Silesian University (Opava)

Recurrence quantification analysis is a powerful tool for identifying and quantifying patterns in dynamical systems, widely used across many disciplines. The rapid growth of data in these fields demands more efficient techniques for analysis. We present AccRQA, a high-performance library available in Python, R, and C/C++, which utilizes novel, scalable, and portable parallel algorithms. AccRQA is parallelized using OpenMP and can leverage NVIDIA GPUs when available, providing portability across computational platforms (CPUs, GPUs) and user environments (PC, HPC), thus offering flexibility between exploration and systematic mapping of a vast parameter space. AccRQA supports long time series and efficient computations for different embedding dimensions m and delay τ with minimal memory requirements. We also present performance benchmarks demonstrating an average 10 × speed-up and at least a 6 × speed-up compared to state-of-the-art RQA packages on both CPUs and GPUs.

The aim of this paper is to determine the optimal advertising strategies for different grids of newly introduced transformed nine-quadrants concept of Foote, Cone and Belding (FCB) model. The author's findings from prior studies on the FCB model, within the context of current conditions in Czechia, suggest that adapting the traditional FCB model is essential. Primary data for this study was gathered through an online questionnaire conducted by the Ipsos research agency, with responses from 1,050 participants from Czechia. The research utilized a modified FCB grid (based on previous studies), positional mapping, and chi-square testing with a post-hoc analysis. The authors propose four major advertisement strategies that are coupled with their corresponding representative product categories. The preference of various media types, emotional and rational appeals, and advertising frequency is discussed for sample identifiers-gender, age, and education. The age group 56-65 years and consumers with university education show the most polarized results in their advertising preferences. Despite the fact that the FCB model is well known, it is rarely applied in scientific research and practical use. Authors' scientific outputs point to this fact and present transformed FCB model.

We construct exact black hole solutions free of curvature singularities, sourced by dark matter halos described by galactic density profiles. Regularity of the geometry is ensured by adopting the relation \(P_{r} = {- \rho}\) between radial pressure and density, which is consistent with the phenomenological freedom of halo models. In particular, the sufficiently dense Einasto and Dehnen-type profiles for the dark matter halo can produce asymptotically flat solutions of singularity-free black holes embedded in the galactic environment. The resulting regular black holes surrounded by dark matter are shown to be stable under axial perturbations. We further compute the shadow radii and Lyapunov exponents associated with the photon circular orbits around these black holes.

We review current challenges in understanding the values and origins of the spins of black holes in binaries. Thanks to recent advances in astrophysical instrumentation, the spins can now be measured using both gravitational waves emitted by merging black holes and electromagnetic radiation from accreting X-ray binaries containing black holes. A key finding of the gravitational-wave observatories is that premerger black holes in binaries have low spin values, with an average dimensionless spin parameter of a* ∼ 0.1–0.2, with 90% having a* ≲ 0.6. This implies that the natal spins of black holes are generally low, and the angular momentum transport in massive stars is efficient. On the other hand, most of the published spins in X-ray binaries are very high, a* ≳ 0.7. In particular, this is the case for binaries with high-mass donors (potential progenitors of mergers), where their published spins range from 0.8 to 1.0. At the same time, their short lifetimes prevent significant spin-up by accretion. Those with low-mass donors could be spun-up to a* ≳ 0.5 by conservative accretion. Spins a* ≳ 0.7 can be achieved only if the donor initial masses were more than several solar masses, which remains unproven. However, the existing methods of spin measurements suffer from significant systematic errors. The method relying on relativistic X-ray line broadening is based on the separation of the observed spectra into incident and reflected ones, which is intrinsically highly uncertain. The method relying on spectral fitting of accretion disk continua uses models that predict the disk to be highly unstable, while stability is observed. Improved stable models yield disk temperatures higher than the standard models, and consequently predict lower spins. The published spin measurements in X-ray binaries are uncertain. The spins of the binaries with high-mass donors may be low, while those with low-mass donors have a broader spin distribution, ranging from low to high, including high spins as required to power relativistic jets.

In most scenarios studied so far, the appearance of echoes in the ringdown signal requires modifications external to the black hole itself, such as the presence of matter in the near-horizon region, quantum field clouds, or exotic compact objects like wormholes that effectively introduce additional peaks in the effective potential. In this work we show that echoes can naturally arise in a different setting: black holes endowed with primary Proca-Gauss-Bonnet hair. We demonstrate that the primary hair modifies the effective potential in such a way that a second peak is formed, giving rise to late-time echoes without invoking any external environment or exotic horizon-scale physics. Using both the higher-order WKB method with Padé resummation and time-domain integration, we compute the quasinormal spectrum for scalar and Dirac test fields and show the appearance of these echoes. Our results highlight a novel mechanism by which primary hairs alone can leave observable imprints on the ringdown signal of black holes in modified gravity.