Dynamics on expanding spaces: modeling the emergence of novelties

Novelties are part of our daily lives. We constantly adopt new technologies, conceive new ideas, meet new people, experiment with new situations. Occasionally, we as individuals, in a complicated cognitive and sometimes fortuitous process, come up with something that is not only new to us, but to our entire society so that what is a personal novelty can turn into an innovation at a global level. Innovations occur throughout social, biological and technological systems and, though we perceive them as a very natural ingredient of our human experience, little is known about the processes determining their emergence. Still the statistical occurrence of innovations shows striking regularities that represent a starting point to get a deeper insight in the whole phenomenology. This paper represents a small step in that direction, focusing on reviewing the scientific attempts to effectively model the emergence of the new and its regularities, with an emphasis on more recent contributions: from the plain Simon's model tracing back to the 1950s, to the newest model of Polya's urn with triggering of one novelty by another. What seems to be key in the successful modelling schemes proposed so far is the idea of looking at evolution as a path in a complex space, physical, conceptual, biological, technological, whose structure and topology get continuously reshaped and expanded by the occurrence of the new. Mathematically it is very interesting to look at the consequences of the interplay between the "actual" and the "possible" and this is the aim of this short review.Comment: 25 pages, 10 figure

Debt, economic growth and interest rates: An empirical study of the Swiss case, presenting a new long-term dataset: 1894-2014

Abstract In this paper, relations between public debt, economic growth, and long-term interest rates in Switzerland from 1894 to 2014 are examined. For this purpose, an original long-term dataset on the general gross public debt in Switzerland, namely the aggregation of the Confederation gross debt, the cantons’ gross debts, and the municipal gross debts, was reconstructed. Three different statistical approaches are performed to study relations between this aggregated debt, economic growth, and interest rates. The first consists of the study of correlations between GDP-weighted variables, the second is the study of the correlation between residuals of ARIMA time series models, and the last one studies vector autoregression (VAR) models, allowing us to test Granger causalities between variables. Every approach is performed on the whole time period but also on boom phases and recession phases independently. All the results suggest that the public debt during this period in Switzerland did not have a negative impact on economic growth and did not raise long-term interest rates

Social dynamics: Emergence of language

Our social behaviour has evolved primarily through contact with a limited number of other individuals. Yet as a species we exhibit uniformities on a global scale. This kind of emergent behaviour is familiar territory for statistical physicists.Peer reviewe