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.

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.

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.

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.

We study quasinormal modes of scalar, electromagnetic, and Dirac perturbations of four-dimensional regular black holes arising in non-polynomial quasi-topological gravity. Starting from a more general class of metric functions constructed within the same framework, from which two representative cases are selected for detailed analysis, we examine their spectral properties. While the fundamental mode changes smoothly with the regularization parameter, higher overtones display a markedly enhanced sensitivity to near-horizon modifications, leading to the characteristic outburst of overtones. Remarkably, pushing the WKB approximation to sufficiently high orders with Padé resummation already allows one to detect the onset of this effect. Time-domain analysis and the Leaver method confirm that the relative error of the higher-order WKB approach is much smaller than the observed effect. Our results indicate that overtone dynamics provides a sensitive probe of geometrically regular black holes and that high-order WKB methods remain capable of capturing nontrivial spectral features beyond the fundamental mode.