Minimal State-Space Representation of Convolutional Product Codes

In this paper, we study product convolutional codes described by state-space representations. In particular, we investigate how to derive state-space representations of the product code from the horizontal and vertical convolutional codes. We present a systematic procedure to build such representation with minimal dimension, i.e., reachable and observable.

One for all: Universal material model based on minimal state-space neural networks

Computational models describing the mechanical behavior of materials are indispensable when optimizing the stiffness and strength of structures. The use of state-of-the-art models is often limited in engineering practice due to their mathematical complexity, with each material class requiring its own distinct formulation. Here, we develop a recurrent neural network framework for material modeling by introducing “Minimal State Cells.” The framework is successfully applied to datasets representing four distinct classes of materials. It reproduces the three-dimensional stress-strain responses for arbitrary loading paths accurately and replicates the state space of conventional models. The final result is a universal model that is flexible enough to capture the mechanical behavior of any engineering material while providing an interpretable representation of their state.

The minimal state in Ukraine as a progressive ideal of the historical criterion of the legal approach to the typology of the state: functional aspect

The article is devoted to the minimal state in Ukraine as a progressive ideal of the historical criterion of the legal approach to the typology of the state. The main attention, at the same time, is paid to features of its functioning. It is this type of state that must overcome the shortcomings of the state of the modern bureaucratic type. It seems that the need for its introduction in Ukraine is influenced by two factors: globalization and a significant increase in the role of civil society. At the same time, despite COVID-19, the processes of globalization have not decreased and the significant narrowing of state influence on economic processes, which is characteristic of globalization, is still continuing. As for civil society, in Ukraine it has gradually begun to realize itself as an important "player" within the country, which not only becomes more independent of the state, but also, to some extent, begins to influence it. Thus, the combination of globalization processes in the world and a powerful "burst" of selfconsciousness of domestic civil society necessitates the introduction in Ukraine of the concept of "minimal state", that is a state whose activities are aimed at implementing as few functions as possible. However, this type of state does not imply an anarchic ideal with its abolition at all. It seems that within the framework of a minimal state, the latter should be deprived of the functions it has assumed for a long historical period, leaving only the fiscal, the function of ensuring the safety of citizens from internal and external threats and the function of organizing work. At the same time, in the conditions of the minimal state the organization of works is transformed into the organization of realization of national and state projects when the state acts only as the coordinator and the financier of work which is carried out by numerous enterprises and corporations. As for the fiscal function, in our opinion, it should be somewhat transformed: the tax system should be enshrined in the principle of one tax, and the budget system should consist of three parts: "expenditure budget", "development budget" and "reserve budget". Regarding the security of citizens, society and the state from external and internal threats and dangers, such activities should take two forms: justice and law enforcement (security within the country) and war and peace (security outside the country). Thus, in the conditions of a minimal state, only the organization of national and state projects, budgetary and financial function, as well as ensuring the security of citizens, society and the state from external and internal threats and dangers should remain behind the latter.

Interpretation of the concept of joint property of spouses in international private legal relations

В настоящей статье рассматриваются вопросы законного и доктринального толкования совместной собственности супругов в Российской Федерации. Проанализирован подход зарубежных стран к составу такого имущества и режимам его регулирования. Семейные отношения относятся к частноправовой сфере, что предполагает минимальное вмешательство государства к вопросам их регулирования. Имущественное положение супругов разниться, в том числе, и в зависимости от правовой семьи, которая характерна для отдельно рассматриваемого государства. This article addresses the issues of legal and doctrinal interpretation of joint property of spouses in the Russian Federation. The approach of foreign countries to the composition of such property and the regimes of its regulation is analyzed. Family relations belong to the private law sphere, which implies minimal state intervention in their regulation. The property statuses of the spouses vary, including, and depending on the legal family, which is characteristic of a separately considered state.