Обеспечение траекторной безопасности в задаче облета статичной круговой зоны

Trajectory accident prevention in a problem of fly-around of static circular zone forbidden for planar motion of a dynamic controlled system is considered. Subproblems which are necessary to solve for tra-jectory accident prevention are developed. Generation of generalized forbidden zone model is realized, description of boundary zone of safe turn-away from forbidden zone is obtained, range limits of dangerous motion directions of the dynamic controlled system are developed.Рассматриваются вопросы, связанные с обеспечением траекторной безопасности в задаче облета статичной круговой зоны, запрещенной для движения динамического управляемого объекта на плоскости. Выявлены подзадачи, решение которых необходимо для обеспечения траекторной безопасности. Проведено формирование модели обобщенной запрещенной зоны, получено описание границы зоны безопасного отворота от запрещенной зоны, определены границы диапазона опасных направлений движения динамического управляемого объекта

Graph homology: Koszul and Verdier duality

We show that Verdier duality for certain sheaves on the moduli spaces of graphs associated to Koszul operads corresponds to Koszul duality of operads. This in particular gives a conceptual explanation of the appearance of graph cohomology of both the commutative and Lie types in computations of the cohomology of the outer automorphism group of a free group. Another consequence is an explicit computation of dualizing sheaves on spaces of metric graphs, thus characterizing to which extent these spaces are different from oriented orbifolds. We also provide a relation between the cohomology of the space of metric ribbon graphs, known to be homotopy equivalent to the moduli space of Riemann surfaces, and the cohomology of a certain sheaf on the space of usual metric graphs.Comment: 13 page

Successful resection of a retroperitoneal giant sarcoma: a case report

Описан клинический случай успешной хирургической резекции гигантскойй 38 килограммовой ретроперитонеальной саркомы у 52 летнего пациента.Описаний клінічний випадок успішної хірургічної резекції гигантскойй 38 кілограмової ретроперитонеальної саркоми у 52 річного пацієнта

One-loop effective action for Einstein gravity in special background gauge

The one-loop effective action for Einstein gravity in a special one-parameter background gauge is calculated up to first order in a gauge parameter. It is shown that the effective action does not depend upon the gauge parameter on shell.Comment: 17 pages, Latex, no figure

Coherent dynamics and decoherence in a superconducting weak link

We demonstrate coherent dynamics of quantized magnetic fluxes in a superconducting loop with a weak link - a nanobridge patterned from the same thin NbN film as the loop. The bridge is a short rounded shape constriction, close to 10 nm long and 20 - 30 nm wide, having minimal width at its center. Quantum state control and coherent oscillations in the driven time evolution of the tunnel-junctionless system are achieved. Decoherence and energy relaxation in the system are studied using a combination of microwave spectroscopy and direct time-domain techniques. The effective flux noise behavior suggests inductance fluctuations as a possible cause of the decoherence.Comment: 5 pages, 3 figure

BRST analysis of general mechanical systems

We study the groups of local BRST cohomology associated to the general systems of ordinary differential equations, not necessarily Lagrangian or Hamiltonian. Starting with the involutive normal form of the equations, we explicitly compute certain cohomology groups having clear physical meaning. These include the groups of global symmetries, conservation laws and Lagrange structures. It is shown that the space of integrable Lagrange structures is naturally isomorphic to the space of weak Poisson brackets. The last fact allows one to establish a direct link between the path-integral quantization of general not necessarily variational dynamics by means of Lagrange structures and the deformation quantization of weak Poisson brackets.Comment: 38 pages, misprints corrected, references and the Conclusion adde

Characteristic classes of gauge systems

We define and study invariants which can be uniformly constructed for any gauge system. By a gauge system we understand an (anti-)Poisson supermanifold provided with an odd Hamiltonian self-commuting vector field called a homological vector field. This definition encompasses all the cases usually included into the notion of a gauge theory in physics as well as some other similar (but different) structures like Lie or Courant algebroids. For Lagrangian gauge theories or Hamiltonian first class constrained systems, the homological vector field is identified with the classical BRST transformation operator. We define characteristic classes of a gauge system as universal cohomology classes of the homological vector field, which are uniformly constructed in terms of this vector field itself. Not striving to exhaustively classify all the characteristic classes in this work, we compute those invariants which are built up in terms of the first derivatives of the homological vector field. We also consider the cohomological operations in the space of all the characteristic classes. In particular, we show that the (anti-)Poisson bracket becomes trivial when applied to the space of all the characteristic classes, instead the latter space can be endowed with another Lie bracket operation. Making use of this Lie bracket one can generate new characteristic classes involving higher derivatives of the homological vector field. The simplest characteristic classes are illustrated by the examples relating them to anomalies in the traditional BV or BFV-BRST theory and to characteristic classes of (singular) foliations.Comment: 23 pages, references added, typos correcte

One loop renormalization of the four-dimensional theory for quantum dilaton gravity.

We study the one loop renormalization in the most general metric-dilaton theory with the second derivative terms only. The general theory can be divided into two classes, models of one are equivalent to conformally coupled with gravity scalar field and also to general relativity with cosmological term. The models of second class have one extra degree of freedom which corresponds to dilaton. We calculate the one loop divergences for the models of second class and find that the arbitrary functions of dilaton in the starting action can be fine-tuned in such a manner that all the higher derivative counterterms disappear on shell. The only structures in both classical action and counterterms, which survive on shell, are the potential (cosmological) ones. They can be removed by renormalization of the dilaton field which acquire the nontrivial anomalous dimension, that leads to the effective running of the cosmological constant. For some of the renormalizable solutions of the theory the observable low energy value of the cosmological constant is small as compared with the Newtonian constant. We also discuss another application of our result.Comment: 21 pages, latex, no figures

Many heads but one brain: FusionBrain – a single multimodal multitask architecture and a competition

Supporting the current trend in the AI community, we present the AI Journey 2021 Challenge called FusionBrain, the first competition which is targeted to make a universal architecture which could process different modalities (in this case, images, texts, and code) and solve multiple tasks for vision and language. The FusionBrain Challenge combines the following specific tasks: Code2code Translation, Handwritten Text recognition, Zero-shot Object Detection, and Visual Question Answering. We have created datasets for each task to test the participants’ submissions on it. Moreover, we have collected and made publicly available a new handwritten dataset in both English and Russian, which consists of 94,128 pairs of images and texts. We also propose a multimodal and multitask architecture – a baseline solution, in the centre of which is a frozen foundation model and which has been trained in Fusion mode along with Single-task mode. The proposed Fusion approach proves to be competitive and more energy-efficient compared to the task-specific one.We would like to thank Sber and SberCloud for granting the GPU-resources to us to experiment with different architectures and also to the participants to train their models, and for supporting the FusionBrain Challenge in general