A note on quasi-similarity of Koopman operators

Answering a question of A. Vershik we construct two non-weakly isomorphic ergodic automorphisms for which the associated unitary (Koopman) representations are Markov quasi-similar. We also discuss metric invariants of Markov quasi-similarity in the class of ergodic automorphisms.Comment: 15 page

The Negative Impact of Varicocele on Basic Semen Parameters, Sperm Nuclear DNA Dispersion and Oxidation-Reduction Potential in Semen

Since varicocele is so common in infertile men, this study intends to analyse the relationships between varicocele and conventional semen characteristics, sperm nuclear DNA dispersion and oxidation-reduction potential (ORP) in semen. Varicocele-positive and varicocele-negative infertile men (study groups) showed significantly lower standard sperm parameters and higher sperm DNA fragmentation (SDF) and ORP in semen than healthy volunteers and subjects with proven fertility (control groups). A lower proportion of low SDF levels (0–15% SDF) and higher incidence of high SDF levels (>30% SDF), as well as a higher prevalence of high ORP values (>1.37 mV/106 sperm/mL), were found in the study groups vs. the control groups. Moreover, infertile men had significantly lower odds ratios (ORs) for low SDF levels and significantly higher ORs for high SDF levels and high ORP. SDF and ORP were negatively correlated with sperm number, morphology, motility and vitality. Furthermore, a significant positive correlation was found between SDF and ORP. The obtained results suggest that disorders of spermatogenesis may occur in varicocele-related infertility. These abnormalities are manifested not only by reduced standard semen parameters but also by decreased sperm DNA integrity and simultaneously increased oxidative stress in semen

The Journey of Cancer Cells to the Brain : Challenges and Opportunities

Cancer metastases into the brain constitute one of the most severe, but not uncommon, manifestations of cancer progression. Several factors control how cancer cells interact with the brain to establish metastasis. These factors include mediators of signaling pathways participating in migration, infiltration of the blood-brain barrier, interaction with host cells (e.g., neurons, astrocytes), and the immune system. Development of novel therapies offers a glimpse of hope for increasing the diminutive life expectancy currently forecasted for patients suffering from brain metastasis. However, applying these treatment strategies has not been sufficiently effective. Therefore, there is a need for a better understanding of the metastasis process to uncover novel therapeutic targets. In this review, we follow the journey of various cancer cells from their primary location through the diverse processes that they undergo to colonize the brain. These processes include EMT, intravasation, extravasation, and infiltration of the blood-brain barrier, ending up with colonization and angiogenesis. In each phase, we focus on the pathways engaging molecules that potentially could be drug target candidates