Mathematical Models Of Complex Systems Research Articles

Artificial Intelligence in Mathematical Modeling of Complex Systems

This article introduces artificial intelligence techniques in mathematical modelling of complex systems and their applications. Mathematical modelling of complex systems is a method of studying the structure and behaviour of complex systems, aiming to understand interactions and nonlinear effects in the system. Commonly used modelling methods include system dynamics, network theory, and algebraic methods. Artificial intelligence technologies include machine learning and deep learning, which can be used for tasks such as prediction and classification, anomaly detection, optimization and decision-making. In mathematical modelling of complex systems, artificial intelligence technology can learn system patterns and laws from large amounts of data, and can be applied to image and speech recognition, time series analysis and other fields. Deep learning and machine learning are important branches of artificial intelligence. They realize the modelling and analysis of complex systems by building neural network models. Data-driven modelling is a modelling method based on actual data that, combined with traditional theoretical modelling, can better describe and predict the behaviour of complex systems. Self-control of complex systems means that the system realizes its own optimization and adjustment through adaptive control algorithms and feedback mechanisms. In summary, artificial intelligence technology has broad application prospects in mathematical modelling of complex systems and will provide new tools and methods for in-depth understanding and solving problems in complex systems.

Алгоритмы дискретной фильтрации на основе модифицированной взвешенной ортогонализации Грама –Шмидта для дискретных стохастических систем с мультипликативными и аддитивными шумами

Discrete-time stochastic systems with multiplicative and additive noises describe a wide class of mathematical models of complex systems, for example, industrial-technological, energy, economic, telecommunication, aerospace systems, etc. An important class of algorithms for processing measure ment information in complex systems are Kalman-type discrete-time filtering algorithms. Purpose. Construction of new discrete-time filtering algorithms for discrete-time linear systems with multiplicative and additive noises based on numerically stable modified weighted Gram – Schmidt orthogonalization (MWGS). Methodology. The methods of computational linear algebra were used, namely, the direct procedu re of MWGS-orthogonalization, the theory of Kalman filtering, methods of scientific programming in MATLAB. Findings. New LD-algorithms for discrete-time filtering in covariance and informational form for discrete-time stochastic systems with multiplicative and additive noises are constructed. The algorithms have an extended array form allowing updates for all necessary filter values. The method employs numerically stable modified weighted Gram – Schmidt orthogonalization. Algebraic equiva lence of LD-filters to Kalman-type covariance and informational algorithms for linear discrete time stochastic systems with multiplicative and additive noises is proved. The conducted numerical experiments have shown the effectiveness of the proposed algorithms using the example of solving the problem of parametric estimation of a model of almost rectilinear motion, as well as their savings in computation time compared to previously constructed UD filters. Value. New discrete-time filtering LD-algorithms can be used as a reliable computational alterna tive to the Kalman-type “standard algorithms” since they have the property being numerically stable to machine round-off errors due to the use of the MWGS orthogonalization computational procedure at each iteration of the algorithm. The results can be used to solve problems of measurement information processing in discrete-time systems with multiplicative and additive noise.

Efficient parameter generation for constrained models using MCMC

Mathematical models of complex systems rely on parameter values to produce a desired behavior. As mathematical and computational models increase in complexity, it becomes correspondingly difficult to find parameter values that satisfy system constraints. We propose a Markov Chain Monte Carlo (MCMC) approach for the problem of constrained model parameter generation by designing a Markov chain that efficiently explores a model’s parameter space. We demonstrate the use of our proposed methodology to analyze responses of a newly constructed bistability-constrained model of protein phosphorylation to perturbations in the underlying protein network. Our results suggest that parameter generation for constrained models using MCMC provides powerful tools for modeling-aided analysis of complex natural processes.

Preface to the Special Issue on “Control, Optimization, and Mathematical Modeling of Complex Systems”

Complex systems have long been an integral part of modern life and can be encountered everywhere [...]

Spatio-temporal combinatorics of resource flows conservation and reduction of risks in conditions of uncertainty of the external environment

Management of non-structured and weakly structured systems for the impacts of the dy-namic changes is not have a developed methodological basis. Management decisions are made on the basis of stochastic recommendations based on the results of existing experience with ex-trapolation to future trends without taking into account risks and possible faults. It is not neces-sary to introduce a great lack of value and inadequacy of acceptance of solutions, related to a wide range of criteria for assessments, without a wide range of factors, and highly direct indicators. When modeling management in the conditions of uncertainties of the environment, which are constantly changing, a large variety of source data is possible. The development of methods and models to support decision-making in terms of geo-graphically distributed processes is a very complex and non-trivial task. All interactions take place within a territorially distributed system. Such model can be built on a continuous basis, but it cannot be used to analyze spatial areas in real time. To reduce the level of risk and the results of possible losses, it is necessary to carefully study the possible carriers of risk, taking into account their individual characteristics, as well as market participants with the development of their original methods of risk management. The initial information on identifying problems of unstable market development is contained in the ratio of internal and external destabilizing factors. Information as an integral part of doing business plays a key role in reducing the risks that ensure the commercialization of proposals. Decision-making in a complex system is that from the available set of acceptable con-trols, it is necessary to identify several options that are the best. The rule that establishes the advantage in many solutions is the principle of optimality. When solving problems of optimal control as a set of valid alternatives use the combinatorics of acceptable management. An important difference between the construction of mathematical models of complex systems is that the modeling is not above the global function and the allocation of the main parts, and below, with the construction of models of individual processes and lower hierar-chical levels. Larger modules and the system as a whole are modeled on the basis of reasona-ble complexity. Combinatorics is directly related to simulation modeling, when it is impossible to apply mathematical solutions to problems in conditions of uncertainty. A perspective area of analysis and management of development under conditions of un-certainty and ambiguity of the external environment is graph theory using the Ford-Falkerson algorithm. Control under the action of constantly changing environments with the onset of change is solved using the Ford-Falkerson algorithm. The network of possible movements is considered as a connected digraph. In the conditions of global risks it is not necessary to count only on one direction of de-velopment. The sudden emergence of restrictions forces to move to another branch of the network, for which the network provides additional vertical edges with their probabilities and bandwidth. As the change of the situation is unpredictable, the transition from one branch to another can occur spontaneously, which is reflected in the presence in the source network of inclined edges that have their own direction and their own weights. The introduction of the method of transition from one branch of the oriented network to another at the time of termination of its implementation due to the unpredictable influence of environmental factors ensures the distribution of risks between the components. The use of combinatorics of the proposed options for interactions in the state space, their implementation at different moments of iterations, their application with the synchronization of flow throughput can reduce the risks arising from the functioning of systems.

MODELING OF INFORMATION TECHNOLOGY OF MATERIAL RESOURCES MANAGEMENT OF A CONSTRUCTION COMPANY

The article's research subject is the information technology of construction company's material resources management. The work's purpose is to construct and implement tools for modeling construction company's material resources management information technology. The article solves the following tasks: determining the place of information technology of construction company's material resources management in the modern construction company's information ecosystem, defining the main components, and building a functional model of construction company's material resources management information technology, taking into account the shortcomings of existing models, сreation of the multicriteria optimization model of the considered information technology. The following methods are used: system analysis, structural analysis, mathematical modeling of complex systems and processes, multicriteria optimization. The following results were obtained: a structural analysis of the existing information ecosystem at the regional level construction company, the composition of which is agreed on the organizational structure elements of the enterprise and the stages of the construction life cycle; considered the functions of construction company's material resources management which are realized at various stages of a construction project life cycle; constructed the set-theoretical model of material resources management information technology; determined the functional characteristics of the considered information technology, offered the criteria of information technology efficiency according to the ITIL strategy; constructed the conceptual model of information technology of material resources management. Conclusions: for the first time, developed tools for modeling construction company's material resources management information technology, including a theoretical-multiple model of material resources management information technology; Offered the information technology's conceptual scheme which realizes specific information technology's functional characteristics. The built modeling strategy will provide an opportunity for further development and software implementation of the information technology.

SPACES OF VARIABLE DIMENSION

Usually scientists build physical models depending on how they perceive the world. But the current state of affairs in science has shown that where the scale is very small compared to our usual world, it is not justified to use models that could be used in the macro world. One of the options that can take place in the micro world, but has no analogues in our ordinary world, which we observe every day, is that space can change or have a fractional dimension. It is possible that the dimension of space will have certain values, depending on the conditions in which our complex system is observed in space, or depending on the frame of reference of the observer. And thus the calculations in the mathematical modeling of complex systems must be adjusted in accordance with the dimension of space.

HCGA: Highly comparative graph analysis for network phenotyping

SummaryNetworks are widely used as mathematical models of complex systems across many scientific disciplines. Decades of work have produced a vast corpus of research characterizing the topological, combinatorial, statistical, and spectral properties of graphs. Each graph property can be thought of as a feature that captures important (and sometimes overlapping) characteristics of a network. In this paper, we introduce HCGA, a framework for highly comparative analysis of graph datasets that computes several thousands of graph features from any given network. HCGA also offers a suite of statistical learning and data analysis tools for automated identification and selection of important and interpretable features underpinning the characterization of graph datasets. We show that HCGA outperforms other methodologies on supervised classification tasks on benchmark datasets while retaining the interpretability of network features. We exemplify HCGA by predicting the charge transfer in organic semiconductors and clustering a dataset of neuronal morphology images.

Descriptive models of the determined systems

Common mathematical models of complex systems are not flexible, their creation is very resource-demanding and they are hard to work with. The numerous problems can arise during the process of building a mathematical model for complex systems. An area of knowledge, facts, and information could be structured badly or not structured at all. Part of the data might be missing or vice versa – we might have too much data available, which makes it difficult to find the necessary information. Therefore building a formal mathematical model, studying its dynamic for the relevant area of knowledge becomes a very hard or even almost impossible task. And that is why the new methods for such task are in much demand, namely, the methods of building descriptive mathematical models. The descriptive mathematical model serves as not a strict and formal model but a qualitative one. Such a qualitative model gives us a possibility to describe the character of the system, behavior of its internal components, and approximate rules of its dynamics. The qualitative model gives us a chance to deny the propositions, which do not fit the model directly at the first stage.

Generating Massive Scale-free Networks

Recently, there has been substantial interest in the study of various random networks as mathematical models of complex systems. As real-life complex systems grow larger, the ability to generate progressively large random networks becomes all the more important. This motivates the need for efficient parallel algorithms for generating such networks. Naïve parallelization of sequential algorithms for generating random networks is inefficient due to inherent dependencies among the edges and the possibility of creating duplicate (parallel) edges. In this article, we present message passing interface-based distributed memory parallel algorithms for generating random scale-free networks using the preferential-attachment model. Our algorithms are experimentally verified to scale very well to a large number of processing elements (PEs), providing near-linear speedups. The algorithms have been exercised with regard to scale and speed to generate scale-free networks with one trillion edges in 6 minutes using 1,000 PEs.

HCGA: Highly Comparative Graph Analysis for Network Phenotyping

Networks are widely used as mathematical models of complex systems across many scientific disciplines, not only in biology and medicine but also in the social sciences, physics, computing and engineering. Decades of work have produced a vast corpus of research characterising the topological, combinatorial, statistical and spectral properties of graphs. Each graph property can be thought of as a feature that captures important (and some times overlapping) characteristics of a network. In the analysis of real-world graphs, it is crucial to integrate systematically a large number of diverse graph features in order to characterise and classify networks, as well as to aid network-based scientific discovery. In this paper, we introduce HCGA, a framework for highly comparative analysis of graph data sets that computes several thousands of graph features from any given network. HCGA also offers a suite of statistical learning and data analysis tools for automated identification and selection of important and interpretable features underpinning the characterisation of graph data sets. We show that HCGA outperforms other methodologies on supervised classification tasks on benchmark data sets whilst retaining the interpretability of network features. We also illustrate how HCGA can be used for network-based discovery through two examples where data is naturally represented as graphs: the clustering of a data set of images of neuronal morphologies, and a regression problem to predict charge transfer in organic semiconductors based on their structure. HCGA is an open platform that can be expanded to include further graph properties and statistical learning tools to allow researchers to leverage the wide breadth of graph-theoretical research to quantitatively analyse and draw insights from network data.

Modeling of polygraphic web-service using colored Petri nets

The use of Petri Networks as a tool for graphical and mathematical modeling of complex systems and processes has recently been widespread. Visual representation techniques and simulations, such as Petri colored networks, are effective at the development stage of complex systems, since they allow formally to describe and model the system at different levels of abstraction and investigate them dynamically. An example of a dynamic system is web-services. Web services and their components can interact with different applications that meet the standards of web services. As a rule, one service does not meet the needs of users, and services are becoming more and more complex. In fact, a modern web service is created by combining different web services and their components to create a component service that offers a set of new functional services. When combining and sharing Web services the most critical is the interaction of Web services and their components among themselves, which requires a detailed study of the functioning of the processes and modeling their behavior to improve their efficiency.Polygraphic web-service is a complex program system that organizes the provision of printing services. It works with the client through the Internet and provides an opportunity to find the necessary service at the printing centers for the best possible means, to make an order, to use various services, to pay for services, to choose a means of payment and delivery of printed products. The complex structure of the web-service requires the study and modeling of the interaction of its components to ensure the effectiveness of the operation.To model the composite web service system, it is necessary to identify the main and auxiliary subsystems by means of structural analysis. The block diagram of a web-service is presented in fig. 1. As a structural analysis tool, we used a data flow diagram (DFD) in the notation of a similar Heine-Sarson notation. A top-level contextual chart contains a set of subsystems connected by data streams.A model of a polygraphic web-service in the form of Petri's network in a hierarchical form was developed and presented for the purpose of analysis of separate networks of the second level. This enables to analyze all parts of the network separately and use the results to formulate conclusions about the correctness of the construction of the entire network. In the presence of links between networks of the second level, it is necessary to add additional criteria for the analysis of networks, which are connected with the addition of the main network of cities and transitions between networks of the second level, the number of which depends on the number of possible states of interaction between networks of the second level.

Analysing modeling methods in the ecology from the systemology positions

To obtain a forecast, models of behavior of specific systems are created, whose adequacy can be judged only within the framework of accepted hypotheses. The increase in the complexity of the object under study causes an increase in the complexity of the mathematical apparatus. However, today’s modeling device does not solve the main problem of increasing the low (or unsatisfactory) predictive ability of models of rather complicated systems. Ecosystems are the objects of complex nature, and the methodological basis for their study is the theory of complex systems. Therefore, when solving this issue, it is necessary to turn to the analysis of the basic principles of systemology. Goal: analysis of the main provisions of systemology for the application of modeling in ecosystem research. The methodological basis for the study of the ecosystem is the theory of complex systems. As a result of the work the analysis of the basic positions of systemology concerning the approaches in the study of simple and complex systems was carried out. The basic principles of systemology and the most important functions of explanation and prediction of the observed phenomena in the studied class of systems are considered, as well as the connection between the complications of the behavior of simulated objects and the methods of their modeling. It is determined that in the study of complex systems, the principle of multiplicity of models is used. In this case, none of the methods of modeling has all sets of model functions at the same time. The principle of feasibility of models is manifested in the block method of constructing simulation models. This to overcome allows to some extent the pro-oath of dimension in models of potential efficiency, where impossible situations can be rejected for real systems. The principle of incompatibility manifests itself in the fact that none of the methods of modeling realizes simultaneously the explanatory and predictive functions of the theory. Finally, the principle of counter-intuitive behavior of complex systems is taken into account when constructing self-organizing models. It is noted that mathematical modeling of complex systems should be considered as an extension of traditional natural science experiment. With regard to the analysis of environmental systems, as well as the analysis of any other complex system, the experiment should replace the power of abstraction and computer simulation.

A dialectical vision of mathematical models of complex systems

Purpose Mathematical models are constructed at the interface between practice, experience and theories. The function of models puts us on guard against the privilege granted to what is accepted as abstract and formal, and at the same time puts us on guard against a static and phenomenological conception of knowledge. The epistemology of models does not suppress in any way the objectives of science: only, a dogmatic conception concerning truth is removed, and dynamic and dialectical aspects of monitoring are stressed to establish the most viable model. The purpose of this paper is to examine hybrid methodologies (inductive-deductive) that may either propose hypothetical causal relations and seek support for them in field data or detect causal relations in field data and propose hypotheses for the relations detected. Design/methodology/approach The authors follow a dialectical analysis for a type of inductive-deductive model. Findings In this work, the authors present an inductive-deductive methodology whose practical result satisfies the Hegelian dialectic. The consequent implication of their mutual reciprocal integration produces abstractions from the concrete that enable thought. The real problem in this case is a given ontological system or reality. Originality/value The essential elements of the models – variables, equations, simulation and feedback – are studied using a dialectic Hegelian theory.

Використання мішаної розрядності у математичному моделюванні

The work proposes a method by which it is possible to accelerate the time of mathematical modeling of complex systems, using a mixed precision in calculations. The mixed precision allows you to improve the computing performance and save memory. Showing this approach in constructing an algorithm for solving systems of linear algebraic equations with sparse matrices

Математичне моделювання складних систем на основі суперкомп’ютерних технологій

Математичне моделювання складних систем на основі суперкомп’ютерних технологій

Technology of hybrid computational intellect and problems associated with intelligent vehicle control systems development

Abstract The authors of this article are presenting the concepts of intelligent vehicle control systems development on the basis of author’s concept of mathematical modeling of complex systems by method of heuristic correction of basic analytical dependences by heuristic knowledge and soft computation. The authors are formulating the basic provisions of “knowledge genesis” method intended for the development of particular class of mathematic models capable (based on flexible computation) (i) to integrate determinate, indeterminate and uncertain knowledge in one and the same system and (ii) to change (accommodate) its structure in the course of modeling the object of evolution. The authors are (i) representing functional scheme of future-oriented on-board intelligent system of motor vehicle (hereinafter referred to as “ATS”) control developed on the basis of hybrid computational intellect and (ii) giving an example of hybrid computational model of unmanned ATS dynamic behavior developed on the basis of “knowledge genesis” method. The proposed methodological and application-oriented concepts of soft mathematical modeling (made on the basis of “knowledge genesis” method) could become the basis for the development of a range of future-oriented intelligent systems capable to exercise control of advanced high-technology vehicles (including unmanned vehicles and vehicles pertaining to civil and military spheres of application).

Recent progress in mathematical modelling of complex systems

Recent progress in mathematical modelling of complex systems

Effect of Operating Point Selection on Non-linear Experimental Identification of iSTC–21v and TKT–1 Small Turbojet Engines

Precise dynamic mathematical models of complex systems are important in control and diagnostic systems design and allow testing a complex system in virtual environment at a low cost. They can be also utilized in rapid prototyping using a concept of hardware in the loop. Ever improving methods of experimental identification and using approaches in non-linear approximation can considerably increase the precision of dynamic models of complex systems. The article deals with non-linear approximation of transfer gains of a complex system and evaluates the influence of operational point selection on precision of the resulting model using methods of experimental data driven identification. The object of control is represented by two similar small turbojet engines at the Departments of the authors, the iSTC-21v and TKT-1, both based on the same power section having two degrees of freedom: fuel mass flow rate and variable convergent nozzle position.

Lumped models of the cardiovascular system of various complexity

PurposeThe main objective is to accelerate the mathematical modeling of complex systems and offer the researchers an accessible and standardized platform for model sharing and reusing. MethodsWe describe a methodology for creating mathematical lumped models, decomposing a system into basic components represented by elementary physical laws and relationships expressed as equations. Our approach is based on Modelica, an object-oriented, equation-based, visual, non-proprietary modeling language, together with Physiolibrary, an open-source library for the domain of physiology. ResultsWe demonstrate this methodology on an open implementation of a range of simple to complex cardiovascular models, with great complexity variance (simulation time from several seconds to hours). The parts of different complexity could be combined together. ConclusionsThanks to the equation-based nature of Modelica, a hierarchy of subsystems can be built with an appropriate connecting component. Such a structural model follows the concept of the system rather than the computational order. Such a model representation retains structural knowledge, which is important for e.g., model maintainability and reusability of the components and multidisciplinary cooperation with domain experts not familiar with modeling methods.