The oxi-inflammatory response is part of the natural process mobilizing leukocytes and satellite cells that contribute to clearance and regeneration of damaged muscle tissue. In sports medicine, a number of post-injury recovery strategies, such as whole-body cryotherapy (WBC), are used to improve skeletal muscle regeneration often without scientific evidence of their benefits. The study was designed to assess the impact of WBC on circulating mediators of skeletal muscle regeneration. Twenty elite athletes were randomized to WBC group (3-min exposure to −120 °C, twice a day for 7 days) and control group. Blood samples were collected before the first WBC session and 1 day after the last cryotherapy exposure. WBC did not affect the indirect markers of muscle damage but significantly reduced the generation of reactive oxygen and nitrogen species (H₂O₂ and NO) as well as the concentrations of serum interleukin 1β (IL-1β) and C-reactive protein (CRP). The changes in circulating growth factors, hepatocyte growth factor (HGF), insulin-like growth factor (IGF-1), platelet-derived growth factor (PDGF^BB), vascular endothelial growth factor (VEGF), and brain-derived neurotrophic factor (BDNF), were also reduced by WBC exposure. The study demonstrated that WBC attenuates the cascade of injury–repair–regeneration of skeletal muscles whereby it may delay skeletal muscle regeneration.

The performance of multivariate kernel density estimation (KDE) depends strongly on the choice of bandwidth matrix. The high computational cost required for its estimation provides a big motivation to develop fast and accurate methods. One of such methods is based on the Fast Fourier Transform. However, the currently available implementation works very well only for the univariate KDE and it's multivariate extension suffers from a very serious limitation as it can accurately operate only with diagonal bandwidth matrices. A more general solution is presented where the above mentioned limitation is relaxed. Moreover, the presented solution can by easily adopted also for the task of efficient computation of integrated density derivative functionals involving an arbitrary derivative order. Consequently, bandwidth selection for kernel density derivative estimation is also supported. The practical usability of the new solution is demonstrated by comprehensive numerical simulations.

The problem of fast computation of multivariate kernel density estimation (KDE) is still an open research problem. In our view, the existing solutions do not resolve this matter in a satisfactory way. One of the most elegant and efficient approach utilizes the fast Fourier transform. Unfortunately, the existing FFT-based solution suffers from a serious limitation, as it can accurately operate only with the constrained (i.e., diagonal) multivariate bandwidth matrices. In this paper we describe the problem and give a satisfactory solution. The proposed solution may be successfully used also in other research problems, for example for the fast computation of the optimal bandwidth for KDE.