Alexander Michael Petersen

Cross-correlations between volume change and price change

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 rate R̃, 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 |R̃|, and their relationship to price changes |R|. We analyze 14,981 daily recordings of the Standard and Poors (S & P) 500 Index over the 59-year period 1950–2009, and find power-law cross-correlations between |R| and |R̃| by using detrended cross-correlation analysis (DCCA). We introduce a joint stochastic process that models these cross-correlations. Motivated by the relationship between |R| and |R̃|, we estimate the tail exponent α̃ of the probability density function P(|R̃|) ∼ |R̃|−1−α̃ 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 estimate α̃, we calculate the time intervals τq between events where R̃ > q. We demonstrate that τ̃q, the average of τq, obeys τ̃q ∼ qα̃. We find α̃ ≈ 3. Furthermore, by aggregating all τq values of 28 global financial indices, we also observe an approximate inverse cubic law.

Languages cool as they expand: Allometric scaling and the decreasing need for new words

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.

On the role of zealotry in the voter model

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 , 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.

Quantitative and empirical demonstration of the Matthew effect in a study of career longevity

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.

Reputation and impact in academic careers

Significance Over a scientist’s career, a reputation is developed, a standing within a research community, based largely upon the quantity and quality of his/her publications. Here, we develop a framework for quantifying the influence author reputation has on a publication’s future impact. We find author reputation plays a key role in driving a paper’s citation count early in its citation life cycle, before a tipping point, after which reputation has much less influence relative to the paper’s citation count. In science, perceived quality, and decisions made based on those perceptions, is increasingly linked to citation counts. Shedding light on the complex mechanisms driving these quantitative measures facilitates not only better evaluation of scientific outputs but also a more transparent evaluation of the scientists producing them. Reputation is an important social construct in science, which enables informed quality assessments of both publications and careers of scientists in the absence of complete systemic information. However, the relation between reputation and career growth of an individual remains poorly understood, despite recent proliferation of quantitative research evaluation methods. Here, we develop an original framework for measuring how a publication’s citation rate Δc depends on the reputation of its central author i, in addition to its net citation count c. To estimate the strength of the reputation effect, we perform a longitudinal analysis on the careers of 450 highly cited scientists, using the total citations Ci of each scientist as his/her reputation measure. We find a citation crossover c×, which distinguishes the strength of the reputation effect. For publications with c < c×, the author’s reputation is found to dominate the annual citation rate. Hence, a new publication may gain a significant early advantage corresponding to roughly a 66% increase in the citation rate for each tenfold increase in Ci. However, the reputation effect becomes negligible for highly cited publications meaning that, for c ≥ c×, the citation rate measures scientific impact more transparently. In addition, we have developed a stochastic reputation model, which is found to reproduce numerous statistical observations for real careers, thus providing insight into the microscopic mechanisms underlying cumulative advantage in science.

Statistical Laws Governing Fluctuations in Word Use from Word Birth to Word Death

We analyze the dynamic properties of 107 words recorded in English, Spanish and Hebrew over the period 1800–2008 in order to gain insight into the coevolution of language and culture. We report language independent patterns useful as benchmarks for theoretical models of language evolution. A significantly decreasing (increasing) trend in the birth (death) rate of words indicates a recent shift in the selection laws governing word use. For new words, we observe a peak in the growth-rate fluctuations around 40 years after introduction, consistent with the typical entry time into standard dictionaries and the human generational timescale. Pronounced changes in the dynamics of language during periods of war shows that word correlations, occurring across time and between words, are largely influenced by coevolutionary social, technological, and political factors. We quantify cultural memory by analyzing the long-term correlations in the use of individual words using detrended fluctuation analysis.

Persistence and uncertainty in the academic career

Understanding how institutional changes within academia may affect the overall potential of science requires a better quantitative representation of how careers evolve over time. Because knowledge spillovers, cumulative advantage, competition, and collaboration are distinctive features of the academic profession, both the employment relationship and the procedures for assigning recognition and allocating funding should be designed to account for these factors. We study the annual production ni(t) of a given scientist i by analyzing longitudinal career data for 200 leading scientists and 100 assistant professors from the physics community. Our empirical analysis of individual productivity dynamics shows that (i) there are increasing returns for the top individuals within the competitive cohort, and that (ii) the distribution of production growth is a leptokurtic “tent-shaped” distribution that is remarkably symmetric. Our methodology is general, and we speculate that similar features appear in other disciplines where academic publication is essential and collaboration is a key feature. We introduce a model of proportional growth which reproduces these two observations, and additionally accounts for the significantly right-skewed distributions of career longevity and achievement in science. Using this theoretical model, we show that short-term contracts can amplify the effects of competition and uncertainty making careers more vulnerable to early termination, not necessarily due to lack of individual talent and persistence, but because of random negative production shocks. We show that fluctuations in scientific production are quantitatively related to a scientist’s collaboration radius and team efficiency.

Bankruptcy Risk Model and Empirical Tests

We analyze the size dependence and temporal stability of firm bankruptcy risk in the US economy by applying Zipf scaling techniques. We focus on a single risk factor—the debt-to-asset ratio R—in order to study the stability of the Zipf distribution of R over time. We find that the Zipf exponent increases during market crashes, implying that firms go bankrupt with larger values of R. Based on the Zipf analysis, we employ Bayes’s theorem and relate the conditional probability that a bankrupt firm has a ratio R with the conditional probability of bankruptcy for a firm with a given R value. For 2,737 bankrupt firms, we demonstrate size dependence in assets change during the bankruptcy proceedings. Prepetition firm assets and petition firm assets follow Zipf distributions but with different exponents, meaning that firms with smaller assets adjust their assets more than firms with larger assets during the bankruptcy process. We compare bankrupt firms with nonbankrupt firms by analyzing the assets and liabilities of two large subsets of the US economy: 2,545 Nasdaq members and 1,680 New York Stock Exchange (NYSE) members. We find that both assets and liabilities follow a Pareto distribution. The finding is not a trivial consequence of the Zipf scaling relationship of firm size quantified by employees—although the market capitalization of Nasdaq stocks follows a Pareto distribution, the same distribution does not describe NYSE stocks. We propose a coupled Simon model that simultaneously evolves both assets and debt with the possibility of bankruptcy, and we also consider the possibility of firm mergers.

Is Europe Evolving Toward an Integrated Research Area

Despite efforts to integrate across borders, Europe remains a collection of national innovation systems. Efforts toward European research and development (R&D) integration have a long history, intensifying with the Fifth Framework Programme (FP) in 1998 (1–3) and the launch of the European Research Area (ERA) initiative at the Lisbon European Council in 2000. A key component of the European Union (EU) strategy for innovation and growth (4, 5), the ERA aims to overcome national borders through directed funding, increased mobility, and streamlined innovation policies.

Statistical regularities in the rank-citation profile of scientists

Recent science of science research shows that scientific impact measures for journals and individual articles have quantifiable regularities across both time and discipline. However, little is known about the scientific impact distribution at the scale of an individual scientist. We analyze the aggregate production and impact using the rank-citation profile ci(r) of 200 distinguished professors and 100 assistant professors. For the entire range of paper rank r, we fit each ci(r) to a common distribution function. Since two scientists with equivalent Hirsch h-index can have significantly different ci(r) profiles, our results demonstrate the utility of the βi scaling parameter in conjunction with hi for quantifying individual publication impact. We show that the total number of citations Ci tallied from a scientists Ni papers scales as . Such statistical regularities in the input-output patterns of scientists can be used as benchmarks for theoretical models of career progress.