Science and Facebook: The same popularity law!

Tree size distribution as the stationary limit of an evolutionary master equation

The diameter distribution of a given species of deciduous trees is well approximated by a Gamma distribution. Here we give new experimental evidence for this conjecture by analyzing deciduous tree size data in mature semi-natural forest and ancient, traditionally managed wood-pasture from Central Europe. These distribution functions collapse on a universal shape if the tree sizes are normalized to the mean value in the considered sample. A new evolutionary master equation is used to model the observed distribution. The model incorporates four ecological processes: tree growth, mortality, recruitment, and diversification. Utilizing simple and realistic kernel functions describing the first three, along with an assumed multiplicative dilution due to diversification, the stationary solution of the master equation yields the experimentally observed Gamma distribution. The model as it is formulated allows an analytically compact solution and has only two fitting parameters whose values are consistent with the experimental data related to these processes. We found that the equilibrium size distribution of tree species with different ecology, originating from two contrastingly different semi-natural ecosystem types can be accurately described by a single dynamical mean-field model.

Thermodynamical Aspects of the LGGR Approach for Hadron Energy Spectra

The local growth global reset (LGGR) dynamical model is reviewed and its performance in describing the hadron energy spectra in relativistic collisions is demonstrated. It is shown that even for dynamical processes a temperature-like quantity can be defined and distributions resembling statistical equilibrium can be reached. With appropriate growth and reset rates the LGGR model is capable of describing the right energy spectra. These findings draw a certain picture of quark–gluon plasma development with random hadronization and re-swallowing steps and signals the fact that observing an exponential spectrum does not necessarily prove thermal equilibrium in the experiment.

Comments on Mathematical Aspects of the Biró–Néda Model

We address two mathematical aspects of the Biró–Néda dynamical model, recently applied in the statistical analysis of several and varied complex phenomena. First, we show that a given implicit assumption ceases to be valid outside the most simple and common cases, and we analyze the consequences thereof, in what the formulation of the model and probability conservation is concerned. Second, we revisit the transient behavior in the case of a constant reset rate and a constant or linear growth rate, improving on a previous analysis by including more general initial conditions.

A typology of research discovery tools

There has been a proliferation of new research discovery tools that aid scientists in finding relevant publications. To obtain a general overview of this development, this article generates a conceptual typology of all possible research discovery tools by drawing from the information-theoretical concepts of redundancy/variety. Bibliometric links between scholarly publications can thus exhibit ‘redundancy’ (i.e. expectable linkages between academic works) or ‘variety’ (i.e. original co-occurrence patterns). On the redundancy-reproducing end of the typology are machines that harness extant co-citations or keyword queries, such as academic search engines and paper recommender systems. The variety end of the spectrum harbours services that enable categorial browsing or that suggest publications randomly, such as journals’ tables of contents or random paper bots. The typology has implications for understanding how the design of research discovery platforms may ultimately shape aggregate citational networks of science.

Transient Dynamics in the Random Growth and Reset Model

A mean-field type model with random growth and reset terms is considered. The stationary distributions resulting from the corresponding master equation are relatively easy to obtain; however, for practical applications one also needs to know the convergence to stationarity. The present work contributes to this direction, studying the transient dynamics in the discrete version of the model by two different approaches. The first method is based on mathematical induction by the recursive integration of the coupled differential equations for the discrete states. The second method transforms the coupled ordinary differential equation system into a partial differential equation for the generating function. We derive analytical results for some important, practically interesting cases and discuss the obtained results for the transient dynamics.

Three dimensions of scientific impact

The growing popularity of bibliometric indexes (whose most famous example is the h index by J. E. Hirsch [J. E. Hirsch, Proc. Natl. Acad. Sci. U.S.A. 102, 16569-16572 (2005)]) is opposed by those claiming that one's scientific impact cannot be reduced to a single number. Some even believe that our complex reality fails to submit to any quantitative description. We argue that neither of the two controversial extremes is true. By assuming that some citations are distributed according to the rich get richer rule (success breeds success, preferential attachment) while some others are assigned totally at random (all in all, a paper needs a bibliography), we have crafted a model that accurately summarizes citation records with merely three easily interpretable parameters: productivity, total impact, and how lucky an author has been so far.

Improving the odds of success in antitumoral drug development using scoring approaches towards heterocyclic scaffolds

One of the most commonly discussed topics in the field of drug discovery is the continuous search for anticancer therapies, in which small-molecule development plays an important role. Although a number of techniques have been established over the past decades, one of the main methods for drug discovery and development is still represented by rational, ligand-based drug design. However, the success rate of this method could be higher if not affected by cognitive bias, which renders many potential druggable scaffolds and structures overlooked. The present study aimed to counter this bias by presenting an objective overview of the most important heterocyclic structures in the development of anti-proliferative drugs. As such, the present study analyzed data for 91,438 compounds extracted from the Developmental Therapeutics Program (DTP) database provided by the National Cancer Institute. Growth inhibition data from these compounds tested on a panel of 60 cancer cell lines representing various tissue types (NCI-60 panel) was statistically interpreted using 6 generated scores assessing activity, selectivity, growth inhibition efficacy and potency of different structural scaffolds, Bemis-Murcko skeletons, chemical features and structures common among the analyzed compounds. Of the most commonly used rings, the most prominent anti-proliferative effects were produced by quinoline, tetrahydropyran, benzimidazole and pyrazole, while overall, the optimal results were produced by complex ring structures that originate from natural compounds. These results highlight the impact of certain ring structures on the anti-proliferative effects in drug design. In addition, considering that medicinal chemists usually focus their research on simpler scaffolds the majority of the time with no significant pay-off, the present study indicates several unused complex scaffolds that could be exploited when designing anticancer therapies for optimal results in the fight against cancer.

Entropic Divergence and Entropy Related to Nonlinear Master Equations

We reverse engineer entropy formulas from entropic divergence, optimized to given classes of probability distribution function (PDF) evolution dynamical equation. For linear dynamics of the distribution function, the traditional Kullback–Leibler formula follows from using the logarithm function in the Csiszár’s f-divergence construction, while for nonlinear master equations more general formulas emerge. As applications, we review a local growth and global reset (LGGR) model for citation distributions, income distribution models and hadron number fluctuations in high energy collisions.

Comparing the topological rank of journals in Web of Science and Mendeley

Recently, there has been a surge of interest in new data emerged due to the rapid development of the information technologies in scholarly communication. Since the 2010s, altmetrics has become a common trend in scientometric research. However, researchers have not treated in much detail the question of the probability distributions underlying these new data. The principal objective of this study was to investigate one of the classic problems of scientometrics-the problem of citation and readership distributions. The study is based on the data obtained from two information systems: Web of Science and Mendeley. Here we based on the concept of the cumulative empirical distribution function to explore the differences and similarities between citations and readership counts of biological journals indexed in Web of Science and Mendeley. The basic idea was to determine, for any journal, a "size" (it is said to be the topological rank) of citation and readership empirical cumulative distributions, and then to compare distributions of the topological ranks of Web of Science and Mendeley. In order to verify our model, we employ it to the bibliometric and altmetric research of 305 biological journals indexed in Journal Citation Reports 2015. The findings show that both distributions of the topological rank of biological journals are statistically close to the Wakeby distribution. The findings presented in this study add to our understanding of information processes of the scholarly communication in the new digital environment.