Moscow Institute of Physics and Technology

Exact solutions describing a fall of a particle to the centre of a non-regularized singular potential in classical and quantum cases are obtained and compared. We inspect the quantum problem with the help of the conventional Schrödinger’s equation. During the fall, the wave function spatial localization area contracts into a single zero-dimensional point. For the fall-admitting potentials, the Hamiltonian is non-Hermitian. Because of that, the wave function norm occurs time-dependent. It demands an extension to this case of the continuity equation and rules for mean value calculations. Surprisingly, the quantum and classical solutions exhibit striking similarities. In particular, both are self-similar as the particle energy equals zero. The characteristic spatial scales of the quantum and classical self-similar solutions obey the same temporal dependence. We present arguments indicating that these self-similar solutions are attractors to a broader class of solutions, describing the fall at finite energy of the particle.

This chapter presents the results of using the set of basic models described in the chapter “Modeling Social Self-Organization and Historical Dynamics. A General Approach” to model the dynamics of an industrial society. Both interactions in the “society–nature” system and social interactions within society between the main social groups (including economic and political interactions) are considered. It is shown that industrial society is characterized by the continuous growth of the main demographic and economic characteristics due to the high pace of technological development and the expansion of the resource base associated with this. Based on the modeling of social interactions, the main structural and functional features of an industrial society are identified, leading to the formation of social structures of the so-called Y-type (which are characterized by a market economy, republican forms of government, and individualism in the socio-psychological sphere). It is shown that a necessary condition for the effective functioning of Y-type social structures is economic growth, in the absence of which they experience crisis and transformation into structures of other types.

Akaev et al. outline their methodological approach to mathematical modeling of social self-organization and historical dynamics, which is used in the study of processes occurring in the world and in forecasting further world development. They describe basic equations (in the demographic, ecological, economic, technological, social, and political spheres) and the order of their use in modeling world dynamics. Based on these equations, a set of basic models has been developed that describes interactions in the “society—nature” system, as well as interactions within society between the main social groups (including economic and political interactions). Finally, Akaev et al. propose a technique for analyzing modeling results based on constructing and studying features of phase portraits of respective equation systems.

This chapter presents the results of the application of the set of basic models outlined in chapter “Modeling Social Self-Organization and Historical Dynamics. A General Approach” (Akaev et al., 2023, this volume) to model the current historical situation and to forecast its further development. Akaev et al. show that the modern historical period is a period of transition from the “epoch of growth,” which followed the industrial revolution of the early nineteenth century, to the “era of deceleration,” one of the strongest indicators of which is a rapid decrease in the growth rate of the Earth's population and its aging. They perform the analysis of the ongoing changes in all spheres of life. Akaev et al show the uniqueness of the ongoing changes and consider alternative options for further development.

Driven-dissipative protocols are proposed to control and create nontrivial quantum many-body correlated states. Protocols conserving the number of particles stand apart. As well-known, in quantum systems with the unitary dynamics the particle number conservation and random scattering yield diffusive behavior of two-particle excitations (diffusons and cooperons). Existence of diffusive modes in the particle-number-conserving dissipative dynamics is not well studied yet. We explicitly demonstrate the existence of diffusons in a paradigmatic model of a two-band system, with dissipative dynamics aiming to empty one fermion band and to populate the other one. The studied model is generalization of the model introduced in F. Tonielli, J. C. Budich, A. Altland, and S. Diehl, Phys. Rev. Lett. 124 , 240404 (2020). We find how the diffusion coefficient depends on details of a model and the rate of dissipation. We discuss how the existence of diffusive modes complicates engineering of macroscopic many-body correlated states.

At the Google Scholar, links to Boris’s books alone exceed 5000. In addition to Boris Mirkin’s starting Ph.D. results in abstract automata, Mirkin’s innovative contributions in various fields of decision-making theory and practice have marked the fourth quarter of the twentieth century and beyond. Boris has done pioneering work in group choice, mathematical psychology, clustering, datamining and knowledge discovery. Here is the list of notions and terms that have been introduced or heavily explored by B. Mirkin: Anomalous cluster, Bi-cluster, Categorical factor analysis, Chain order partition, Complementary partition criterion, Core-shell cluster, Data recovery approach, Distance between partitions, Federation consensus rule, Generalization in taxonomy, Interval order, Linear stratification, Mapping between evolutionary trees, Minkowski weighted feature clustering, Parsimonious gene history reconstruction, Single cluster clustering, Structured partition, Prebase (in automata theory), Taxonomic rank of research results, Tri-clustering.

Extensive application of technologies like phage display in screening peptide and protein combinatorial libraries has not only facilitated creation of new recombinant antibodies but has also significantly enriched repertoire of the protein binders that have polypeptide scaffolds without homology to immunoglobulins. These innovative synthetic binding protein (SBP) platforms have grown in number and now encompass monobodies/adnectins, DARPins, lipocalins/anticalins, and a variety of miniproteins such as affibodies and knottins, among others. They serve as versatile modules for developing complex affinity tools that hold promise in both diagnostic and therapeutic settings. An optimal scaffold typically has low molecular weight, minimal immunogenicity, and demonstrates resistance against various challenging conditions, including proteolysis – making it potentially suitable for peroral administration. Retaining functionality under reducing intracellular milieu is also advantageous. However, paramount to its functionality is the scaffold’s ability to tolerate mutations across numerous positions, allowing for the formation of a sufficiently large target binding region. This is achieved through the library construction, screening, and subsequent expression in an appropriate system. Scaffolds that exhibit high thermodynamic stability are especially coveted by the developers of new SBPs. These are steadily making their way into clinical settings, notably as antagonists of oncoproteins in signaling pathways. This review surveys the diverse landscape of SBPs, placing particular emphasis on the inhibitors targeting the oncoprotein KRAS, and highlights groundbreaking opportunities for SBPs in oncology.

In this work, we consider the problem of strongly convex online optimization with convex inequality constraints. A scheme with switching over productive and non-productive steps is proposed for these problems. The convergence rate of the proposed scheme is proven for the class of relatively Lipschitz-continuous and strongly convex minimization problems. Moreover, we study the extensions of the Mirror Descent algorithms that eliminate the need for a priori knowledge of the lower bound on the (relative) strong convexity parameters of the observed functions. Some numerical experiments were conducted to demonstrate the effectiveness of one of the proposed algorithms with a comparison with another adaptive algorithm for convex online optimization problems.

We consider three problems in combinatorial geometry in which the search for counterexamples and improvement of known estimates is reduced to a finite-dimensional multi-extremal optimization problem with piecewise-smooth constraints. The first problem is to find a distance embedding of some graph into a given surface, i.e. to find a set of points for which a part of pairwise distances and some additional condition are given. The other two problems consist in minimization of some functional computed for partitions of a compact set into a given number of subsets. The solutions found have improved some quantitative estimates in generalizations of the Borsuk hypothesis and variants of the Hadwiger–Nelson–Erdös problem on the chromatic number of space.

One of the key challenges in developing autonomous vehicles is planning safe and efficient trajectories in complex environments, such as intersections. This paper proposes an offline RL approach for planning trajectories for autonomous vehicles at crossroads with other actors. It enables the possibility of using pre-recorded expert trajectories for algorithm tuning. We study the influence of the quality of collected trajectories on various offline reinforcement learning methods. Our approach has the potential to overcome the limitations of online RL and provide an effective planning solution for autonomous vehicles in dynamic environments.

Place Recognition is a fundamental task in mobile robotics and autonomous systems, enabling vehicles to navigate and perform tasks in previously visited environments. LiDAR-based Place Recognition has become increasingly popular due to its robustness to changes in illumination, weather conditions, and dynamic objects. One critical aspect of training effective Place Recognition models is the selection of an appropriate loss function. In this paper, we investigate the impact of various loss functions on the training and evaluation of LiDAR voxel-based Place Recognition. To the best of our knowledge, no previous works have compared the performance of different loss functions in this context. We compare the performance of trained models on popular public datasets Oxford RobotCar and NCLT. We also tested them on the data collected in a real-world scenario. The results prove that selecting an effective loss function results in improving the performance of the trained model.

The conditional gradient idea proposed by Marguerite Frank and Philip Wolfe in 1956 was so well received by the community that new algorithms (also called Frank–Wolfe type algorithms) are still being actively created. In this paper, we study a non-smooth stochastic convex optimization problem with constraints. Using a smoothing technique and based on an accelerated batched first-order Stochastic Conditional Gradient Sliding method, we propose a novel gradient-free Frank–Wolfe type algorithm called Zero-Order Stochastic Conditional Gradient Sliding (ZO-SCGS). This algorithm is robust not only for the class of non-smooth problems, but surprisingly also for the class of smooth black box problems, outperforming the SOTA algorithms in the smooth case in term oracle calls. In practical experiments we confirm our theoretical results.