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This book deals with methods to evaluate scientific productivity. In the book statistical methods, deterministic and stochastic models and numerous indexes are discussed that will help the reader to understand the nonlinear science dynamics and to be able to develop or construct systems for appropriate evaluation of research productivity and management of research groups and organizations. The dynamics of science structures and systems is complex, and the evaluation of research productivity requires a combination of qualitative and quantitative methods and measures. The book has three parts. The first part is devoted to mathematical models describing the importance of science for economic growth and systems for the evaluation of research organizations of different size. The second part contains descriptions and discussions of numerous indexes for the evaluation of the productivity of researchers and groups of researchers of different size (up to the comparison of research productivities of research communities of nations). Part three contains discussions of non-Gaussian laws connected to scientific productivity and presents various deterministic and stochastic models of science dynamics and research productivity. The book shows that many famous fat tail distributions as well as many deterministic and stochastic models and processes, which are well known from physics, theory of extreme events or population dynamics, occur also in the description of dynamics of scientific systems and in the description of the characteristics of research productivity. This is not a surprise as scientific systems are nonlinear, open and dissipative.



Science and Society. Research Organizations and Assessment of Research


Chapter 1. Science and Society. Assessment of Research

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.
Nikolay K. Vitanov

Indicators and Indexes for Assessment of Research Production


Chapter 2. Commonly Used Indexes for Assessment of Research Production

In this chapter, selected indicators and indexes (constructed on the basis of research publications and/or on the basis of a set of citations of these publications) are discussed. These indexes are frequently used for assessment of production of individual researchers. The chapter begins with several general remarks about indicators and indexes used in scientometrics. Then the famous h-index of Hirsch, its variants, and indexes complementary to the h-index are discussed. Next the g-index of Egghe as well as the \(i_n\)-indexes are described. The h-index, g-index, and \(i_n\)-indexes may provide a minimum of information for the quantitative part of assessment of the production of a researcher. Numerous indexes are described further in the text such as the m-index, p-index, \(IQ_p\)-index, A-index, R-index. The discussion of indexes continues with a discussion of indexes for the success of a researcher. In addition, a short list of indexes for quantitative characterization of research networks and their dynamics is presented.
Nikolay K. Vitanov

Chapter 3. Additional Indexes and Indicators for Assessment of Research Production

About forty-five indexes for assessment of research production of single researchers have been discussed in Chap. 2. These indexes are based mainly on citations of publications of the evaluated researcher. The indexes form Chap. 2 can be calculated also for groups of researchers. In addition to indexes from Chap. 2, other indexes useful for assessment of production of groups of researchers may be used. About ninety such indexes are discussed in this chapter. The indexes are grouped in the following classes: simple indexes; indexes for deviation from simple tendency; indexes for difference; indexes for concentration, dissimilarity, coherence, and diversity; indexes for advantage and inequality; indexes for stratified data; indexes for imbalance and fragmentation; indexes based on the concept of entropy; Lorenz curve and associated indexes. In addition, the set of indexes connected to the RELEV method for assessment of scientific research performance within public institutes as well as indicators and indexes for scientific research performance of nations and about comparing national scientific productions are discussed. Finally, we discuss briefly several journal citation measures as well as an example of an application of a geometric tool for detection of scientific elites in a group of institutes on the basis of Lorenz curves.
Nikolay K. Vitanov

Statistical Laws and Selected Models


Chapter 4. Frequency and Rank Approaches to Research Production. Classical Statistical Laws

We discuss several classical statistical laws that are important for understanding characteristics of research production and for its assessment. The statistical laws are grouped in such a way that the two much-used statistical approaches for the study of research systems and especially for the study of research publications (frequency approach and rank approach) are appropriately addressed. We begin with some remarks on the frequency and rank approaches to distributions and discuss why the frequency approach is much used in the natural sciences and the rank approach is widely used in the social sciences. Then the stable non-Gaussian distributions are described, and their importance for statistical methodology of research dynamics is emphasized. The laws of Lotka, Pareto, Zipf, Zipf–Mandelbrot, and Bradford are discussed from the point of view of their application to describing different aspects of scientific production. In addition to the discussion of statistical laws, we discuss two important effects: the concentration–dispersion effect (which reflects the separation of the researchers into a small group of highly productive ones and a large group of researchers with limited productivity) and the Matthew effect in science (which reflects the larger attention to the research production of the highly ranked researchers). In addition, we mention the invitation paradox (many papers accepted in highly ranked journals are not cited as much as expected) and the Ortega hypothesis (the big discoveries in science are supported by the everyday hard work of ordinary researchers). At the end of the chapter we discuss more general questions; relationships between the statistical laws and power laws as informetric distributions.
Nikolay K. Vitanov

Chapter 5. Selected Models for Dynamics of Research Organizations and Research Production

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.
Nikolay K. Vitanov

Chapter 6. Concluding Remarks

In this chapter, several concluding remarks are provided about the importance of science for society and about general characteristics of research systems. The importance of statistical laws for research systems is emphasized, and we stress the usefulness of mathematical models and methods for the study and understanding of the dynamics of science and scientific production.
Nikolay K. Vitanov


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