a narrow energy bin around this line, with physical emission models embedded in a 3D geometry to constrain the density distribution of the warm-hot gas around our Galaxy, with a focus on mid and high (absolute) Galactic latitudes. By masking out the eROSITA bubbles and other bright extended foreground sources, we find that an oblate geometry of the warm-hot gas (T~0.15-0.17 keV), flattened around the Galactic disk with scale height z_h~1-3 kpc, best describes the eRASS1 O VIII map, with most of the observed emission resulting to be produced within a few kpc from the Sun. The additional presence of a large scale warm-hot spherical halo, while providing a minor contribute to the X-ray emission, accounts for the high O VII absorption column densities detected with XMM-Newton, as well as most of the baryon budget of the CGM of the MW. The eROSITA data carry the largest amount of information and detail of O VIII CGM intensities to date, allowing for a significant reduction of the statistical uncertainties of the inferred physical parameters., Comment: Accepted for publication in Astronomy & Astrophysics

We propose a parallel (distributed) version of the spectral proper orthogonal decomposition (SPOD) technique. The parallel SPOD algorithm distributes the spatial dimension of the dataset preserving time. This approach is adopted to preserve the non-distributed fast Fourier transform of the data in time, thereby avoiding the associated bottlenecks. The parallel SPOD algorithm is implemented in the PySPOD (https://github.com/MathEXLab/PySPOD) library and makes use of the standard message passing interface (MPI) library, implemented in Python via mpi4py (https://mpi4py.readthedocs.io/en/stable/). An extensive performance evaluation of the parallel package is provided, including strong and weak scalability analyses. The open-source library allows the analysis of large datasets of interest across the scientific community. Here, we present applications in fluid dynamics and geophysics, that are extremely difficult (if not impossible) to achieve without a parallel algorithm. This work opens the path toward modal analyses of big quasi-stationary data, helping to uncover new unexplored spatio-temporal patterns.

Complex interactions between two opposing agents frequently occur in domains of machine learning, game theory, and other application domains. Quantitatively analyzing the strategies involved can provide an objective basis for decision-making. One such critical scenario is shot-taking in football, where decisions, such as whether the attacker should shoot or pass the ball and whether the defender should attempt to block the shot, play a crucial role in the outcome of the game. However, there are currently no effective data-driven and/or theory-based approaches to analyzing such situations. To address this issue, we proposed a novel framework to analyze such scenarios based on game theory, where we estimate the expected payoff with machine learning (ML) models, and additional features for ML models were extracted with a theory-based shot block model. Conventionally, successes or failures (1 or 0) are used as payoffs, while a success shot (goal) is extremely rare in football. Therefore, we proposed the Expected Probability of Shot On Target (xSOT) metric to evaluate players' actions even if the shot results in no goal; this allows for effective differentiation and comparison between different shots and even enables counterfactual shot situation analysis. In our experiments, we have validated the framework by comparing it with baseline and ablated models. Furthermore, we have observed a high correlation between the xSOT and existing metrics. This alignment of information suggests that xSOT provides valuable insights. Lastly, as an illustration, we studied optimal strategies in the World Cup 2022 and analyzed a shot situation in EURO 2020.

SRG/eROSITA is situated in a halo orbit around L2 where the highly variable solar wind charge exchange (SWCX) emission from Earth's magnetosheath is expected to be negligible. The soft X-ray foreground emissions from the local hot bubble (LHB) and the remaining heliospheric SWCX emissions could be studied in unprecedented detail with eROSITA All-Sky Survey (eRASS) data in a 6-month cadence and better spectral resolution than ROSAT. We aim to use eRASS data of the sight lines towards three giant molecular clouds away from the Galactic plane to isolate and study the soft X-ray diffuse foreground emission. These X-ray shadows will serve as calibration baselines for the future three-dimensional structural study of the LHB. We conducted spectral analysis on the diffuse X-ray spectra of these clouds from the first four eRASSs to estimate and separate the heliospheric SWCX contribution from the LHB emission. We find the density of the LHB to be independent of the sight line with $n_e \sim 4 \times 10^{-3}\,$cm$^{-3}$, but not the temperature. We report a lower temperature of $kT_{\mathrm{LHB}}=0.084\pm0.004\,$keV towards Chamaeleon$~$II & III (Cha$~$II & III) than Ophiuchus (Oph) and Corona Australis (CrA), in which we measured $0.102\pm0.006$ and $0.112\pm0.009\,$keV, respectively. We measured the emission measure of the LHB to be $\sim 2\times10^{-3}\,$cm$^{-6}\,$pc at medium Galactic latitudes ($|b| \sim 20^{\circ}$). A monotonic increase in the SWCX contribution has been observed since the start of 2020, coincidental with the beginning of solar cycle 25. For Oph, SWCX has dominated the LHB in the $0.3$-$0.7\,$keV band intensity since eRASS2. We observed lower SWCX contributions in Cha$~$II & III and CrA, consistent with the expected decreasing solar wind ion density at high heliographic latitudes., Comment: 22 pages, 15 figures. Accepted for publication in A&A

Unveiling the true nature of Dark Matter (DM), which manifests itself only through gravity, is one of the principal quests in physics. Leading candidates for DM are weakly interacting massive particles (WIMPs) or ultralight bosons (axions), at opposite extremes in mass scales, that have been postulated by competing theories to solve deficiencies in the Standard Model of particle physics. Whereas DM WIMPs behave like discrete particles ($\varrho$DM), quantum interference between DM axions is manifested as waves ($\psi$DM). Here, we show that gravitational lensing leaves signatures in multiply-lensed images of background galaxies that reveal whether the foreground lensing galaxy inhabits a $\varrho$DM or $\psi$DM halo. Whereas $\varrho$DM lens models leave well documented anomalies between the predicted and observed brightnesses and positions of multiply-lensed images, $\psi$DM lens models correctly predict the level of anomalies left over by $\varrho$DM lens models. More challengingly, when subjected to a battery of tests for reproducing the quadruply-lensed triplet images in the system HS 0810+2554, $\psi$DM is able to reproduce all aspects of this system whereas $\varrho$DM often fails. The ability of $\psi$DM to resolve lensing anomalies even in demanding cases like HS 0810+2554, together with its success in reproducing other astrophysical observations, tilt the balance toward new physics invoking axions., Comment: Updated with accepted version. The Version of Record of this article is published in Nature Astronomy, and is available online at https://www.nature.com/articles/s41550-023-01943-9. Free online version : https://rdcu.be/damHj

With recently available football match event data that record the details of football matches, analysts and researchers have a great opportunity to develop new performance metrics, gain insight, and evaluate key performance. However, most sports sequential events modeling methods and performance metrics approaches could be incomprehensive in dealing with such large-scale spatiotemporal data (in particular, temporal process), thereby necessitating a more comprehensive spatiotemporal model and a holistic performance metric. To this end, we proposed the Transformer-Based Neural Marked Spatio Temporal Point Process (NMSTPP) model for football event data based on the neural temporal point processes (NTPP) framework. In the experiments, our model outperformed the prediction performance of the baseline models. Furthermore, we proposed the holistic possession utilization score (HPUS) metric for a more comprehensive football possession analysis. For verification, we examined the relationship with football teams' final ranking, average goal score, and average xG over a season. It was observed that the average HPUS showed significant correlations regardless of not using goal and details of shot information. Furthermore, we show HPUS examples in analyzing possessions, matches, and between matches., Comment: 36 pages, 25 figures

Despite their vital importance to understand galaxy evolution and our own Galactic ecosystem, our knowledge of the physical properties of the hot phase of the Milky Way is still inadequate. However, sensitive SRG/eROSITA large area surveys are now providing us with the long sought-after data needed to mend this state of affairs. We present the properties of the soft X-ray emission as observed by eROSITA in the eFEDS field. We measure the temperature and metal abundance of the hot circum-Galactic medium (CGM) to be within $kT_{CGM}=0.153-0.178$ keV and $Z_{CGM}=0.052-0.072$ $Z_\odot$, depending on the contribution of solar wind charge exchange (SWCX). Slightly larger CGM abundances $Z_{CGM}=0.05-0.10$ $Z_\odot$ are possible, considering the uncertain extrapolation of the extragalactic Cosmic X-ray background (CXB) emission below $\sim1$ keV. To recover CGM abundances as large as $Z_{CGM}=0.3$ $Z_\odot$, it must be postulated the presence of an additional component, likely associated with the warm-hot intergalactic medium, providing $\sim15-20$% of the flux in the soft X-ray band. The emission in the soft band is dominated by the CGM, with contributions from the CXB and the local hot bubble. Moreover, the eROSITA data require the presence of an additional component associated with the elusive Galactic corona plus a possible contribution from unresolved M dwarf stars. This component has a temperature of $kT\sim0.4-0.7$ keV and it might be out of thermal equilibrium. It contributes $\sim9$% to the total emission in the 0.6--2 keV band, therefore it is a likely candidate to produce part of the unresolved CXB flux observed in X-ray ultra-deep fields. We also observe a significant contribution to the soft X-ray flux due to SWCX, during periods characterised by stronger solar wind activity, and causing the largest uncertainty on the determination of the CGM temperature., Comment: Accepted for publication in Astronomy and Astrophysics

We address the nature and origin of Super Star Clusters (SSCs) discovered by Holtzman et al. (1992) within a radius of $\sim$$5\,\rm kpc$ from the center of NGC 1275, the giant elliptical galaxy at the center of the Perseus Cluster. We show that, in contrast with the much more numerous population of SSCs subsequently discovered up to $\sim$$30\,\rm kpc$ from the center of this galaxy, the central SSC population have maximal masses an order of magnitude higher and a mass function with a shallower power-law slope. Furthermore, whereas the outer SSC population have ages spanning a few $\rm Myr$ to at least $\sim$$1\,\rm Gyr$, the central SSC population have ages strongly concentrated around $\sim$$500 \rm \, Myr$ with a $1\,\sigma$ dispersion of $\sim$$100\,\rm Myr$. These SSCs share a close spatial and temporal relationship with the "central spiral," which also has a radius $\sim$$5\,\rm kpc$ centered on NGC 1275 and a characteristic stellar age of $\sim$$150\,\rm Myr$ (Paper I). We argue that both the central SSC population and the central spiral formed from gas deposited by a residual cooling flow, with the SSCs forming first followed by the formation of the stellar body of the central spiral $\sim$$300$-$400\,\rm Myr$ later. The ages of the central SSC population imply that they are able to withstand very strong tidal fields near the center of NGC 1275, making them genuine progenitor globular clusters. Evidently, a spiral disk hosting progenitor globular clusters has recently formed at the center of a giant elliptical galaxy., Comment: 11 pages, 6 figures, accepted by ApJ

We address the nature and origin of a spiral disk at the center of NGC 1275, the giant elliptical galaxy at the center of the Perseus cluster, that spans a radius of $\sim$$5\,\rm kpc$. By comparing stellar absorption lines measured in long-slit optical spectra with synthetic spectra for single stellar populations, we find that fitting of these lines requires two stellar populations: (i) a very young population that peaks in radial velocity at $\pm 250 {\rm \, km \, s^{-1}}$ of the systemic velocity within a radius of $\sim$$720\,\rm pc$ of the nucleus, a $1\,\sigma$ velocity dispersion significantly lower than $140 {\rm \, km \, s^{-1}}$, and an age of $0.15 \pm 0.05 \rm\,Gyr$; and (ii) a very old population having a constant radial velocity with a radius corresponding to the systemic velocity, a much broader velocity dispersion of $\sim$$250 {\rm \, km \, s^{-1}}$, and an age of around $10\,\rm Gyr$. We attribute the former to a post-starburst population associated with the spiral disk, and the latter to the main stellar body of NGC 1275 along the same sight line. If the spiral disk is the remnant of a cannibalized galaxy, then its progenitor would have had to retain an enormous amount of gas in the face of intensive ram-pressure stripping so as to form a total initial mass in stars of $\sim 3 \times 10^9 \,M_\odot$. More likely, the central spiral originally comprised a gaseous body accreted over the distant past from a residual cooling flow, before experiencing a starburst $\sim$$0.15\,\rm Gyr$ ago to form its stellar body., Comment: 34 pages, 14 figures, accepted by ApJ

We search for signatures of gravitational lensing in the gravitational-wave signals from compact binary coalescences detected by Advanced LIGO and Advanced Virgo during O3a, the first half of their third observing run. We study: 1) the expected rate of lensing at current detector sensitivity and the implications of a non-observation of strong lensing or a stochastic gravitational-wave background on the merger-rate density at high redshift; 2) how the interpretation of individual high-mass events would change if they were found to be lensed; 3) the possibility of multiple images due to strong lensing by galaxies or galaxy clusters; and 4) possible wave-optics effects due to point-mass microlenses. Several pairs of signals in the multiple-image analysis show similar parameters and, in this sense, are nominally consistent with the strong lensing hypothesis. However, taking into account population priors, selection effects, and the prior odds against lensing, these events do not provide sufficient evidence for lensing. Overall, we find no compelling evidence for lensing in the observed gravitational-wave signals from any of these analyses., Comment: 31 pages and 6 figures. Accepted by the Astrophysical Journal