Analysis of player speed and angle toward the ball in soccer.

The study analyzes how the magnitude and angle of the speed of soccer players change according to the distance to the ball and the phases of the game, namely the defensive and attacking phases. We observed how the role played in the team (goalkeeper, defender, midfielder, or forward) strongly determines the speed pattern of players. As a general trend, the speed's modulus is incremented as their position is closer to the ball, however, it is slightly decreased when arriving at it.

Distance Between Players During a Soccer Match: The Influence of Player Position.

In this study, we analyse the proximity between professional players during a soccer match. Specifically, we are concerned about the time a player remains at a distance to a rival that is closer than 2 m, which has a series of consequences, from the risk of contagion during a soccer match to the understanding of the tactical performance of players during the attacking/defensive phases. Departing from a dataset containing the Euclidean positions of all players during 60 matches of the Spanish national league (30 from and 30 from , respectively, the first and second divisions), we analysed 1,670 participations of elite soccer players.

Entropy of Badminton Strike Positions.

The aim of the current study was twofold: (i) to investigate the distribution of the strike positions of badminton players while quantifying the corresponding standard entropy and using an alternative metric (spatial entropy) related to winning and losing points and random positions; and (ii) to evaluate the standard entropy of the receiving positions. With the datasets of 259 badminton matches, we focused on the positions of players' strokes and the outcome of each point. First, we identified those regions of the court from which hits were most likely to be struck.

Antiphase synchronization in multiplex networks with attractive and repulsive interactions.

A series of recent publications, within the framework of network science, have focused on the coexistence of mixed attractive and repulsive (excitatory and inhibitory) interactions among the units within the same system, motivated by the analogies with spin glasses as well as to neural networks, or ecological systems. However, most of these investigations have been restricted to single layer networks, requiring further analysis of the complex dynamics and particular equilibrium states that emerge in multilayer configurations. This article investigates the synchronization properties of dynamical systems connected through multiplex architectures in the presence of attractive intralayer and repulsive interlayer connections.

Players' physical performance in LaLiga across the season: insights for competition continuation after COVID-19.

Due to the COVID-19 outbreak, professional football players competing in LaLiga were confined at home for ~8 weeks and then they were allowed to train to prepare the first competitive match for 4 weeks. As the duration of summer break in the prior four seasons of LaLiga (from 2015-2016 to 2018-2019) was of similar length to the suspension of the championship due to COVID-19 (~12 weeks), we have analysed the running performance of teams competing in LaLiga in these four seasons to anticipate players' physical performance after the resumption of the competition. The analysis includes the average running distance per game for each of the 38 matchdays that compose LaLiga.

Spatial and Temporal Entropies in the Spanish Football League: A Network Science Perspective.

We quantified the spatial and temporal entropy related to football teams and their players by means of a pass-based interaction. First, we calculated the spatial entropy associated to the positions of all passes made by a football team during a match, obtaining a spatial entropy ranking of Spanish teams during the 2017/2018 season. Second, we investigated how the player's average location in the field is related to the amount of entropy of his passes.

Permutation Entropy and Statistical Complexity in Mild Cognitive Impairment and Alzheimer's Disease: An Analysis Based on Frequency Bands.

We present one of the first applications of Permutation Entropy (PE) and Statistical Complexity (SC) (measured as the product of PE and Jensen-Shanon Divergence) on Magnetoencephalography (MEG) recordings of 46 subjects suffering from Mild Cognitive Impairment (MCI), 17 individuals diagnosed with Alzheimer's Disease (AD) and 48 healthy controls. We studied the differences in PE and SC in broadband signals and their decomposition into frequency bands ( δ , θ , α and β ), considering two modalities: (i) raw time series obtained from the magnetometers and (ii) a reconstruction into cortical sources or regions of interest (ROIs). We conducted our analyses at three levels: (i) at the group level we compared SC in each frequency band and modality between groups; (ii) at the individual level we compared how the [PE, SC] plane differs in each modality; and (iii) at the local level we explored differences in scalp and cortical space.

Influence of Players' Maximum Running Speed on the Team's Ranking Position at the End of the Spanish .

The maximum running speed that a football player can attain during match play has become one of the most popular variables to assess a player's physical talent. However, the influence of a player's maximum running speed on football performance has not yet been properly investigated. The aim of this study was to determine the influence of a player's peak/maximum running speed on the team's ranking position at the end of a national league.

The resumption of sports competitions after COVID-19 lockdown: The case of the Spanish football league.

In this work, we present a stochastic discrete-time model adapted to describe the propagation of COVID-19 during a football tournament. Specifically, we are concerned about the re-start of the Spanish national football league, , which is currently -May 2020- stopped with 11 fixtures remaining. Our model includes two additional states of an individual, confined and quarantined, which are reached when an individual presents COVID-19 symptoms or has undergone a virus test with a positive result.

Using symbolic networks to analyse dynamical properties of disease outbreaks.

We introduce a new methodology, which is based on the construction of epidemic networks, to analyse the evolution of epidemic time series. First, we translate the time series into ordinal patterns containing information about local fluctuations in disease prevalence. Each pattern is associated with a node of a network, whose (directed) connections arise from consecutive appearances in the series.

Experimental datasets of networks of nonlinear oscillators: Structure and dynamics during the path to synchronization.

The analysis of the interplay between structural and functional networks require experiments where both the specific structure of the connections between nodes and the time series of the underlying dynamical units are known at the same time. However, real datasets typically contain only one of the two ways (structural or functional) a network can be observed. Here, we provide experimental recordings of the dynamics of 28 nonlinear electronic circuits coupled in 20 different network configurations.

Taming out-of-equilibrium dynamics on interconnected networks.

A wide variety of social, biological or technological systems can be described as processes taking place on networked structures in continuous interaction with other networks. We propose here a new methodology to describe, anticipate and manage, in real time, the out-of-equilibrium dynamics of processes that evolve on interconnected networks. This goal is achieved through the full analytical treatment of the phenomenology and its reduction to a two-dimensional flux diagram, allowing us to predict at every time step the dynamical consequences of modifying the links between the different ensembles.

Frequency-based brain networks: From a multiplex framework to a full multilayer description.

We explore how to study dynamical interactions between brain regions by using functional multilayer networks whose layers represent different frequency bands at which a brain operates. Specifically, we investigate the consequences of considering the brain as (i) a multilayer network, in which all brain regions can interact with each other at different frequency bands; and as (ii) a multiplex network, in which interactions between different frequency bands are allowed only within each brain region and not between them. We study the second-smallest eigenvalue of the combinatorial supra-Laplacian matrix of both the multiplex and multilayer networks, as has been used previously as an indicator of network synchronizability and as a biomarker for several brain diseases.

Functional brain networks reveal the existence of cognitive reserve and the interplay between network topology and dynamics.

We investigated how the organization of functional brain networks was related to cognitive reserve (CR) during a memory task in healthy aging. We obtained the magnetoencephalographic functional networks of 20 elders with a high or low CR level to analyse the differences at network features. We reported a negative correlation between synchronization of the whole network and CR, and observed differences both at the node and at the network level in: the average shortest path and the network outreach.

Biological conservation law as an emerging functionality in dynamical neuronal networks.

Scientists strive to understand how functionalities, such as conservation laws, emerge in complex systems. Living complex systems in particular create high-ordered functionalities by pairing up low-ordered complementary processes, e.g.

Competition among networks highlights the power of the weak.

The unpreventable connections between real networked systems have recently called for an examination of percolation, diffusion or synchronization phenomena in multilayer networks. Here we use network science and game theory to explore interactions in networks-of-networks and model these as a game for gaining importance. We propose a viewpoint where networks choose the connection strategies, in contrast with classical approaches where nodes are the active players.

Synchronization of networks of chaotic oscillators: Structural and dynamical datasets.

We provide the topological structure of a series of =28 Rössler chaotic oscillators diffusively coupled through one of its variables. The dynamics of the variable describing the evolution of the individual nodes of the network are given for a wide range of coupling strengths. Datasets capture the transition from the unsynchronized behavior to the synchronized one, as a function of the coupling strength between oscillators.

Synchronization-based computation through networks of coupled oscillators.

The mesoscopic activity of the brain is strongly dynamical, while at the same time exhibits remarkable computational capabilities. In order to examine how these two features coexist, here we show that the patterns of synchronized oscillations displayed by networks of neural mass models, representing cortical columns, can be used as substrates for Boolean-like computations. Our results reveal that the same neural mass network may process different combinations of dynamical inputs as different logical operations or combinations of them.

Inferring the connectivity of coupled oscillators from time-series statistical similarity analysis.

A system composed by interacting dynamical elements can be represented by a network, where the nodes represent the elements that constitute the system, and the links account for their interactions, which arise due to a variety of mechanisms, and which are often unknown. A popular method for inferring the system connectivity (i.e.

Evaluating the effect of aging on interference resolution with time-varying complex networks analysis.

In this study we used graph theory analysis to investigate age-related reorganization of functional networks during the active maintenance of information that is interrupted by external interference. Additionally, we sought to investigate network differences before and after averaging network parameters between both maintenance and interference windows. We compared young and older adults by measuring their magnetoencephalographic recordings during an interference-based working memory task restricted to successful recognitions.