Science Dynamics and Research Production: Indicators, Indexes, Statistical Laws and Mathematical Mod

Part I Society, economics and science.- Scientific structures and systems.- Complex structure and system of science.- Nonlinear dynamics of scientific entities.- Science is so important.- On the connection between science and technology.- Several features of technological progress.- Science as important component of the economic growth of a country: global point of view.- Role of technology for the growth of a GDP of a country.- Role of science for development of technology.- Factors for growth of science.- Science as important component of economic growth of a country: local point of view.- Why the size of the scientific community is important?.- The effective solutions of the scientific problems depend on the size of the scientific community.- Increasing complexity of problems requires increase of the size of group of scientists that has to solve them.- Science structures are dissipative. Three levels of the structure of science.- Science as open system.- Financial, material, and human resource flows keep science in an organized state.- Levels and characteristic features of science structures.- Role of instability for evolution of science.- Model of science as a part of global model of a social system.- Two scenarios based on the model of science as a part of the social system.- Scientific competition among the nations. Extended academic diamond.- Several concluding remarks.- References.- Quality and quantity in the study of science, research work and research productivity. The role of mathematics.- Remarks about publications and other aspects of evaluation of performance in science.- Quality management systems. Processes and process indicators.- Performance measurement systems.- Analysis of key processes.- Analysis of the needs of the organization and its stakeholders.- Plan of the system and plan for implementation of the system.- An example of quality management model: EFQM.- Latent variables and their operational definition by means of groups of indicators.- Measurements, qualitative analysis, quantitative analysis.- Scales and 2 kinds of measurements.- Qualitative analysis and measurement.- Differences in statistical characteristics of processes in Nature and society.- About the non-Gaussian nature of processes in society and science.- Well, many distributions in social sciences are non-Gaussian.What follows from this?.- Several notes on scientometrics.- Examples of quantities that can be analyzed in the process of study of science dynamics.- Inequality of scientific achievements.- Knowledge landscapes.- Scientific productivity and its evaluation.- Role of science structure and system for scientific productivity.- Age effects in scientific productivity.- Notes on statistical analysis of scientific productivity.- Other factors that affect scientific productivity.- Complexity of scientific productivity.- Method of expert evaluation.- Scientific publications as a characteristic of scientific productivity.- Notes on scientce indicators and inequality.- Examples of evaluation and assessment of research work.- How to perform a complex evaluation of a researcher.- How to assess basic research.- An example of institute evaluation system: The SEP system of Netherlands.- Second example of institutes evaluation system: AERES (France).- Example for system of indicators for evaluation of national research policy: OECD indicators.- On mathematics and quantification of research performance.- English-Czerwon method for quantification of performance of research units.- Scientific performance from the point of view of information production processes.- Additional notes on application of mathematics for quantifications of scientific achievements.- Part II Indicators and indexes of scientific productivity.- Scientific productivity of individual researchers.- Introduction remarks.- Money cuts and "value for money". Peer review and evaluation by a sets of indicators and indices.- Indicators and indexes.- The h-index of Hirsch.- Advantages and disadvantage of the h-index. Use the h-index carefully.- Normalized h-index.- Tapered h-index.- Temporally bounded h-index. Age dependent h-index.- The problem of multiple authorship. h-index of Hirsch and gh-index of Galam.- m-index.- The g-index of Egghe.- The in-index.- The p-index.- IQp-index.- A-index and R-index.- Additional indexes.- h-like indexes and indexes complementary to the Hirsch.- Index.- Indexes based on normalization mechanisms.- PI-indexes.- Indexes for personal success of a researcher.- Indexes for characterization of scientific networks.- References.- Indexes for characteristics of research productivity in a group of researchers.- Indexes based on simple statistical concepts.- A simple index of quality of scientific output based on the publications in major journals.- MII-index.- Shutz coefficient of inequality.- Wilcox deviation from the mode (from the maximum percentage).- Nagel's index of equality.- Coefficient of variation.- Gini's mean relative difference.- Gini's coefficient of inequality.- Herfindahl-Hirschmann index of concentration.- Horvath's index of concentration.- RTS-index of concentration.- Diversity index of Lieberson.- Index of imbalance of Taagepera.- RT-index of fragmentation.- Indexes based on the concept of entropy.- Theil's index of entropy.- Redundancy index of Theil.- Negative entropy index.- Expected information content of Theil.- The Lorenz curve and associated indicators.- Lorenz curve.- The index of Gini from the point of view of the Lorenz curve.- Index of Kuznets.- Pareto diagram (Pareto chart).- Indexes for the case of stratified data.- References.- Comparison of research productivities of groups of researchers.- Indexes of dissimilarity and diversity.- Index of dissimilarity.- Index of diversity of Lieberson.- Indexes of difference and advantage.- Other indexes.- Index of net difference of Lieberson.- Index of average relative advantage.- Index of inequity of Coulter.- Proportionality index of Nagel.- RELEV method for assessment of scientific research performance within public institutes.- Comparison among scientific communities in different countries.- Efficiency of scientific production based on papers and patents.- Additional characteristics of scientific productivity of a nation.- Scientific elites.- Several characteristics of a scientific elite.- Several words about studied groups of institutes.- Size of elite.- Sizes of superelite, hyperelite, etc.- Strength of elite.- Remarks about some characteristics of the scientific elites of the two groups of institutes.- References.- Part III Basic laws and selected models.- Frequency and the rank approaches to scientific productivity.- Measurement of scientific productivity by publications.- Frequency approach and rank approach: general remarks.- Differential and integral form of the frequency and rank distributions.- Why frequency distributions are dominant in the natural sciences and rank distributions are frequently used in the social sciences?.- Status of Zipf distribution in the world of non-Gaussian distributions.- Importance of the stable non-Gaussian distributions for the organization of science.- Non-Gaussian distributions. Characteristic features.- Stable non-Gaussian distributions.- Frequently used stable non-Gaussian distributions.- Frequency approach. Law of Lotka for scientific publications.- Presence of extremely productive scientists: imax ¥.- imax: finite - the most productive scientists have finite productivity. Scientific elite according to Price.- The exponent a: measure of inequality.- The continuous limit: from law of Lotka to the distribution of Pareto.- The shortcomings of Pareto distribution and overcoming them by Pareto II distribution.- Rank approach.- Law of Zipf.- Zipf-Mandelbrot law.- Law of Bradford for scientific journals.- Distributions connected to citation analysis.- Citation analysis.- Modeling citation behavior in journals.- Quantities connected to the age of citation.- Growth dynamics of citations.- References.- Selected models for evolution of research organizations and scientific productivity.- Variation approach to scientific productivity.- A hint for a possible applicability of an variation approach.- Variation principle of Boltzmann and distribution of research productivity in the equilibrium state of the scientific system.- "Temperature".- Scientific productivity,Yule distribution and the random branching process.- Definition, initial conditions, and differential equations for the process.- How Yule process arises.- Properties of the scientific productivity according to the model.- Modeling production/citation process.- Model of h-index based on Paretian distributions.- Model of h-index based on Poisson distribution.- Matthew effect in science.- Deterministic models.- Logistic curve and its generalizations.- Aging of scientific information and importance of fundamental research.- Price model of knowledge growth. Cycles of growth of knowledge.- SI (susceptibles-infectives) discrete model of the change in the number of publications for a scientific field.- Goffman-Newill continuous model for the dynamics of populations of scientists and papers.- Continuous model of competition between systems of ideas.- Stochastic models.- Aging of scientific information as a death stochastic process.- Aging of scientific literature as nonhomogeneous birth process.- Stochastic model of scientific productivity.- Reproduction-transport equation model of the evolution of scientific subfields.- References.- Several concluding remarks.- Importance of science for society.- General characteristics of science structures and systems.- Quality management systems and performance measurement systems.