Dissimilarity between synchronization processes on networks.

In this study, we present a general framework for comparing two dynamical processes that describe the synchronization of oscillators coupled through networks of the same size. We introduce a measure of dissimilarity defined in terms of a metric on a hypertorus, allowing us to compare the phases of coupled oscillators. In the first part, this formalism is implemented to examine systems of networked identical phase oscillators that evolve with the Kuramoto model. In particular, we analyze the effect of the weight of an edge in the synchronization of two oscillators, the introduction of new sets of edges in interacting cycles, the effect of bias in the couplings, and the addition of a link in a ring. We also compare the synchronization of nonisomorphic graphs with four nodes. Finally, we explore the dissimilarities generated when we contrast the Kuramoto model with its linear approximation for different random initial phases in deterministic and random networks. The approach introduced provides a general tool for comparing synchronization processes on networks, allowing us to understand the dynamics of a complex system as a consequence of the coupling structure and the processes that can occur in it.

Temporal visitation patterns of points of interest in cities on a planetary scale: a network science and machine learning approach.

We aim to study the temporal patterns of activity in points of interest of cities around the world. In order to do so, we use the data provided by the online location-based social network Foursquare, where users make check-ins that indicate points of interest in the city. The data set comprises more than 90 million check-ins in 632 cities of 87 countries in 5 continents. We analyzed more than 11 million points of interest including all sorts of places: airports, restaurants, parks, hospitals, and many others. With this information, we obtained spatial and temporal patterns of activities for each city. We quantify similarities and differences of these patterns for all the cities involved and construct a network connecting pairs of cities. The links of this network indicate the similarity of temporal visitation patterns of points of interest between cities and is quantified with the Kullback-Leibler divergence between two distributions. Then, we obtained the community structure of this network and the geographic distribution of these communities worldwide. For comparison, we also use a Machine Learning algorithm-unsupervised agglomerative clustering-to obtain clusters or communities of cities with similar patterns. The main result is that both approaches give the same classification of five communities belonging to five different continents worldwide. This suggests that temporal patterns of activity can be universal, with some geographical, historical, and cultural variations, on a planetary scale.

Optimal exploration of random walks with local bias on networks.

We propose local-biased random walks on general networks where a Markovian walker is defined by different types of biases in each node to establish transitions to its neighbors depending on their degrees. For this ergodic dynamics, we explore the capacity of the random walker to visit all the nodes characterized by a global mean first passage time. This quantity is calculated using eigenvalues and eigenvectors of the transition matrix that defines the dynamics. In the first part, we illustrate how our framework leads to optimal exploration for small-size graphs through the analysis of all the possible bias configurations. In the second part, we study the most favorable configurations in each node by using simulated annealing. This heuristic algorithm allows obtaining approximate solutions of the optimal bias in different types of networks. The results show how the local bias can optimize the exploration of the network in comparison with the unbiased random walk. The methods implemented in this research are general and open the doors to a broad spectrum of tools applicable to different random walk strategies and dynamical processes on networks.

Activity of vehicles in the bus rapid transit system Metrobús in Mexico City.

In this paper, we analyze a massive dataset with registers of the movement of vehicles in the bus rapid transit system Metrobús in Mexico City from February 2020 to April 2021. With these records and a division of the system into 214 geographical regions (segments), we characterize the vehicles' activity through the statistical analysis of speeds in each zone. We use the Kullback-Leibler distance to compare the movement of vehicles in each segment and its evolution. The results for the dynamics in different zones are represented as a network where nodes define segments of the system Metrobús and edges describe similarity in the activity of vehicles. Community detection algorithms in this network allow the identification of patterns considering different levels of similarity in the distribution of speeds providing a framework for unsupervised classification of the movement of vehicles. The methods developed in this research are general and can be implemented to describe the activity of different transportation systems with detailed records of the movement of users or vehicles.

When Cyclodextrins Met Data Science: Unveiling Their Pharmaceutical Applications through Network Science and Text-Mining.

We present a data-driven approach to unveil the pharmaceutical technologies of cyclodextrins (CDs) by analyzing a dataset of CD pharmaceutical patents. First, we implemented network science techniques to represent CD patents as a single structure and provide a framework for unsupervised detection of keywords in the patent dataset. Guided by those keywords, we further mined the dataset to examine the patenting trends according to CD-based dosage forms. CD patents formed complex networks, evidencing the supremacy of CDs for solubility enhancement and how this has triggered cutting-edge applications based on or beyond the solubility improvement. The networks exposed the significance of CDs to formulate aqueous solutions, tablets, and powders. Additionally, they highlighted the role of CDs in formulations of anti-inflammatory drugs, cancer therapies, and antiviral strategies. Text-mining showed that the trends in CDs for aqueous solutions, tablets, and powders are going upward. Gels seem to be promising, while patches and fibers are emerging. Cyclodextrins' potential in suspensions and emulsions is yet to be recognized and can become an opportunity area. This is the first unsupervised/supervised data-mining approach aimed at depicting a landscape of CDs to identify trending and emerging technologies and uncover opportunity areas in CD pharmaceutical research.

Mean encounter times for multiple random walkers on networks.

We introduce a general approach for the study of the collective dynamics of noninteracting random walkers on connected networks. We analyze the movement of R independent (Markovian) walkers, each defined by its own transition matrix. By using the eigenvalues and eigenvectors of the R independent transition matrices, we deduce analytical expressions for the collective stationary distribution and the average number of steps needed by the random walkers to start in a particular configuration and reach specific nodes the first time (mean first-passage times), as well as global times that characterize the global activity. We apply these results to the study of mean first-encounter times for local and nonlocal random walk strategies on different types of networks, with both synchronous and asynchronous motion.

Technological evolution of cyclodextrins in the pharmaceutical field.

We herein disclose how global cyclodextrin-based pharmaceutical technologies have evolved since the early 80s through a 1998 patents dataset retrieved from Derwent Innovation Index. We used text-mining techniques based on the patents semantic content to extract the knowledge contained therein, to analyze technologies related to the principal attributes of CDs: solubility, stability, and taste-masking enhancement. The majority of CDs pharmaceutical technologies are directed toward parenteral aqueous solutions. The development of oral and ocular formulations is rapidly growing, while technologies for nasal and pulmonary routes are emerging and seem to be promising. Formulations for topical, transdermal, vaginal, and rectal routes do not account for a high number of patents, but they may be hiding a great potential, representing opportunity research areas. Certainly, the progress in materials sciences, supramolecular chemistry, and nanotechnology, will influence the trend of that, apparently neglected, research. The bottom line, CDs pharmaceutical technologies are still increasing, and this trend is expected to continue in the coming years. Patent monitoring allows the identification of relevant technologies and trends to prioritize research, development, and investment in both, academia and industry. We expect the scope of this approach to be applied in the pharmaceutical field beyond CDs technological applications.