We present an analysis of citations accrued over time by patents granted by the United States Patent and Trademark Office in 1998. In contrast to previous studies, a disaggregation by technology category is performed, and exogenously caused citation-number growth is controlled for. Our approach reveals an intrinsic citation rate that clearly separates into an-in the long run, exponentially time-dependent-aging function and a completely time-independent preferential-attachment-type growth kernel. For the general case of such a separable citation rate, we obtain the time-dependent citation distribution analytically in a form that is valid for any functional form of its aging and growth parts. Good agreement between theory and long-time characteristics of patent-citation data establishes our work as a useful framework for addressing still open questions about knowledge-propagation dynamics, such as the observed excess of citations at short times.

We analyze the time evolution of citations acquired by articles from journals of the American Physical Society (PRA, PRB, PRC, PRD, PRE and PRL). The observed change over time in the number of papers published in each journal is considered an exogenously caused variation in citability that is accounted for by a normalization. The appropriately inflation-adjusted citation rates are found to be separable into a preferential-attachment-type growth kernel and a purely obsolescence-related (i.e., monotonously decreasing as a function of time since publication) aging function. Variations in the empirically extracted parameters of the growth kernels and aging functions associated with different journals point to research-field-specific characteristics of citation intensity and knowledge flow. Comparison with analogous results for the citation dynamics of technology-disaggregated cohorts of patents provides deeper insight into the basic principles of information propagation as indicated by citing behavior.

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We have constructed a fitness parameter, characterizing the intrinsic attractiveness for patents to be cited, from attributes of the associated inventions known at the time a patent is granted. This exogenously obtained fitness is shown to determine the temporal growth of the citation network in conjunction with mechanisms of preferential attachment and obsolescence-induced ageing that operate without reference to characteristics of individual patents. Our study opens a window on understanding quantitatively the interplay of the rich-gets-richer and fit-gets-richer paradigms that have been suggested to govern the growth dynamics of real-world complex networks.A wide variety of social and economic processes evolve such that success or popularity appear to be selfreinforcing. Significant attention has been given to trying to distinguish the extent to which the apparently selfreinforcing behavior of popularity is purely a property of the dynamic system, versus being generated by intrinsic heterogeneity that allows inherently better agents or products to persistently succeed [1][2][3][4][5][6][7][8][9]. With our increasingly data-rich world enabling more effective ways for measuring quality as well as popularity, this question can now be explored more deeply and in a greater variety of fields [10]. Here we provide an answer within the context of technological innovation, where an accepted measure of popularity is the intensity with which patents accumulate citations [11]. Our construction of a technologydependent single quality score for individual patents from a broad range of patent-quality measures that are exogenous to citations and available at the time of grant is shown to quantify the innate attractiveness of patents to be cited in the future. The ability to account for inherent quality as a driver of citation dynamics enables better observation of other important influences, including the time scale for knowledge obsolescence [12].Empirically, the average rateλ at which the number of citations k accrued by patents [13] increases over time t is observed [12,14,15] to follow an aging-tempered [16] preferential-attachment-type [17][18][19] growth modelλ = A(t) f (k). The asymptotic form f (k) ∼ k α for large k with α > 0 embodies a rich-gets-richer feedback loop whereby more highly cited patents are more likely to gain future citations. Similar behavior is exhibited by the citation dynamics of scientific articles, e.g., those published in the journals of the American Physical Society [20][21][22]. However, the special purpose and associated legal ramifications of citations in patents [11,13] enforce a greater * Present address: degree of caution in citing behavior than is commonly practiced for scientific articles, making patent citations particularly suitable for investigating the relationship between popularity and quality [23].On a phenomenological level, purely preferentialattachment-based models seem to be able to successfully describe the dynamics of how patents receive forward citations. However, they are...

Quantitative methods to describe the participation to debate of Members of Parliament and the parties they belong to are lacking. Here we propose a new approach that combines topic modeling with complex networks techniques, and use it to characterize the political discourse at the New Zealand Parliament. We implement a Latent Dirichlet Allocation model to discover the thematic structure of the government’s digital database of parliamentary speeches, and construct from it two-mode networks linking Members of the Parliament to the topics they discuss. Our results show how topic popularity changes over time and allow us to relate the trends followed by political parties in their discourses with specific social, economic and legislative events. Moreover, the community analysis of the two-mode network projections reveals which parties dominate the political debate as well as how much they tend to specialize in a small or large number of topics. Our work demonstrates the benefits of performing quantitative analysis in a domain normally reserved for qualitative approaches, providing an efficient way to measure political activity.