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The subject of the article is a model of correlation between anti-corruption institutions of international and national law. The research methodology involved the use of formal and dialectical logic, historical and legal, comparative legal, anthropological and legal, economic and legal, hermeneutical, synergetic, systemic, and statistical methods. The purpose of the article is to reveal the model of correlation between anti-corruption institutions of international and national law. It is determined that anti-corruption policy becomes a value when it is implemented on an institutional basis. Such a basis means its independence from the acquisition of public power by any person. The sustainability and completeness of the manifestation of virtues in legal relations are ontologically determined by the processes of nation-building, which, in turn, are based on the values of law inherent in human nature. The anti-corruption model is influenced by historical, spiritual, cultural, external conditions, climatic, geographical and other living conditions. Such a model becomes effective when all these factors and their conditions form the best basis for the development of the nation, compared to others, through the full use of the energy potential of the virtues of all its members. Any delay, irresponsibility and/or unjustified loss of vigilance regarding the components of this model leads to decline. It is emphasised that the national anti-corruption model is ternary, since it is based on three main elements, namely, anthropospatial legislation, the practice of its application within the framework of administrative and jurisdictional procedures. The configuration of both elements of the model and their parts is determined by its uniqueness. The most superficial classification of these models is based on the system of criminal justice components. The fundamental classifications of national anti-corruption models are based on the anthropological dimension of legislation and practices of its application outside the criminal process. This is the strategy of anti-corruption work. The role of a person in the strategy process is not to remain in office as long as possible, but to remain in office as useful and effective as possible. Corruption distortions in legal relations disappear where the individual nourishes the institutions of law and power rather than replaces them. The author establishes that the correlation between national and international anti-corruption models is conditional, since the international model has not yet been formed and largely reflects the worldview of the Western legal tradition. It is also precocious to discuss an international anti-corruption model because the international community has not reached a sincere agreement on a universal set of human rights and freedoms and their scope. However, such a substantive understanding is the essence of anti-corruption policy, where its rules and practices reveal the nature of human virtues in legal relations. Currently, there is no complete description of the counterbalance to this tradition of law. Eastern, Muslim, Hindu and other non-Western cultures have adopted legal institutions for the declaration of assets and interests of public officials, conflicts of interest, financial audits of public procurement and anti-corruption criminal justice systems. The Republics of Singapore, Japan and Hong Kong have been the most successful in this anti-corruption legislative reception. The implementation of these institutions by other nations requires their adaptation to unique existential conditions, so that the potential for the liberation of human virtues by the force of legislative requirements is organically strengthened by the conditions of the nation's development. This will manifest the features of both innovation and anthropo-dimensionality of law.

The subject of the article is the means of international law to eliminate corruption threats to national security. The research methodology involved the use of logical, historical and legal, systemic, natural law, formal and dogmatic, hermeneutical, economic and legal (analysis, comparison), axiological, statistical and economic methods. The purpose of the article is to reveal the means of international law to eliminate corruption threats to national security. Carrying out the study made it possible to draw the following conclusions. It was found that most countries of the world have implemented international anti-corruption norms into their national legal frameworks and have the support of international organisations specialising in the fight against corruption. The resources of foreign legal doctrine become an important source of support for domestic scientists to convince of the correctness of their scientific conclusions regarding successful anti-corruption measures. An extensive system of international anti-corruption assistance allows to minimise the costs of own relevant infrastructure. On this basis and against the background of access to powerful anti-corruption resources at the European and world level, there is essentially sabotage of anti-corruption policy in Ukraine, which has critically affected the security of the Ukrainian nation. It was emphasised that military threats from the outside are an exceptional danger for corrupt countries. At the same time, even the stabilising effect of microcorruption becomes dangerous for them in today's unstable development environment. All the positive effects of corruption in the form of improved communication through small gifts that comply with legal customs disappear when top corruption spreads in a country. Then this level of corruption multiplies a series of official crimes, treason and other crimes that destroy the foundations of national security. Already after the point of no return – the beginning of military aggression from outside against the background of prolonged high-level corruption inside the country – external support for anti-corruption reforms becomes a condition for the survival of the nation, the reduction of human losses in the war, and so forth. The need to neutralise these two challenges to national security becomes urgent after years of procrastination on accountability and other dimensions of integrity in public positions. In these cases, the national legal standard falls under the critical conditions of ultra-fast transformation, according to the successful anti-corruption models of countries that saved their nation from war and high-level corruption. It is noted that the standards set for Ukraine are quite close. These are EU standards, which are achieved through the adoption and implementation of those legal norms that reflect the current state of ensuring human opportunities. It is stressed that the specification of anti-corruption norms and the structural units of their implementation in legal reality are nativemorphic. They always differ in the degree of unification within the contexts common to nations, namely, legal traditions, mentality, historical conditions, economy, etc. Transnational anti-corruption assistance in the mutual enrichment of some nations through the possibility of using the experience of other nations. The author concludes that knowledge about the practices of building virtuous relations is the capital of the nation that possesses it. Conscious disregard of this knowledge by the recipient should be remedied by charging a fee for it. It is proposed to establish an International Organisation for Integrity Development, which would include the top 20 countries in terms of corruption and rule of law perception indices.

The article reveals the strategy for elimination of corruption threats to national security. It is a system of knowledge about legal and organisational measures aimed at ensuring the supremacy of human virtues in public-legal relations at a level that excludes both potential and real threats to human rights, territorial integrity, safe living conditions of citizens and other constitutional values. It is a molar set, the content capacity of which is divided into at least two atomic units – legal norms and the implementation of legal norms. Taken together, both components of the strategy are capable of ensuring the preservation of these values and the development of the nation on this basis on an ongoing basis. The first component is intended to cover the content of legal relations. The second component involves the practical implementation of legal norms. These two variables equally saturate the functional and structural content of the security of national interests. Accordingly, the security of the nation exists only under the condition of the implementation of law-making and law-enforcement operations, which is possible only at the level of the institutionalisation of these processes. Any replacement of an institution by a person, of public interest by private interest, of law by its visibility, of freedom by force, determines the operational and/or strategic dysfunction of law, which leads to the loss of meaningful national values. It is determined that the hierarchy of initial relations of key concepts for understanding corruption distortions, the essential content of national interests and the relationship of corruption acts with the level of threats to Ukraine's national security form the ontological basis of the strategy for eliminating such threats. This basis should also include the principles of its creation, updating, implementation and monitoring of effectiveness. This is the introductory part of the strategy. In the substantive part of the strategy, it is necessary to specify the goal, tasks and areas of national interests, as well as the subjects of its implementation, effectiveness control and renewal. These subjects include all public authorities, civil organisations and each citizen. The main responsibility for the effectiveness of this approach lies not only with specialised anti-corruption bodies, but necessarily with all national public authorities. It is emphasised that there will be a system of control over such performers within the already existing infrastructure of public authorities and with detailed rules on the limits of control by citizens, the legal possibilities of which should be wide enough to ensure that this control remains an effective tool for ensuring the provisions of the specified strategy, including the possibility for citizens to use legal procedures of vigilantism. Separate sections of this strategy should be devoted to detailed rules for strengthening national security through transnational connections and digital technological resources. The secret part of the strategy should contain rules for using the nation's permanent and situational advantages, its individual features and other resources at a particular moment in time, as well as in the short, medium and long term. This part should also reflect the algorithms for determining the nature and qualities of these advantages, timely verification of their emergence and transformation. The author establishes that all these rules and algorithms should be combined with the rules for determining the changing nature of corruption acts and corruption subjects and their criminal accomplices.

This paper gives an experimentally supported review and comparison of several indices based on the conventional K-means inertia criterion for determining the number of clusters, $K$ , in datasets, using the popular Silhouette width index as a benchmark. Our experiments involve a novel version of the Elbow index, defined using values of $K$ two or three steps apart. We also discuss alternative ways of computing the inertia and summarizing its values. Even though there are no overall winners in our experiments, some of our results are very conclusive and can be used as a guide for indices determining the number of clusters in K-means.

Given the recognition of the priority of the European integration and North Atlantic vectors of modern state-building and law-making processes in most countries of the world, the issue of "high terminological quality", "terminological purity", with the implementation of relevant international and European legal standards for the formation of "basic terminology", the basis for combating the legalisation of "dirty money" is not only relevant, but also of paramount importance, as it plays the role of "key provisions" of the entire regulatory framework. The purpose of the study is to analyse the existing international legal and European standards and national regulatory models for defining "politically exposed persons", with the aim of identifying "defects in their quality" and formulating proposals for their elimination. The object of the study is social relations directly related to the state financial monitoring of politically exposed persons. The subject of the study is the regulatory models for determining politically exposed persons in terms of state financial monitoring. The methodological basis was formed by both general scientific and special research methods, which made it possible to present a comprehensive cross-section of the relevant issue. Results. The "quality" of the regulatory definition of PEPs implies the following: a) consideration of international legal and European standards for preventing and combating the legalisation of "dirty money" as a "basis" for national thematic rulemaking; b) regulatory distinction between "main PEPs", with criteria that allow determining the "uniqueness" of their legal status, and "additional PEPs" (persons who do not have the main features of PEPs, but may potentially be involved in relations with them); c) "criterionality" of the "main PEPs" is directly related to the "influential" position and significant public functions performed by the person (it is mandatory to have these positions enshrined in the law, with the corresponding correlation of functions); d) delimitation of "additional PEPs", with the identification of those persons who are "related" by family and other relations with the "main PEP". For each category of such persons, the guideline is to standardise their list, which makes it impossible to vary the interpretation of the relevant provisions and diversify law enforcement practice.

The article reveals the formal-legal basis for the institutionalisation of international commercial arbitration. It is found that states are still far from a unified understanding of the basic scope of human rights, but they have a clear common vision of the mechanism for protecting the interests of international commerce. Against the background of the economic and innovative successes of the EU and other countries in the world that have made human rights a priority, it would appear that the source of modern transnational trade problems lies precisely in another group of states in which commercial interests dominate human rights. This second type of state nourishes its development at the expense of the innovations of the first type of state, its constructive and passionate representatives. Innovative solutions are formulated by the freest people, whose freedom is legally and organisationally guaranteed, which becomes a source of release for their creative, productive existential energy. Therefore, the contradictions between these two types of entrepreneurs of nations give rise to commercial disputes regarding the path of development, as well as legal conflicts within each of these types of nations regarding the vector of development or decline. Strategically, it is an ontology of modern problems of international commercial disputes. It is emphasised that the institutionalisation of international commercial arbitration is conceived as the creation of legal models for interpretation, determination of cause-effect relations, assessment of all essential circumstances of commercial relations, about which the parties of this type of social interaction have not reached an agreement and are forced to turn to mediators, to whom they entrust jurisdiction over the dispute between them. It was noted that the legal reality of the institutionalisation of international commercial arbitration reflects the path of human development, which at the present stage is marked by crisis. Logical, rational, clear law is in a permanent process of critical evaluation of the synergy of creative, risky, adventurous, pragmatic entrepreneurship. Ideal legal models absorb the constructive activity of entrepreneurship, foreseeing its long-term prospects as positive. At the same time, it is the task of lawyers to reject those types of economic relationships that threaten common humanity. In conclusion, the UN Commission on International Trade Law is the only global body designed to ensure the optimal course of correlation processes between private international law and transnational commercial activity. At the same time, however, this Commission suffers from all the consequences of the UN's dysfunction. This is particularly evident in the UN's inability to prevent wars, famines, environmental disasters, military crimes and other global crises. It is advisable for the states to create a separate organisation in which they can coordinate their legal standards of joint entrepreneurship in the extractive industries, production, trade, finance, as well as the global environmental, national economic and other consequences of commercial projects. This organisation would become a convenient platform for honest parity in the unification of the legal practice of transnational entrepreneurship and the settlement of its disputes, based on the legal customs and traditions of different nations. This would provide a significant impetus for the healthy creation and application of international private law, capable of determining the vector both of global progress and of appropriate transformations in domestic national economic policies.

The article reveals the epistemological context of transformations of anti-corruption legal requirements in the conditions of European economic integration of Ukraine. It has been established that the elimination of the dominance of human defects by the tools of legislation and law enforcement practices becomes effective when the reproducible knowledge reflects the scientific awareness. The subject of knowledge is the whole complex of issues of fostering the manifestation of good virtues and their suppression. Otherwise, both economic reproduction and economic progress are excluded. For Ukraine, both processes now depend on an understanding of the respective progressive solutions that the highly developed nations of the EU have to offer. In fact, integration into the EU is historically determined and currently historically inevitable, and therefore requires meaningful dynamic transformations of domestic legislation. The most urgent direction of these transformations requires interdisciplinary knowledge related to the fight against corruption and its minimisation. It has been established that the epistemological context of the creation and application of anti-corruption legal norms consists of scientifically proven, comprehensive knowledge about the mechanism of neutralisation of corruption by means of coercion and stimulation. The methodology of gaining knowledge through human consciousness involves the use of logical resources, namely 1) rational conclusions of formal logic; 2) contradictions and patterns of dialectical logic; 3) actions and events of historical logic; 4) artefacts of art logic. The truth of knowledge, verified by these means of reasoning and empirical experience, is then partly expressed by mathematical and linguistic symbols, and the rest is conveyed in an intuitive way. The understanding of that which does not fit into the forms of words and numbers is done mentally and sensitively. At this point, it should be emphasised that the praxeological dimension of pure epistemology requires taking into account the characteristics of the cognitive subjects of a specific social community. This requirement extends the scientist's sphere of responsibility beyond epistemology and involves mastering knowledge of its historical determinants. It is concluded that the teleological attitudes of the Ukrainian nation include the study of the values of European nations, which have united for the purpose of economic well-being. Integration into the EU requires knowledge of the mechanisms for combating human vices, eliminating corrupt distortions and using human virtues in EU structures. Regional civilisational stratification persists due to both intra-national and international dishonesty. Accordingly, global integration based on fundamentally unified legal standards requires the elimination of counterproductive factors at both levels of social communication. The focus of attention on good virtues is determined differently from the existing configuration of national associations. Economic and other issues of cultural heritage are first a consequence and then a cause of the manifestation of good virtues. At the same time, military alliances confirm the deep ideological contradictions of nations. This shows the denial of the possibility of creating a global union of nations based on the manifestation in legal reality of the good virtues of its members. It is on the basis of the legal manifestation of the degree of virtue that nations and their associations are formed in the modern world.

The aim of the work. To summarize and expand knowledge about current methods used for visualization of coronary arteries, their evolution, capabilities, effectiveness, indications for use, safety for patients, guided by the principles of evidence-based medicine. Coronary artery disease (CАD) is an extremely common clinical cardiovascular disease, which is caused by atherosclerosis of the subepicardial coronary arteries (CAs) and can have both acute and chronic course. The incidence of CАD is increasing every year and getting younger. CАD has not only a high morbidity rate, but also a high mortality rate. In Ukraine, mortality from CАD is the main cause of population mortality. Without timely diagnosis and effective treatment, myocardial infarction or sudden cardiac death may develop. It is possible to ascertain the etiological cause of myocardial ischemia only after visualization of the СAs. A practicing physician is able to visualize the СAs using X-ray contrast coronary angiography or contrast-enhanced computed tomography of the chest. СA visualization methods have been used in clinical practice for more than half a century. The hardware and software are constantly upgraded, the diagnostic options of these methods are improved and expanded, and recommendations regarding their use in general clinical practice are updated. The main task for clinicians is to confirm or rule out the presence of a СA atherosclerotic lesion, as well as to determine its localization, extent, degree of stenosis and its significance for coronary blood flow, the presence of СA calcification, collateral pathways, plaque composition and its internal structure. Only after identifying the anatomical and physiological aspects of the atherosclerotic process in СA, it is possible to choose the right strategy for the treatment of patients by a multidisciplinary heart team including pharmacological therapy, a method of cardiac revascularization, and measures for primary or secondary prevention. Conclusions. CАD is a common disease worldwide. Today, two methods of the CА visualization are available – invasive coronary angiography and non-invasive coronary CT angiography. Further research is needed on the efficacy and safety of different СA imaging methods in CAD. Better results of the diagnostic search depend on both the capabilities of the clinic hardware component and on the optimal sequence for diagnostic processes rationally constructed by physicians.

Relevance. In connection with the introduction of various types of chelated microfertilizers into production, it is necessary to develop new elements of varietal technology for the cultivation of melons and gourds in order to obtain stable yields in the arid conditions of the Volgograd Trans-Volga region. These studies will be relevant in this period of time.Material and technique. The object of research is watermelon, variety Meteor. We studied the types and methods of using chelate microfertilizers: Helaton Extra, Chelate B, Chelate Fe. Fertilizers were used for soaking seeds before sowing and for foliar treatment of plants during the growing season.Results. During the research period of 2019-2021, new forms of microfertilizers were studied. As a result of the research, new preparations for different methods of processing had a positive effect on the growth and development of table watermelon plants. The evaluation of the results obtained showed a positive effect of new microfertilizers on the germination energy and seed germination. The maximum growth of lashes was recorded when seeds were soaked before sowing: Helaton Extra preparation and foliar feeding of plants during the growing season with microfertilizer boron chelate. The best results of increasing the leaf surface were obtained in variants with the use of Helaton Extra microfertilizer for soaking seeds and treating plants on vegetative organs. Accordingly, the highest yield was obtained when using Helaton Extra fertilizer for seed treatment before sowing and spraying plants during the growing season. The output of marketable products was noted at a fairly high level. The average weight of the fetus in all studied variants ranged from 5.9 kg to 7.8 kg. The length of the growing season in all variants increased slightly. Comparative analysis of growth processes and productivity of watermelon variety Meteor when using new forms of water-soluble fertilizers for seed soaking and foliar treatment of plants showed greater efficiency from their use.

The rimless wheel model appears in engineering literature as a zero dynamics reduction of the model of a biped walking down a slope. Nonuniformity in the rimless wheel (i.e. unequal lengths of spokes and unequal angles between successive spokes) can be viewed as nonuniformity of the walking terrain. Existence of a limit cycle for nonuniform rimless wheel model was established in the earlier literature but stability was addressed just briefly. The present paper formulates conditions for asymptotic stability of the limit cycle and verifies the findings with numeric simulations (Wolfram Mathematica notebook is uploaded with this paper as supplementary material).

Understanding the evolution of Severe Acute Respiratory Syndrome Coronavirus (SARS-CoV-2) and its relationship to other coronaviruses in the wild is crucial for preventing future virus outbreaks. While the origin of the SARS-CoV-2 pandemic remains uncertain, mounting evidence suggests the direct involvement of the bat and pangolin coronaviruses in the evolution of the SARS-CoV-2 genome. To unravel the early days of a probable zoonotic spillover event, we analyzed genomic data from various coronavirus strains from both human and wild hosts. Bayesian phylogenetic analysis was performed using multiple datasets, using strict and relaxed clock evolutionary models to estimate the occurrence times of key speciation, gene transfer, and recombination events affecting the evolution of SARS-CoV-2 and its closest relatives. We found strong evidence supporting the presence of temporal structure in datasets containing SARS-CoV-2 variants, enabling us to estimate the time of SARS-CoV-2 zoonotic spillover between August and early October 2019. In contrast, datasets without SARS-CoV-2 variants provided mixed results in terms of temporal structure. However, they allowed us to establish that the presence of a statistically robust clade in the phylogenies of gene S and its receptor-binding (RBD) domain, including two bat (BANAL) and two Guangdong pangolin coronaviruses (CoVs), is due to the horizontal gene transfer of this gene from the bat CoV to the pangolin CoV that occurred in the middle of 2018. Importantly, this clade is closely located to SARS-CoV-2 in both phylogenies. This phylogenetic proximity had been explained by an RBD gene transfer from the Guangdong pangolin CoV to a very recent ancestor of SARS-CoV-2 in some earlier works in the field before the BANAL coronaviruses were discovered. Overall, our study provides valuable insights into the timeline and evolutionary dynamics of the SARS-CoV-2 pandemic.