We introduce a 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. The transition matrix of the random walk depends on the network weights, while in turn the weight of an edge is reinforced by the passage of a walker. The presence of the network naturally accounts for the mechanism of the adjacent possible, and the model reproduces both the rate at which novelties emerge and the correlations among them observed empirically. We show this by using synthetic networks and by studying real data sets on the growth of knowledge in different scientific disciplines. Edge-reinforced random walks on complex topologies offer a new modeling framework for the dynamics of correlated novelties and are another example of coevolution of processes and networks.
In this paper we develop a theory to describe innovation processes in a network of interacting units. We introduce a stochastic picture that allows for the clarification of the role of fluctuations for the survival of innovations in such a non-linear system. We refer to the theory of complex networks and introduce the notion of sensitive networks. Sensitive networks are networks in which the introduction or the removal of a node/vertex dramatically changes the dynamic structure of the system. As an application we consider interaction networks of firms and technologies and describe technologica…
Taylor's law quantifies the scaling properties of the fluctuations of the number of innovations occurring in open systems. Urn based modelling schemes have already proven to be effective in modelling this complex behaviour. Here, we present analytical estimations of Taylor's law exponents in such models, by leveraging on their representation in terms of triangular urn models. We also highlight the correspondence of these models with Poisson-Dirichlet processes and demonstrate how a non-trivial Taylor's law exponent is a kind of universal feature in systems related to human activities. We base …
In this paper we have proposed a basic agent-based model based on evolutionary dynamics for investigating innovation initiation process. In our model we suppose each agent will represent a firm which is interacting with other firms through a given network structure. We consider a two-hit process for presenting a potentially successful innovation in this model and therefore at each time step each firm can be in on of three different stages which are respectively, Ordinary, Innovative, and Successful. We design different experiments in order to investigate how different interaction networks may …
We study the competition of two spreading entities, for example innovations, in complex contagion processes in complex networks. We develop an analytical framework and examine the role of dual users, i.e. agents using both technologies. Searching for the spreading transition of the new innovation and the extinction transition of a preexisting one, we identify different phases depending on network mean degree, prevalence of preexisting technology, and thresholds of the contagion process. Competition with the preexisting technology effectively suppresses the spread of the new innovation, but it …
The dynamics of urban systems can be understood from an evolutionary perspective, in some sense extending biological and cultural evolution. Models for systems of cities implementing elementary evolutionary processes remain however to be investigated. We propose here such a model for urban dynamics at the macroscopic scale, in which the diffusion of innovations between cities captures transformation processes (mutations) and transmission processes (diffusion), using two coupled spatial interaction models. Explorations of the model on synthetic systems of cities show the role of spatial interac…
A fundamental question related to innovation diffusion is how the social network structure influences the process. Empirical evidence regarding real-world influence networks is very limited. On the other hand, agent-based modeling literature reports different and at times seemingly contradictory results. In this paper we study innovation diffusion processes for a range of Watts-Strogatz networks in an attempt to shed more light on this problem. Using the so-called Sznajd model as the backbone of opinion dynamics, we find that the published results are in fact consistent and allow to predict th…
Understanding the innovation process, that is the underlying mechanisms through which novelties emerge, diffuse and trigger further novelties is undoubtedly of fundamental importance in many areas (biology, linguistics, social science and others). The models introduced so far satisfy the Heaps' law, regarding the rate at which novelties appear, and the Zipf's law, that states a power law behavior for the frequency distribution of the elements. However, there are empirical cases far from showing a pure power law behavior and such a deviation is present for elements with high frequencies. We exp…
We study the introduction of lexical innovations into a community of language users. Lexical innovations, i.e., new terms added to people's vocabulary, play an important role in the process of language evolution. Nowadays, information is spread through a variety of networks, including, among others, online and offline social networks and the World Wide Web. The entire system, comprising networks of different nature, can be represented as a multi-layer network. In this context, lexical innovations diffusion occurs in a peculiar fashion. In particular, a lexical innovation can undergo three diff…
We introduce a heterogeneous network structure into the Bass diffusion model, in order to study the diffusion times of innovation or information in networks with a scale-free structure, typical of regions where diffusion is sensitive to geographic and logistic influences (like for instance Alpine regions). We consider both the diffusion peak times of the total population and of the link classes. In the familiar trickle-down processes the adoption curve of the hubs is found to anticipate the total adoption in a predictable way. In a major departure from the standard model, we model a trickle-up…
This paper outlines a framework for the study of innovation that treats discoveries as additions to evolving networks. As inventions enter they expand or limit the reach of the ideas they build on by influencing how successive discoveries use those ideas. The approach is grounded in novel measures of the extent to which an innovation amplifies or disrupts the status quo. Those measures index the effects inventions have on subsequent uses of prior discoveries. In so doing, they characterize a theoretically important but elusive feature of innovation. We validate our approach by showing it: (1) …
Innovation and evolution are two processes of paramount relevance for social and biological systems. In general, the former allows to introduce elements of novelty, while the latter is responsible for the motion of a system in its phase space. Often, these processes are strongly related, since an innovation can trigger the evolution, and the latter can provide the optimal conditions for the emergence of innovations. Both processes can be studied by using the framework of Evolutionary Game Theory, where evolution constitutes an intrinsic mechanism, while innovation requires an opportune represe…
Axelrod model describes the dissemination of a set of cultural traits in a society constituted by individual agents. In a social context, nevertheless, individual choices toward a specific attitude are also at the basis of the formation of communities, groups, parties. The membership in a group changes completely the behavior of single agents who start acting according to a social identity. Groups act and interact among them as single entities, but still conserve an internal dynamics. We show that, under certain conditions on social dynamics, the introduction of group dynamics in a cultural di…
Based on a recent model of paradigm shifts by Bornholdt et al., we studied mean-field opinion dynamics in an infinite population where an infinite number of ideas compete simultaneously with their values publicly known. We found that a highly innovative society is not characterized by heavy concentration in highly valued ideas: Rather, ideas are more broadly distributed in a more innovative society with faster progress, provided that the rate of adoption is constant, which suggests a positive correlation between innovation and technological disparity. Furthermore, the distribution is generally…
We examine the innovation of researchers with long-lived careers in Computer Science and Physics. Despite the epistemological differences between such disciplines, we consistently find that a researcher's most innovative publication occurs earlier than expected if innovation were distributed at random across the sequence of publications in their career, and is accompanied by a peak year in which researchers publish other work which is more innovative than average. Through a series of linear models, we show that the innovation achieved by a researcher during their peak year is higher when it is…
We propose a simple model where the innovation rate of a technological domain depends on the innovation rate of the technological domains it relies on. Using data on US patents from 1836 to 2017, we make out-of-sample predictions and find that the predictability of innovation rates can be boosted substantially when network effects are taken into account. In the case where a technology$'$s neighborhood future innovation rates are known, the average predictability gain is 28$\%$ compared to simpler time series model which do not incorporate network effects. Even when nothing is known about the f…
Quantifying the Dynamics of Innovation Abandonment Across Scientific, Technological, Commercial, and Pharmacological Domains
Center for Science of Science and Innovation（科学科学与创新研究中心）；Northwestern Institute on Complex Systems (NICO)（西北大学复杂系统研究所）；Kellogg School of Management（凯洛格管理学院）；Centre for Interdisciplinary Methodologies, University of Warwick（华威大学跨学科方法中心）；Department of Physics, University of Miami（迈阿密大学物理系）；Telenor Research and Development（泰伦诺研发部）
While great emphasis has been placed on the role of social interactions as driver of innovation growth, very few empirical studies have explicitly investigated the impact of social network structures on the innovation performance of cities. Past research has mostly explored scaling laws of socio-economic outputs of cities as determined by, for example, the single predictor of population. Here, by drawing on a publicly available dataset of the startup ecosystem, we build the first Workforce Mobility Network among US metropolitan areas. We found that node centrality computed on this network acco…
The interaction among the three sub-dynamics of economic exchange, technological innovation, and institutional control can be captured with a generalized Triple Helix model. We propose to use the information contained in the configuration among the three sub-dynamics as an indicator of the synergy in a configuration. This measure indicates the reduction of the uncertainty which prevails at the level of an innovation system. On the basis of data at the district level in Germany, the conclusions of a previous study about the Netherlands are tested: medium-tech manufacturing is the main driver of…
Thermodynamics of Innovation: A Statistical Mechanics Framework of Social Adoption
Sanghi College of Engineering (SCE) and School of Informatics, Computing, and Cyber Systems (SICCS), Northern Arizona University（桑基工程学院与北方亚利桑那大学信息学、计算与网络系统学院）
Novelty is an inherent part of innovations and discoveries. Such processes may be considered as an appearance of new ideas or as an emergence of atypical connections between the existing ones. The importance of such connections hints for investigation of innovations through network or graph representation in the space of ideas. In such representation, a graph node corresponds to the relevant concept (idea), whereas an edge between two nodes means that the corresponding concepts have been used in a common context. In this study we address the question about a possibility to identify the edges b…
We study the dynamics of the adoption of new products by agents with continuous opinions and discrete actions (CODA). The model is such that the refusal in adopting a new idea or product is increasingly weighted by neighbor agents as evidence against the product. Under these rules, we study the distribution of adoption times and the final proportion of adopters in the population. We compare the cases where initial adopters are clustered to the case where they are randomly scattered around the social network and investigate small world effects on the final proportion of adopters. The model pred…
Innovation diffusion in the networked population is an essential process that drives the progress of human society. Despite the recent advances in network science, a fundamental understanding of network properties that regulate such processes is still lacking. Focusing on an innovation diffusion model with pairwise transmission and macro-level social influence, i.e., more adopters in the networked population lead to a higher adoption tendency among the remaining individuals, we observe discontinuous phase transitions when the influence is sufficiently strong. Through extensive analyses of a la…
We investigate some of the properties and extensions of a dynamic innovation network model recently introduced in \citep{koenig07:_effic_stabil_dynam_innov_networ}. In the model, the set of efficient graphs ranges, depending on the cost for maintaining a link, from the complete graph to the (quasi-) star, varying within a well defined class of graphs. However, the interplay between dynamics on the nodes and topology of the network leads to equilibrium networks which are typically not efficient and are characterized, as observed in empirical studies of R&D networks, by sparseness, presence of c…
Diffusion of innovation can be interpreted as a social spreading phenomena governed by the impact of media and social interactions. Although these mechanisms have been identified by quantitative theories, their role and relative importance are not entirely understood, since empirical verification has so far been hindered by the lack of appropriate data. Here we analyse a dataset recording the spreading dynamics of the world's largest Voice over Internet Protocol service to empirically support the assumptions behind models of social contagion. We show that the rate of spontaneous service adopti…
