Biomedical research has been previously reported to primarily focus on a minority of all known genes. Here, we demonstrate that these differences in attention can be explained, to a large extent, exclusively from a small set of identifiable chemical, physical, and biological properties of genes. Together with knowledge about homologous genes from model organisms, these features allow us to accurately predict the number of publications on individual human genes, the year of their first report, the levels of funding awarded by the National Institutes of Health (NIH), and the development of drugs against disease-associated genes. By explicitly identifying the reasons for gene-specific bias and performing a meta-analysis of existing computational and experimental knowledge bases, we describe gene-specific strategies for the identification of important but hitherto ignored genes that can open novel directions for future investigation.

One of the most celebrated findings in complex systems in the last decade is that different indexes y (e.g. patents) scale nonlinearly with the population x of the cities in which they appear, i.e. y∼xβ,β≠1. More recently, the generality of this finding has been questioned in studies that used new databases and different definitions of city boundaries. In this paper, we investigate the existence of nonlinear scaling, using a probabilistic framework in which fluctuations are accounted for explicitly. In particular, we show that this allows not only to (i) estimate β and confidence intervals, but also to (ii) quantify the evidence in favour of β≠1 and (iii) test the hypothesis that the observations are compatible with the nonlinear scaling. We employ this framework to compare five different models to 15 different datasets and we find that the answers to points (i)–(iii) crucially depend on the fluctuations contained in the data, on how they are modelled, and on the fact that the city sizes are heavy-tailed distributed.

We propose a stochastic model for the number of different words in a given database which incorporates the dependence on the database size and historical changes. The main feature of our model is the existence of two different classes of words: (i) a finite number of core-words which have higher frequency and do not affect the probability of a new word to be used; and (ii) the remaining virtually infinite number of noncore-words which have lower frequency and once used reduce the probability of a new word to be used in the future. Our model relies on a careful analysis of the google-ngram database of books published in the last centuries and its main consequence is the generalization of Zipf's and Heaps' law to two scaling regimes. We confirm that these generalizations yield the best simple description of the data among generic descriptive models and that the two free parameters depend only on the language but not on the database. From the point of view of our model the main change on historical time scales is the composition of the specific words included in the finite list of core-words, which we observe to decay exponentially in time with a rate of approximately 30 words per year for English.

A new approach to topic models finds topics through community detection in word-document networks.

No abstract

Zipf's law is just one out of many universal laws proposed to describe statistical regularities in language. Here we review and critically discuss how these laws can be statistically interpreted, fitted, and tested (falsified). The modern availability of large databases of written text allows for tests with an unprecedent statistical accuracy and also a characterization of the fluctuations around the typical behavior. We find that fluctuations are usually much larger than expected based on simplifying statistical assumptions (e.g., independence and lack of correlations between observations). These simplifications appear also in usual statistical tests so that the large fluctuations can be erroneously interpreted as a falsification of the law. Instead, here we argue that linguistic laws are only meaningful (falsifiable) if accompanied by a model for which the fluctuations can be computed (e.g., a generative model of the text). The large fluctuations we report show that the constraints imposed by linguistic laws on the creativity process of text generation are not as tight as one could expect.

Quantifying the similarity between symbolic sequences is a traditional problem in information theory which requires comparing the frequencies of symbols in different sequences. In numerous modern applications, ranging from DNA over music to texts, the distribution of symbol frequencies is characterized by heavy-tailed distributions (e.g., Zipf's law). The large number of low-frequency symbols in these distributions poses major difficulties to the estimation of the similarity between sequences; e.g., they hinder an accurate finite-size estimation of entropies. Here, we show analytically how the systematic (bias) and statistical (fluctuations) errors in these estimations depend on the sample size N and on the exponent. of the heavy-tailed distribution. Our results are valid for the Shannon entropy (alpha = 1), its corresponding similarity measures (e.g., the Jensen-Shanon divergence), and also for measures based on the generalized entropy of order a. For small alpha's, including alpha = 1, the errors decay slower than the 1/N decay observed in short-tailed distributions. For a larger than a critical value alpha* = 1 + 1/gamma <= 2, the 1/N decay is recovered. We show the practical significance of our results by quantifying the evolution of the English language over the last two centuries using a complete alpha spectrum of measures. We find that frequent words changemore slowly than less frequent words and that alpha = 2 provides the most robust measure to quantify language change

In this paper we combine statistical analysis of written texts and simple stochastic models to explain the appearance of scaling laws in the statistics of word frequencies. The average vocabulary of an ensemble of fixed-length texts is known to scale sub-linearly with the total number of words (Heaps' law). Analyzing the fluctuations around this average in three large databases (Google-ngram, English Wikipedia, and a collection of scientific articles) we find that the standard deviation scales linearly with the average (Taylor's law), in contrast to the prediction of decaying fluctuations obtained using simple sampling arguments. We explain both scaling laws (Heaps and Taylor) by modeling the usage of words by a Poisson process with a fattailed distribution of word-frequencies (Zipf's law) and topic-dependent frequencies of individual words (as in topic models). Taking into account topical variations lead to quenched averages, turn the vocabulary size a non-self-averaging quantity, and explain the empirical observations. For the numerous practical applications relying on estimations of vocabulary size, our results show that uncertainties remain large even for long texts. We show how to account for these uncertainties in measurements of lexical richness of texts with different lengths.