Yaroslavl State University

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.

The theory of electrical networks, in its current state, covers a number of areas of contemporary mathematics and mathematical physics including the combinatorics of paths, forests and groves on graphs, discrete harmonic analysis, problems of random walks, exactly solved models in statistical mechanics, cluster varieties related to spaces of totally positive matrices, discrete integrable systems, algebraic structures similar to Zamolodchikov's tetrahedron equation, and many others. The main aim of this survey is to present some of these topics, classical and recently discovered ones alike.

Semi-discrete (differential-difference) matrix Lax representations (Lax pairs) play an essential role in the theory of integrable differential-difference equations. Fix a (1+1)-dimensional evolutionary differential-difference (semi-discrete) equation and consider matrix Lax representations (MLRs) of this equation. Two MLRs are said to be gauge equivalent if one of them can be obtained from the other by applying a (local) matrix gauge transformation. Gauge transformations (GTs) form an infinite-dimensional group, which acts on the set of MLRs of a given equation. Two MLRs are gauge equivalent iff they belong to the same orbit of this action. When one tries to establish integrability (in the sense of soliton theory) for a given equation, one is interested in MLRs which depend on a parameter (usually called the spectral parameter) such that the parameter cannot be removed by any GT. We introduce and study explicit invariants with respect to the action of GTs on the set of MLRs for a given (1+1)-dimensional evolutionary differential-difference equation with any number of components. Using these invariants, we obtain the following results: - Consider a MLR with a parameter λ. If at least one of the invariants computed for this MLR depends nontrivially on λ, then the parameter cannot be removed by any GT. - When we have two different MLRs for a given equation, we present necessary conditions for these two MLRs to be gauge equivalent. Our results on semi-discrete MLRs of differential-difference equations are inspired by results of S.Yu. Sakovich and M. Marvan on (continuous) zero-curvature representations of partial differential equations. A comparison with some of the results of S.Yu. Sakovich and M. Marvan is presented.