The Russian invasion of Ukraine damaged or compromised astronomical facilities and has prompted the displacement of researchers. A plan to restore Ukrainian astronomy, rooted in a deeper integration with the international community, is now being developed.

Quantum computing promises exponential improvements in solving large systems of partial differential equations (PDE), which forms a bottleneck in high-resolution computational fluid dynamics (CFD) simulations, in, among others, aerospace applications and weather forecasting. One approach is via mapping classical CFD problems to a quantum Hamiltonian evolution, for which recently an explicit quantum circuit construction has been shown in simple cases, allowing proof-of-concept execution on quantum processors. Here we extended this method to more complex and practically relevant cases. We first demonstrate how boundary conditions corresponding to arbitrary complex-shaped obstacles can be introduced in the quantum representations of elementary difference operators used to implement the PDE. We provide explicit and efficient circuit constructions, and show they neither increase the Trotter error, nor asymptotic gate complexity with respect to the free space equation. Using these methods we then derive quantum circuits for simulating the linearized Euler equations in a presence of a background fluid flow and obstacles. We illustrate our results by simulating the obtained quantum circuits for a number of boundary conditions, and compare the errors of the quantum solution to classical finite difference methods.

Early interaction of supernova blast waves with CSM has the potential to accelerate particles to PeV energies, although this has not yet been detected. Current models for this interaction assume the shock expands into a smooth stellar wind, although observations of many SNe do not support this assumption. We extend previous work by considering shocks expanding into complex density profiles consisting of smooth winds with dense CSM shells at various distances from the progenitor star. We aim to predict the gamma-ray and multiwavelength signatures of CSM interaction. We used the PION code to model the CSM around LBV including a brief episode of enhanced mass-loss and to simulate the formation of photoionization-confined shells around RSGs. Consequently, we used the time-dependent acceleration-code RATPaC to study the acceleration of cosmic rays in SNe expanding into these media and to evaluate the emitted radiation across the whole electromagnetic spectrum. We find that the interaction with the CSM shells can significantly boost the gamma-ray emission, with the emission peaking weeks to years after the explosion. The peak luminosity for Type-IIP and Type-IIn remnants can exceed the luminosity expected for smooth winds by orders of magnitude. For Type-IIP explosions, the light-curve peak is only reached years after the explosion. We evaluate the multiwavelength signatures expected from the interaction of the blast wave with a dense CSM shell from radio, over optical, to thermal X-rays. We identify high-cadence optical surveys and continuous monitoring of nearby SN in radio and mm wavelengths as the best-suited strategies for identifying targets that should be followed-up by gamma-ray observatories. We predict that gamma-rays from interaction with dense CSM shells may be detectable out to a few Mpc for late interaction, and tens of Mpc for early interaction.

In this work, we study the use of logistic regression in manufacturing failures detection. As a data set for the analysis, we used the data from Kaggle competition Bosch Production Line Performance. We considered the use of machine learning, linear and Bayesian models. For machine learning approach, we analyzed XGBoost tree based classifier to obtain high scored classification. Using the generalized linear model for logistic regression makes it possible to analyze the influence of the factors under study. The Bayesian approach for logistic regression gives the statistical distribution for the parameters of the model. It can be useful in the probabilistic analysis, e.g. risk assessment.

The paper considers the possibility of fine-tuning Llama 2 large language model (LLM) for the disinformation analysis and fake news detection. For fine-tuning, the PEFT/LoRA based approach was used. In the study, the model was fine-tuned for the following tasks: analysing a text on revealing disinformation and propaganda narratives, fact checking, fake news detection, manipulation analytics, extracting named entities with their sentiments. The obtained results show that the fine-tuned Llama 2 model can perform a deep analysis of texts and reveal complex styles and narratives. Extracted sentiments for named entities can be considered as predictive features in supervised machine learning models.

This article considers the current problem of investigation and development of the method of web-members' socio-demographic characteristics' profile validation based on analysis of socio-demographic characteristics. The topicality of the paper is determined by the necessity to identify the web-community member by means of computer-linguistic analysis of their information track (all information about web-community members, which posted on the Internet). The formal model of basic socio-demographic characteristics of virtual communities' member is formed. The algorithm of these characteristics verification is developed.

Context. The youngest Galactic supernova remnant G1.9+0.3 is an interesting target for next generation gamma-ray observatories. So far, the remnant is only detected in the radio and the X-ray bands, but its young age of ~100 yrs and inferred shock speed of ~14,000 km/s could make it an efficient particle accelerator. Aims. We aim to model the observed radio and X-ray spectra together with the morphology of the remnant. At the same time, we aim to estimate the gamma-ray flux from the source and evaluated the prospects of its detection with future gamma-ray experiments. Methods. We performed spherical symmetric 1-D simulations with the RATPaC code, in which we simultaneously solve the transport equation for cosmic rays, the transport equation for magnetic turbulence, and the hydro-dynamical equations for the gas flow. Separately computed distributions of the particles accelerated at the forward and the reverse shock are then used to calculate the spectra of synchrotron, inverse Compton, and pion-decay radiation from the source. Results. The emission from G1.9+0.3 can be self-consistently explained within the test-particle limit. We find that the X-ray flux is dominated by emission from the forward shock while most of the radio emission originates near the reverse shock, which makes G1.9+0.3 the first remnant with non-thermal radiation detected from the reverse shock. The flux of very-high-energy gamma-ray emission from G1.9+0.3 is expected to be close to the sensitivity threshold of the Cherenkov Telescope Array, CTA. The limited time available to grow large-scale turbulence limits the maximum energy of particles to values below 100 TeV, hence G1.9+0.3 is not a PeVatron.

The maximum energy of electrons in supernova remnant (SNR) shocks is typically limited by radiative losses, where the synchrotron cooling time equals the acceleration time. The low speed of shocks in a dense medium increases the acceleration time, leading to lower maximum electron energies and fainter X-ray emissions. However, in Kepler's SNR, an enhanced electron acceleration, which proceeds close to the Bohm limit, occurs in the north of its shell, where the shock is slowed by a dense circumstellar medium (CSM). To investigate whether this scenario still holds at smaller scales, we analyzed the temporal evolution of the X-ray synchrotron flux in filamentary structures, using the two deepest Chandra/ACIS X-ray observations, performed in 2006 and 2014. We examined spectra from different filaments, we measured their proper motion and calculated the acceleration to synchrotron time-scale ratios. The interaction with the turbulent and dense northern CSM induces competing effects on electron acceleration: on one hand, turbulence reduces the electron mean free path enhancing the acceleration efficiency, on the other hand, lower shock velocities increase the acceleration time-scale. In most filaments, these effects compensate each other, but in one region the acceleration time-scale exceeds the synchrotron time-scale, resulting in a significant decrease in nonthermal X-ray emission from 2006 to 2014, indicating fading synchrotron emission. Our findings provide a coherent understanding of the different regimes of electron acceleration observed in Kepler's SNR through various diagnostics.

We investigate how primordial magnetic fields (PMFs) affect the formation kinetics of the first molecules, H$_2$, HD, and HeH$^+$, as well as the populations of rovibrational levels and the global signals in the rovibrational transitions of H$_2$ and HD. We show that PMFs can significantly speed up the formation and destruction of the first molecules, leading to an increase in the number density of H$_2$ and HD molecules and a decrease in the number density of HeH$^+$ ion-molecules compared to the case without PMFs. We demonstrate that more frequent collisions of the gas particles in such models alter the ortho-to-para ratio of hydrogen molecules, making it a potential probe of the thermal history of gas in the early Universe. In contrast to the standard cosmological model, where the global signal from the first molecules appears as an absorption feature in the cosmic microwave background spectrum, cosmological models with PMFs can produce an emission signal. Specifically, for non-helical PMFs with $n_B = -2.9$ and a strength of $\sim 1$~nG, the signal transforms into emission with an amplitude of about $\sim 0.5$~Jy/sr. This signal is comparable in magnitude to other known CMB spectral distortions and falls within the detection capabilities of several proposed missions, including Super-PIXIE, Multi-SIMBAD (4 units), and Voyage2050. We show that both the amplitude and the spectral range of the global signals from the first molecules are highly sensitive to the spectral index $n_B$, the strength $B_0$, and the helicity of the PMFs. Therefore, the global signals from the first molecules can serve as a potential probe of PMFs.

We present the results of Monte Carlo simulations for the critical dynamics of the three-dimensional site-diluted quenched Ising model. Three different dynamics are considered, these correspond to the local update Metropolis scheme as well as to the Swendsen-Wang and Wolff cluster algorithms. The lattice sizes of L=10-96 are analysed by a finite-size-scaling technique. The site dilution concentration p=0.85 was chosen to minimize the correction-to-scaling effects. We calculate numerical values of the dynamical critical exponents for the integrated and exponential autocorrelation times for energy and magnetization. As expected, cluster algorithms are characterized by lower values of dynamical critical exponent than the local one: also in the case of dilution critical slowing down is more pronounced for the Metropolis algorithm. However, the striking feature of our estimates is that they suggest that dilution leads to decrease of the dynamical critical exponent for the cluster algorithms. This phenomenon is quite opposite to the local dynamics, where dilution enhances critical slowing down.

We introduce a functor of functionals which preserve maximum of comonotone functions and addition of constants. This functor is a subfunctor of the functor of order-preserving functionals and contains the idempotent measure functor as subfunctor. The main aim of this paper is to show that this functor is isomorphic to the capacity functor. We establish such isomorphism using the fuzzy max-plus integral. In fact, we can consider this result as an idempotent analogue of Riesz Theorem about a correspondence between the set of $\sigma$-additive regular Borel measures and the set of linear positively defined functionals.

The formation of large voids in the Cosmic Web from the initial adiabatic cosmological perturbations of space-time metric, density and velocity of matter is investigated in cosmological model with the dynamical dark energy accelerating expansion of the Universe. It is shown that the negative density perturbations with the initial radius of about 50 Mpc in comoving to the cosmological background coordinates and the amplitude corresponding to the r.m.s. temperature fluctuations of the cosmic microwave background lead to the formation of voids with the density contrast up to $-$0.9, maximal peculiar velocity about 400 km/s and the radius close to the initial one. An important feature of voids formation from the analyzed initial amplitudes and profiles is establishing the surrounding overdensity shell. We have shown that the ratio of the peculiar velocity in units of the Hubble flow to the density contrast in the central part of a void does not depend or weakly depends on the distance from the center of the void. It is also shown that this ratio is sensitive to the values of dark energy parameters and can be used to find them based on the observational data on mass density and peculiar velocities of galaxies in the voids.

The three-dimensional velocity structure of the shock-heated Si-reach and S-reach ejecta were reconstructed in Tycho supernova remnant from Doppler-shifted lines. The vector components along the line of sight were restored from the spatially resolved spectral analysis of the Doppler shifts of Si XIII and S XV lines. The components in the plane of the sky were derived from analysis of the proper motion of the remnant's edge at different azimuths. This has been done by using the data of X-ray observations from Chandra observatory as well as the radio data from the Very Large Array. Differences in Doppler velocities over the Tycho's SNR are of the order of thousands of km/s. The speed of the ejecta on the opposite sides of the remnant as a three-dimensional object differs on 20-30%. There are asymmetries and differences in the spatial distributions between the Si-reach and S-reach ejecta components. Namely, the level of isotropy is higher in Si while the vector components directed outward of the observer are larger in S. This puts limitations on the level of deviation of the internal structure of the progenitor star from the ideal layered structure as well as on the level of asymmetries in supernova explosion.

We quantify the geometric measure of entanglement in terms of mean values of observables of entangled system. For pure states we find the relation of geometric measure of entanglement with the mean value of spin one-half for the system composed of spin and arbitrary quantum system. The geometric measure of entanglement for mixed states of rank-2 is studied as well. We find the explicit expression for geometric entanglement and the relation of entanglement in this case with the values of spin correlations. These results allow to find experimentally the value of entanglement by measuring a value of the mean spin and the spin correlations for pure and mixed states, respectively. The obtained results are applied for calculation of entanglement during the evolution in spin chain with Ising interaction , two-spin Ising model in transverse fluctuating magnetic field, Schr\"odinger cat in fluctuating magnetic field.

We consider the direct and inverse spectral problems for Dirac operators that are generated by the differential expressions $$ \mathfrak t_q:=\frac{1}{i}[I&0 0&-I]\frac{d}{dx}+[0&q q^*&0] $$ and some separated boundary conditions. Here $q$ is an $r\times r$ matrix-valued function with entries belonging to $L_2((0,1),\mathbb C)$ and $I$ is the identity $r\times r$ matrix. We give a complete description of the spectral data (eigenvalues and suitably introduced norming matrices) for the operators under consideration and suggest an algorithm of reconstructing the potential $q$ from the corresponding spectral data.

We have investigated the effect of changing two microscopic parameters in a cell model with Curie-Weiss-type interaction on its phase behavior, namely the cell volume and ratio between repulsion and attraction intensities. The results are based on an exact solution previously derived for this model in the grand canonical ensemble. At sufficiently low temperatures, the cell model exhibits multiple first-order phase transitions. Varying the cell volume and the repulsion-to-attraction ratio, we represent a quantitative comparison of the chemical potential and pressure isotherms, as well as the pressure-temperature and temperature-density phase diagrams. The analysis of provided data shows that altering microscopic parameters does not lead to qualitative changes in the overall phase behavior of the cell model.

In the paper, different approaches for the analysis of news trends on Twitter has been considered. For the analysis and case study, informational trends on Twitter caused by Russian invasion of Ukraine in 2022 year have been studied. A deep learning approach for fake news detection has been analyzed. The use of the theory of frequent itemsets and association rules, graph theory for news trends analytics have been considered.

The two-component mixture of Bose particles with short-range pairwise interaction at finite temperatures in three dimensions is considered. Particularly we examine, by means of the large-$N$ expansion technique, the stability of mixed state below the Bose-Einstein transition point and the temperature dependence of the condensate density for symmetric mixture of Bose gases. The presented analysis reveals the importance of finite-temperature excitations of the non-condensed particles in formation of the phase diagram of two-component Bose systems.