We construct a faithful representation of the semiring of all order-preserving decreasing transformations of a chain with $n+1$ elements by Boolean upper triangular $n\times n$-matrices.

The Weyl geometric gravity theory, in which the gravitational action is constructed from the square of the Weyl curvature scalar and the strength of the Weyl vector, has been intensively investigated recently. The theory admits a scalar-vector-tensor representation, obtained by introducing an auxiliary scalar field, and can therefore be reformulated as a scalar-vector-tensor theory in a Riemann space, in the presence of a nonminimal coupling between the Ricci scalar and the scalar field. By assuming that the Weyl vector has only a radial component, an exact spherically symmetric vacuum solution of the field equations can be obtained, which depends on three integration constants. As compared to the Schwarzschild solution, the Weyl geometric gravity solution contains two new terms, linear and quadratic in the radial coordinate, respectively. In the present work we consider the possibility of testing and obtaining observational restrictions on the Weyl geometric gravity black hole at the scale of the Solar System, by considering six classical tests of general relativity (gravitational redshift, the Eötvös parameter and the universality of free fall, the Nortvedt effect, the planetary perihelion precession, the deflection of light by a compact object, and the radar echo delay effect, respectively) for the exact spherically symmetric black hole solution of the Weyl geometric gravity. All these gravitational effects can be fully explained and are consistent with the vacuum solution of the Weyl geometric gravity. Moreover, the study of the classical general relativistic tests also allows to constrain the free parameter of the solution.

We consider the implications of the modified dispersion relations, due to the noncommutativity of the spacetime, for a photon gas filling the early Universe in the framework of the Big Bang Nucleosynthesis (BBN) processes, during the period of light elements formation. We consider three types of deformations present in the dispersion relations for the radiation gas, from which we obtain the low temperature corrections to the energy density and pressure. The cosmological implications of the modified equations of state in the BBN era are explored in detail for all radiation models. The effects induced on the nucleosynthesis process by spacetime noncommutativity are investigated by evaluating the abundances of relic nuclei (Hydrogen, Deuterium, Helium-3, Helium-4, and Lithium-7). The primordial mass fraction estimates and their deviations due to changes in the freezing temperature impose an upper limit on the energy density of the deformed photon gas, which follows from the modified Friedmann equations. The deviations from the standard energy density of the radiative plasma are therefore constrained by the abundances of the Helium-4 nuclei. Upper limits on the free parameters of the spacetime noncommutativity are obtained via a numerical analysis performed using the \texttt{PRyMordial} software package. The primordial abundances of the light elements are obtained by evaluating the thermonuclear reaction rates for the considered noncommutative spacetime models. An MCMC (Markov Chain Monte Carlo) analysis allows to obtain restrictions on the free parameters of the modified dispersion relations. The numerical and statistical approach is implemented in the python code \texttt{PRyNCe}, available on GitHub.

We present the serendipitous radio-continuum discovery of a likely Galactic supernova remnant (SNR) G305.4-2.2. This object displays a remarkable circular symmetry in shape, making it one of the most circular Galactic SNRs known. Nicknamed Teleios due to its symmetry, it was detected in the new Australian Square Kilometre Array Pathfinder (ASKAP) Evolutionary Map of the Universe (EMU) radio-continuum images with an angular size of 1320"x1260" and PA = 0 deg. While there is a hint of possible H$\alpha$ and gamma-ray emission, Teleios is exclusively seen at radio-continuum frequencies. Interestingly, Teleios is not only almost perfectly symmetric, but it also has one of the lowest surface brightnesses discovered among Galactic SNRs and a steep spectral index of $\alpha=-0.6\pm 0.3$. Our estimates from HI studies and the Sigma-D relation place Teleios as a type Ia SNR at a distance of either ~2.2 kpc of ~7.7 kpc. This indicates two possible scenarios, either a young (under 1000 yr) or an older SNR (over 10000 yr). With a corresponding diameter of 14/48 pc, our evolutionary studies place Teleios at the either early or late Sedov phase, depending on the distance estimate. However, our modelling also predicts X-ray emission, which we do not see in the present generation of eROSITA images. We also explored a type Iax explosion scenario that points to a much closer distance of <1 kpc and Teleios size of only ~3.3 pc, which would be similar to the only known type Iax remnant SN1181. Unfortunately, all examined scenarios have their challenges, and no definitive supernova (SN) origin type can be established at this stage. Teleios's symmetrical shape suggests expansion into a rarefied and isotropic ambient medium. The low radio surface brightness and the lack of pronounced polarisation can be explained by a high level of ambient rotation measure (RM), with the largest RM being observed at centre.

We report the results of a search for long-period ($100

We present ExoMiner++, an enhanced deep learning model that builds on the success of ExoMiner to improve transit signal classification in 2-minute TESS data. ExoMiner++ incorporates additional diagnostic inputs, including periodogram, flux trend, difference image, unfolded flux, and spacecraft attitude control data, all of which are crucial for effectively distinguishing transit signals from more challenging sources of false positives. To further enhance performance, we leverage multi-source training by combining high-quality labeled data from the Kepler space telescope with TESS data. This approach mitigates the impact of TESS's noisier and more ambiguous labels. ExoMiner++ achieves high accuracy across various classification and ranking metrics, significantly narrowing the search space for follow-up investigations to confirm new planets. To serve the exoplanet community, we introduce new TESS catalog containing ExoMiner++ classifications and confidence scores for each transit signal. Among the 147,568 unlabeled TCEs, ExoMiner++ identifies 7,330 as planet candidates, with the remainder classified as false positives. These 7,330 planet candidates correspond to 1,868 existing TESS Objects of Interest (TOIs), 69 Community TESS Objects of Interest (CTOIs), and 50 newly introduced CTOIs. 1,797 out of the 2,506 TOIs previously labeled as planet candidates in ExoFOP are classified as planet candidates by ExoMiner++. This reduction in plausible candidates combined with the excellent ranking quality of ExoMiner++ allows the follow-up efforts to be focused on the most likely candidates, increasing the overall planet yield.

We present results of the first investigations on the correlated nature of electronic states that cross the Fermi level in Pb$_9$Cu(PO$_4$)$_6$O aka LK-99 obtained within the DFT + DMFT approach. Coulomb correlations between Cu-$d$ electrons led to the opening of the band gap between the extra-O $p$ and Cu $d_{xz}/d_{yz}$ states. We state that oxygen $p$ states play a significant role in the electronic properties of LK-99. We also assume that doping with electrons is necessary to turn the stoichiometric Pb$_9$Cu(PO$_4$)$_6$O into conducting state.

Dust attenuation in galaxies has often been used as a proxy for the extinction of point sources, such as supernovae, even though this approach ignores fundamental differences between the two cases. We present an analysis of the impact of geometric effects and scattering within dusty media on recovered galaxy dust properties. We use SKIRT, a radiative transfer code, to simulate observations of point sources embedded in dust clouds, as well as spiral and elliptical galaxies. We examine various galaxy morphologies, inclinations, and instrument apertures. We find that in galaxies the scattering of light into the line of sight and the presence of sources at different depths within the galaxy make attenuation fundamentally different from extinction. For a medium with intrinsic extinction slope Rv=3.068, we recover effective attenuation slopes Rv_e ranging from 0.5 to 7, showing that the two quantities are not analogous, even for local resolved observations. We find that Rv_e greatly depends on dust density, galaxy morphology, and inclination, the latter being the most significant. A single simulated galaxy, viewed from different angles, can reproduce the well-known relation between attenuation strength Av_e and Rv_e observed for star-forming galaxy samples. An increase in dust density leads to higher Rv_e across all inclinations, which, assuming a correlation between stellar mass and dust density, explains the increase in Rv_e with mass observed in star-forming galaxies. However, we are unable to explain the differences in Rv_e between star-forming and quiescent high-mass galaxies. We conclude that highly attenuated regions of simulated face-on galaxies yield Rv_e within 10% of the intrinsic extinction slope of the medium, allowing for the distinction of different dust types. For edge-on spirals, however, the median Rv_e for low Av_e regions appears to better approximate the extinction slope.

We examine geodesics for scalar-tensor black holes in the Horndeski-Galileon non-minimal kinetic coupling framework. Our analysis shows that bound orbits may not be present within some model parameters range. Using the observational data we pose bounds on possible solution parameter values, as well as initial model parameters.

Astrometric microlensing events occur when a massive object passes between a distant source and the observer, causing a shift of the light centroid. The precise astrometric measurements of the Gaia mission provide an unprecedented opportunity to detect and analyze these events, revealing properties of lensing objects such as their mass and distance. We develop and test the Gaia Astrometric Microlensing Events (GAME) Filter, a software tool to identify astrometric microlensing events and derive lensing object properties. We generated mock Gaia observations for different magnitudes, number of Gaia visits, and events extending beyond Gaia's observational run. We applied GAME Filter to these datasets and validated its performance. We also assessed the rate of false positives where binary astrometric systems are misidentified as microlensing events. GAME Filter successfully recovers microlensing parameters for strong events. Parameters are more difficult to recover for short events and those extending beyond Gaia's run, where only a fraction of the events is observed. The astrometric effect breaks the degeneracy in the microlensing parallax present in photometric microlensing. For fainter sources, the observed signal weakens, reducing recovered events and increasing parameter errors. However, even for Gaia G-band magnitude 19, parameters can be recovered for Einstein radii above two mas. Observing regions with varying numbers of Gaia visits has minimal impact on filter accuracy when the number of visits exceeds 90. Additionally, even if the peak of a microlensing event lies outside Gaia's run, microlensing parameters can still be recovered. GAME Filter characterizes lenses with astrometry-only data for lens masses from approximately 1 to 20 solar masses and distances up to 6 kpc.

Machine-learned interatomic potentials (MLIPs) have become the gold standard for atomistic simulations, yet their extension to magnetic materials remains challenging because spin fluctuations must be captured either explicitly or implicitly. We address this problem for the technologically vital Fe-Cr-C system by constructing two deep machine learning potentials in DeePMD realization: one trained on non-magnetic DFT data (DP-NM) and one on spin-polarised DFT data (DP-M). Extensive validation against experiments reveals a striking dichotomy. The dynamic, collective properties, viscosity and melting temperatures are reproduced accurately by DP-NM but are incorrectly estimated by DP-M. Static, local properties, density, and lattice parameters are captured excellently by DP-M, especially in Fe-rich alloys, whereas DP-NM fails. This behaviour is explained by general properties of paramagnetic state: at high temperature, local magnetic moments self-average in space and time, so their explicit treatment is unnecessary for transport properties but essential for equilibrium volumes. Exploiting this insight, we show that a transfer-learning protocol, pre-training on non-magnetic DFT and fine-tuning on a small set of spin-polarised data, reduces the computational cost to develop magnetic MLIPs by more than an order of magnitude. Developing general-purpose potentials that capture static and dynamic behaviors throughout the whole composition space requires proper accounting for temperature-induced spin fluctuations in DFT calculations and correctly incorporating spin degrees of freedom into classical force fields.

The work considers a model of charged "semi-hard-core" bosons on a square lattice with a possible filling number at each node, ranging from 0 to 2. Temperature phase diagrams of the model are obtained using numerical Monte Carlo quantum simulation methods, and the influence of local charge correlations is examined. Comparison with results from mean-field methods shows that local charge correlations contribute to an increased role of quantum fluctuations in the formation of phase states.

With the surge in blockchain-based cryptocurrencies, illegal mining for cryptocurrency has become a popular cyberthreat. Host-based cryptojacking, where malicious actors exploit victims systems to mine cryptocurrency without their knowledge, is on the rise. Regular cryptojacking is relatively well-known and well-studied threat, however, recently attackers started switching to GPU cryptojacking, which promises greater profits due to high GPU hash rates and lower detection chance. Additionally, GPU cryptojackers can easily propagate using, for example, modified graphic card drivers. This article considers question of GPU cryptojacking detection. First, we discuss brief history and definition of GPU cryptojacking as well as previous attempts to design a detection technique for such threats. We also propose complex exposure mechanism based on GPU load by an application and graphic card RAM consumption, which can be used to detect both browser-based and host-based cryptojacking samples. Then we design a prototype decision tree detection program based on our technique. It was tested in a controlled virtual machine environment with 80% successful detection rate against selected set of GPU cryptojacking samples and 20% false positive rate against selected number of legitimate GPU-heavy applications.

In this paper we investigate a Yukawa gravity modification of the Newtonian gravitational potential in a weak field approximation. For that purpose we derived the corresponding equations of motion and used them to perform two-body simulations of the stellar orbits. In 2020 the GRAVITY Collaboration detected the orbital precession of the S2 star around the supermassive black hole (SMBH) at the Galactic Center (GC) and showed that it is close to the general relativity (GR) prediction. Using this observational fact, we evaluated parameters of the Yukawa gravity (the range of Yukawa interaction $\Lambda$ and universal constant $\delta$) with the Schwarzschild precession of the S-stars assuming that the observed values as indicated by the GRAVITY Collaboration will have a small deviation from GR prediction. GR provides the most natural way to fit observational data for S-star orbits, however, their precessions can be fitted by Yukawa gravity. Our main goal was to study the possible influence of the strength of Yukawa interaction, i.e. the universal constant $\delta$, on the precessions of S-star orbits. We analyze S-star orbits assuming different strength of Yukawa interaction $\delta$ and find that this parameter has strong influence on range of Yukawa interaction $\Lambda$. For that purpose we use PPN equations of motion in order to calculate the simulated orbits of S-stars in GR and Yukawa gravity. Using MCMC simulations we obtain the best-fit values and uncertainties of Yukawa gravity parameters for S-stars. Also, we introduce a new criterion which can be used for classification of gravitational systems in this type of gravity, according to their scales. We demonstrated that performed analysis of the observed S-stars orbits around the GC in the frame of the Yukawa gravity represent a tool for constraining the Yukawa gravity parameters and probing the predictions of gravity theories.

The results of numerical simulation using a modified Monte Carlo method with a heat bath algorithm for the pseudospin model of cuprates are presented. The temperature phase diagrams are constructed for various degrees of doping and for various parameters of the model, and the effect of local correlations on the critical temperatures of the model cuprate is investigated. It is shown that, in qualitative agreement with the results of the mean field, the heat bath algorithm leads to a significant decrease in the estimate of critical temperatures due to more complete accounting of fluctuations, and also makes it possible to detect phase inhomogeneous states. The possibility of using machine learning to accelerate the heat bath algorithm is discussed.

We conducted observations of multiple HC3N (J = 10-9, 12-11, and 16-15) lines and the N2H+ (J = 1-0) line toward a large sample of 61 ultracompact (UC) H II regions, through the Institutde Radioastronomie Millmetrique 30 m and the Arizona Radio Observatory 12 m telescopes. The N2H+ J = 1-0 line is detected in 60 sources and HC3N is detected in 59 sources, including 40 sources with three lines, 9 sources with two lines, and 10 sources with one line. Using the rotational diagram, the rotational temperature and column density of HC3N were estimated toward sources with at least two HC3N lines. For 10 sources with only one HC3N line, their parameters were estimated, taking one average value of Trot. For N2H+, we estimated the optical depth of the N2H+ J = 1-0 line, based on the line intensity ratio of its hyperfine structure lines. Then the excitation temperature and column density were calculated. When combining our results in UC H II regions and previous observation results on high-mass starless cores and high-mass protostellar cores, the N(HC3N)/N(N2H+) ratio clearly increases from the region stage. This means that the abundance ratio changes with the evolution of high-mass star-forming regions (HMSFRs). Moreover, positive correlations between the ratio and other evolutionary indicators (dust temperature, bolometric luminosity, and luminosity-to-mass ratio) are found. Thus we propose the ratio of N(HC3N)/N(N2H+) as a reliable chemical clock of HMSFRs.

In this paper, we present NEREL, a Russian dataset for named entity recognition and relation extraction. NEREL is significantly larger than existing Russian datasets: to date it contains 56K annotated named entities and 39K annotated relations. Its important difference from previous datasets is annotation of nested named entities, as well as relations within nested entities and at the discourse level. NEREL can facilitate development of novel models that can extract relations between nested named entities, as well as relations on both sentence and document levels. NEREL also contains the annotation of events involving named entities and their roles in the events. The NEREL collection is available via this https URL

The weighted ancestor problem is a well-known generalization of the predecessor problem to trees. It is known to require $\Omega(\log\log n)$ time for queries provided $O(n\mathop{\mathrm{polylog}} n)$ space is available and weights are from $[0..n]$, where $n$ is the number of tree nodes. However, when applied to suffix trees, the problem, surprisingly, admits an $O(n)$-space solution with constant query time, as was shown by Gawrychowski, Lewenstein, and Nicholson (Proc. ESA 2014). This variant of the problem can be reformulated as follows: given the suffix tree of a string $s$, we need a data structure that can locate in the tree any substring $s[p..q]$ of $s$ in $O(1)$ time (as if one descended from the root reading $s[p..q]$ along the way). Unfortunately, the data structure of Gawrychowski et al. has no efficient construction algorithm, limiting its wider usage as an algorithmic tool. In this paper we resolve this issue, describing a data structure for weighted ancestors in suffix trees with constant query time and a linear construction algorithm. Our solution is based on a novel approach using so-called irreducible LCP values.

The transformer architecture has become an integral part of the field of modern neural networks, playing a crucial role in a variety of tasks, such as text generation, machine translation, image and audio processing, among others. There is also an alternative approach to building intelligent systems, proposed by Jeff Hawkins and inspired by the processes occurring in the neocortex. In our article we want to combine some of these ideas and to propose the use of homeostasis mechanisms, such as RFB-kWTA and "Smart" Inhibition, in the attention mechanism of the transformer and at the output of the transformer block, as well as conducting an experiment involving the introduction of sparse distributed representations of the transformer at various points. RFB-kWTA utilizes statistics of layer activations across time to adjust the entire layer, enhancing the values of rare activations while reducing those of frequent ones. "Smart" Inhibition also uses activation statistics to sample sparsity masks, with rarer activation times are more likely to be activated. Our proposed mechanisms significantly outperform the classical transformer 0.2768 BLEU and a model that only makes use of dropout in the attention mechanism and output of the transformer block 0.3007 BLEU, achieving a score of 0.3062 on the Multi30K dataset.

By taking into account relativistic corrections to the magnetic dipole operator, the theoretical [OIII] 5006.843/4958.511 line intensity ratio of 2.98 is obtained. In order to check this new value using AGN spectra we present the measurements of the flux ratio of the [OIII] 4959,5007 emission lines for a sample of 62 AGN, obtained from the Sloan Digital Sky Survey (SDSS) Database and from published observations. We select only high signal-to-noise ratio spectra for which the line shapes of the [OIII] 4959,5007 lines are the same. We obtained an averaged flux ratio of 2.993 +/- 0.014, which is in a good agreement with the theoretical one.