Yaroslavl State University

We study noncommutative analogues and integrable discretisations of nonlinear Schrödinger (NLS)-type systems associated with reduction groups. In particular, we consider the Ablowitz–Kaup–Newell–Segur (AKNS) system, the Kaup–Newell derivative NLS system, and the Mikhailov–Shabat–Yamilov deformation of the derivative NLS system together with their Darboux–Bäcklund transformations and associated lattice equations. We derive the continuum limits of previously constructed integrable lattice systems and recover the corresponding NLS-type partial differential equations. We then construct a noncommutative deformation of the Mikhailov–Shabat–Yamilov system and show that, unlike the AKNS and Kaup–Newell cases, its Lax representation requires the introduction of nonlocal variables. Furthermore, we derive Darboux–Bäcklund transformations and integrable discretisations for the noncommutative derivative NLS and deformation derivative NLS systems in the form of vertex–bond lattice equations. We also construct explicit solutions for a six-point derivative NLS-type lattice equation and for its noncommutative analogue.

Background. Elevated cholesterol levels are among the leading risk factors for the development of cardiovascular diseases and are a cause of mortality worldwide. Literature data indicate significant differences in the prevalence of hypercholesterolemia among various populations and age groups. Purpose. Investigation of the age- and sex-specific characteristics of total cholesterol levels in the blood and the prevalence of hypercholesterolemia among the working-age population living in Yaroslavl. Materials and methods. A single, uncontrolled, non-randomized observational study was conducted, involving 890 participants, aged 20-59, of both sexes. Fasting total cholesterol levels in the blood were measured using the SD LipidoCare rapid analyzer. Results. The average level of total cholesterol among males was 4.6±1.21 mmol/L and among females – 4.8±1.16 mmol/L. As age increased, the level of total cholesterol in blood plasma increased by 37.8% among men and by 34.1% among women. Optimal levels of total cholesterol were recorded in 66.1% of men and 62.7% of women. However, with age, the proportion of individuals with optimal levels decreased by 1.4 times among men and 2.5 times among women. Elevated and high levels of cholesterol were observed in 17.2% of men and 9.3% of women and in 23.6% of women and 10.8% women, respectively. The distribution of total cholesterol levels, both among men (χ²=66.217, Df=9, p<0.01) and among women (χ²=113.907, Df=9, p<0.01), showed significant differences depending on age. The odds of developing hypercholesterolemia increased with age 10.6-fold among men (OR=10,198, 95% CI: 4.481-23.208, p<0.001), in women – 16.5 times (OR=16,427, 95% CI: 7.741-34.861, p<0.001). The median values of total cholesterol in the blood and the prevalence of hypercholesterolemia in Yaroslavl men and women aged 20–59 are lower compared to national data.

The availability of unmanned aerial vehicles (UAVs) has led to a significant increase in the number of offenses involving their use. This makes the development of UAV detection systems relevant. Solutions based on deep neural networks show the best results in detecting UAVs on video. This article presents a study of various neural network detectors and focuses on identifying objects as small as possible, up to the size of $4\times4$ and even $3\times3$ pixels. The work investigates architectures SSD (VGG16) and YOLOv3 and it's modifications. Precision and recall metrics are calculated separately for different intervals of the object areas. The best result have been shown by YOLOv3 model with bbox parameters chosen as the result of object sizes clustering. Small ($3\times3$ px) drones have been successfully identified with 76% precision and a very small recall of 26%. For objects between 10 and 20 pixels in area, the recall is 64% with an accuracy of 75%. For objects with an area more than 20px the recall is about 90%, the precision is 89%, and the F1 score is 90%. These results show that it is possible to recognize even $4\times4$ pixel drones, which can be used in video surveillance systems.

We show how to derive noncommutative versions of integrable partial difference equations using Darboux transformations. As an illustrative example, we use the nonlinear Schr & ouml;dinger system. We derive a noncommutative nonlinear Schr & ouml;dinger equation and we construct its integrable discretisations via the compatibility condition of Darboux transformations around the square. In particular, we construct a noncommutative Adler-Yamilov type system and a noncommutative discrete Toda equation. For the noncommutative Adler-Yamilov type system we construct B & auml;cklund transformations.

Antimony (Sb) is a toxic metalloid and a global pollutant. Sb exposure is known to cause pulmonary, cardiovascular, liver and kidney damage, as well as cancer. In addition, data showing neurotoxic effects of Sb have been also obtained recently. Therefore, the objective of the present review was to discuss existing epidemiological findings linking Sb exposure to brain diseases and the underlying molecular mechanisms of Sb neurotoxicity. Laboratory findings revealed neurotoxic effects of high-dose Sb exposure. Specifically, in vitro and in vivo studies show that Sb induces neuronal apoptosis through induction of oxidative stress, altered Akt/mTOR and Wnt/β-catenin signaling, and potentially increased Ca2 + flux. Activation of ferroptosis due to reactive oxygen species (ROS) overproduction, autophagic GPX4 degradation, and NCOA4-mediated ferritinophagy also appear to mediate Sb neurotoxicity. Other mechanisms linked to adverse effects of Sb in brain include altered neurotransmitter metabolism, neuroinflammation, as well as impaired gut-brain axis and neurogenesis. Epidemiological findings show also that Sb exposure, both in single metal and multiple metal exposure models, is associated with increased risk of depression, sleep disorders, anxiety, cognitive dysfunction, and neurodevelopmental disorders like autism spectrum disorder (ASD) and attention deficit/hyperactivity disorder (ADHD), although controversial data exist. Evidence showing that maternal Sb exposure is also associated with adverse neurodevelopmental outcome in children also exists. While the precise role of Sb exposure in development of neurological diseases has yet to be established due to limited data, a complex of epidemiological and laboratory findings show that Sb should be considered a potential environmental neurotoxicant.