Schutzenberger's promotion operator, pro, is a fundamental map in dynamical algebraic combinatorics. At first, its action was mainly considered on standard Young tableaux. But pro was subsequently shown to have interesting properties when applied to natural labelings of other posets. Pechenik defined a K-theoretic version of promotion, pro_K, on m-packed labelings of tableaux. The operator pro was then extended to increasing labelings of other posets. The purpose of the current work is to show that the original action of pro_K on m-packed labelings yields interesting results when applied to partially ordered sets in general, and to rooted trees in particular. We show that under certain conditions, the sizes of the orbits and order of pro_K exhibit nice divisibility properties. We also completely determine, for certain values of m, the orbit sizes for the action on various types of rooted trees such as extended stars, combs, zippers, and a type of three-leaved tree.

This study first examines how APC expenditures, authorship patterns, and publishing venues of Ukrainian scholars changed between the pre-war (2020-2021) and wartime (2022-2023) periods. Second, it explores the extent to which APC levels are associated with the field-normalized citation impact (FNCI) of Gold Open Access articles authored by Ukrainian scholars. Statistical analysis revealed a small but significant correlation between APC amounts and citation impact, though the effect size was minimal, suggesting higher APCs did not substantially boost citations. APC waivers offered by major publishers such as Springer and Elsevier since 2022 resulted in only a slight increase in the number of articles authored solely by Ukrainian scholars. Despite these waivers, MDPI and Aluna maintained the largest shares. Between 2020 and 2023, the number of articles authored solely by Ukrainian scholars in foreign journals fell by 25.7 percent, and total APC spending declined by 24.6 percent, from 1.24 million EUR to 0.93 million EUR. Medicine accounted for the largest share of both articles and APC expenditure, with the majority published in Aluna journals.

We examine the splashback structure of galaxy clusters using hydrodynamical simulations from the GIZMO run of The Three Hundred Project, focusing on the relationship between the stellar and dark matter components. We dynamically decompose clusters into orbiting and infalling material and fit their density profiles. We find that the truncation radius $r_{\mathrm{t}}$, associated with the splashback feature, coincides for stars and dark matter, but the stellar profile exhibits a systematically steeper decline. Both components follow a consistent $r_{\mathrm{t}}{-}Γ$ relation, where $Γ$ is the mass accretion rate, which suggests that stellar profiles can be used to infer recent cluster mass growth. We also find that the normalisation of the density profile of infalling material correlates with $Γ$, and that stellar and dark matter scale radii coincide when measured non-parametrically. By fitting stellar profiles in projection, we show that $r_{\mathrm{t}}$ can, in principle, be recovered observationally, with a typical scatter of $\sim 0.3\,R_{200\mathrm{m}}$. Our results demonstrate that the splashback feature in the stellar component provides a viable proxy for the cluster's physical boundary and recent growth by mass accretion, offering a complementary observable tracer to satellite galaxies and weak lensing.

The emission of continuous gravitational waves (CWs) possibly explains why pulsars spinning with a period shorter than a millisecond have not been observed so far. Neutron stars accreting mass at the highest rates are the most promising targets for a search for CWs, because a strong emission of gravitational waves is required to balance the torque exerted by mass accretion onto the neutron star. Detecting coherent pulsations in the electromagnetic emission maximizes the search sensitivity, but has so far not been successful for most of the brightest accreting neutron stars. Here, we present the first search for pulsations in the optical band from the brightest accreting neutron star known, Sco X-1. To this end, we tailored semi-coherent search strategies to data obtained over four years, for a total of $\sim$$56$ ks, by the SiFAP2 fast photometer mounted at the Telescopio Nazionale Galileo (TNG). These searches are especially suited to analysing long observations of systems for which only limited knowledge on the orbital parameters is available, and involve joining coherent analyses on shorter segments without connecting the spin phase between them. The large count rates afforded by an optical telescope and the efficiency of the search strategy employed allowed us to set an upper limit of $9 \times 10^{-5}$ to the pulsed amplitude, which is lower by a factor of four with respect to previous searches in the X-ray band. We also show that the application of semi-coherent searches to SiFAP2 observations of the first detected optical millisecond pulsar, PSR J1023+0038, could have preceded its detection in the radio band. These results highlight the role played by high-time-resolution optical observations in performing deep searches of quickly rotating pulsars.

Partial differential equations describing the dynamics of physical systems rarely have closed-form solutions. Fourier spectral methods, which use Fast Fourier Transforms (FFTs) to approximate solutions, are a common approach to solving these equations. However, mapping Fourier integrals to discrete FFTs is not straightforward, as the selection of the grid as well as the coordinate-dependent phase and scaling factors require special care. Moreover, most software packages that deal with this step integrate it tightly into their full-stack implementations. Such an integrated design sacrifices generality, making it difficult to adapt to new coordinate systems, boundary conditions, or problem-specific requirements. To address these challenges, we present FFTArray, a Python library that automates the general discretization of Fourier transforms. Its purpose is to reduce the barriers to developing high-performance, maintainable code for pseudo-spectral Fourier methods. Its interface enables the direct translation of textbook equations and complex research problems into code, and its modular design scales naturally to multiple dimensions. This makes the definition of valid coordinate grids straightforward, while coordinate grid specific corrections are applied with minimal impact on computational performance. Built on the Python Array API Standard, FFTArray integrates seamlessly with array backends like NumPy, JAX and PyTorch and supports Graphics Processing Unit acceleration. The code is openly available at https://github.com/QSTheory/fftarray under Apache-2.0 license.

The Euclid survey aims to trace the evolution of cosmic structures up to redshift $z$ $\sim$ 3 and beyond. Its success depends critically on obtaining highly accurate mean redshifts for ensembles of galaxies $n(z)$ in all tomographic bins, essential for deriving robust cosmological constraints. However, photometric redshifts (photo-$z$s) suffer from systematic biases arising from various sources of uncertainty. To address these challenges, we utilised self-organising maps (SOMs) with mock samples resembling the Euclid Wide Survey (EWS), to validate Euclid's uncertainty requirement of $|Δ\langle z \rangle| = \langle z_{\text{est}} \rangle - \langle z \rangle \leq 0.002 (1+z)$ per tomographic bin, assuming DR3-level data. We observe that defining the redshift tomography using the mean spectroscopic redshift (spec-$z$) per SOM cell, results in none of the ten tomographic redshift bins satisfying the requirement. In contrast, the redshift tomography on the photo-$z$s of the EWS-like sample yields superior results, with eight out of ten bins [$0 < z\leq 2.5$] meeting the Euclid requirement. To enhance the realism of our study, we morph our calibration sample to mimic the C3R2 survey in incremental steps. In this context, a maximum of six out of ten bins meet the requirement, strongly advocating the adoption of a redshift tomography defined by the photo-$z$s of individual galaxies rather than the commonly used mean spec-$z$ of SOM cells. To examine the impact on the expected biases for $Ω_{\text{m}}$, $σ_{8}$, and $Δw_{0}$ measured by Euclid, we perform a Fisher forecast for cosmic shear only, based on our redshift uncertainties. Here, we find that even under an evaluation of the uncertainty where the impact of the redshift bias is substantial, most absolute biases remain below 0.1$σ$ in the idealised scenario and below 0.3$σ$ in the more realistic case.

We introduce a new point of view to present classical notions related to set-theoretic solutions of the Yang-Baxter equation: left skew braces, dirings, left skew rings. The idea is to replace the single multiplication on a left near-ring by two operations, one associative and the other left distributive. Two algebraic structures naturally appear: left skew rings and left weak rings, whose categories turn out to be canonically isomorphic.

The first stars, the chemically pristine Population III, likely played an important role in heating the intergalactic medium during the epoch of cosmic dawn. The very high effective temperatures ($\sim 10^5$ K) predicted for the most massive Population III stars could also give rise to tell-tale signatures in the emission-line spectra of early star clusters or small galaxies dominated by such stars. Important quantities in modelling their observational signatures include their photon production rates at ultraviolet energies at which photons are able to ionize hydrogen and helium, dissociate molecular hydrogen and cause Lyman-$α$ heating. Here, we model the spectral energy distributions of Population III stars to explore how these key quantities are affected by the initial mass and rotation of Population III stars given a wide range of models for the evolution of these stars. Our results indicate that rotating Population III stars that evolve to effective temperatures $\sim 2\times 10^5$ K could potentially give rise to a very strong HeII 1640 emission line in the spectra from primordial star clusters, without requiring stellar masses of $\gtrsim 100\ \mathrm{M}_\odot$ indicated by previous models for non-rotating Population III stars. The observable impact on 21-cm signatures from cosmic dawn and the epoch of reionization from our set of rotating stars that evolve to $\sim 2\times 10^5$ K is modest, except in case of high Population~III star formation efficiencies which imprint potentially detectable features in the global 21-cm signal and 21-cm power spectrum.

Despite their discovery fifteen years ago, the nature and origin of the Fermi bubbles remain unclear. We here investigate the effect a magnetic field can have on a subsonic breeze outflow emanating from the Galactic centre region. The presence of this magnetic field allows anisotropic diffusion of cosmic rays within the outflow, shaping the resultant cosmic ray distribution obtained out at large distances within the Galactic halo. We show that our magnetohydrodynamic Galactic breeze model, in combination with an opening angle for the injection of cosmic rays, leads to $γ$-ray emission from the Fermi bubble region with relatively sharp edges.

Ideal quantum measurement requires divergent thermodynamic resources. This is a consequence of the third law of thermodynamics, which prohibits the preparation of the measurement pointer in a fully erased, pure state required for the acquisition of perfect, noiseless measurement information. In this work, we investigate the consequences of finite resources in the emergence of intersubjectivity as a model for measurement processes with multiple observers. Here, intersubjectivity refers to a condition in which observers agree on the observed outcome (agreement), and their local random variables exactly reproduce the original random variable for the system observable (probability reproducibility). While agreement and reproducibility are mutually implied in the case of ideal measurement, finite thermodynamic resources constrain each of them. Starting from the third law of thermodynamics, we derive how the achievability of ideal intersubjectivity is affected by restricted thermodynamic resources. Specifically, we establish a no-go theorem concerning perfect intersubjectivity and present a deviation metric to account for the influence of limited resources. We further present attainable bounds for the agreement and bias that are exclusively dependent on the initial state of the environment. In addition, we show that either by cooling or coarse-graining, we can approximate ideal intersubjectivity even with finite resources. This work bridges quantum thermodynamics and the emergence of classicality in the form of intersubjectivity.

We investigate the Type I migration of planets in low-density cavities and inner discs of strongly magnetized young stars using global three-dimensional (3D) magnetohydrodynamic (MHD) simulations, where the strong magnetic field carves the low-density cavity. Simulations show that a planet in the cavity migrates inwards up to the radius at which the outer Lindblad resonances are inside the cavity. At smaller radii, the migration stalls. The migration is faster if a star accretes in the unstable regime where the temporary tongues penetrate the magnetosphere. If a planet is in a highly inclined orbit, it interacts with the disc, and the eccentricity increases due to the Kozai-Lydov mechanism. A planet may stop or reverse its migration in the inner disc before entering the cavity. The magnetosphere interacts with the inner disc, changing its density distribution such that migration slows down or is even reversed. A tilted magnetosphere also excites density and bending waves in the disc, which may slow down migration and also increase the inclination and eccentricity of the planet. When a planet reaches the disc-cavity boundary, it is typically trapped at the boundary by asymmetric corotation torque. A planet moves together with the boundary when the cavity expands. Overall, a magnetized star provides an environment for slow or reverse migration.

Large language models (LLMs) fail on over one-third of multi-hop questions with counterfactual premises and remain vulnerable to adversarial prompts that trigger biased or factually incorrect responses, which exposes a fundamental deficit in self-regulated reasoning. We propose \textbf{MetaCrit}, a multi-agent framework grounded in Nelson and Narens' metacognitive regulation theory. MetaCrit decomposes reasoning regulation into four agents: object-level generation, a \emph{monitoring} agent that assesses response validity, a \emph{control} agent that critiques logical soundness, and a meta-level synthesizer that integrates all signals into a final response. Evaluation across eight benchmarks, four model backbones, and a college-level analytical writing study shows that MetaCrit significantly improves content truthfulness and logical soundness while eliminating toxic outputs. Its modular design allows individual agents to be integrated into existing frameworks as drop-in components without architectural modifications.

The paper describes the objectives, design and findings of the pre-launch ground characterisation campaigns of the Euclid infrared detectors. The pixel properties, including baseline, bad pixels, quantum efficiency, inter pixel capacitance, quantum efficiency, dark current, readout noise, conversion gain, response nonlinearity, and image persistence were measured and characterised for each pixel. We describe in detail the test flow definition that allows us to derive the pixel properties and we present the data acquisition and data quality check software implemented for this purpose. We also outline the measurement protocols of all the pixel properties presented and we provide a comprehensive overview of the performance of the Euclid infrared detectors as derived after tuning the operating parameters of the detectors. The main conclusion of this work is that the performance of the infrared detectors Euclid meets the requirements. Pixels classified as non-functioning accounted for less than 0.2% of all science pixels. IPC coupling is minimal and crosstalk between adjacent pixels is less than 1% between adjacent pixels. 95% of the pixels show a QE greater than 80% across the entire spectral range of the Euclid mission. The conversion gain is approximately 0.52 ADU/e-, with a variation less than 1% between channels of the same detector. The reset noise is approximately equal to 23 ADU after reference pixels correction. The readout noise of a single frame is approximately 13 $e^-$ while the signal estimator noise is measured at 7 $e^-$ in photometric mode and 9 $e^-$ in spectroscopic acquisition mode. The deviation from linear response at signal levels up to 80 k$e^-$ is less than 5% for 95% of the pixels. Median persistence amplitudes are less than 0.3% of the signal, though persistence exhibits significant spatial variation and differences between detectors.

The Near-Infrared Spectrometer and Photometer (NISP) onboard Euclid includes several optical elements in its path, which introduce artefacts into the data from non-nominal light paths. To ensure uncontaminated source photometry, these artefacts must be accurately accounted for. This paper focuses on two specific optical features in NISP's photometric data (NISP-P): ghosts caused by the telescope's dichroic beamsplitter, and the bandpass filters within the NISP fore-optics. Both ghost types exhibit a characteristic morphology and are offset from the originating stars. The offsets are well modelled using 2D polynomials, with only stars brighter than approximately 10 magnitudes in each filter producing significant ghost contributions. The masking radii for these ghosts depend on both the source-star brightness and the filter wavelength, ranging from 20 to 40 pixels. We present the final relations and models used in the near-infrared (NIR) data pipeline to mask these ghosts for Euclid's Quick Data Release (Q1).

We present the discovery and confirmation of the ultra-short period (USP) planet TOI-2431 b orbiting a nearby ($d\sim36$ pc) late K star ($T_{\mathrm{eff}}$ = $4109 \pm 28 \, {\rm K}$) using observations from the Transiting Exoplanet Survey Satellite (TESS), precise radial velocities with the NEID and the Habitable-zone Planet Finder (HPF) spectrographs, as well as ground-based high contrast imaging from NESSI. TOI-2431 b has a period of 5 hours and 22 minutes, making it one of the shortest-period exoplanets known to date. TOI-2431 b has a radius of $1.536 \pm 0.033\, \rm{R_\oplus}$, and a mass of $6.2 \pm 1.2\, \rm{M_\oplus}$, suggesting it has a density compatible with an Earth-like composition and, due to its high irradiation, is likely a 'lava-world' with a $T_{\mathrm{eq}}$ = $2063 \pm 30 \, {\rm K}$. We estimate that the current orbital period is only 30% larger than the Roche-limit orbital period, and that it has an expected orbital decay timescale of only $\sim$31 Myr. Finally, due to the brightness of the host star ($V = 10.9$, $K = 7.6$), TOI-2431 b has a high Emission Spectroscopy Metric of 27, making it one of the best USP systems for atmospheric phase-curve analysis.

Studying the composition and origin of the inner region of our Galaxy -- the "Galactic bulge" -- is crucial for understanding the formation and evolution of the Milky Way and other galaxies. We present new observational constraints based on a sample of around 18,000 stars in the inner Galaxy, combining Gaia DR3 RVS and APOGEE DR17 spectroscopy. Gaia-RVS complements APOGEE by improving sampling of the metallicity, [Fe/H] in the -2.0 to -0.5 dex range. This work marks the first application of Gaia-RVS spectroscopy to the bulge region, enabled by a novel machine learning approach (hybrid-CNN) that derives stellar parameters from intermediate-resolution spectra with precision comparable to APOGEE's infrared data. We performed full orbit integrations using a barred Galactic potential and applied orbital frequency analysis to disentangle the stellar populations in the inner Milky Way. For the first time, traced by the field stars, we are able to robustly identify the long-sought pressure supported bulge. We show this stellar population to be chemically and kinematically distinct from the other main components co-existing in the same region. The spheroidal bulge has a metallicity distribution function (MDF) peak at around -0.70 dex extending to solar value, is dominated by a high-[alpha/Fe] population with almost no dependency on metallicity, consistent with very rapid early formation, predating the thick disc and the bar. We find evidence that the bar has influenced the dynamics of the spheroidal bulge, introducing a mild triaxiality and radial extension. We identify a group of stars on X4 orbits, likely native to the early spheroid, as this population mimics the chemistry of the spheroidal bulge, with a minor contamination from the more metal-poor ([Fe/H] < -1.0) halo. We find the inner-thick disc to be kinematically hotter (mean Vphi ~125 km/s) than the local-thick disc. ...

Two fast radio bursts, FRB 20121102A and FRB 20180916B, show periodic activity with cycles of 159.3 and 16.33 days, respectively. These cycles consist of active and inactive windows, with the peak activity centred within the active phase. For FRB 20180916B, studies reported a frequency-dependent or chromatic behaviour, for which the activity window starts earlier and becomes narrower at higher frequencies. The activity across frequencies is typically modelled with a power law. We developed a simple model that combines the phase and frequency dependence of the activity windows of FRB 20121102A and FRB 20180916B. Our goal was to perform a chromaticity study for FRB 20121102A that incorporates model improvements to account for the cyclic nature of its activity window and to compare the chromatic behaviour of the two periodic FRBs. We standardised the detections from the 425 observing epochs for FRB 20121102A and the 214 epochs for FRB20180916B to account for differences in the radio telescope sensitivity. To the normalised detection-rate phase distribution, we fitted a von Mises distribution and extracted the peak activity phase and activity width. These quantities as a function of frequency were then modelled as power laws to construct the chromatic model. The activity window starts earlier at higher frequencies for the two sources. The activity window of FRB 20121102A broadens at higher frequencies, however, and that of FRB 20180916B broadens at lower frequencies. Interestingly, it appears to remain active during at least 80% of the cycle at C band. The observed chromatic behaviour of FRB 20180916B is consistent with previous findings. For FRB 20121102A, a chromaticity in its activity window is also seen, but the source appears to be active for longer at higher frequencies, which is different from the behaviour of FRB 20180916B.

The escape fraction of Lyman continuum photons (fesc(LyC)) is the last key unknown in our understanding of cosmic reionization. Directly estimating the escape fraction (fesc) of ionizing photons in the epoch of reionization (EoR) is impossible, due to the opacity of the intergalactic medium (IGM). However, a high fesc leaves clear imprints in the spectrum of a galaxy, due to reduced nebular line and continuum emission, which also leads to bluer UV continuum slopes (betaUV). Here, we exploit the large archive of deep JWST/NIRSpec spectra from the DAWN JWST Archive to analyze over 1'400 galaxies at 5 < zspec < 10 and constrain their fesc based on SED fitting enhanced with a picket fence model. We identify 71 high-confidence sources with significant fesc based on Bayes factor analysis strongly favouring fesc > 0 over fesc = 0 solutions. We compare the characteristics of this high-escape subset against both the parent sample and established diagnostics including betaUV slope, O32, and SFR surface density (SigmaSFR). For the overall sample, we find that most sources have a low escape fraction (<1%), however, a small subset of sources seems to emit a large number of their ionizing photons into the IGM, such that the average fesc is found to be ~10%, as needed for galaxies to drive reionization. Although uncertainties remain regarding recent burstiness and the intrinsic stellar ionizing photon output at low metallicities, our results demonstrate the unique capability of JWST/NIRSpec to identify individual LyC leakers, measure average fesc and thus constrain the drivers of cosmic reionization.

We investigate the accuracy and range of validity of the perturbative model for the 2-point (2PCF) and 3-point (3PCF) correlation functions in real space in view of the forthcoming analysis of the Euclid mission spectroscopic sample. We take advantage of clustering measurements from four snapshots of the Flagship I N-body simulations at z = {0.9, 1.2, 1.5, 1.8}, which mimic the expected galaxy population in the ideal case of absence of observational effects such as purity and completeness. For the 3PCF we consider all available triangle configurations given a minimal separation. First, we assess the model performance by fixing the cosmological parameters and evaluating the goodness-of-fit provided by the perturbative bias expansion in the joint analysis of the two statistics, finding overall agreement with the data down to separations of 20 Mpc/h. Subsequently, we build on the state-of-the-art and extend the analysis to include the dependence on three cosmological parameters: the amplitude of scalar perturbations As, the matter density ωcdm and the Hubble parameter h. To achieve this goal, we develop an emulator capable of generating fast and robust modelling predictions for the two summary statistics, allowing efficient sampling of the joint likelihood function. We therefore present the first joint full-shape analysis of the real-space 2PCF and 3PCF, testing the consistency and constraining power of the perturbative model across both probes, and assessing its performance in a combined likelihood framework. We explore possible systematic uncertainties induced by the perturbative model at small scales finding an optimal scale cut of rmin = 30 Mpc/h for the 3PCF, when imposing an additional limitation on nearly isosceles triangular configurations included in the data vector. This work is part of a Euclid Preparation series validating theoretical models for galaxy clustering.

Spatially resolved stellar kinematics has become a key ingredient in time-delay cosmography to break the mass-sheet degeneracy in the mass profile and in turn provide a precise constraint on the Hubble constant and other cosmological parameters. In this paper, we present the first measurements of 2D resolved stellar kinematics for the lens galaxy in the quadruply lensed quasar system RXJ1131$-$1231 using integral field spectroscopy from JWST's Near-Infrared Spectrograph (NIRSpec), marking the first such measurement conducted with JWST. In extracting robust kinematic measurements from this first-of-its-kind dataset, we have made methodological improvements both in the data reduction and kinematic extraction. In our kinematic extraction procedure, we performed joint modeling of the lens galaxy, the quasar, and its host galaxy's contributions in the spectra to deblend the lens galaxy component and robustly constrain its stellar kinematics. Our improved methodological frameworks are released as software pipelines for future use: squirrel, for extracting stellar kinematics, and RegalJumper, for JWST-NIRSpec data reduction. We incorporated additional artifact cleaning beyond the standard JWST pipeline. We compared our measured stellar kinematics from the JWST NIRSpec with previously obtained ground-based measurements from the Keck Cosmic Web Imager integral field unit and find that the two datasets are statistically consistent at a $\sim$1.1$σ$ confidence level. Our measured kinematics will be used in a future study to improve the precision of the Hubble constant measurement.

Quantum signal processing (QSP) and quantum singular value transformation (QSVT), have emerged as unifying frameworks in the context of quantum algorithm design. These techniques allow to carry out efficient polynomial transformations of matrices block-encoded in unitaries, involving a single ancilla qubit. Recent efforts try to extend QSP to the multivariate setting (M-QSP), where multiple matrices are transformed simultaneously. However, this generalization faces problems not encountered in the univariate counterpart: in particular, the class of polynomials achievable by M-QSP seems hard to characterize. In this work we borrow tools from query complexity, namely the state conversion problem and the adversary bound: we first recast QSP as a state conversion problem over the Hilbert space of square-integrable functions. We then show that the adversary bound for a state conversion problem in this space precisely identifies all and only the QSP protocols in the univariate case. Motivated by this first result, we extend the formalism to several variables: the existence of a feasible solution to the adversary bound implies the existence of a M-QSP protocol, and the computation of a protocol of minimal space is reduced to a rank minimization problem involving the feasible solution space of the adversary bound.

Recurrent events often serve as key endpoints in clinical studies but may be prematurely truncated by terminal events such as death, creating selection bias and complicating causal inference. To address this challenge, we develop a Bayesian nonparametric framework to address potential selection bias due to truncation by death within the continuous-time principal stratification framework. We introduce causal estimands for recurrent events in the presence of a terminal event and derive a partial identification result for the estimand under a dual-frailty framework, enabling transparent sensitivity analysis for non-identifiable parameters. We then propose a flexible Bayesian nonparametric prior, the enriched dependent Dirichlet process, specifically designed for joint modeling of recurrent and terminal events, addressing a limitation where standard Dirichlet process priors create random partitions dominated by recurrent events, yielding poor predictive performance for terminal events. Simulations are carried out to show that our method has superior performance compared to existing methods. We apply the proposed new Bayesian nonparametric methods to infer the causal effect of a structured exercise program on rehospitalizations, which are subject to truncation by death.

The hot circumgalactic medium (CGM), probed by X-ray observations, plays a central role in understanding gas flows that drive a galaxy's evolution. While CGM properties have been widely studied, the influence of a galaxy's large-scale cosmic environment on the hot gas content remains less explored. We investigate how the large-scale cosmic web affects the X-ray surface brightness (XSB) profiles of galaxies in the context of cosmological simulations. We use our novel IllustrisTNG-based lightcone, spanning $0.03 \leq z \leq 0.3$, first developed in our previous work, and generate self-consistent mock X-ray observations, using intrinsic gas cell information. We apply the filament finder DisPerSE on the galaxy distributions to identify the cosmic filaments within the lightcone. We classify central galaxies into five distinct large-scale environment (LSE) categories: clusters and massive groups, cluster outskirts, filaments, filament-void transition regions, and voids/walls. We find that the X-ray surface brightness profiles (XSB) of central galaxies of dark matter halos in filaments with $M_{\rm 200m} >10^{12}\ M_\odot$ are X-ray brighter than those in voids and walls, with $20-45%$ deviations in the radial range of $\sim (0.3-0.5) R_{\rm 200m}$. We investigate the source of this enhancement and find that the filament galaxies show higher average gas densities, temperatures, and metallicities compared to voids/walls galaxies. Our results demonstrate that the impact of the large-scale cosmic environment is imprinted on the hot CGM's X-ray emission. Future theoretical work on studying the effect of assembly history, connectivity, and gas accretion on galaxies in filaments and voids would help to further our understanding of the impact of the environment on X-ray observations.

Within the deep gravitational potential of galaxy clusters lies the intracluster medium (ICM). At the first order, it is considered to be at hydrostatic equilibrium within the potential well. However, evidence is growing that the ICM dynamics is non-negligible, is mostly turbulent in origin, and provides a non-thermal pressure support to the equilibrium. In this work, we intend to characterise the properties of the velocity field in the ICM of a simulated replica of the Virgo cluster. We first study the 3D and projected properties of the ICM velocity field by computing its probability density functions (PDFs) and its statistical moments. We then estimate the non-thermal pressure fraction from an effective turbulent Mach number, including the velocity dispersion. We finally compute the velocity structure function (VSF) from projected maps of the sightline velocity. We first show that the components of the 3D velocity field and the projected quantities along equivalent sightlines are anisotropic and affected by the accretion of gas from filaments. Then, we compare the mean statistical moments of the 3D velocity field to the mean properties of a hundred random projections. We show, in particular, an almost linear relation between the standard deviation estimated from direct simulation outputs and sightline velocity dispersion projections, comparable to the line broadening of X-ray atomic lines. However, this linear relation does not hold between the direct simulation outputs and the standard deviation of the sightline velocity projections, comparable to the line shift of X-ray atomic lines. We find a non-thermal pressure fraction around $6\%$ within $R_{500}$ and $9\%$ within $R_{vir}$ from sightline velocity dispersion, which is in good agreement with direct simulation outputs. Finally, we show that the VSF might probe the Active Galactic Nuclei (AGN) feedback turbulent injection scale.

Finding the ground state of strongly-interacting fermionic systems is often the prerequisite for fully understanding both quantum chemistry and condensed matter systems. The Sachdev--Ye--Kitaev (SYK) model is a representative example of such a system; it is particularly interesting not only due to the existence of efficient quantum algorithms preparing approximations to the ground state such as Hastings--O'Donnell (STOC 2022), but also known no-go results for many classical ansatzes in preparing low-energy states. However, this quantum-classical separation is known to \emph{not} persist when the SYK model is sufficiently sparsified, i.e., when terms in the model are discarded with probability $1-p$, where $p=Θ(1/n^3)$ and $n$ is the system size. This raises the question of how robust the quantum and classical complexities of the SYK model are to sparsification. In this work we initiate the study of the sparse SYK model where $p \in [Θ(1/n^3),1]$ and show there indeed exists a certain robustness of sparsification. We prove that with high probability, Gaussian states achieve only a $Θ(1/\sqrt{n})$-factor approximation to the true ground state energy of sparse SYK for all $p\geqΩ(\log n/n^2)$, and that Gaussian states cannot achieve constant-factor approximations unless $p \leq O(\log^2 n/n^3)$. Additionally, we prove that the quantum algorithm of Hastings--O'Donnell still achieves a constant-factor approximation to the ground state energy when $p\geqΩ(\log n/n)$. Combined, these show a provable separation between classical algorithms outputting Gaussian states and efficient quantum algorithms for the goal of finding approximate sparse SYK ground states whenever $p \geq Ω(\log n/n)$, extending the analogous $p=1$ result of Hastings--O'Donnell.

ESA's Euclid cosmology mission relies on the very sensitive and accurately calibrated spectroscopy channel of the Near-Infrared Spectrometer and Photometer (NISP). With three operational grisms in two wavelength intervals, NISP provides diffraction-limited slitless spectroscopy over a field of $0.57$ deg$^2$. A blue grism $\text{BG}_\text{E}$ covers the wavelength range $926$--$1366$\,nm at a spectral resolution $R=440$--$900$ for a $0.5''$ diameter source with a dispersion of $1.24$ nm px$^{-1}$. Two red grisms $\text{RG}_\text{E}$ span $1206$ to $1892$\,nm at $R=550$--$740$ and a dispersion of $1.37$ nm px$^{-1}$. We describe the construction of the grisms as well as the ground testing of the flight model of the NISP instrument where these properties were established.

We present the Non-Relativistic QCD (NRQCD) calculations at the next-to-leading order (NLO) of $α_s$ for $B_c^*\to η_c$ vector, axial-vector, tensor and axial-tensor form factors, and obtain complete analytical expressions for the form factors, along with their asymptotic forms in the hierarchical heavy quark limit. Our results show that the NLO corrections are both sizable and well-behaved in the low squared transfer momentum $(q^2)$ region. Using the NRQCD + lattice + $z$-series method, we further provide theoretical predictions for $B_c^*\to η_c$ form factors across the full physical $q^2$ range. Based on these predicted form factors, we finally compute the decay widths and branching fractions for the semileptonic decays $B_c^*\to η_c+l{ν_l}$.

We study a nonlinear analogue of additive commutators, known as \textit{polynomial commutators}, defined by $p(ab) - p(ba)$ for a polynomial $p \in F[x]$ and elements $a, b$ in an algebra $R$ over a field $F$. Originally introduced by Laffey and West for matrices over fields, this notion is here extended to broader algebraic settings. We first show that in division rings, polynomial commutators can generate maximal subfields and even the entire ring as an algebra. In the matrix setting, we prove that matrices similar to ones with zero diagonal are polynomial commutators, and under mild assumptions, every matrix can be written as a product of at most three such commutators. Furthermore, we demonstrate that the matrix algebra can be decomposed as the sum of its center and the linear span of all polynomial commutators. Using the theory of rational identities in division rings, we also exhibit that the trace of a polynomial commutator in the matrix ring can be nonzero in noncommutative cases. Lastly, we explore the size of polynomial commutators via matrix norms.

The reionisation of the intergalactic medium (IGM) was driven by the first stars, galaxies, and accreting black holes. However, the relative importance of these sources and the efficiency by which ionising photons escape into the IGM remain poorly understood. Most reionisation modelling frameworks assume idealised, isotropic emissions. We investigate this assumption by examining a suite of simulations incorporating directed, anisotropic photon emissions. We find that such anisotropic emissions of ionising photons yield a different reionisation geometry compared to the standard, isotropic, case. During the early stages of reionisation (when less than 30 per cent of the Universe is ionised), simulations with narrow photon leakage channels produce smaller ionised bubbles on average. However, these bubbles grow to similar sizes during the middle stages of reionisation. This anisotropy not only produces a distinctive evolution of the size distribution of the ionised regions, but also imprints a feature onto the spherically averaged power spectra of the 21-cm signal throughout reionisation. We observe a suppression in power by about 10-40 per cent at scales corresponding to wavenumbers $k = 0.1-1 \, h \, \mathrm{Mpc}^{-1}$, corresponding to the range in which current radio interferometers are most likely to measure the power spectrum. The simulation with the narrowest channel of ionisation emission shows the strongest suppression. However, this anisotropic emission process does not introduce any measurable anisotropy in the 21-cm signal.

The spherical Jeans equation is commonly used to infer dark matter distributions in dwarf spheroidal satellites of the Milky Way to constrain the nature of dark matter. One of its assumptions is that of dynamical equilibrium while the dwarfs are under the influence of Galactic tides. We carry out tailored simulations of Carina, Draco, Fornax, Sculptor and Ursa Minor and test the accuracy of dark matter density profiles and annihilation rates (J-factors) recovered with the Jeans analysis code pyGravSphere. We find that tides do not significantly affect the quality of density profile inference; however, pyGravSphere tends to underestimate the inner densities of dwarf galaxies, which, together with tidal mass loss, leads to an inference of flatter density slopes, although all of our dwarfs have cuspy Navarro-Frenk-White haloes. This is because the default broken power-law model is unable to describe the outer halo density profile. The recovered J-factors are generally underestimated. While the difference with the true J-factor is small, the error bars are also often underestimated. We also test the accuracy of the Wolf et al. 2010 mass estimator and find that it can be sensitive to orbital stage and eccentricity. Still, for our sample of dwarf galaxies, the estimates agree with the truth within 10 percent. Consistency of our simulated dwarfs with the mass-concentration relation in LambdaCDM requires a light Milky Way, or limited action of tides, which may be in tension with a "tidal stirring" origin of dwarf spheroidals.