We analyze the SCARDO model in the case of the 3-element opinion space under specific constraints on the transition table parameters that allows to link the problem at stake to the case of the 2-element opinion space that has been thoroughly studied previously. We characterize the properties of fixed points and support our findings by numerical experiments. Further, we manage to find out those settings that ensure the system almost surely reaches a specific domain in the phase space, after which its behavior can be predicted analytically.

The paper is devoted to solving the problem of determining the relative spatial arrangement and orientation of objects. The task was set: to show the fundamental possibility of spatial and angular relative positioning when using the parameters of the magnetic field gradient in tensor form and in the form of gradient of an absolute value vector as measurement information for the magnetic field of a local dipole source. The solution of the problem is presented along with the features and limitations for both forms of representation are considered. The principles of construction of magnetic gradiometry measurement systems are briefly described, the limitations of technical implementation are considered, and the benefits of using an alternating magnetic field source is outlined. The results of modelling are presented, proving the possibility of using the proposed positioning method for various engineering problems.

The paper is devoted to a comparison of open source power flow solvers: Pandapower, PyPower, PyPSA, GridCal, and a custom-developed solver. The core objective was to evaluate and contrast their performance in solving the power flow problem. The widely-used Newton-Raphson method has been tested as the primary analytical tool across all solvers, focusing on two primary metrics: computation time and the number of iterations required for convergence. The analysis was conducted under standard operating conditions, followed by stress-testing scenarios, where the solvers' resilience was examined under increased load conditions.

The paper discusses industrial production management in an Industry 4.0 enterprise based on digital twins of manufacturing process and products. The principles of applying digital twins in the production cycle are defined. We present an example structure of an integrated automated production management system that includes the digital twins and a number of other systems. The functions of digital twins in such a system are indicated. The order of formation and development of digital twins in the course of the enterprise design and construction is considered. At the initial stage of collecting requirements and drawing up technical specifications for the enterprise design, we propose to create an approximate simulation model of the production cycle, which allows the feasibility assessment of key requirements. At the subsequent stages of the enterprise life cycle, the simulation model is enriched up to a full-fledged digital twin and augmented with other components of the management system. We show that the digital twin development can be performed at a high level of formal rigor and automation utilizing the mathematical device of category theory. For this purpose, the novel construction called flexible multicomma category is introduced, representing all possible enterprise architecture variants from a given viewpoint in the sense of the ISO/IEC/IEEE 42010 standard. A flexible multicomma is defined by a signature composed of functors that represent the architecture components from the selected viewpoint. We prove that a multicomma of any fixed shape derived from the signature is embedded into the flexible multicomma.

The paper introduces a new approach to modeling Internet shutdown during the process of protest mobilization. The central point of the approach is the sequential use of two networks, with different topologies built upon the same set of individuals. Some endogenously set proportion of connections is shared by both networks. A model of protest dynamics is built on the developed approach. Numerical experiments with the model show that the effect of shutdown depends crucially on the degree of anger that triggers the protest campaign. This anger may arise, for example, from contested elections or an act of unjustified repression. The inference from the numerical experiments is that shutdown basically stifles protest activity if the triggering anger is high, and fuels protest activity if the triggering anger is low.