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## Методы построения тензоров преобразования для сетевых моделей сложных систем

The methods of constructing tensors transform (TT) used in the analysis and synthesis of network models of complex systems, presented in different coordinate systems are described in the article. The general method of construction of the TT, as well as a method of building TT for network models, decomposed into many of the automate synchronization networks, and primitive system is presented. It is shown that the complexity of the proposed methods for constructing the TT does not depend on the dimensionality of network models and defined a simple procedure for constructing a binary matrix.

Some methodological foundations for elaboration of the modern strategies of ecological thinking based on the theoretical biology and on the theory of complex adaptive systems статье are under review in the article. Ecology, being a science of interaction of living organisms and their communities with environment, goes far beyond its primary frames of the biological knowledge and becomes a nodal discipline from which vectors of perspective interdisciplinary synthesis of knowledge diverge. The ecological approach turns to be fruitful in social and humanitarian researches. Ecology of action, ecology of mind, ecology of life, of cognition and of creativity, ecology of thoughts and words, ecology of ideas, ecology of communication and ecology of management – all these conceptual attitudes give evidence of audacious integration of the ecological thinking in wide spheres of the humanitarian and social knowledge, where it gives opportunities for some fresh approaches. The concept of Umwelt coined by Jakob von Uexküll in 1909 and his study of Umwelt (Umweltslehre) are of great significance for the development of the modern ecological universalism and for elaboration of strategic imperatives of the ecological thinking. The concept of Umwelt as a specific environment to which any biological species or its separate individual is adapted and which is constructed by it allows us to elaborate a real interdisciplinary platform for development of the theory of ecology, for holding a reasonable position in discussions about sustainable development and sustainable futures as well as about the role of education for sustainable development of the world.

Some texts written by me together with corresponding member of the Russian Academy of science Sergei P. Kurdyumov (1928-2004) and under his direct ideological influence are collected in the book. These texts are elaborated, systematized, brought together in the book and supplemented with new materials. Sergei P. Kurdyumov were possessed of a deep metaphysical flair and put forward ideas, the matter of which are not fully clear up to now. These are, first of all, the idea of co-evolution and the notion of complex structures developing at different tempos as co-existing tempo-worlds. Owing to developments in the field of nonlinear dynamics and of synergetics, the classical problem of time and the problems of evolutionary holism disclose some new and non-traditional aspects. The matter of new notions of nonlinearity of the course of time in the processes of evolution and coevolution and of nonlinear links between different modi of time – between the past, the present and the future - come to the light in the book. Analyses of four interconnected aspects of the course of processes in open and nonlinear dissipative systems – of evolutionarity, temporality, emergent nature and holism – are carried out. A whole series of paradoxical notions, such as “the influence of the future upon the present”, “the possibility of touch of a remote future in praesenti”, irreversibility and elements of reversibility of the course of time appear in synergetics, non-traditional and nonlinear notion of time being at the heart of all of them. It is shown that the best pictorial view of the nonlinear time is apparently the tree of evolution or the tree of time that represent one of archetypes in the human psyche. This image is widely used in myths and religious doctrines of the world nations (the tree of evolution of languages from some united parent language or the tree of evolution of biological species), the image is often drawn by children, appears in consciousness of a man in his sleep, etc. The synergetics methodology under development is applied to study of cognitive systems. The emergent structures of evolution and of self-organization of the individual consciousness, their spatiotemporal peculiarities, and the complexity of the human Self are considered in detail. The radical changes in the understanding of the problems of time that occur due to synergetics are compared with images of time and with the notions of connection between the past, the present and the future in the history of philosophy and of culture. The obtained methodological inferences are of great importance for a reform of systems of education, for forecasting (for building of scenarios of future development), for effective management activity in the modern globalizing world, for elaboration of methods of stimulation of the creative thinking, for the growth of personality and its adequate building into the social media.

This book constitutes the proceedings of the 37th International Conference on Application and Theory of Petri Nets and Concurrency, PETRI NETS 2016, held in Toruń, Poland, in June 2016. Petri Nets 2016 was co-located with the Application of Concurrency to System Design Conference, ACSD 2016. The 16 papers including 3 tool papers with 4 invited talks presented together in this volume were carefully reviewed and selected from 42 submissions. Papers presenting original research on application or theory of Petri nets, as well as contributions addressing topics relevant to the general field of distributed and concurrent systems are presented within this volume.

These are the proceedings of the International Workshop on Petri Nets and Software Engineering (PNSE’13) and the International Workshop on Modeling and Business Environments (ModBE’13) in Milano, Italy, June 24–25, 2013. These are co-located events of Petri Nets 2013, the 34th international conference on Applications and Theory of Petri Nets and Concurrency.

PNSE'13 presents the use of Petri Nets (P/T-Nets, Coloured Petri Nets and extensions) in the formal process of software engineering, covering modelling, validation, and veriﬁcation, as well as their application and tools supporting the disciplines mentioned above.

ModBE’13 provides a forum for researchers from interested communities to investigate, experience, compare, contrast and discuss solutions for modeling in business environments with Petri nets and other modeling techniques.

Resource-driven automata (RDA) are finite automata, sitting in the nodes of a finite system net and asynchronously consuming/producing shared resources through input/output system ports (arcs of the system net). RDAs themselves may be resources for each other, thus allowing the highly flexible structure of the model. It was proved earlier, that RDA-nets are expressively equivalent to Petri nets. In this paper the new formalism of *cellular RDAs* is introduced. Cellular RDAs are RDA-nets with an infinite regularly structured system net. We build a hierarchy of cellular RDA classes on the basis of restrictions on the underlying grid. The expressive power of several major classes of 1-dimensional grids is studied.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.

Operational processes leave trails in the information systems supporting them. Such event data are the starting point for process mining – an emerging scientific discipline relating modeled and observed behavior. The relevance of process mining is increasing as more and more event data become available. The increasing volume of such data (“Big Data”) provides both opportunities and challenges for process mining. In this paper we focus on two particular types of process mining: process discovery (learning a process model from example behavior recorded in an event log) and conformance checking (diagnosing and quantifying discrepancies between observed behavior and modeled behavior). These tasks become challenging when there are hundreds or even thousands of different activities and millions of cases. Typically, process mining algorithms are linear in the number of cases and exponential in the number of different activities. This paper proposes a very general divide-and-conquer approach that decomposes the event log based on a partitioning of activities. Unlike existing approaches, this paper does not assume a particular process representation (e.g., Petri nets or BPMN) and allows for various decomposition strategies (e.g., SESE- or passage-based decomposition). Moreover, the generic divide-and-conquer approach reveals the core requirements for decomposing process discovery and conformance checking problems.

Process mining is a relatively new field of computer science which deals with process discovery and analysis based on event logs. In this work we consider the problem of discovering workflow nets with cancellation regions from event logs. Cancellations occur in the majority of real-life event logs. In spite of huge amount of process mining techniques little has been done on cancellation regions discovery. We show that the state-based region algorithm gives labeled Petri nets with overcomplicated control flow structure for logs with cancellations. We propose a novel method to discover cancellation regions from the transition systems built on event logs and show the way to construct equivalent workflow net with reset arcs to simplify the control flow structure.

In this work we consider modeling of services with workflow modules, which are a subclass of Petri nets. The service compatibility problem is to answer the question, whether two Web services fit together, i.e. whether the composed system is sound. We study complementarity of service produced/consumed resources, that is a necessary condition for the service compatibility. Resources, which are produced/consumed by a Web service, are described as a multiset language. We define an algebra of multiset languages and present an algorithm for checking the conformance of resources for two given structured workflow modules.

Process mining aims to discover and analyze processes by extracting information from event logs. Process mining discovery algorithms deal with large data sets to learn automatically process models. As more event data become available there is the desire to learn larger and more complex process models. To tackle problems related to the readability of the resulting model and to ensure tractability, various decomposition methods have been proposed. This paper presents a novel decomposition approach for discovering more readable models from event logs on the basis of a priori knowledge about the event log structure: regular and special cases of the process execution are treated separately. The transition system, corresponding to a given event log, is decomposed into a regular part and a specific part. Then one of the known discovery algorithms is applied to both parts, and finally these models are combined into a single process model. It is proven, that the structural and behavioral properties of submodels are inherited by the unified process model. The proposed discovery algorithm is illustrated using a running example.

The paper presents a dicision rule forming a mathematical basis of earthquake forecasting problem. We develop an axiomatic approach to earthquake forecasting in terms of a multicomponent random fields on a lattice.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.