BACKGROUND The increasing availability of digital data on scholarly inputs and outputs—from research funding, productivity, and collaboration to paper citations and scientist mobility—offers unprecedented opportunities to explore the structure and evolution of science. The science of science (SciSci) offers a quantitative understanding of the interactions among scientific agents across diverse geographic and temporal scales: It provides insights into the conditions underlying creativity and the genesis of scientific discovery, with the ultimate goal of developing tools and policies that have the potential to accelerate science. In the past decade, SciSci has benefited from an influx of natural, computational, and social scientists who together have developed big data–based capabilities for empirical analysis and generative modeling that capture the unfolding of science, its institutions, and its workforce. The value proposition of SciSci is that with a deeper understanding of the factors that drive successful science, we can more effectively address environmental, societal, and technological problems. ADVANCES Science can be described as a complex, self-organizing, and evolving network of scholars, projects, papers, and ideas. This representation has unveiled patterns characterizing the emergence of new scientific fields through the study of collaboration networks and the path of impactful discoveries through the study of citation networks. Microscopic models have traced the dynamics of citation accumulation, allowing us to predict the future impact of individual papers. SciSci has revealed choices and trade-offs that scientists face as they advance both their own careers and the scientific horizon. For example, measurements indicate that scholars are risk-averse, preferring to study topics related to their current expertise, which constrains the potential of future discoveries. Those willing to break this pattern engage in riskier careers but become more likely to make major breakthroughs. Overall, the highest-impact science is grounded in conventional combinations of prior work but features unusual combinations. Last, as the locus of research is shifting into teams, SciSci is increasingly focused on the impact of team research, finding that small teams tend to disrupt science and technology with new ideas drawing on older and less prevalent ones. In contrast, large teams tend to develop recent, popular ideas, obtaining high, but often short-lived, impact. OUTLOOK SciSci offers a deep quantitative understanding of the relational structure between scientists, institutions, and ideas because it facilitates the identification of fundamental mechanisms responsible for scientific discovery. These interdisciplinary data-driven efforts complement contributions from related fields such as sciento-metrics and the economics and sociology of science. Although SciSci seeks long-standing universal laws and mechanisms that apply across various fields of science, a fundamental challenge going forward is accounting for un...

We study the voter model with a finite density of zealots-voters that never change opinion. For equal numbers of zealots of each species, the distribution of magnetization (opinions) is Gaussian in the mean-field limit as well as in one and two dimensions, with a width that is proportional to 1/ √ Z, where Z is the number of zealots, independent of the total number of voters. Thus just a few zealots can prevent consensus or even the formation of a robust majority.

The Matthew effect refers to the adage written some two-thousand years ago in the Gospel of St. Matthew: "For to all those who have, more will be given." Even two millennia later, this idiom is used by sociologists to qualitatively describe the dynamics of individual progress and the interplay between status and reward. Quantitative studies of professional careers are traditionally limited by the difficulty in measuring progress and the lack of data on individual careers. However, in some professions, there are well-defined metrics that quantify career longevity, success, and prowess, which together contribute to the overall success rating for an individual employee. Here we demonstrate testable evidence of the age-old Matthew "rich get richer" effect, wherein the longevity and past success of an individual lead to a cumulative advantage in further developing his or her career. We develop an exactly solvable stochastic career progress model that quantitatively incorporates the Matthew effect and validate our model predictions for several competitive professions. We test our model on the careers of 400,000 scientists using data from six high-impact journals and further confirm our findings by testing the model on the careers of more than 20,000 athletes in four sports leagues. Our model highlights the importance of early career development, showing that many careers are stunted by the relative disadvantage associated with inexperience. T he rate of individual progress is fundamental to career development and success. In practice, the rate of progress depends on many factors, such as an individual's talent, productivity, reputation, as well as other external random factors. Using a stochastic model, here we find that the relatively small rate of progress at the beginning of the career plays a crucial role in the evolution of the career length. Our quantitative model describes career progression using two fundamental ingredients: (i) random forward progress "up the career ladder" and (ii) random stopping times, terminating a career. This model quantifies the "Matthew effect" by incorporating into ingredient (i) the common cumulative advantage property (1-8) that it is easier to move forward in the career the further along one is in the career. A direct result of the increasing progress rate with career position is the large disparity between the numbers of careers that are successful long tenures and the numbers of careers that are unsuccessful short stints.Surprisingly, despite the large differences in the numbers of long and short careers, we find a scaling law that bridges the gap between the frequent short and the infrequent long careers. We test this model for both scientific and sports careers, two careers where accomplishments are methodically recorded. We analyze publication careers within six high-impact journals: Nature, Science, the Proceedings of the National Academy of Science (PNAS), Physical Review Letters (PRL), New England Journal of Medicine (NEJM), and CELL. We also analyze sports careers within ...

We analyze the occurrence frequencies of over 15 million words recorded in millions of books published during the past two centuries in seven different languages. For all languages and chronological subsets of the data we confirm that two scaling regimes characterize the word frequency distributions, with only the more common words obeying the classic Zipf law. Using corpora of unprecedented size, we test the allometric scaling relation between the corpus size and the vocabulary size of growing languages to demonstrate a decreasing marginal need for new words, a feature that is likely related to the underlying correlations between words. We calculate the annual growth fluctuations of word use which has a decreasing trend as the corpus size increases, indicating a slowdown in linguistic evolution following language expansion. This “cooling pattern” forms the basis of a third statistical regularity, which unlike the Zipf and the Heaps law, is dynamical in nature.

In finance, one usually deals not with prices but with growth rates R, defined as the difference in logarithm between two consecutive prices. Here we consider not the trading volume, but rather the volume growth rateR, the difference in logarithm between two consecutive values of trading volume. To this end, we use several methods to analyze the properties of volume changes |R|, and their relationship to price changes |R|. We analyze 14, 981 daily recordings of the Standard and Poor's (S & P) 500 Index over the 59-year period 1950-2009, and find power-law cross-correlations between |R| and |R| by using detrended cross-correlation analysis (DCCA). We introduce a joint stochastic process that models these crosscorrelations. Motivated by the relationship between |R| and |R|, we estimate the tail exponentα of the probability density function P(|R|) ∼ |R| −1−α for both the S & P 500 Index as well as the collection of 1819 constituents of the New York Stock Exchange Composite Index on 17 July 2009. As a new method to estimateα, we calculate the time intervals τ q between events whereR > q. We demonstrate thatτ q , the average of τ q , obeysτ q ∼ qα. We findα ≈ 3. Furthermore, by aggregating all τ q values of 28 global financial indices, we also observe an approximate inverse cubic law. econophysics | finance | volatility There is a saying on Wall Street that "it takes volume to move stock prices." A number of studies have analyzed the relationship between price changes and the trading volume in financial markets (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14). Some of these studies (1, 3-6) have found a positive relationship between price change and the trading volume. In order to explain this relationship, Clarke assumed that the daily price change is the sum of a random number of uncorrelated intraday price changes (3), so predicted that the variance of the daily price change is proportional to the average number of daily transactions. If the number of transactions is proportional to the trading volume, then the trading volume is proportional to the variance of the daily price change.The cumulative distribution function (cdf) of the absolute logarithmic price change |R| obeys a power lawIt is believed (15-18) that α ≈ 3 ("inverse cubic law"), outside the range α < 2 characterizing a Lévy distribution (18,19). A parallel analysis of Q, the volume traded, yields a power law (20-28)To our knowledge, the logarithmic volume change-R and its relation to the logarithmic price change R-has not been analyzed, and this analysis is our focus here. For each of the 1,819 companies and 28 indices, we calculate over the time interval of one day the logarithmic change in price S(t), Data Analyzedand also the logarithmic change in trading volume Q(t) (29),For each of the 3,694 time series, we also calculate the absolute values |R t | and |R t | and define the "price volatility" (30) and "volume volatility," respectively,andwhere σ R ≡ ( |R t | 2 − |R t | 2 ) 1/2 and σR ≡ ( |R t | 2 − |R t | 2 ) 1/2 are the respective standard deviat...