Estimation of the world economic system stability from 1963 to 2013 by using a discrete dynamic model

<abstract> <p>The current global economic crisis has actualized the problem of studying non-equilibrium processes in the economy. To approach the problem, a discrete dynamic model (DDM) was developed that describes the dynamics of the rate of change in the global GDP for the period 1961-2021. This paper publishes the results of studies of two types of stability. The first is connected with the global economic system stability, which can be described by a DDM in different time periods. The second studies sensitivity of the DDM to the annual GDP growth values that were used to construct it (sensitivity analysis). The conducted research depicted the various periods of development of the global economic system, characterized by varying degrees of stability. The DDM determined that during periods of crises, the stability of the global economic system decreases. Our studies have shown that at present the world economic system is on the verge of a complete loss of stability. To assess the sensitivity of the DDM to the input data, a sensitivity indicator was introduced. It was found that the DDM is insensitive to input data during periods of crisis, i.e., the results obtained are reliable. In turn, periods of stable development of the global economic system are characterized by less reliability in the DDM results.</p> </abstract>

The current English teaching mode focuses on the traditional offline teaching and online teaching. In order to solve the problems that some students are inefficient and cannot teach students according to their aptitude in the teaching process, this paper uses the big data analysis strategy based on a neural network algorithm. This paper studies the discrete dynamic modeling method of learner behavior analysis in English teaching. Firstly, it summarizes the current situation of English teaching and the research status of the hybrid application of discrete dynamic modeling technology. Secondly, combined with English teaching content and teaching objectives, through the analysis of various data of students' learning behavior, this paper evaluates students' English teaching quality from five aspects that affect the students' English teaching quality and puts forward a personalized English teaching quality evaluation model based on discrete dynamic modeling technology and learners' behavior analysis. Finally, through the practical teaching application in a university, the feasibility of the discrete dynamic English teaching model is verified. The results show that compared with the current innovative English teaching methods based on a dynamic iterative decision algorithm, the personalized discrete dynamic English teaching model based on learner behavior analysis significantly improves the quality of English teaching and students' academic performance.

Estimation of dynamic discrete models from time aggregated data

A simplified method of 3‐D dynamic analysis, named 3‐D quasi‐dynamic analysis, is presented. This method has been primarily used to evaluate stress states at identified times of peak dynamic responses of structures with flexible diaphragms. The quasi‐dynamic analysis consists of extracting the accelerations predicted by the time‐step integration analyses of two 2‐D discrete MDOF dynamic models of a given structure (each discrete model corresponding to one of the principal orthogonal directions of the structure) at given times of interest. These accelerations are imposed on a 3‐D representation of the structure (for example, a finite element mesh) as equivalent static forces. Accelerations at the diaphragms are assumed to act over the same tributary areas of the diaphragms considered in the 2‐D discrete dynamic models.The study of the firehouse of Gilroy (an unreinforced masonry structure with flexible diaphragms) during the Loma Prieta Earthquake is presented to illustrate the 3‐D quasi‐dynamic seismic analysis. This method was compared to the more traditional 3‐D modal time‐step integration and 3‐D response spectra analyses. The quasi‐dynamic analysis had a general good agreement with the more formal, complex and computationally extensive modal time‐step integration analysis. The 3‐D response spectra analysis was very conservative and had a poor correlation with both the quasi‐dynamic and the modal time‐step integration analyses. The case study of the firehouse of Gilroy suggested that if 3‐D effects have to be considered in the evaluation of a given structure, the quasi‐dynamic analysis constitutes a reliable and computationally cheaper alternative to the more traditional methods of 3‐D dynamic analysis.

Discrete dynamical modeling and analysis of the R– S flip-flop circuit

The identification of the discount factor in dynamic discrete models is important for counterfactual analysis, but hard. Existing approaches either take the discount factor to be known or rely on high level exclusion restrictions that are difficult to interpret and hard to satisfy in applications, in particular in industrial organization. We provide identification results under an exclusion restriction on primitive utility that is more directly useful to applied researchers. We also show that our and existing exclusion restrictions limit the choice and state transition probability data in different ways; that is, they give the model nontrivial and distinct empirical content.

In biomolecular systems, various non-identical molecules interact in diverse ways. The field of systems biology aims to understand how the components and interactions of biological systems give rise to the system’s behavior and phenotypes. Researchers have used molecular networks and dynamic models to represent and understand biological systems. In this chapter, we introduce the network representation and the graph measures that quantify its topological properties. We describe how to build a discrete dynamic (Boolean) model of a biological system from experimental data, and how to use the model to provide insights into emergent phenomena and make useful predictions. We also introduce methods to bridge the network’s topological and dynamical properties. We use real biological system involved in complex disease to demonstrate the theoretical framework. Discrete dynamical models, especially Boolean networks, benefit from the current high-throughput technologies and large amounts of qualitative data and provide insight to large-scale systems, where continuous modeling is not possible yet.

Systems pharmacology is an interdisciplinary field that aims to apply the theoretical and experimental tools of systems biology to drug development. The goal is to go beyond the interaction between a drug and the target to which it binds to explore drug effects on the cellular networks affected by disease. Over the years, vast amounts of information about the regulatory relationships among genes, proteins, and small molecules have been acquired. Similarly, there is much known about the deregulation of these systems during disease. However, many knowledge gaps still exist. There is an abundance of qualitative or relative information related to the activation of signaling pathways, but a paucity of kinetic and temporal information. Discrete dynamic modeling provides a means to create predictive models of signal transduction pathways by integrating fragmentary and qualitative interaction information. Using discrete dynamic modeling, a structural (static) network of biological regulatory relationships can be translated into a mathematical model without the use of kinetic parameters. This model can describe the dynamics of a biological system over time, both in normal and in perturbation scenarios. In this chapter, we discuss the fundamentals of discrete dynamic modeling as it pertains to systems pharmacology. As an example, we apply this methodology to a previously constructed pharmacodynamic model of epidermal derived growth factor receptor (EGFR) signaling. We (1) translate this model into two types of discrete models, a Boolean model and a three-state model, (2) show how the effects of an EGFR inhibitor (such as gefitinib) can suppress tumor growth, and (3) model how genomic variants can augment the effect of EGFR inhibition in tumor growth. We argue that discrete dynamic models can be used to facilitate many of the goals of systems pharmacology. These include understanding how individual differences contribute to variability in drug response and determining which drugs would be best depending on individual genetic differences.

Chapter 11 - Discrete Dynamic Modeling of Cellular Signaling Networks

The driving force of high-quality development of regional economy is inseparable from the support of technology. With the support of big data, we need to solve this problem in order to solve the difficulty of large-scale experimental testing and accurately reflect the feasibility growth of data sample changes. This paper proposes a discrete dynamic modeling technology based on big data background to analyze the development and change of regional economy. The reliability AMSAA model is usually used for dynamic discrete modeling. It can be combined with the change data provided by big data to form a dynamic modeling method for reliability growth evaluation. Then, the Bayesian regression method is used to predict the change parameters of the model, and the spatial econometric method is used to analyze the regional economic change. The results show that compared with the traditional methods, the discrete dynamic modeling method is more accurate and can effectively solve the problem of reliable growth under the condition of big data. After introducing the spatial effect measurement model, it can also reflect the main factors of the growth and change of regional economic real output value. In addition to the development of high and new technology, terrain factors, investment, and government support have also had different effects. Therefore, according to the above results, it is proved that the discrete dynamic modeling technology can accurately obtain the experimental data and provide reliable technical support for dynamic data processing.

With the increasing proportion of renewable energy in the new power system, the grid-connected capacity of photovoltaic (PV) units shows an obvious upward trend, but its dynamic behavior under different penetration rates significantly affects the transient stability of the power system, so it is crucial to establish a dynamic model that meets the actual working conditions and select a suitable parameter identification method. Therefore, in this paper, based on the electromechanical transient characteristics of the grid-connected PV power generation system, the corresponding dynamic discrete equivalent model is established, and the simulation platform of the grid-connected PV power generation system is built in MATLAB/Simulink to study the adaptability of the dynamic discrete equivalent model of the grid-connected PV power generation system from the single and multiple scenarios using the ordinary least squares (OLS) and bat algorithm (BA) while comparing the generalization ability of the parameters identified by the two methods to the model. The simulation results show that the generalization ability of the parameters identified by the OLS and BA for the model in the single scenario is better, indicating that the model has good adaptability; the generalization ability of a set of general parameters identified by the BA for the model in the multiple scenarios is better than that of the OLS, indicating that the parameters identified by the BA have better adaptability. In conclusion, the dynamic discrete equivalent model of the grid-connected PV power generation system proposed in this paper can accurately reflect the dynamic characteristics of the grid-connected PV power generation system, and the parameters identified by the BA are more generalized than the OLS.

The state of the global economic system is described by a large number of parameters. It is interesting to find out whether it is possible to collapse these parameters into a single symbol (image, logograph) that would describe the state of the global economic system as a whole. A discrete dynamic model (DDM) was used to describe the global economic system. DDM states can be divided into unstable and stable. The degree of instability of the DDM can be used to assess the likelihood that the economic system would emerge from an unstable state. In turn, stable states are divided into stable points, stable cycles and strange attractors. It was discovered that stable states are characterized by areas of convergence that represent fractal formations. The unique nature of fractals encourages us to assess their usefulness and informative value when describing the state of the world economic system. In this work, we are trying to carry out such an assessment and formalize the characteristics of fractals in order to give a rough description of the states of the world economic system. To get input data, we used information on the rate of change in world GDP provided on the World Bank website as of June 29, 2023.

Newly available experimental data characterizing different processes involved in signaling pathways have provided the opportunity for network analysis and modeling of these interacting pathways. Current approaches in studying the dynamics of signaling networks fall into two major groups, namely, continuous and discrete models. The lack of kinetic information for biochemical interactions has limited the wide applicability of continuous models. To address this issue, discrete dynamic models, based on a qualitative description of a system's variables, have been applied for the analysis of biological systems with many unknown parameters. The purpose of this chapter is to give a detailed description of Boolean modeling, the simplest type of discrete dynamic modeling, and the ways in which it can be applied to analyze the dynamics of signaling networks. This is followed by practical examples of a Boolean dynamic framework applied to the modeling of the abscisic acid signal transduction network in plants as well as the T-cell survival signaling network in humans.

The article considers economic and mathematical models and studies the socio-economic processes that develop over time, as well as mathematical models that describe them. These are dynamic models. All variables in dynamic models generally depend on the time that acts as an independent variable. In economic research, there are often problems in which variables acquire discrete numerical values. For example, at the end of the month, quarter, year, etc., production results are optimized; accrual of interest on the bank deposit at the end of the month, six months, at the end of the year. In addition, because computers operate only with numbers, so when using computer technology, all continuous processes are reduced to discrete. In this case, from differential equations that describe certain economic processes, we move to difference equations. There are dynamic models with continuous and discrete time, ie continuous and discrete models. Therefore, depending on the type of dynamics of the system under study, dynamic models can be divided into discrete and continuous. In discrete dynamic models, difference equations or systems of difference equations are used; differential equations or systems of differential equations are used in continuous dynamic models. In addition, in some cases there may be systems with mixed dynamics, then differential-equation equations are used to describe them. Difference equations and systems of equations are used successfully in modeling dynamic processes (in economics, banking, etc.). It is when the change of process occurs abruptly, or discretely, that it is convenient and expedient to apply difference equations and systems of equations. The theory of dynamical systems with discrete time, which arose as a result of building mathematical models of real economic and physical processes at the junction of the theory of difference equations and discrete random processes, is currently experiencing a period of rapid development and widespread use in various spheres of human life. In this paper, we investigate the following equations, as well as show their application to solve economic problems. In particular, discrete models described by first-order difference equations are considered. Considerable attention is paid to the analysis of specific models that are meaningful and widely used in economic theory, banking, etc.

With the advent of the big data era, information technology and intelligent algorithms are more and more widely used. In the engineering project management industry, big data technology and dynamic modeling have achieved good results. Enterprises attach great importance to the innovation of engineering project management. The establishment of engineering management and quality optimization innovation model can improve the management efficiency of engineering project process and enable enterprises to obtain great advantages in market competition. The use of big data technology can make project management and quality innovation more information‐based and intelligent. Based on the above situation, this paper puts forward the research on discrete dynamic modeling of engineering management and optimization innovation mode based on big data intelligent algorithm. It mainly uses big data technology to collect and classify the obtained data information and uses discrete dynamic modeling technology to optimize the management system, focus on the management and innovation of green engineering, use big data dynamic modeling technology to build engineering management model, and improve the balance of project model through intelligent planning algorithm. The experimental results show that the big data intelligent algorithm combined with discrete dynamic modeling technology increases the applicability and feasibility of the system. The accurate data after big data analysis can be used for quality supervision and detection, which not only improves the project quality problems but also improves the management efficiency of the project.