Science Dynamics and Research Production

Science is a driving force of positive social evolution. And in the course of this evolution, research systems change as a consequence of their complex dynamics. Research systems must be managed very carefully, for they are dissipative, and their evolution takes place on the basis of a series of instabilities that may be constructive (i.e., can lead to states with an increasing level of organization) but may be also destructive (i.e., can lead to states with a decreasing level of organization and even to the destruction of corresponding systems). For a better understanding of relations between science and society, two selected topics are briefly discussed: the Triple Helix model of a knowledge-based economy and scientific competition among nations from the point of view of the academic diamond. The chapter continues with a part presenting the minimum of knowledge necessary for understanding the assessment of research activity and research organizations. This part begins with several remarks on the assessment of research and the role of research publications for that assessment. Next, quality and performance as well as measurement of quality and latent variables by sets of indicators are discussed. Research activity is a kind of social process, and because of this, some differences between statistical characteristics of processes in nature and in society are mentioned further in the text. The importance of the non-Gaussianity of many statistical characteristics of social processes is stressed, because non-Gaussianity is connected to important requirements for study of these processes such as the need for multifactor analysis or probabilistic modeling. There exist entire branches of science, scientometrics, bibliometrics, informetrics, and webometrics, which are devoted to the quantitative perspective of studies on science. The sets of quantities that are used in scientometrics are mentioned, and in addition, we stress the importance of understanding the inequality of scientific achievements and the usefulness of knowledge landscapes for understanding and evaluating research performance. Next, research production and its assessment are discussed in greater detail. Several examples for methods and systems for such assessment are presented. The chapter ends with a description of an example for a combination of qualitative and quantitative tools in the assessment of research: the English–Czerwon method for quantification of scientific performance.

The understanding of dynamics of research organizations and research production is very important for their successful management. In the text below, selected deterministic and probability models of research dynamics are discussed. The idea of the selection is to cover mainly the areas of publications dynamics, citations dynamics, and aging of scientific information. From the class of deterministic models we discuss models connected to research publications (SI-model, Goffmann–Newill model, model of Price for growth of knowledge), deterministic model connected to dynamics of citations (nucleation model of growth dynamics of citations), deterministic models connected to research dynamics (logistic curve models, model of competition between systems of ideas, reproduction–transport equation model of evolution of scientific subfields), and a model of science as a component of the economic growth of a country. From the class of probability models we discuss a probability model connected to research publications (based on the Yule process), probability models connected to dynamics of citations (Poisson and mixed Poisson models, models of aging of scientific information (death stochastic process model and birth stochastic process model connected to Waring distribution)). The truncated Waring distribution and the multivariate Waring distribution are described, and a variational approach to scientific production is discussed. Several probability models of production/citation process (Paretian and Poisson distribution models of the h-index) as well as GIGP model distribution of bibliometric data are presented. A stochastic model of scientific productivity based on a master equation is described, and a probability model for the importance of the human factor in science is discussed. The chapter ends by providing information about some models and distributions connected to informetrics: limited dependent variable models for data analysis and the generalized Zipf distribution and its connection to the Waring distribution and Yule distribution.