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Prof. Javier Buldú
University Rey Juan Carlos

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0 Complex Systems
0 Network Science
0 Nonlinear Dynamics
0 Sports Science
0 Brain Networks

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Network Science
Nonlinear Dynamics
Complex Systems

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Journal article
Published: 23 June 2021 in Entropy
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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. Second, we computed the standard entropy of stroke positions, and then the spatial entropy, which also considers the order and clustering of the hitting locations in a two-dimensional Euclidean space. Both entropy quantifiers revealed high uncertainty in the striking position; however, specific court locations (i.e., the four corners) are preferred over the rest. When the outcome of each point was taken into account, we observed that the hitting patterns with lower entropy were associated with higher probabilities of winning points. On the contrary, players striking from more random positions were more prone to losing the points.

ACS Style

Javier Galeano; Miguel-Ángel Gomez; Fernando Rivas; Javier Buldú. Entropy of Badminton Strike Positions. Entropy 2021, 23, 799 .

AMA Style

Javier Galeano, Miguel-Ángel Gomez, Fernando Rivas, Javier Buldú. Entropy of Badminton Strike Positions. Entropy. 2021; 23 (7):799.

Chicago/Turabian Style

Javier Galeano; Miguel-Ángel Gomez; Fernando Rivas; Javier Buldú. 2021. "Entropy of Badminton Strike Positions." Entropy 23, no. 7: 799.

Journal article
Published: 23 May 2021 in Chaos, Solitons & Fractals
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We investigate, numerically and experimentally, the phenomenon of dynamical consistency in a network of nonlinear oscillators. Dynamical consistency is defined as the ability of a dynamical system to respond in the same way when it is perturbed by the same external signal. This property, fulfilled by specific dynamical systems, has been mainly studied in single oscillators (e.g., lasers or electronic circuits), but just a few works have focused on dynamical systems connected through a non-regular network. Using an electronic array, we can connect a series of nonlinear (analog) electronic circuits to create complex networks, where nodes are coupled between them in a given structure, and an external signal can also be introduced into each particular circuit. Furthermore, the strength of the connections is re-configurable. Next, we analyze the consequences of varying the network’s coupling strength and investigate how synchronization and consistency of the whole ensemble arise. Variations in both coupling strengths, i.e. (i) between oscillators and (ii) with the external signal, show the existence of a region where electronic oscillators can respond in the same way to an external perturbation even though they are not completely synchronized with the external signal. We use the Pearson correlation coefficient to measure the consistency of the network, which is characterized by a high correlation between the network output signals and, at the same time, a low correlation with the input signal.

ACS Style

V.P. Vera-Ávila; J.R. Sevilla-Escoboza; R.R. Rivera Durón; J.M. Buldú. Dynamical consistency in networks of nonlinear oscillators. Chaos, Solitons & Fractals 2021, 148, 111017 .

AMA Style

V.P. Vera-Ávila, J.R. Sevilla-Escoboza, R.R. Rivera Durón, J.M. Buldú. Dynamical consistency in networks of nonlinear oscillators. Chaos, Solitons & Fractals. 2021; 148 ():111017.

Chicago/Turabian Style

V.P. Vera-Ávila; J.R. Sevilla-Escoboza; R.R. Rivera Durón; J.M. Buldú. 2021. "Dynamical consistency in networks of nonlinear oscillators." Chaos, Solitons & Fractals 148, no. : 111017.

Article
Published: 18 March 2021 in Physical Review E
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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. This setting enables the emergence of antisynchronization, i.e., intralayer synchronization coexisting with antiphase dynamics between coupled systems of different layers. We demonstrate the existence of a transition from interlayer antisynchronization to antiphase synchrony in any connected bipartite multiplex architecture when the repulsive coupling is introduced through any spanning tree of a single layer. We identify, analytically, the required graph topologies for interlayer antisynchronization and its interplay with intralayer and antiphase synchronization. Next, we analytically derive the invariance of intralayer synchronization manifold and calculate the attractor size of each oscillator exhibiting interlayer antisynchronization together with intralayer synchronization. The necessary conditions for the existence of interlayer antisynchronization along with intralayer synchronization are given and numerically validated by considering Stuart-Landau oscillators. Finally, we also analytically derive the local stability condition of the interlayer antisynchronization state using the master stability function approach.

ACS Style

Sayantan Nag Chowdhury; Sarbendu Rakshit; Javier M. Buldú; Dibakar Ghosh; Chittaranjan Hens. Antiphase synchronization in multiplex networks with attractive and repulsive interactions. Physical Review E 2021, 103, 032310 .

AMA Style

Sayantan Nag Chowdhury, Sarbendu Rakshit, Javier M. Buldú, Dibakar Ghosh, Chittaranjan Hens. Antiphase synchronization in multiplex networks with attractive and repulsive interactions. Physical Review E. 2021; 103 (3):032310.

Chicago/Turabian Style

Sayantan Nag Chowdhury; Sarbendu Rakshit; Javier M. Buldú; Dibakar Ghosh; Chittaranjan Hens. 2021. "Antiphase synchronization in multiplex networks with attractive and repulsive interactions." Physical Review E 103, no. 3: 032310.

Editorial
Published: 08 December 2020 in Chaos, Solitons & Fractals
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ACS Style

Javier M. Buldú; Miguel-Ángel Gómez; José Luis Herrera-Diestra; Johann H. Martínez. Editorial: Nonlinear dynamics and networks in sports. Chaos, Solitons & Fractals 2020, 142, 110518 .

AMA Style

Javier M. Buldú, Miguel-Ángel Gómez, José Luis Herrera-Diestra, Johann H. Martínez. Editorial: Nonlinear dynamics and networks in sports. Chaos, Solitons & Fractals. 2020; 142 ():110518.

Chicago/Turabian Style

Javier M. Buldú; Miguel-Ángel Gómez; José Luis Herrera-Diestra; Johann H. Martínez. 2020. "Editorial: Nonlinear dynamics and networks in sports." Chaos, Solitons & Fractals 142, no. : 110518.

Journal article
Published: 27 November 2020 in International Journal of Environmental Research and Public Health
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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. A second aim was to investigate differences in maximum running speed among playing positions. To fulfil this aim, the peak/maximum running speeds of 475 male professional football players were recorded for 38 fixtures of the Spanish first-division league (LaLiga) from the 2017–2018 season (7838 data points). Players’ peak running speeds in each match were assessed with a validated multicamera tracking system and associated software (Mediacoach®). Players’ maximum running speed was established as the fastest running speed they attained during the entire season. Most players (53.5% of the total) had a maximum running speed in the range of 32.0–33.9 km/h, with only three players (0.6%) with a maximum running speed of over 35.0 km/h. Overall, forwards were faster than defenders and both types of players were faster than midfielders (33.03 ± 1.35 > 32.72 ± 1.32 > 32.08 ± 1.63 km/h; p < 0.001). There was no association between teams’ maximum running speed and ranking position at the end of the league (r = −0.356, p = 0.135). The correlations between teams’ maximum speeds and ranking position were low for defenders (r = −0.334, p = 0.163), midfielders (r = 0.125, p = 0.610), and forwards (r = −0.065, p = 0.791). As a result, the variance in the ranking position at the end of the season explained by a team’s maximum speed was of only 7.5%. Finally, as an average for all teams, players’ peak running speeds remained stable at ~30.7 ± 0.6 km/h throughout the whole season. These results suggest that successful and less successful football teams have squads with players able to obtain similar maximum running speeds during match play throughout the season. Hence, players’ maximum running speeds have a poor association with the team’s ranking position at the end of the Spanish professional national league.

ACS Style

Juan Del Coso; Diego Brito De Souza; Víctor Moreno-Perez; Javier M. Buldú; Fabio Nevado; Ricardo Resta; Roberto López-Del Campo. Influence of Players’ Maximum Running Speed on the Team’s Ranking Position at the End of the Spanish LaLiga. International Journal of Environmental Research and Public Health 2020, 17, 8815 .

AMA Style

Juan Del Coso, Diego Brito De Souza, Víctor Moreno-Perez, Javier M. Buldú, Fabio Nevado, Ricardo Resta, Roberto López-Del Campo. Influence of Players’ Maximum Running Speed on the Team’s Ranking Position at the End of the Spanish LaLiga. International Journal of Environmental Research and Public Health. 2020; 17 (23):8815.

Chicago/Turabian Style

Juan Del Coso; Diego Brito De Souza; Víctor Moreno-Perez; Javier M. Buldú; Fabio Nevado; Ricardo Resta; Roberto López-Del Campo. 2020. "Influence of Players’ Maximum Running Speed on the Team’s Ranking Position at the End of the Spanish LaLiga." International Journal of Environmental Research and Public Health 17, no. 23: 8815.

Journal article
Published: 12 November 2020 in Scientific Reports
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We investigated the ability of football teams to develop a particular playing style by looking at their passing patterns. Using the information contained in the pass sequences during matches, we constructed the pitch passing networks of teams, whose nodes are the divisions of the pitch for a given spatial scale and links account for the number of passes from region to region. We translated football passings networks into their corresponding adjacency matrices. We calculated the correlations between matrices of the same team to quantify how consistent the passing patterns of a given team are. Next, we quantified the differences with other teams’ matrices and obtained an identifiability parameter that indicates how unique are the passing patterns of a given team. Consistency and identifiability rankings were calculated during a whole season, allowing to detect those teams of a league whose passing patterns are different from the rest. Furthermore, we found differences between teams playing at home or away. Finally, we used the identifiability parameter to investigate what teams imposed their passing patterns over the rivals during a given match.

ACS Style

D. Garrido; D. R. Antequera; J. Busquets; R. López Del Campo; R. Resta Serra; S. Jos Vielcazat; J. M. Buldú. Consistency and identifiability of football teams: a network science perspective. Scientific Reports 2020, 10, 1 -10.

AMA Style

D. Garrido, D. R. Antequera, J. Busquets, R. López Del Campo, R. Resta Serra, S. Jos Vielcazat, J. M. Buldú. Consistency and identifiability of football teams: a network science perspective. Scientific Reports. 2020; 10 (1):1-10.

Chicago/Turabian Style

D. Garrido; D. R. Antequera; J. Busquets; R. López Del Campo; R. Resta Serra; S. Jos Vielcazat; J. M. Buldú. 2020. "Consistency and identifiability of football teams: a network science perspective." Scientific Reports 10, no. 1: 1-10.

Journal article
Published: 04 September 2020 in Scientific Reports
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The interplay between structure and function is critical in the understanding of complex systems, their dynamics and their behavior. We investigated the interplay between structural and functional networks by means of the differential identifiability framework, which here quantifies the ability of identifying a particular network structure based on (1) the observation of its functional network and (2) the comparison with a prior observation under different initial conditions. We carried out an experiment consisting of the construction of $$M=20$$ different structural networks composed of $$N=28$$ nonlinear electronic circuits and studied the regions where network structures are identifiable. Specifically, we analyzed how differential identifiability is related to the coupling strength between dynamical units (modifying the level of synchronization) and what are the consequences of increasing the amount of noise existing in the functional networks. We observed that differential identifiability reaches its highest value for low to intermediate coupling strengths. Furthermore, it is possible to increase the identifiability parameter by including a principal component analysis in the comparison of functional networks, being especially beneficial for scenarios where noise reaches intermediate levels. Finally, we showed that the regime of the parameter space where differential identifiability is the highest is highly overlapped with the region where structural and functional networks correlate the most.

ACS Style

V. P. Vera-Ávila; R. Sevilla-Escoboza; J. Goñi; Roberto R. Rivera-Durón; J. M. Buldú. Identifiability of structural networks of nonlinear electronic oscillators. Scientific Reports 2020, 10, 1 -11.

AMA Style

V. P. Vera-Ávila, R. Sevilla-Escoboza, J. Goñi, Roberto R. Rivera-Durón, J. M. Buldú. Identifiability of structural networks of nonlinear electronic oscillators. Scientific Reports. 2020; 10 (1):1-11.

Chicago/Turabian Style

V. P. Vera-Ávila; R. Sevilla-Escoboza; J. Goñi; Roberto R. Rivera-Durón; J. M. Buldú. 2020. "Identifiability of structural networks of nonlinear electronic oscillators." Scientific Reports 10, no. 1: 1-11.

Journal article
Published: 10 July 2020 in Chaos, Solitons & Fractals
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We investigated the particular organization of Guardiola’s F.C. Barcelona during season 2009/2010, using datasets from the Spanish National League La Liga. Specifically, we constructed the corresponding pitch networks, obtained from all passes successfully performed by a team during a football match. Pitch networks are composed of nodes consisting of particular subdivisions of the field, which are connected through links whose weight ωi,j corresponds to the number of passes made from region i to region j. We performed a multi-scale analysis focused on evaluating the properties of pitch networks at different scales, from a partition of the pitch into 2 × 2 to 10 × 10 areas. For each scale, we calculated a diversity of network parameters of F.C. Barcelona and its opponents during the whole season. Next, we compared the properties of F.C. Barcelona pitch networks with the networks of its rivals. Our results show how, depending on the spatial scale, there are statistically significant differences between F.C. Barcelona and the rest of the teams of the Spanish league. These differences are particularly significant at the clustering coefficient, the network average shortest-path, and the number of nodes occupied by a team for partitions with a high number of subdivisions.

ACS Style

J.L. Herrera-Diestra; I. Echegoyen; J.H. Martínez; D. Garrido; J. Busquets; F.Seirul. Io; J.M. Buldú. Pitch networks reveal organizational and spatial patterns of Guardiola’s F.C. Barcelona. Chaos, Solitons & Fractals 2020, 138, 109934 .

AMA Style

J.L. Herrera-Diestra, I. Echegoyen, J.H. Martínez, D. Garrido, J. Busquets, F.Seirul. Io, J.M. Buldú. Pitch networks reveal organizational and spatial patterns of Guardiola’s F.C. Barcelona. Chaos, Solitons & Fractals. 2020; 138 ():109934.

Chicago/Turabian Style

J.L. Herrera-Diestra; I. Echegoyen; J.H. Martínez; D. Garrido; J. Busquets; F.Seirul. Io; J.M. Buldú. 2020. "Pitch networks reveal organizational and spatial patterns of Guardiola’s F.C. Barcelona." Chaos, Solitons & Fractals 138, no. : 109934.

Journal article
Published: 24 June 2020 in Symmetry
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We investigate the relation between the number of passes made by a football team and the number of goals. We analyze the 380 matches of a complete season of the Spanish national league “LaLiga" (2018/2019). We observe how the number of scored goals is positively correlated with the number of passes made by a team. In this way, teams on the top (bottom) of the ranking at the end of the season make more (less) passes than the rest of the teams. However, we observe a strong asymmetry when the analysis is made depending on the part of the match. Interestingly, fewer passes are made in the second half of a match, while, at the same time, more goals are scored. This paradox appears in the majority of teams, and it is independent of the number of passes made. These results confirm that goals in the first half of matches are more “costly” in terms of passes than those scored in second halves.

ACS Style

Daniel R. Antequera; David Garrido; Ignacio Echegoyen; Roberto López Del Campo; Ricardo Resta Serra; Javier M. Buldú. Asymmetries in Football: The Pass—Goal Paradox. Symmetry 2020, 12, 1052 .

AMA Style

Daniel R. Antequera, David Garrido, Ignacio Echegoyen, Roberto López Del Campo, Ricardo Resta Serra, Javier M. Buldú. Asymmetries in Football: The Pass—Goal Paradox. Symmetry. 2020; 12 (6):1052.

Chicago/Turabian Style

Daniel R. Antequera; David Garrido; Ignacio Echegoyen; Roberto López Del Campo; Ricardo Resta Serra; Javier M. Buldú. 2020. "Asymmetries in Football: The Pass—Goal Paradox." Symmetry 12, no. 6: 1052.

Journal article
Published: 04 June 2020 in Chaos, Solitons & Fractals
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In this work, we present a stochastic discrete-time SEIR Susceptible-Exposed-Infectious-Recoveredmodel 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, La Liga, 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. The model also accounts for the interaction dynamics of players, considering three different sources of infection: the player social circle, the contact with his/her team colleagues during training sessions, and the interaction with rivals during a match. Our results highlight the influence of the days between matches, the frequency of virus tests and their sensitivity on the number of players infected at the end of the season. Following our findings, we finally propose a variety of strategies to minimise the probability that COVID-19 propagates in case the season of La Liga was re-started after the current lockdown.

ACS Style

Javier M. Buldú; Daniel R. Antequera; Jacobo Aguirre. The resumption of sports competitions after COVID-19 lockdown: The case of the Spanish football league. Chaos, Solitons & Fractals 2020, 138, 109964 .

AMA Style

Javier M. Buldú, Daniel R. Antequera, Jacobo Aguirre. The resumption of sports competitions after COVID-19 lockdown: The case of the Spanish football league. Chaos, Solitons & Fractals. 2020; 138 ():109964.

Chicago/Turabian Style

Javier M. Buldú; Daniel R. Antequera; Jacobo Aguirre. 2020. "The resumption of sports competitions after COVID-19 lockdown: The case of the Spanish football league." Chaos, Solitons & Fractals 138, no. : 109964.

Journal article
Published: 02 February 2020 in Entropy
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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. Next, we constructed the temporal passing networks of each team and computed the deviation of their network parameters along the match. For each network parameter, we obtained the permutation entropy and the statistical complexity of its temporal fluctuations. Finally, we investigated how the permutation entropy (and statistical complexity) of the network parameters was related to the total number of passes made by a football team. Our results show that (i) spatial entropy changes according to the position of players in the field, and (ii) the organization of passing networks change during a match and its evolution can be captured measuring the permutation entropy and statistical complexity of the network parameters, allowing to identify what parameters evolve more randomly.

ACS Style

Johann H. Martínez; David Garrido; José L. Herrera-Diestra; Javier Busquets; Ricardo Sevilla-Escoboza; Javier M. Buldú. Spatial and Temporal Entropies in the Spanish Football League: A Network Science Perspective. Entropy 2020, 22, 172 .

AMA Style

Johann H. Martínez, David Garrido, José L. Herrera-Diestra, Javier Busquets, Ricardo Sevilla-Escoboza, Javier M. Buldú. Spatial and Temporal Entropies in the Spanish Football League: A Network Science Perspective. Entropy. 2020; 22 (2):172.

Chicago/Turabian Style

Johann H. Martínez; David Garrido; José L. Herrera-Diestra; Javier Busquets; Ricardo Sevilla-Escoboza; Javier M. Buldú. 2020. "Spatial and Temporal Entropies in the Spanish Football League: A Network Science Perspective." Entropy 22, no. 2: 172.

Journal article
Published: 18 January 2020 in Entropy
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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. We recovered classical results that considered only broadband signals and found a nontrivial pattern of alterations in each frequency band, showing that SC does not necessarily decrease in AD or MCI.

ACS Style

Ignacio Echegoyen; David López-Sanz; Johann H. Martínez; Fernando Maestú; Javier M. Buldú. Permutation Entropy and Statistical Complexity in Mild Cognitive Impairment and Alzheimer’s Disease: An Analysis Based on Frequency Bands. Entropy 2020, 22, 116 .

AMA Style

Ignacio Echegoyen, David López-Sanz, Johann H. Martínez, Fernando Maestú, Javier M. Buldú. Permutation Entropy and Statistical Complexity in Mild Cognitive Impairment and Alzheimer’s Disease: An Analysis Based on Frequency Bands. Entropy. 2020; 22 (1):116.

Chicago/Turabian Style

Ignacio Echegoyen; David López-Sanz; Johann H. Martínez; Fernando Maestú; Javier M. Buldú. 2020. "Permutation Entropy and Statistical Complexity in Mild Cognitive Impairment and Alzheimer’s Disease: An Analysis Based on Frequency Bands." Entropy 22, no. 1: 116.

Journal article
Published: 22 November 2019 in Nature Communications
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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. Our results are consistent with real data and the methodology can be translated to clustered networks and/or interconnected networks of any size, topology or origin, from the struggle for knowledge on innovation structures to international economic relations or disease spreading on social groups.

ACS Style

Javier M. Buldú; Federico Pablo-Martí; Jacobo Aguirre. Taming out-of-equilibrium dynamics on interconnected networks. Nature Communications 2019, 10, 1 -9.

AMA Style

Javier M. Buldú, Federico Pablo-Martí, Jacobo Aguirre. Taming out-of-equilibrium dynamics on interconnected networks. Nature Communications. 2019; 10 (1):1-9.

Chicago/Turabian Style

Javier M. Buldú; Federico Pablo-Martí; Jacobo Aguirre. 2019. "Taming out-of-equilibrium dynamics on interconnected networks." Nature Communications 10, no. 1: 1-9.

Journal article
Published: 19 September 2019 in Scientific Reports
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The application of Network Science to social systems has introduced new methodologies to analyze classical problems such as the emergence of epidemics, the arousal of cooperation between individuals or the propagation of information along social networks. More recently, the organization of football teams and their performance have been unveiled using metrics coming from Network Science, where a team is considered as a complex network whose nodes (i.e., players) interact with the aim of overcoming the opponent network. Here, we combine the use of different network metrics to extract the particular signature of the F.C. Barcelona coached by Guardiola, which has been considered one of the best teams along football history. We have first compared the network organization of Guardiola’s team with their opponents along one season of the Spanish national league, identifying those metrics with statistically significant differences and relating them with the Guardiola’s game. Next, we have focused on the temporal nature of football passing networks and calculated the evolution of all network properties along a match, instead of considering their average. In this way, we are able to identify those network metrics that enhance the probability of scoring/receiving a goal, showing that not all teams behave in the same way and how the organization Guardiola’s F.C. Barcelona is different from the rest, including its clustering coefficient, shortest-path length, largest eigenvalue of the adjacency matrix, algebraic connectivity and centrality distribution.

ACS Style

J. M. Buldú; J. Busquets; I. Echegoyen; F. Seirul.Lo. Defining a historic football team: Using Network Science to analyze Guardiola’s F.C. Barcelona. Scientific Reports 2019, 9, 1 -14.

AMA Style

J. M. Buldú, J. Busquets, I. Echegoyen, F. Seirul.Lo. Defining a historic football team: Using Network Science to analyze Guardiola’s F.C. Barcelona. Scientific Reports. 2019; 9 (1):1-14.

Chicago/Turabian Style

J. M. Buldú; J. Busquets; I. Echegoyen; F. Seirul.Lo. 2019. "Defining a historic football team: Using Network Science to analyze Guardiola’s F.C. Barcelona." Scientific Reports 9, no. 1: 1-14.

Preprint
Published: 19 September 2019
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The application of Network Science to social systems has introduced new methodologies to analyze classical problems such as the emergence of epidemics, the arousal of cooperation between individuals or the propagation of information along social networks. More recently, the organization of football teams and their performance have been unveiled using metrics coming from Network Science, where a team is considered as a complex network whose nodes (i.e., players) interact with the aim of overcoming the opponent network. Here, we combine the use of different network metrics to extract the particular signature of the F.C. Barcelona coached by Guardiola, which has been considered one of the best teams along football history. We have first compared the network organization of Guardiola's team with their opponents along one season of the Spanish national league, identifying those metrics with statistically significant differences and relating them with the Guardiola's game. Next, we have focused on the temporal nature of football passing networks and calculated the evolution of all network properties along a match, instead of considering their average. In this way, we are able to identify those network metrics that enhance the probability of scoring/receiving a goal, showing that not all teams behave in the same way and how the organization Guardiola's F.C. Barcelona is different from the rest, including its clustering coefficient, shortest-path length, largest eigenvalue of the adjacency matrix, algebraic connectivity and centrality distribution.

ACS Style

J. M. Buldu; J. Busquets; I. Echegoyen; F. Seirul. Lo. Defining a historic football team: Using Network Science to analyze Guardiola's F.C. Barcelona. 2019, 1 .

AMA Style

J. M. Buldu, J. Busquets, I. Echegoyen, F. Seirul. Lo. Defining a historic football team: Using Network Science to analyze Guardiola's F.C. Barcelona. . 2019; ():1.

Chicago/Turabian Style

J. M. Buldu; J. Busquets; I. Echegoyen; F. Seirul. Lo. 2019. "Defining a historic football team: Using Network Science to analyze Guardiola's F.C. Barcelona." , no. : 1.

Journal article
Published: 19 December 2018 in Chaos, Solitons & Fractals
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We introduce Ordinal Synchronization (OS) as a new measure to quantify synchronization between dynamical systems. OS is calculated from the extraction of the ordinal patterns related to two time series, their transformation into D-dimensional ordinal vectors and the adequate quantification of their alignment. OS provides a fast and robust-to noise tool to assess synchronization without any implicit assumption about the distribution of data sets nor their dynamical properties, capturing in-phase and anti-phase synchronization. Furthermore, varying the length of the ordinal vectors required to compute OS it is possible to detect synchronization at different time scales. We test the performance of OS with data sets coming from unidirectionally coupled electronic Lorenz oscillators and brain imaging datasets obtained from magnetoencephalographic recordings, comparing the performance of OS with other classical metrics that quantify synchronization between dynamical systems.

ACS Style

I. Echegoyen; V. Vera-Ávila; R. Sevilla-Escoboza; J.H. Martínez; J.M. Buldú. Ordinal synchronization: Using ordinal patterns to capture interdependencies between time series. Chaos, Solitons & Fractals 2018, 119, 8 -18.

AMA Style

I. Echegoyen, V. Vera-Ávila, R. Sevilla-Escoboza, J.H. Martínez, J.M. Buldú. Ordinal synchronization: Using ordinal patterns to capture interdependencies between time series. Chaos, Solitons & Fractals. 2018; 119 ():8-18.

Chicago/Turabian Style

I. Echegoyen; V. Vera-Ávila; R. Sevilla-Escoboza; J.H. Martínez; J.M. Buldú. 2018. "Ordinal synchronization: Using ordinal patterns to capture interdependencies between time series." Chaos, Solitons & Fractals 119, no. : 8-18.

Opinion article
Published: 08 October 2018 in Frontiers in Psychology
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Using Network Science to Analyse Football Passing Networks: Dynamics, Space, Time, and the Multilayer Nature of the Game

ACS Style

Javier M. Buldú; Javier Busquets; Johann H. Martínez; Jose Herrera Diestra; Ignacio Echegoyen; Javier Galeano; Jordi Luque. Using Network Science to Analyse Football Passing Networks: Dynamics, Space, Time, and the Multilayer Nature of the Game. Frontiers in Psychology 2018, 9, 1900 .

AMA Style

Javier M. Buldú, Javier Busquets, Johann H. Martínez, Jose Herrera Diestra, Ignacio Echegoyen, Javier Galeano, Jordi Luque. Using Network Science to Analyse Football Passing Networks: Dynamics, Space, Time, and the Multilayer Nature of the Game. Frontiers in Psychology. 2018; 9 ():1900.

Chicago/Turabian Style

Javier M. Buldú; Javier Busquets; Johann H. Martínez; Jose Herrera Diestra; Ignacio Echegoyen; Javier Galeano; Jordi Luque. 2018. "Using Network Science to Analyse Football Passing Networks: Dynamics, Space, Time, and the Multilayer Nature of the Game." Frontiers in Psychology 9, no. : 1900.

Journal article
Published: 01 October 2018 in Network Neuroscience
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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 λ2 of the combinatorial supra-Laplacian matrix of both the multiplex and multilayer networks, as λ2 has been used previously as an indicator of network synchronizability and as a biomarker for several brain diseases. We show that the heterogeneity of interlayer edge weights and, especially, the fraction of missing edges crucially modify the value of λ2, and we illustrate our results with both synthetic network models and real data obtained from resting-state magnetoencephalography. Our work highlights the differences between using a multiplex approach and a full multilayer approach when studying frequency-based multilayer brain networks.

ACS Style

Javier M. Buldú; Mason A. Porter. Frequency-based brain networks: From a multiplex framework to a full multilayer description. Network Neuroscience 2018, 2, 418 -441.

AMA Style

Javier M. Buldú, Mason A. Porter. Frequency-based brain networks: From a multiplex framework to a full multilayer description. Network Neuroscience. 2018; 2 (4):418-441.

Chicago/Turabian Style

Javier M. Buldú; Mason A. Porter. 2018. "Frequency-based brain networks: From a multiplex framework to a full multilayer description." Network Neuroscience 2, no. 4: 418-441.

Preprint
Published: 19 September 2018
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ACS Style

Ignacio Echegoyen; Victor Vera-Ávila; Ricardo Sevilla-Escoboza; Johann H. Martínez; Javier M. Buldú. Ordinal Synchronization: Using ordinal patterns to capture interdependencies between time series. 2018, 1 .

AMA Style

Ignacio Echegoyen, Victor Vera-Ávila, Ricardo Sevilla-Escoboza, Johann H. Martínez, Javier M. Buldú. Ordinal Synchronization: Using ordinal patterns to capture interdependencies between time series. . 2018; ():1.

Chicago/Turabian Style

Ignacio Echegoyen; Victor Vera-Ávila; Ricardo Sevilla-Escoboza; Johann H. Martínez; Javier M. Buldú. 2018. "Ordinal Synchronization: Using ordinal patterns to capture interdependencies between time series." , no. : 1.

Journal article
Published: 17 July 2018 in Physica A: Statistical Mechanics and its Applications
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The way the topological structure goes from a decoupled state into a coupled one in multiplex networks has been widely studied by means of analytical and numerical studies, involving models of artificial networks. In general, these experiments assume uniform interconnections between layers offering, on the one hand, an analytical treatment of the structural properties of multiplex networks but, on the other hand, loosing applicability to real networks where heterogeneity of the links’ weights is an intrinsic feature. In this paper, we study 2-layer multiplex networks of musicians whose layers correspond to empirical datasets containing, and linking the information of: (i) collaboration between them and (ii) musical similarities. In our model, connections between the collaboration and similarity layers exist, but they are not ubiquitous for all nodes. Specifically, inter-layer links are created (and weighted) based on structural resemblances between the neighborhood of an artist, taking into account the level of interaction at each layer. Next, we evaluate the effect that the heterogeneity of the weights of the inter-layer links has on the structural properties of the whole network, namely the second smallest eigenvalue of the Laplacian matrix (algebraic connectivity). Our results show a transition in the value of the algebraic connectivity that is far from classical theoretical predictions where the weight of the inter-layer links is considered to be homogeneous.

ACS Style

Johann H. Martínez; Stefano Boccaletti; Vladimir V. Makarov; Javier M. Buldú. Multiplex networks of musical artists: The effect of heterogeneous inter-layer links. Physica A: Statistical Mechanics and its Applications 2018, 510, 671 -677.

AMA Style

Johann H. Martínez, Stefano Boccaletti, Vladimir V. Makarov, Javier M. Buldú. Multiplex networks of musical artists: The effect of heterogeneous inter-layer links. Physica A: Statistical Mechanics and its Applications. 2018; 510 ():671-677.

Chicago/Turabian Style

Johann H. Martínez; Stefano Boccaletti; Vladimir V. Makarov; Javier M. Buldú. 2018. "Multiplex networks of musical artists: The effect of heterogeneous inter-layer links." Physica A: Statistical Mechanics and its Applications 510, no. : 671-677.