The dynamics of correlated novelties

Human language, the most powerful communication system in history, is closely associated with cognition. Written text is one of the fundamental manifestations of language, and the study of its universal regularities can give clues about how our brains process information and how we, as a society, organize and share it. Still, only classical patterns such as Zipf's law have been explored in depth. In contrast, other basic properties like the existence of bursts of rare words i...

The word-stock of a language is a complex dynamical system in which words can be created, evolve, and become extinct. Even more dynamic are the short-term fluctuations in word usage by individuals in a population. Building on the recent demonstration that word niche is a strong determinant of future rise or fall in word frequency, here we introduce a model that allows us to distinguish persistent from temporary increases in frequency. Our model is illustrated using a 10^8-wor...

Innovation is the driving force of human progress. Recent urn models reproduce well the dynamics through which the discovery of a novelty may trigger further ones, in an expanding space of opportunities, but neglect the effects of social interactions. Here we focus on the mechanisms of collective exploration and we propose a model in which many urns, representing different explorers, are coupled through the links of a social network and exploit opportunities coming from their...

Innovation and obsolescence describe dynamics of ever-churning and adapting social and biological systems, concepts that encompass field-specific formulations. We formalize the connection with a reduced model of the dynamics of the "space of the possible" (e.g. technologies, mutations, theories) to which agents (e.g. firms, organisms, scientists) couple as they grow, die, and replicate. We predict three regimes: the space is finite, ever growing, or a Schumpeterian dystopia i...

Empirical studies of scientific discovery---so-called Eurekometrics---have indicated that the output of exploration proceeds as a logistic growth curve. Although logistic functions are prevalent in explaining population growth that is resource-limited to a given carrying capacity, their derivation do not apply to discovery processes. This paper develops a generative model for logistic \emph{knowledge discovery} using a novel extension of coupon collection, where an explorer i...

Recent advances in the quantitative, computational methodology for the modeling and analysis of heterogeneous large-scale data are leading to new opportunities for understanding of human behaviors and faculties, including the manifestation of creativity that drives creative enterprises such as science. While innovation is crucial for novel and influential achievements, quantifying these qualities in creative works remains a challenge. Here we present an information-theoretic ...

In recent times there has been a surge of interest in seeking out patterns in the aggregate behavior of socio-economic systems. One such domain is the emergence of statistical regularities in the evolution of collective choice from individual behavior. This is manifested in the sudden emergence of popularity or "success" of certain ideas or products, compared to their numerous, often very similar, competitors. In this paper, we present an empirical study of a wide range of po...

Innovation is to organizations what evolution is to organisms: it is how organisations adapt to changes in the environment and improve. Governments, institutions and firms that innovate are more likely to prosper and stand the test of time; those that fail to do so fall behind their competitors and succumb to market and environmental change. Yet despite steady advances in our understanding of evolution, what drives innovation remains elusive. On the one hand, organizations in...

Background: Zipf's discovery that word frequency distributions obey a power law established parallels between biological and physical processes, and language, laying the groundwork for a complex systems perspective on human communication. More recent research has also identified scaling regularities in the dynamics underlying the successive occurrences of events, suggesting the possibility of similar findings for language as well. Methodology/Principal Findings: By consider...

The World Wide Web is fast becoming a source of information for a large part of the world's population. Because of its sheer size and complexity users often resort to recommendations from others to decide which sites to visit. We present a dynamical theory of recommendations which predicts site visits by users of the World Wide Web. We show that it leads to a universal power law for the number of users that visit given sites over periods of time, with an exponent related to t...