# Researchers Develop Mathematical Model for How Innovations Emerge

*An international team of scientists has developed a mathematical model for the emergence of innovations, in which cognitive processes are described as random walks on the network of links among ideas or concepts, and an innovation corresponds to the first visit of a node. Their work is published in the journal Physical Review Letters.*

The study, led by Professor Vito Latora from Queen Mary University of London, introduces a new mathematical framework that correctly reproduces the rate at which novelties emerge in real systems, known as Heaps’ law, and can explain why discoveries are strongly correlated and often come in clusters.

It does this by translating the theory of the ‘adjacent possible,’ initially formulated by American theoretical biologist Stuart Kauffman in the context of biological systems, into the language of complex networks.

The adjacent possible is the set of all novel opportunities that open up when a new discovery is made.

Networks have emerged as a powerful way to both investigate real world systems, by capturing the essential relations between the components, and to model the hidden structure behind many complex social phenomena.

In this work, networks are used to model the underlying space of relations among concepts.

“This research opens up new directions for the modeling of innovation, together with a new framework that could become important in the investigation of technological, biological, artistic, and commercial systems,” Professor Latora said.

In the study, the discovery process is modeled as a particular class of random walks, named ‘reinforced’ walks, on an underlying network of relations among concepts and ideas.

An innovation corresponds to the first visit of a site of the network, and every time a walker moves from a concept to another, such association (an edge in the network) is reinforced so that it will be used more frequently in the future.

Professor Latora and co-authors named this the ‘edge-reinforced random walk’ model.

To show how the model works in a real case, they also constructed a dataset of 20 years of scientific publications in different disciplines, such as astronomy, ecology, economics and mathematics to analyze the appearance of new concepts.