Comparing the evolutionary dynamics of predominant SARS-CoV-2 virus lineages co-circulating in Mexico.

Over 200 different SARS-CoV-2 lineages have been observed in Mexico by November 2021. To investigate lineage replacement dynamics, we applied a phylodynamic approach and explored the evolutionary trajectories of five dominant lineages that circulated during the first year of local transmission. For most lineages, peaks in sampling frequencies coincided with different epidemiological waves of infection in Mexico. Lineages B.1.1.222 and B.1.1.519 exhibited similar dynamics, constituting clades that likely originated in Mexico and persisted for >12 months. Lineages B.1.1.7, P.1 and B.1.617.2 also displayed similar dynamics, characterized by multiple introduction events leading to a few successful extended local transmission chains that persisted for several months. For the largest B.1.617.2 clades, we further explored viral lineage movements across Mexico. Many clades were located within the south region of the country, suggesting that this area played a key role in the spread of SARS-CoV-2 in Mexico.

Intermunicipal travel networks of Mexico during the COVID-19 pandemic.

Human mobility networks are widely used for diverse studies in geography, sociology, and economics. In these networks, nodes usually represent places or regions and links refer to movement between them. They become essential when studying the spread of a virus, the planning of transit, or society's local and global structures. Therefore, the construction and analysis of human mobility networks are crucial for a vast number of real-life applications. This work presents a collection of networks that describe the human travel patterns between municipalities in Mexico in the 2020-2021 period. Using anonymized mobile location data, we constructed directed, weighted networks representing the volume of travels between municipalities. We analysed changes in global, local, and mesoscale network features. We observe that changes in these features are associated with factors such as COVID-19 restrictions and population size. In general, the implementation of restrictions at the start of the COVID-19 pandemic in early 2020, induced more intense changes in network features than later events, which had a less notable impact in network features. These networks will result very useful for researchers and decision-makers in the areas of transportation, infrastructure planning, epidemic control and network science at large.

Modeling the popularity of twitter hashtags with master equations.

In this work we introduce a simple mathematical model, based on master equations, to describe the time evolution of the popularity of hashtags on the Twitter social network. Specifically, we model the total number of times a certain hashtag appears on user's timelines as a function of time. Our model considers two kinds of components: those that are internal to the network (degree distribution) as well as external factors, such as the external popularity of the hashtag. From the master equation, we are able to obtain explicit solutions for the mean and variance and construct confidence regions. We propose a gamma kernel function to model the hashtag popularity, which is quite simple and yields reasonable results. We validate the plausibility of the model by contrasting it with actual Twitter data obtained through the public API. Our findings confirm that relatively simple semi-deterministic models are able to capture the essentials of this very complex phenomenon for a wide variety of cases. The model we present distinguishes from other existing models in its focus on the time evolution of the total number of times a particular hashtag has been seen by Twitter users and the consideration of both internal and external components.

Population patterns in World's administrative units.

Whereas there has been an extended discussion concerning city population distribution, little has been said about that of administrative divisions. In this work, we investigate the population distribution of second-level administrative units of 150 countries and territories and propose the discrete generalized beta distribution (DGBD) rank-size function to describe the data. After testing the balance between the goodness of fit and number of parameters of this function compared with a power law, which is the most common model for city population, the DGBD is a good statistical model for 96% of our datasets and preferred over a power law in almost every case. Moreover, the DGBD is preferred over a power law for fitting country population data, which can be seen as the zeroth-level administrative unit. We present a computational toy model to simulate the formation of administrative divisions in one dimension and give numerical evidence that the DGBD arises from a particular case of this model. This model, along with the fitting of the DGBD, proves adequate in reproducing and describing local unit evolution and its effect on the population distribution.

Size distribution of function-based human gene sets and the split-merge model.

The sizes of paralogues-gene families produced by ancestral duplication-are known to follow a power-law distribution. We examine the size distribution of gene sets or gene families where genes are grouped by a similar function or share a common property. The size distribution of Human Gene Nomenclature Committee (HGNC) gene sets deviate from the power-law, and can be fitted much better by a beta rank function. We propose a simple mechanism to break a power-law size distribution by a combination of splitting and merging operations. The largest gene sets are split into two to account for the subfunctional categories, and a small proportion of other gene sets are merged into larger sets as new common themes might be realized. These operations are not uncommon for a curator of gene sets. A simulation shows that iteration of these operations changes the size distribution of Ensembl paralogues and could lead to a distribution fitted by a rank beta function. We further illustrate application of beta rank function by the example of distribution of transcription factors and drug target genes among HGNC gene families.

Beyond Zipf's Law: The Lavalette Rank Function and Its Properties.

Although Zipf's law is widespread in natural and social data, one often encounters situations where one or both ends of the ranked data deviate from the power-law function. Previously we proposed the Beta rank function to improve the fitting of data which does not follow a perfect Zipf's law. Here we show that when the two parameters in the Beta rank function have the same value, the Lavalette rank function, the probability density function can be derived analytically. We also show both computationally and analytically that Lavalette distribution is approximately equal, though not identical, to the lognormal distribution. We illustrate the utility of Lavalette rank function in several datasets. We also address three analysis issues on the statistical testing of Lavalette fitting function, comparison between Zipf's law and lognormal distribution through Lavalette function, and comparison between lognormal distribution and Lavalette distribution.