Mapping the local and distant Universe is key to our understanding of it. For decades, the Sloan Digital Sky Survey (SDSS) has made a concerted effort to map millions of celestial objects to constrain the physical processes that govern our Universe. The most recent and fifth generation of SDSS (SDSS-V) is organized into three scientific ``mappers". Milky Way Mapper (MWM) that aims to chart the various components of the Milky Way and constrain its formation and assembly, Black Hole Mapper (BHM), which focuses on understanding supermassive black holes in distant galaxies across the Universe, and Local Volume Mapper (LVM), which uses integral field spectroscopy to map the ionized interstellar medium in the local group. This paper describes and outlines the scope and content for the nineteenth data release (DR19) of SDSS and the most substantial to date in SDSS-V. DR19 is the first to contain data from all three mappers. Additionally, we also describe nine value added catalogs (VACs) that enhance the science that can be conducted with the SDSS-V data. Finally, we discuss how to access SDSS DR19 and provide illustrative examples and tutorials.

The dynamical low-rank approximation of time-dependent matrices is a low-rank factorization updating technique. It leads to differential equations for factors of the matrices, which need to be solved numerically. We propose and analyze a fully ex- plicit, computationally inexpensive integrator that is based on splitting the orthogonal projector onto the tangent space of the low-rank manifold. As is shown by theory and illustrated by numerical experiments, the integrator enjoys robustness properties that are not shared by any standard numerical integrator. This robustness can be exploited to change the rank adaptively. Another application is in optimization algorithms for low-rank matrices where truncation back to the given low rank can be done efficiently by applying a step of the integrator proposed here.

We address the problem of solving strongly convex and smooth minimization problems using stochastic gradient descent (SGD) algorithm with a constant step size. Previous works suggested to combine the Polyak-Ruppert averaging procedure with the Richardson-Romberg extrapolation to reduce the asymptotic bias of SGD at the expense of a mild increase of the variance. We significantly extend previous results by providing an expansion of the mean-squared error of the resulting estimator with respect to the number of iterations $n$. We show that the root mean-squared error can be decomposed into the sum of two terms: a leading one of order $\mathcal{O}(n^{-1/2})$ with explicit dependence on a minimax-optimal asymptotic covariance matrix, and a second-order term of order $\mathcal{O}(n^{-3/4})$, where the power $3/4$ is best known. We also extend this result to the higher-order moment bounds. Our analysis relies on the properties of the SGD iterates viewed as a time-homogeneous Markov chain. In particular, we establish that this chain is geometrically ergodic with respect to a suitably defined weighted Wasserstein semimetric.

In this paper, I apply linguistic methods of analysis to non-linguistic data, chess plays, metaphorically equating one with the other and seeking analogies. Chess game notations are also a kind of text, and one can consider the records of moves or positions of pieces as words and statements in a certain language. In this article I show how word embeddings (word2vec) can work on chess game texts instead of natural language texts. I don't see how this representation of chess data can be used productively. It's unlikely that these vector models will help engines or people choose the best move. But in a purely academic sense, it's clear that such methods of information representation capture something important about the very nature of the game, which doesn't necessarily lead to a win.

The stylo package includes a frequency table that can be used to calculate distances between texts and thus independently solve the problem of attribution of The Cuckoo's Calling, a novel that J.K. Rowling said she wrote. However, the set of texts for this table is very vulnerable to criticism. The authors there are not modern, they wrote in a different genre. I set out to test the performance of the method on texts that are more relevant to the research question.

Decision-making, motion planning, and trajectory prediction are crucial in autonomous driving systems. By accurately forecasting the movements of other road users, the decision-making capabilities of the autonomous system can be enhanced, making it more effective in responding to dynamic and unpredictable environments and more adaptive to diverse road scenarios. This paper presents the FFStreams++ approach for decision-making and motion planning of different maneuvers, including unprotected left turn, overtaking, and keep-lane. FFStreams++ is a combination of sampling-based and search-based approaches, where iteratively new sampled trajectories for different maneuvers are generated and optimized, and afterward, a heuristic search planner is called, searching for an optimal plan. We model the autonomous diving system in the Planning Domain Definition Language (PDDL) and search for the optimal plan using a heuristic Fast-Forward planner. In this approach, the initial state of the problem is modified iteratively through streams, which will generate maneuver-specific trajectory candidates, increasing the iterating level until an optimal plan is found. FFStreams++ integrates a query-connected network model for predicting possible future trajectories for each surrounding obstacle along with their probabilities. The proposed approach was tested on the CommonRoad simulation framework. We use a collection of randomly generated driving scenarios for overtaking and unprotected left turns at intersections to evaluate the FFStreams++ planner. The test results confirmed that the proposed approach can effectively execute various maneuvers to ensure safety and reduce the risk of collisions with nearby traffic agents.

Temperature of the hot gas in galaxy clusters is known to be a reliable proxy for their total gravitating mass, allowing one to use spectroscopic X-ray observations for halo mass function measurements. Data of shallow wide area surveys, however, often precludes direct fitting of the X-ray spectra, given possible biases arising due to unresolved (multi-temperature) inner structure of the intracluster medium (ICM), projection effects and necessity of certain model assumptions to be made to allow for robust spectral fitting. We consider using a simple observable value - the average energy of the observed cluster X-ray spectrum - as a model-independent proxy for the ICM temperature, and consequently cluster's mass. We calibrate relation of this proxy to the cluster parameters using mock observations for a sample of 84 massive galaxy clusters extracted from the \textit{Magneticum} cosmological hydro simulations. We consider observational parameters corresponding to the all-sky survey observations by \textit{SRG/eROSITA}. Taking into account contributions of various background and foreground signals, average energy of the simulated X-ray spectra in the $0.4-7.0$ keV band is shown to be a stable indicator of the ICM temperature with $\sim10\%$ scatter and cluster's mass $M_{500}$ with a $\sim 20\%$ scatter. A database containing simulated X-ray images and their spectra (subtracted in several concentric rings) is publicly available.

Burrows' Delta was introduced in 2002 and has proven to be an effective tool for author attribution. Despite the fact that these are different languages, they mostly belong to the same grammatical type and use the same graphic principle to convey speech in writing: a phonemic alphabet with word separation using spaces. The question I want to address in this article is how well this attribution method works with texts in a language with a different grammatical structure and a script based on different principles. There are fewer studies analyzing the effectiveness of the Delta method on Chinese texts than on texts in European languages. I believe that such a low level of attention to Delta from sinologists is due to the structure of the scientific field dedicated to medieval Chinese poetry. Clustering based on intertextual distances worked flawlessly. Delta produced results where clustering showed that the samples of one author were most similar to each other, and Delta never confused different poets. Despite the fact that I used an unconventional approach and applied the Delta method to a language poorly suited for it, the method demonstrated its effectiveness. Tang dynasty poets are correctly identified using Delta, and the empirical pattern observed for authors writing in European standard languages has been confirmed once again.

In this paper, we present extended gas kinematic maps of the Perseus cluster by combining five new XRISM/Resolve pointings observed in 2025 with four Performance Verification datasets from 2024, totaling 745 ks net exposure. To date, Perseus remains the only cluster that has been extensively mapped out to ~0.7$r_{2500}$ by XRISM/Resolve, while simultaneously offering sufficient spatial resolution to resolve gaseous substructures driven by mergers and AGN feedback. Our observations cover multiple radial directions and a broad dynamical range, enabling us to characterize the intracluster medium kinematics up to the scale of ~500 kpc. In the measurements, we detect high velocity dispersions ($\simeq$300 km/s) in the eastern region of the cluster, corresponding to a nonthermal pressure fraction of $\simeq$7-13%. The velocity field outside the AGN-dominant region can be effectively described by a single, large-scale kinematic driver based on the velocity structure function, which statistically favors an energy injection scale of at least a few hundred kpc. The estimated turbulent dissipation energy is comparable to the gravitational potential energy released by a recent merger, implying a significant role of turbulent cascade in the merger energy conversion. In the bulk velocity field, we observe a dipole-like pattern along the east-west direction with an amplitude of $\simeq\pm$200-300 km/s, indicating rotational motions induced by the recent merger event. This feature constrains the viewing direction to ~30$^\circ$-50$^\circ$ relative to the normal of the merger plane. Our hydrodynamic simulations suggest that Perseus has experienced at least two energetic mergers since redshift z~1, the latest associated with the radio galaxy IC310. This study showcases exciting scientific opportunities for future missions with high-resolution spectroscopic capabilities (e.g., HUBS, LEM, and NewAthena).

Relativistic leptons in galaxy clusters lose their energy via radiation (synchrotron and inverse Compton losses) and interactions with the ambient plasma. At z~0, pure radiative losses limit the lifetime of electrons emitting at ~GHz frequencies to t<100 Myr. Adiabatic losses can further lower Lorentz factors of electrons trapped in an expanding medium. If the propagation speed of electrons relative to the ambient weakly magnetized (plasma $\beta\sim10^2$) Intracluster Medium (ICM) is limited by the Alfvén speed, $v_{a,ICM}=c_{s,ICM}/\beta^{1/2}\sim 10^7\,{\rm cm\,s^{-1}}$, GHz-emitting electrons can travel only $l \sim v_{a,ICM}t_r\sim 10\,kpc$ relative to the underlying plasma. Yet, elongated structures spanning hundreds of kpc or even a few Mpc are observed, requiring either a re-acceleration mechanism or another form of synchronization, e.g., by a large-scale shock. We argue that filaments with ordered magnetic fields supported by non-thermal pressure have $v_{a}\gg v_{a,{\rm ICM}}$ and so can provide such a synchronization even without re-acceleration or shocks. In particular, along quasi-stationary filaments, electrons can propagate without experiencing adiabatic losses, and their velocity is not limited by the Alfvén or sound speeds of the ambient thermal plasma. This model predicts that along filaments that span significant pressure gradients, e.g., in the cores of galaxy clusters, the synchrotron break frequency $\nu_b\propto B$ should scale with the ambient gas pressure as $P^{1/2}$, and the emission from such filaments should be strongly polarized. While some of these structures can be observed as "filaments", i.e., long and narrow bright structures, others can be unresolved and have a collective appearance of a diffuse structure, or be too faint to be detected, while still providing channels for electrons' propagation.

Mass currents in astrophysics generate gravitomagnetic fields of enormous complexity. Gravitomagnetic helicity, in direct analogy with magnetic helicity, is a measure of entwining of the gravitomagnetic field lines. We discuss gravitomagnetic helicity within the gravitoelectromagnetic (GEM) framework of linearized general relativity. Furthermore, we employ the spacetime curvature approach to GEM in order to determine the gravitomagnetic helicity for static observers in Kerr spacetime.

The discovery of the most metal-poor stream, C-19, provides us with a fossil record of a stellar structure born very soon after the Big Bang. In this work, we search for new C-19 members over the whole sky by combining two complementary stream-searching algorithms, STREAMFINDER and StarGO,, and utilizing low-metallicity star samples from the Pristine survey as well as Gaia BP/RP spectro-photometric catalogues. We confirm twelve new members, spread over more than 100$^\circ$, using velocity and metallicity information from a set of spectroscopic follow-up programs that targeted a quasi-complete sample of our bright candidates ($G \lesssim 16.0$). From the updated set of stream members, we confirm that the stream is wide, with a stream width of $\sim200$ pc, and dynamically hot, with a derived velocity dispersion of $10.9^{+2.1}_{-1.5}$ km/s. The tension remains between these quantities and a purely baryonic scenario in which the relatively low-mass stream (even updated to a few $10^4M_{\odot}$) stems from a globular cluster progenitor, as suggested by its chemical abundances. Some heating mechanism, such as preheating of the cluster in its own dark matter halo or through interactions with halo sub-structures appears necessary to explain the tension. The impact of binaries on the measured dispersion also remains unknown. Detailed elemental abundances of more stream members as well as multi-epoch radial velocities from spectroscopic observations are therefore crucial to fully understand the nature and past history of the most metal-poor stream of the Milky Way.

The C-19 stream is the most metal poor stellar system ever discovered, with a mean metallicity $[Fe/H] = -3.38\pm0.06$. Its low metallicity dispersion ($\sigma_{\rm [Fe/H]}$ &lt; 0.18 at the 95\% confidence level) as well as variations in sodium abundances strongly suggest a globular cluster origin. In this work, we use VLT/UVES spectra of seven C-19 stars to derive more precise velocity measurements for member stars, and to identify two new members with radial velocities and metallicities consistent with the stream's properties. One of these new member stars is located 30 $\deg$ away from the previously identified body of C-19, implying that the stream is significantly more extended than previously known and that more members likely await discovery. In the main part of C-19, we measure a radial velocity dispersion $\sigma_v$ = 6.2$^{+2.0}_{-1.4}$ km s$^{-1}$ from nine members, and a stream width of 0.56$\deg\pm0.08\deg$, equivalent to $\sim$158 pc at a heliocentric distance of 18 kpc. These confirm that C-19 is comparatively hotter, dynamically, than other known globular cluster streams and shares the properties of faint dwarf galaxy streams. On the other hand, the variations in the Na abundances of the three newly observed bright member stars, the variations in Mg and Al for two of them, and the normal Ba abundance of the one star where it can be measured provide further evidence for a globular cluster origin. The tension between the dynamical and chemical properties of C-19 suggests that its progenitor experienced a complex birth environment or disruption history.

When a polarized light beam is incident upon the surface of a magnetic material, the reflected light undergoes a polarization rotation. This magneto-optical Kerr effect (MOKE) has been intensively studied in a variety of ferro- and ferrimagnetic materials because it provides a powerful probe for electronic and magnetic properties as well as for various applications including magneto-optical recording. Recently, there has been a surge of interest in antiferromagnets (AFMs) as prospective spintronic materials for high-density and ultrafast memory devices, owing to their vanishingly small stray field and orders of magnitude faster spin dynamics compared to their ferromagnetic counterparts. In fact, the MOKE has proven useful for the study and application of the antiferromagnetic (AF) state. Although limited to insulators, certain types of AFMs are known to exhibit a large MOKE, as they are weak ferromagnets due to canting of the otherwise collinear spin structure. Here we report the first observation of a large MOKE signal in an AF metal at room temperature. In particular, we find that despite a vanishingly small magnetization of $M \sim$0.002 $\mu_{\rm B}$/Mn, the non-collinear AF metal Mn$_3$Sn exhibits a large zero-field MOKE with a polar Kerr rotation angle of 20 milli-degrees, comparable to ferromagnetic metals. Our first-principles calculations have clarified that ferroic ordering of magnetic octupoles in the non-collinear Neel state may cause a large MOKE even in its fully compensated AF state without spin magnetization. This large MOKE further allows imaging of the magnetic octupole domains and their reversal induced by magnetic field. The observation of a large MOKE in an AF metal should open new avenues for the study of domain dynamics as well as spintronics using AFMs.

The ability of our semi-empirical irregular dipole-moment functions (2022) and (2025) to predict the intensities of the yet unobserved lines, as well as to describe the observed ones not used in the fitting, is demonstrated by comparison with recent measurements in the 0-0, 1-0, 3-0, and 7-0 bands.

We report the discovery of X-ray polarization from the X-ray-bright filament. G0.13-0.11 in the Galactic center (GC) region. This filament features a bright, hard X-ray source that is most plausibly a pulsar wind nebula (PWN) and an extended and structured diffuse component. Combining the polarization signal from IXPE with the imaging/spectroscopic data from Chandra, we find that X-ray emission of G0.13-0.11 is highly polarized PD=$57(\pm18)$% in the 3-6 keV band, while the polarization angle is PA=$21^\circ(\pm9^\circ)$. This high degree of polarization proves the synchrotron origin of the X-ray emission from G0.13-0.11. In turn, the measured polarization angle implies that the X-ray emission is polarized approximately perpendicular to a sequence of nonthermal radio filaments that may be part of the GC Radio Arc. The magnetic field on the order of $100\,{\rm\mu G}$ appears to be preferentially ordered along the filaments. The above field strength is the fiducial value that makes our model self-consistent, while the other conclusions are largely model independent.

This is a collection of open problems in group theory proposed by hundreds of mathematicians from all over the world. It has been published every 2--4 years since 1965. This is the 20th edition, which contains 126 new problems and a number of comments on problems from the previous editions.

The W50 nebula around microquasar SS~433, powered by supercritical accretion, features two `extended jets' (tens of pc long and a few pc wide) from which polarized X-ray and very high energy radiation above 100 TeV is detected. Here we present a model of very high energy particle acceleration in these extended jets. In the `minimalist' model (discussed in Churazov, Khabibullin, and Bykov, 2024), a collimated outflow aligned with the rotation axis is propagating through a more isotropic wind produced by the accretion disk. The observed extended X-ray jets with bright knots in this model are associated with the formation of strong recollimation MHD shocks after the collision of the collimated outflow with the isotropic wind termination surface. The spectra of electrons and protons up to PeV energies are simulated with a nonlinear Monte Carlo model of diffusive shock acceleration with turbulent magnetic field amplification. The overall efficiency of the jets power transfer to accelerated protons in this model is above 10\% and about 0.5\% for electrons above 50 TeV. The magnetic field amplification by Bell's instability due to the electric current of cosmic rays escaping the accelerator produces highly anisotropic magnetic turbulence in the shock downstream. This results in the polarized synchrotron X-ray emission with the photon electric vector predominantly transverse to the jet direction and the degree of polarization above 20\%. The model is able to reproduce the observed spectra and intensity profiles of non-thermal X-ray and gamma-ray emission, which are both dominated by the leptonic radiation.

The logarithmically enhanced alpha^7 ln(1/alpha) contribution to the hyperfine splitting of the positronium ground-state energy levels is calculated in the framework of dimensionally regularized nonrelativistic quantum electrodynamics. The correction is negative and amounts to about 1/3 of the leading logarithmic alpha^7 ln^2(1/alpha) one. The discrepancy between the experimental measurements and the theoretical prediction is reduced.