Physics.

Complex Systems and Networks (COSNET Lab)

Head of the Research Line:

Professor Yamir Moreno

Researchers:

Yamir Moreno (Group Leader)
Carlos Gracia-Lázaro (Researcher)
Thomas Perón (Postdoctoral Researcher)
Guilherme F de Arruda (ISI Postdoctoral Researcher)
Sergio Arregui (PhD Student)
Alberto Aleta (PhD Student)
Felipe M. Cardoso (PhD Student)
Dan Lu (PhD Student)
Clàudia Payrató Borràs (PhD Student)
Mario Tovar (M.Sc Student)

BIFI members linked to the research line who work at the Department of Condensed Matter Physics, Faculty of Sciences, University of Zaragoza:
Professor Luis Mario Floría Peralta

MAIN LINE OF RESEARCH

The Complex Systems and Networks Lab (COSNET) was founded in 2003 by Professor Yamir Moreno and has an extensive scientific background in Statistical Physics and in the Physics of Complex Systems. During the last decade, the group has consolidated as a leading team at international level in the study of several topics related to the structure and dynamics of Complex Networks, Epidemiology, Systems Biology, Multiplex Networks, synchronization phenomena, technological and social networks, specially, in the emergence and evolution of online social movements, Evolutionary Game Theory, as well as in the analysis of human collective behavior and in the development of large-scale experiments to study cooperation in humans.

Complex Network Theory

Networked systems are all around us. The accumulated evidence that complex systems cannot be fully understood by studying only their isolated constituents, has given rise to the birth of a new movement of interest and research in the study of complex networks. The expectancy is that understanding and modeling the structure of a complex network would lead to a better cottoning on its dynamical and functional behavior. Though modern network theory has produced a number of relevant results in the last few years, it is still in its infancy, particularly, when it comes to applications in real systems and to the comprehension of the relation between structure and function (dynamics). The main purpose of this research line is the study of complex networks and the collective behavior of dynamical agents that interact among them following the couplings given by the topology of these complex networks. As a result, the fundamental objectives are:

• The simultaneous characterization of the interactions and dynamics at a local scale and the study of their integration into a global and coherent dynamics at a system-wide scale.
• The study of how global dynamics affects local interactions.
• The statistical characterization of real networks.
• The design of realistic models.
• The study of other dynamical processes on complex networks and the emergence of collective behavior.
• The development and application of analytical tools to study complex networks.
• Fostering of a community of multidisciplinary scientists, who master the discipline of complex systems and use it for their research.
• Identify the best course of action to transfer the acquired knowledge from the basic sciences to the application level for a proper characterization and exploitation of real systems.

Complex network theory is particularly advantageous to explore several aspects of complexity. The fundamental idea is to discover the structure of interactions between the components of the system and the emergent behavior of many-body systems coupled to the underlying structure. This would improve our understanding and modeling capabilities so that we may control or predict the dynamics and function of complex networked systems. In addition, this approach does not rely on a detailed knowledge of the system’s constituents, but in the analysis of the relationship between them and therefore, allows obtaining universal results that can be generalized with relative ease (the study of epidemic spreading processes is equivalent to the spread of computer viruses). For example, biological networks like protein interaction networks, share many structural (scale-freeness) and dynamical (functional modules) features with other seemingly different systems such as the Internet and interaction patterns in social systems. Thus, systems as diverse as peer-to-peer networks, neural systems, socio-technical phenomena or complex biological networks can be studied with a unique theoretical and computational tool.

On the other hand, there are still many unknown systems and processes in which the new discoveries and techniques developed in the last years can shed light and provide novel results. For example, why scale-free networks are ubiquitous in Nature? Are there universal principles that govern the growth and evolution of these networks? How the dynamics of local interactions are spread and integrated into the global scale? And, in turn, how the macroscopic behavior of the system modulates interactions at lower scales? Finally, are there common patterns that can be identified not only structurally, but also in the functional organization of these systems? The latter and other questions should be studied by adopting new perspectives and approaches based on multidisciplinary research. The research results have important applications in problems such as: the modeling of biological processes at the molecular and cellular levels (metabolism, gene expression, etc.), the study of epidemic dynamics, the characterization of transport and diffusion processes in networks and communication technologies, several synchronization phenomena and the emergence of collective effects with applications in neuroscience and social systems. The ultimate goal is to understand the general principles governing these biological, social and technological systems in order to be able to predict, design and control the behavior of a wide range of real systems.

“The Science of Complexity”

The Science of Complexity has become extremely important in the study of many real systems. Complexity theory is based on the holistic principle antireductionist that considers the whole greater than the sum of its parts. This perspective allows an accurate analysis of different phenomena so as to predict the evolution of them over time. Complex behavior occurs when many interactions at the local scale collectively lead to unpredictable larger-scale outcomes. However, only very recently scientists have started to reconsider the traditional reductionism viewpoint that has frequently driven science. The accumulated evidence that systems as complex as a group of social animals, or the cells of a living system, cannot be fully understood by simply reducing them to a sum of their fundamental parts, has produced an increasingly large interest in the study of complex systems. These studies are revealing and explaining a range of emergent system behaviors and providing a deeper understanding of entire systems and their responses, with often surprising and unexpected results.

Multiplex Networks

Until very recently, most of the studies on the structure and dynamics of networks considered them as single layer graphs, in which all the interactions, no matter whether they were obtained in different conditions, appeared aggregated. However, as more data about real systems became available, it was evident that many systems are indeed made up by different interaction layers that are interdependent. Think of, for instance, a transportation system, where different transportation modes coexist in space. An accurate representation of such a system would represent each mode of transportation as one layer, with connections among them representing the possibility of commuting from one to another: from a bus line to a metro line, to a tram, etc. The same applies to online social systems, where an individual could be in several platforms (Twitter, Facebook, Google Plus, etc.) concurrently, thus communicating and being exposed to info through many information channels. A final example in the biological domain is given by cellular processes, where there are many biochemical pathways operating at the same time.

This new structural paradigm poses important challenges. First, we need to figure out when the multilayer structure is important and then, develop new metrics, algorithms and representations of such systems. In addition, dynamical processes such as diffusion and spreading dynamics should be reassessed, as it is expected that new phenomenology arises. In our group, we have been studying these networks since a few years and have already produced a significant number of contributions that have had a deep impact on the general subject of network science. This includes the study of diffusion processes, the spreading of multistrain and interacting diseases, new metrics and formalisms to characterize the structure of multilayer networks and the dynamics of multichannel information dissemination. We continue to explore this line and plan to tackle several interesting problems in the biological domain.

A multilayer perspective for the analysis of urban transportation systems, Scientific Reports 7:44359 (2017)

Multiplex Networks: Basic Formalism and Structural Properties, Monograph Springer Briefs in Complexity, ISBN 978-3-319-92255-3 (2018).

Diffusion Dynamics and Optimal Coupling in Multiplex Networks with Directed Layers, Physical Review X 8, 031071 (2018)

Epidemiology

Epidemic spreading is a central issue in a variety of fields. In this context, both epidemic modeling and data collection about contact networks are intensively contributing to the development of an accurate computational and theoretical framework to simulate how diseases spread and evolve as well as to the search of efficient immunization and vaccination policies. However, the lack of a complete description of connectivity maps and the singularities of the transmission mechanisms make the analysis extremely difficult. Much effort should still be invested in the design of efficient and reliable epidemic spreading models that benefit from data of connectivity patterns given by social maps of contacts (directionality, age, gender, etc.) and also to understand the dynamics of multi-strain or interacting diseases. Our research is mainly focus on the study of situations in which multiple pathogens coexist within the same host population, including systems of competing pathogens (e.g., seasonal influenza) or the so-called syndemic systems (e.g. HIV and Tuberculosis), i.e., the convergence of two or more diseases that act synergistically in a population to magnify the burden of disease. For these latter scenarios, considering multiple networks of contacts or layers is paramount.

Data-driven model for the assessment of M. tuberculosis transmission in evolving demographic structures, Proceedings of the National Academy of Sciences USA 115, E3238-E3245 (2018).

Epidemiological Framework & Multilevel Approach

The study of epidemic spreading processes from a quantitative point of view is a vast field under intense investigation for nearly a century. Mathematical and computational modeling of infectious diseases is a collective endeavor of scientists coming from many scientific fields, from applied mathematicians and epidemiologists, to computer scientists and physicists. Physicist’s approaches to problems in Epidemiology invoke statistical physics, the theory of phase transitions and critical phenomena, to grasp the macroscopic behavior of epidemic outbreaks. It is not adventurous to claim that one of the main successful frameworks is the Mean-Field (MF) approximation, where homogeneity and isotropy are hypothesized to reduce the complexity of the system under study. This approach is mainly used to study the spreading of a disease in a system in which individuals are identified with the nodes of a (complex) network of contacts. Another important alternative approach aimed at describing the large-scale spreading of infectious diseases mathematically is the so-called meta-population approach. This framework describes a set of spatially structured interacting subpopulations as a network whose links denote the mobility of individuals across subpopulations. Each subpopulation consists of a number of individuals that are divided into several classes according to their dynamical state with respect to the modeled disease, for instance: susceptible, infected, removed, etc. The internal compartmental dynamics models the contagion dynamics by considering that people in the same subpopulation are in contact and may change their state according to their interactions and the disease dynamics. Finally, subpopulations also interact and exchange individuals due to mobility from one subpopulation to another.

Being able to understand analytically how the various model components influence the dynamics and interact is not always possible. More often, this is achieved numerically. We therefore pay particular attention to the development of efficient numerical methods that complement, when possible, analytical insights. The constraint of modeling a real process in which myriads of sources of complexity are involved makes the combination of massive data bases with relatively simple models the only sensible approach to model fitting, projection and understanding. Finally, it is worth mentioning that epidemiological research nowadays faces problems related to the lack of appropriate, disease-specific theoretical and computational models to understand the transmission mechanisms behind global public health threats. This is amplified by our current limited knowledge about the interplay among the various scales involved in the transmission of infectious diseases at the global scale.

Most epidemic models are developed assuming that the spreading process takes place on a single level (be it a single population, a meta-population system or a network of contacts). Therefore, pressing problems rooted at the interdependency of multi-scales call for the development of a whole new set of theoretical and simulation approaches. Our research is related the emergence and evolution of global diseases from the new paradigm of multi-scale, interdependent complex systems. Taking into consideration not only a single interaction level but also the interdependency between many levels and scales is a radical change, a change that makes a substantial difference as it allows to address problems such as comorbidity and the spreading of persistent infections and multi-strain diseases, among others. The outcomes may be rewarding and the resulting framework would be invaluable to better comprehend global health threats.

As a result, our goal is to develop a contemporary epidemiological framework that integrates the many aspects involved in the spreading of global diseases: from single networks of contacts to metapopulation systems, to the interaction between different diseases and strains and to the influence of human behavioral changes and mobility patterns.

In this context, our main objectives are:

• To integrate individual-level approaches into meta-population schemes with the aim of adding 
further realism to the structure of subpopulations.
• To generate new mathematical and computational modeling schemes to accurately describe the 
impact of human behavioral changes on the course of an epidemic.
• To develop models that will allow addressing the effects of the interaction between persistent 
infections (and specifically, between TB and AIDS) in structured populations.
• To significantly advance in a brand new theoretical and modeling framework to better grasp the role 
of competition between cross-reacting strains of infection in multi-scale diseases.
• To compare the structural and dynamical properties of epidemic multi-scale models looking for similarities, organizational principles and universal dynamical patterns with other multi-level, interdependent complex systems.

 Dynamics of interacting diseases, Physical Review X 4, 041005 (2014)

Disease Localization in Multilayer Networks, Physical Review X 7, 011014 (2017)

Structure and Dynamics of Online Social Systems

The collection and mining of large amounts of digital data is allowing gaining deep insights into the structure and dynamics of large-scale socio-technical systems. In order to advance more in our current understanding of such systems, we need to develop a proper and efficient way to handle these datasets as well as to implement new algorithms and modeling tools that will ultimately allow to extract new knowledge from them. In this respect, it has become apparent that online social systems are playing a role in the development of different collective phenomena that manifest in the off-line world. Therefore, the analysis of the emergence and evolution of influential social movements in social platforms like Twitter is extremely useful if we aim at making further predictions about human collective behavior.

Today, techno-social systems pervade our world. ICT systems are leading to profound transformations in the way our society self-organize and generate and use information as well as on how humans interact, travel, behave, etc. Such transformations are not always traduced in an improved human society, as they can also lead to new forms of instabilities or make social and economic systems more fragile. Moreover, the ongoing technological revolution is taking place at a never-saw pace, which makes it even more urgent the development of tools that allow understanding the emerging properties of complex techno-social systems and to anticipate the consequences of new regulations, actions, or systems’ failures.

Although outstanding results have recently been obtained in modeling collective behavior in techno- social systems, we have not yet progressed enough in basic theoretical aspects and in the application of the generated knowledge to the characterization and understanding of real social phenomena. Moreover, with the unprecedented amount of data at our disposal nowadays, new challenges arise.

Present-day tools simply fail to keep up with the shifting challenges that the interaction between humans and complex ICT systems poses. For instance, think of a techno-social system like online social networks in which individuals engage in a multitude of categorical (politics, science, sports, technology, etc.) layers, giving to each of them a specific weight. Could we predict or simply understand how likely it is that a given rumor, idea or belief reaches system-wide proportions? Is there a general mechanism behind such kind of social phenomenon or are there different mechanisms unique to each categorical level or social niche? Are influential individuals globally defined or instead are they system’s dependent? Can we understand what gives rise to social uproar as recently witnessed? Or even more, are we in a position to answer those questions that we would ideally like to ask?

Emergence of consensus as a modular-to-nested transition in communication dynamics”, Scientific Reports 7, 41673 (2017)

 Effects of network structure, competition and memory time on social spreading phenomena”, Physical Review X 6, 021019 (2016)

Evolutionary Game Theory and The Socio-Technical Man

Evolutionary Game Theory is a branch of mathematics that analyzes the strategic interaction between rational or irrational agents that can be individuals, groups, corporations, etc. The game consists of a set of players and strategies. Each player earns a reward that depends not only on his/her own strategy, but also on the strategy carried out by his/her competitors. This theory is very useful to reveal and predict human behavior and provides a framework and analytical tools for understanding a wide range of phenomena that occur in real life and are linked to decision-making by individuals or groups of individuals who interact with each other (see contributions of John von Neumann, Oskar Morgenstern and John Nash). The Prisoner’s Dilemma is the most studied model in Evolutionary Game Theory and is a symmetric, bi-personal, finite, static and non-zero-sum game in which players must choose between two strategies: Cooperate or defect. From an individual perspective, defect is always the best strategy. Nevertheless, cooperation gives the highest payoff collectively. This is the dilemma.

If we want to describe the Socio-technical man, we need to understand first, some basic problems such as: how humans interact with the environment and other individuals, how cooperative behavior emerges and survives, and how social networks evolve and shape the way we communicate and interact with each other. To this end, we should develop new ways to analyze existing data, perform controlled experiments with groups –of different sizes- of humans facing social dilemmas and hypothetical scenarios and come out with new theoretical and computational methods and algorithms. By doing this, we will be in the position to better understand what are the factors determining human behavior in a plethora of situations, and hopefully, provide hints to, e.g., policy makers, with the aim of creating a better and more sustainable Society for the future. On its turn, given the universality of many concepts and methods of Complexity Science, we are also sure that the new methods will contribute to the development of other areas (for instance, the Physics of non-equilibrium systems, Economics and even Ecology).

Finally, Evolutionary Game Theory is also very useful tool to study different phenomena and biological processes such as the ecology of bacterial population and the evolution of virus and species, in general.

The aim of the Laboratory of Experimental Economics “NECTUNT LAB” is the study of cooperative phenomena in humans as well as the applications of Evolutionary Game Theory in different fields of science. Methodologically, we make use of this theory and computer simulations to build more realistic models based on our findings in controlled experiments, both onsite and online. Currently, we are involved in a European Research Project (IBSEN). The main objective of the project is to develop the largest simulator of human behavior up to date, with the ultimate goal of answering questions such as: What are the mechanisms and real motivations that promote the emergence and evolution of cooperation in humans? How individuals behave in different contexts? How financial bubbles are formed?

On December 20, 2011, the largest experiment developed up to now with thousands of subjects playing a Prisoner’s Dilemma Game took place in Zaragoza, Spain. Almost 1300 students coming from 42 schools and institutes of the Autonomous Community of Aragon were involved in this unprecedented real-time experiment. The design, software and visualization platform were developed by BIFI researchers.

Relevant publications

1.- Complex Networks: Structure and Dynamics. S. Boccaletti, V. Latora, Y. Moreno, M. Chávez and D.-U. Hwang. Physics Reports 424, 175-308 (2006).

2.- Heterogeneous networks do not promote cooperation when humans play a Prisoner’s Dilemma. C. Gracia-Lázaro, A. Ferrer, G. Ruíz, A. Tarancón, J. A. Cuesta, A. Sánchez, and Y. Moreno. Proceedings of the National Academy of Sciences USA 109, 12922-12926 (2012).

3.- Evolutionary dynamics of group interactions on structured populations – A review. M. Perc, J. Gómez-Gardeñes, A. Szolnoki, L. M. Floría and Y. Moreno. Journal of the Royal Society Interface 10, 20120997 (2013).

4.- Multilayer Networks. M. Kivela, A. Arenas, M. Barthelemy, J. P. Gleeson, Y. Moreno, and M. A. Porter. Journal of Complex Networks 2, 203-271 (2014).

5.- Behavioral transition with age in social dilemmas: From reciprocal youth to persistent response in adulthood. M. Gutiérrez-Roig, C. Gracia-Lázaro, J. Perelló, Y. Moreno, and A. Sánchez. Nature Communications 5:4362, doi: 10.1038/ncomms5362 (2014).

6.- Dynamics of interacting diseases. J. Sanz, C. -Y. Xia, S. Meloni and Y. Moreno. Physical Review X 4, 041005 (2014).

7.- Characterizing two-pathogen competition in spatially structured environments. C. Poletto, S. Meloni, A. Van Metre, V. Colizza, Y. Moreno and A. Vespignani. Scientific Reports 5:7895 (2015).

8.- Spatiotemporal characterization of information-driven collective phenomena through transfer entropy. J. Borge-Holthoefer, N. Perra, B. Gonçalves, S. Gonzalez-Bailón, A. Arenas, Y. Moreno, and A. Vespignani. Science Advances 2, e1501158 (2016).

9.- Modeling the effects of network structure, competition and memory time on social spreading phenomena. J. P. Gleeson, K. P. O’Sullivan, R. A. Baños, Y. Moreno. Physical Review X 6, 021019 (2016).

10.- Humans conform to a reduced set of behavioral phenotypes when facing social dilemmas. J. Poncela-Casasnovas, M. Gutiérrez-Roig, C. Gracia-Lázaro, J. Vicens, J. Gomez-Gardeñes, J. Perelló, Y. Moreno, J. Duch, and A. Sánchez. Science Advances 2, e1600451 (2016).

11.- Disease Localization in Multilayer Networks. G. Ferraz de Arruda, E. Cozzo, T. P. Peixoto, F. A. Rodrigues, and Y. Moreno. Physical Review X 7, 011014 (2017).

12.- Onymity promotes cooperation in social dilemma experiments. Z. Wang, M. Jusup, R.-W. Wang, L. Shi, Y. Iwasa, Y. Moreno and J. Kurths. Science Advances 3:e1601444 (2017).

13.- Data-driven model for the assessment of M. Tuberculosis transmission in evolving demographic structures. Sergio Arregui, Dessislava Marinova, Maria Jose Iglesias, Sofia Samper, Carlos Martin, Joaquin Sanz, and Yamir Moreno. Proceedings of the National Academy of Sciences USA 115, E3238-E3245 (2018).

14.- Multiplex Networks: Basic Formalism and Structural Properties. E. Cozzo, G. Ferraz de Arruda, F. A. Rodrigues, and Y. Moreno. Monograph Springer Briefs in Complexity, ISBN 978-3-319-92255-3 (2018).

15.- Physics of humans, physics for society. Guido Caldarelli, Sarah Wolf, and Yamir Moreno. Nature Physics 14, 870 (2018).

16.- Diffusion Dynamics and Optimal Coupling in Multiplex Networks with Directed Layers. Alejandro Tejedor, Anthony Longjas, Efi Foufoula-Georgiou, Tryphon Georgiou, and Yamir Moreno. Physical Review X 8, 031071 (2018).

Main research projects

1.- BRIDGING THE GAP: FROM INDIVIDUAL BEHAVIOR TO THE SOCIO-TECHNICAL MAN (IBSEN), European Commission. H2020 FET Open, Project number 662725, 2015-2018.

2.- DISTRIBUTED GLOBAL FINANCIAL SYSTEMS FOR SOCIETY (DOLFINS), European Commission. H2020 FET Proactive GSS, Project number 640772, 2015-2017.

3.- FOUNDATIONAL RESEARCH ON MULTILEVEL COMPLEX NETWORKS AND SYSTEMS (MULTIPLEX), European Commission. FET Proactive IP Project number 317532, 2012-2016.

4.- MATHEMATICAL FRAMEWORK FOR MULTIPLEX NETWORKS (PLEXMATH), European Commission. FET Proactive STREP Project number 317614, 2012-2015.

Collaborators

• Alessandro Vespignani (Sternberg Distinguished University Professor College of Computer and Information Science, College of Science, Bouvé College of Health Sciences, Northeastern University, Boston, US)
• Vittoria Colizza (Inserm and UPMC Université Paris 06, Faculté de Médecine, Paris & ISI Foundation, Turin, Italy)
• Chiara Poletto (Researcher (Chargé de Recherche 2ème classe) EPICX-Lab, iPLESP, INSERM & UPMC UMR-S 1136)
• Carlos Martín (Group of Mycobacterial Genetics, Faculty of Medicine, University of Zaragoza, Spain)
• James Gleeson (Department of Mathematics and Statistics, University of Limerick, Ireland)
• Javier Borge-Holthoefer (Internet Interdisciplinary Institute, IN3, Group: CoSIN3, Barcelona, Catalunya)-External BIFI Member.
• Sandra González-Bailón (University of Pennsylvania’s Annenberg School for Communication, US)
• Francisco Rodriguez (Department of Applied Mathematics and Statistics, Institute of Mathematics and Computer Science, University of São Paulo, Brazil)
• Angel Sánchez (Universidad Carlos III, Madrid, Spain. External BIFI Member)
• José Cuesta (Universidad Carlos III, Madrid, Spain. External BIFI Member)
• Josep Perelló (OpenSystems-UB, Departament de Física Fonamental, Universitat de Barcelona)
• Matjaz Perc (Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia)
• Zhen Wang (Research Associate, School of Computer Science and Engineering, Nanyang Technological University)

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Human Behavioral Lab (NECTUNT Lab)

Head of the Research Line:

Professor Yamir Moreno

Researchers:

Yamir Moreno (Group Leader)
Carlos Gracia-Lázaro (Senior Researcher)
Felipe M. Cardoso (Ph.D Student)
Alfredo Ferrer (Software Developer)

BIFI members linked to the research line:
Professor Ángel Sánchez (UC3M)
Professor José A. Cuesta (UC3M)

MAIN LINE OF RESEARCH

The Nectunt Lab was founded in 2014 and is mainly devoted to performing high-level research, both experimental and theoretical, in Human Behavior, Evolutionary Game Theory, and Behavioral Sciences.

Summary of Research

We are living the advent of the Big Data era. Hundreds of millions of connected people and billions of sensors yield previously unimaginable amounts of information. Similarly, more data is generated by people simply going about their lives, as a byproduct of other activities such as their Internet browsing and searching or moving around with their smartphones in their pocket. One field in which big data will foster enormous advances in social science, in particular, when involving computational approaches through data analysis, model design, and simulations.

However, big data alone will not be enough for this purpose. By itself, having the data does not produce new knowledge about human behavior and Information and Communication Technology (ICT) systems. We need to develop new tools for the categorization and characterization of human-generated datasets that ultimately will allow the identification of new patterns exhibited in social collective behavior. As a matter of fact, the question of whether the online world is representative of the population at large is a pressing challenge, whose answer will determine to some extent, the usefulness of such big data sets for improving human welfare or for promoting positive changes and social good.

Finally, the data gathering and mining processes themselves need to be standardized so as to allow for the reproducibility of experiments and for meaningful comparisons between different datasets. To date, such standard protocol is lacking. From the modeling perspective, prevalent models still miss a lot of temporal and spatial details and information. If we were to understand large-scale and generic social phenomena, we need to generate new theoretical models that incorporate the patterns emerging out of real data analyses as well as to validate them through large-scale data-driven simulations.

To date, there are many problems in the social sciences that in principle are more tractable than they were a few years ago. However, there is one process that is believed to be at the root of many diverse phenomena, ranging from the spreading of ideas and information to the adoption of behaviors and fashions, to marketing campaigns and large-scale social mobilizations. It is transversal and rich enough as to constitute one of the fundamental problems not only in the social sciences, but also in complexity: the problem of social contagion. The phenomenon of social contagion accounts for processes in which rumors, ideas, behaviors –no matter the nature of it- spread in a population of individuals by the influence they exert to each other.

What we know today as Computational Social Sciences (CSS) was born in this context. Scientists from very diverse fields use methods and tools imported from Statistical Physics and Complex Systems Science to study how humans organize, act and interact with each other. In the last years, it has been possible to discover new universal patterns in the functioning of social and economic systems applying these tools to the data obtained from online social networks.

Evolutionary Game Theory

The Evolutionary Game Theory is based on a mathematical application that is able to analyze the strategic interaction between rational or irrational agents that can be individuals, groups, companies, large corporations, etc. The game consists of a set of players and strategies. Each player wins a reward that depends not only on his own strategy, but also on the strategy carried out by his competitors. This theory is very useful for revealing and predicting human behavior and provides a framework and essential analytical tools for understanding a wide range of phenomena that occur in real life and are linked to decision making by individuals or groups of individuals that interact with each other (see contributions by John von Neumann, Oskar Morgenstern and John Nash). The Prisoner’s Dilemma is the most studied model in Evolutionary Game Theory and consists of a symmetrical, bipersonal, finite, static and non-zero sum game in which players must choose between two strategies: cooperate or not. The dilemma is based on the fact that from a purely individual point of view, not cooperating would always be the best strategy, but certainly, mutual cooperation is much better than not cooperating individually. This is the dilemma.

NECTUNT Behavioral Lab

The Experimental Economics Lab: “NECTUNT” is dedicated to studying human cooperation with tools, methods and the approach of evolutionary game theory. In the last decades, this important theory has gained the interests of economists, sociologists, physicists and many other researchers from different fields and it has expanded far beyond its original inspiration in Biology.

Methodologically, we use this theory and computer simulations to build models based on our findings in controlled experiments, both onsite and online. The main purpose is to study the patterns of human behavior in different strategic contexts in order to implement, evaluate and redesign more efficiently new policies and strategies in all areas of society. At present, we have a database of more than 6000 volunteers in Zaragoza who actively participate in different experiments.

It is essential to determine how we (humans) act in certain strategic situations, what is our position when facing the conflict between individual and collective interests (dilemma related to climate change), how decisions are reached, what are the psychological motivations that promote and lead a given behavior and what are the real mechanisms that allow the emergence and prevalence of cooperation. Cooperation is one of the pillars of evolution that has allowed the transition from a primitive society based on hunting, fishing and gathering to the modern society characterized by new technologies and infrastructures and in which everything is interconnected.

Humans display a reduced set of consistent behavioral phenotypes in dyadic games, Science Advances 2, e1600451 (2016)

The experiments we carry out allow us to have a repertoire of behavioral patterns that we can incorporate into agent-based models, which are therefore more realistic. Previously, these models (in general) were assigned certain properties that were rather irrational or unrealistic and did not take into account essential aspects like human psychology, for example. It is what is known as simulation of artificial societies.

Many of the experiments carried out during the last years have taken place with tens or hundreds of participants and in very limited environments. The largest large-scale and real-time experiment performed to date took place in Zaragoza in 2011 and involved 1229 volunteers from different schools and institutes of Aragon.

Heterogeneous networks do not promote cooperation when humans play a Prisoner’s Dilemma, Proceedings of the National Academy of Sciences USA 109, 12922-12926 (2012)

During the last years, we have been part of the European project IBSEN2020 whose main objective was to create a Global Simulator of Human Behavior. The global simulator is, essentially, a database with thousands of individuals from different countries (Holland, United Kingdom, Finland, and Spain) who participate in large-scale controlled experiments (onsite and online). It is the first time that a database of such dimensions (+ 20,000 volunteers up to date) is created to carry out social experiments in different strategic contexts. Participants always receive an initial amount of not less than 5 Euros that can be increased depending on the results obtained in the game. No details about the game are provided until the session begins. All those from Zaragoza and surrounding areas can register in Nectunt lab to participate in the calls.

As part of the Dolfins2020 project, our tasks (together with other members of the consortium) have been to develop fundamental research to deliver data-driven insights on policies in the following areas: systemic risk and financial stability, sustainable finance and climate finance, impact investing and social impact finance.

Experiments carried out in our Lab in the last 3 years:

• Joint experiment Spain-China (Forest resources and sustainability).
• Experiment on Climate Change (Spain- China).
• Experiment “Impact Investing” (Economics & Finance).
• Collective experiment on dynamic resources (Sustainability).
• Experiment “Trading in Networks” (International trade routes and networks).

Relevant publications

1.- Physics of humans, physics for society. Guido Caldarelli, Sarah Wolf, and Yamir Moreno. Nature Physics 14, 870 (2018).

2.- The Contagion Effects of Repeated Activation in Social Networks. P. Piedrahita, J. Borge-Holthoefer, Y. Moreno, and S. González-Bailón. Social Networks 54, 326-335 (2018).

3.- Robustness of Cultural Communities in an Open-ended Axelrod’s Model. Alexis R. Hernandez, Carlos Gracia-Lázaro, Edgardo Brigatti, Yamir Moreno. Physica A 509, 492-500 (2018)

4.- A Networked Voting Rule for Democratic Representation. Alexis R. Hernández, Carlos Gracia-Lázaro, Edgardo Brigatti, Yamir Moreno. Royal Society Open Science 5:172265160914 (2018).

5.- Onymity Promotes Cooperation in Social Dilemma Experiments. Z. Wang, M. Jusup, R. -W. Wang, L. Shi, Y. Iwasa, Y. Moreno and J. Kurths. Science Advances 3:e1601444 (2017).

6.- Evolutionary Dynamics of N-person Hawk-Dove Games. W. Chen, C. Gracia-Lázaro, Z. Li, L. Wang, and Y. Moreno. Scientific Reports 7:4800 (2017).

7.- Heterogeneous Resource Allocation can change Social Hierarchy in Public Goods Games. S. Meloni, C. Xia and Y. Moreno. Royal Society Open Science 4:170092 (2017).

8.- From Degree-Correlated to Payoff-Correlated Activity for an Optimal Resolution of Social Dilemmas. A. Aleta, S. Meloni, M. Perc, and Y. Moreno. Physical Review E 94, 062315 (2016).

9.- Humans Display a Reduced Set of Consistent Behavioral Phenotypes in Dyadic Games. J. Poncela-Casasnovas, M. Gutiérrez-Roig, C. Gracia-Lázaro, J. Vicens, J. Gomez-Gardeñes, J. Perelló, Y. Moreno, J. Duch, and A. Sánchez. Science Advances 2, e1600451 (2016).

10.- Dynamic Instability of Cooperation due to Diverse Activity Patterns in Evolutionary Social Dilemmas. C.-Y. Xia, S. Meloni, M. Perc and Y. Moreno. Europhysics Letters 109, 58002 (2015)

11.- Reputation Drives Cooperative Behavior and Network Formation in Human Groups. J. A. Cuesta, C. Gracia-Lázaro, A. Ferrer, Y. Moreno, and A. Sánchez. Scientific Reports 5:7843 (2015).

12.- Behavioral transition with age in social dilemmas: From reciprocal youth to persistent response in adulthood. M. Gutiérrez-Roig, C. Gracia-Lázaro, J. Perelló, Y. Moreno, and A. Sánchez. Nature Communications 5:4362, doi: 10.1038/ncomms5362 (2014).

13.- A Comparative Analysis of Spatial Prisoner’s Dilemma Experiments: Conditional Cooperation and Payoff Irrelevance. J. Grujic, C. Gracia-Lázaro, M. Milinski, D. Semmann, A. Traulsen, J. A. Cuesta, Y. Moreno, A. Sánchez. Scientific Reports 4, 4615 (2014).

14.- Evolutionary dynamics of group interactions on structured populations – A review. M. Perc, J. Gómez-Gardeñes, A. Szolnoki, L. M. Floría and Y. Moreno. Journal of the Royal Society Interface 10, 20120997 (2013).

15.- Heterogeneous networks do not promote cooperation when humans play a Prisoner’s Dilemma. C. Gracia-Lázaro, A. Ferrer, G. Ruíz, A. Tarancón, J. A. Cuesta, A. Sánchez, and Y. Moreno. Proceedings of the National Academy of Sciences USA 109, 12922-12926 (2012).

Main research projects

1.- BRIDGING THE GAP: FROM INDIVIDUAL BEHAVIOR TO THE SOCIO-TECHNICAL MAN (IBSEN), European Commission. H2020 FET Open, Project number 662725, 2015-2018.

2.- DISTRIBUTED GLOBAL FINANCIAL SYSTEMS FOR SOCIETY (DOLFINS), European Commission. H2020 FET Proactive GSS, Project number 640772, 2015-2017.

Collaborators

• Matjaz Perc (Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia)
• Zhen Wang (Research Associate, School of Computer Science and Engineering, Nanyang Technological University)
• Marko Jusup (Tokyo Institute of Technology, Tokyo, Japan)
• Zhen Wang (Research Associate, School of Computer Science and Engineering, Nanyang Technological University)
• Sandro Meloni (IFISC Mallorca, Spain)
• Josep Perelló (OpenSystems-UB, Departament de Física Fonamental, Universitat de Barcelona)
• Arne Traulsen (Max-Planck Institute for Evolutionary Biology, Plön, Germany)
• Sanjeev Goyal (Founding Director of the Cambridge-INET Institute, Faculty of Economics, U.K)
• Cars Hommes (Faculty of Economics and Business, University of Amsterdam)
• Penélope Hernández Rojas (LINEEX Lab, Universitat de Valéncia)
• Kimmo Kaski (School of Science, Aalto University, Finland)
• Stefano Battiston (Department of Banking and Finance of the University of Zurich)
• Guido Caldarelli (IMT School for Advanced Studies, Lucca, Italy)
• José Alberto Molina (Facultad de Economía y Empresa, UNIZAR)
• Alberto Antonioni (UC3M Madrid & BIFI Institute)
• María Pereda García (GESIS Leibniz Institut für Sozialwissenschaften, Germany)

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Statistical-physics modeling of biomolecules

Head of the Research Line:

Pierpaolo Bruscolini

Researchers:

Pierpaolo Bruscolini, Researcher UZ
Antonio Rey Gayo, Full Professor UCM
Ana Ma Rubio Caparrós, Associate professor UCM
Fernando Falo Forniés, Full professor UZ
Alessandro Fiasconaro, Assistant Professor UZ

SUMMARY OF THE RESEARCH LINE

The research line of “Physical modeling of biomolecules” is articulated around three research groups which share the same approach to the physics of biological molecules as well as the analysis techniques from statistical mechanics.

Bruscolini’s Group (Statistical-physics modeling of biomolecules)

We apply coarse-grained models and statistical mechanics methods to protein folding, protein function, protein design and sequencing, seeking the best balance between the quantitative accuracy of the predictions (increasing with the complexity of the model) and the viability in terms of computational costs and time (increasing with the simplicity of the approach). We are also interested in statistical inference and its applications, and we are using it to investigate protein signaling and redesign. Our view is that the big-data explosion that we are witnessing in biology can be best tackled with simple models and approaches that help rationalizing and understanding the biological processes.

In more detail, our recent activity encompasses:

a) Protein Folding: we use simple models, and especially the Wako-Saito-Muñoz-Eaton model, for which an exact solution can be given (PRL 88, 258101, 2002). In particular, we have developed the latter model to provide a quantitative description of the experimental data from different experimental techniques.

b) Protein design and “antibody humanization”: we have applied statistical-physics methods to protein design at fixed backbone. More recently, we have worked on a statistical inference approach to the “humanization” of antibodies; that is, the design of a human antibody sequence, to be used in pre-clinical studies, starting from a murine antibody, by optimizing a “humanness score” derived by statistical inference from public databases of human sequences. Anyone interested in applications/collaborations please contact: pier “at” unizar.es

c) Protein Sequencing: we are interested in de-novo sequencing by Tandem Mass Spectrometry, and have proposed a novel algorithm, T-NovoMS, which relies on the mapping of the sequencing of a parent peptide on the thermodynamics of a one-dimensional system, with the experimental MSMS spectrum acting as an external field. We have developed a web server implementing the method: http://webapps.bifi.es/tnovoms/

d) Protein function: we have applied a simple worm-like-chain model to explain the interplay between the catalytic and lectine domain of GalNAC transferase 2 in determining the structure and function of the enzyme.

Rey’s Group (Computer modeling of protein folding and aggregation)

We use molecular modeling and coarse-grained models to explore the stability of the native structure in proteins and the protein folding process.

We design ourselves the simulation models in order to properly analyze structural, thermodynamic and kinetic aspects of the folding process. The most important part in this design is the interaction potential, which has to permit to reach the native conformation from the unfolded state. In the last decade, we have been mainly devoted to structure-based (Gō-type) models, also known as native-centric models. They consider the contacts between amino acid pairs which can be found in the native structure, in order to define the attractive interactions which rank the different conformations sampled along the simulation. We have designed simulation models which combine these potentials with mean field interactions which take into account the chemical sequence of the considered protein sequence. In addition, we have introduced new interactions to describe the hydrogen bonds present in the protein backbone, which play a fundamental role in the study of the aggregation processes which frequently appear when proteins are kept at moderate or high concentrations.

Our main sampling technique to study the thermal transition between the native and unfolded states of the desired proteins has been an in-house designed Monte Carlo method, together with replica exchange (parallel tempering). Our research work involves a strong methodological part, by dissecting the different physicochemical contributions to the behavior of the simulation models. By using this approach to the problem, we have been able to build models which can be widely used is different systems of interest in relevant scientific and applied problems: two state proteins vs downhill folding, proteins with thermodynamic intermediates, knotted proteins, unfolding transitions under pressure, proteins in highly confined environments or the competition between folding and aggregation.

Falo´s Group (Modeling and Simulation of biological systems)

We use mesoscopic models at different scales to address different biological problems:

a) Transport by molecular motors. We investigate the transport of cargos inside cell by processive directional motors (kinesin and dynein). Our work is focused now on the study of the influence of microtubule network structure in cargo transport and as a mean of effective motor-motor interaction.

b) Translocation of polymers. The polymers passage through membranes is an important phenomenon both from the point of view of biological and technological processes. We are developing models of translocation driven by time-dependent forces (deterministic or stochastic) to simulate a molecular motor.

c) Free energy landscape of biomolecules: we apply Markov Network Models to the process of mechanical and thermal unfolding of proteins. Besides, we are studying the modelling of the mechanical unbinding of molecular complexes in order to understand the underlying free energy profile.

d) Models of non-canonical DNA structures: We focus on the behavior of guanine quadruplex of DNA (G-quaduplex) under external forces as those generated by AFM or optical tweezers. We are developing mesoscopic models of such molecules as well as performing “all atom” molecular dynamics simulations. Our goal is to bridge the gap between the theory and simulation regimes and the realistic experimental conditions.

e) Other fields of study comprise biological water behaviour, system biology of cellular differentiation, DNA models of denaturation and unzipping.

Relevant publications

1.- Active translocation of a semifexible polymer assisted by an ATP-based molecular motor. A. Fiasconaro, J.J. Mazo and F. Falo. Scientific Reports 7, 4188 (2017).

2.-Mesoscopic model for DNA G-quadruplex unfolding A. E. Bergues-Pupo, I. Gutiérrez, J. R. Arias-Gonzalez F. Falo, and A. Fiasconaro. Scientific Reports 7, 11756 (2017).

3.-Humanization of Antibodies using a Statistical Inference Approach. A. Clavero- Álvarez , T. Di Mambro , S. Pérez-Gaviro , M. Magnani, P. Bruscolini. Scientific Reports, accepted.

4.-Steric confinement and enhanced local flexibility assist knotting in simple models of protein folding. Miguel Soler, Antonio Rey, and Patrícia FN Faísca. Phys. Chem. Chem. Phys. DOI: 10.1039/c6cp05086g (2016).

5.- Dynamic interplay between catalytic and lectin domains of GalNAc-transferases modulates protein O-glycosylation. Lira-Navarrete, E.; De Las Rivas; Compañón, I.; Pallarés, M. C.; Kong, Y.; Iglesias-Fernández, J.; Bernardes, G. J. L.; Peregrina, J. M.; Rovira, C.; Bernadó, P.; Bruscolini, P.; Clausen, H.; Lostao, A.; Corzana, F.; Hurtado-Guerrero, R. Nature Communications 6: 6937, 2015.

6.- Mapping the Topography of a Protein Energy Landscape. Hutton, R. D.; Wilkinson, J.; Faccin, M.; Sivertsson, E. M.; Pelizzola, A.; Lowe, A. R.; Bruscolini, P.; Itzhaki, L. S. J. Am. Chem Soc. 137 – 46, pp. 14610 – 14625. 2015.

7.- Active polymer translocation in the 3d domain. A. Fiasconaro, J. J. Mazo, F. Falo. Physical Review E 91, 022113 (2015).

8.- An integrative approach for modeling and simulation of Heterocyst pattern formation in Cyanobacteria filaments. A. Torres-Sánchez, J. Gómez-Gardeñes, F. Falo. PLoS Comput Biol 11(3) e1004129. (2015).

9.- Role of the central cations in the mechanical unfolding of DNA and RNA G-quadruplexes. A. E. Bergues-Pupo, J. R. Arias-Gonzalez, M. C. Morón, A. Fiasconaro and F. Falo. Nucleic Acids Research 43(15) 7638-7647 (2015).

10.- How determinant is N-terminal to C-terminal coupling for protein folding?. Heinrich Krobath, Antonio Rey, and Patrícia FN Faísca. Phys. Chem. Chem. Phys. 17, 3512 – 3524 (2015).

11.- Intermediates in the folding equilibrium of repeat proteins from the TPR family. Vicente González and Antonio Rey. Eur. Biophys. J. 43, 433 – 443 (2014).

12.- Design of a rotamer library for coarse-grained models in protein folding simulations. María Larriva and Antonio Rey. J. Chem. Inform. Model. 54, 302 – 313 (2014).

13.- Binary interactions between dendrimer molecules. A simulation study. Ana M. Rubio, Carl C. McBride and Juan J. Freire. Macromolecules, 47, 5379 – 5387 (2014).

14.- MS/MS spectra interpretation as a statistical-mechanics problem. Faccin, M.; Bruscolini, P. Analytical Chemistry. 85 – 10, pp. 4884 – 4892. 2013.

15.- Quantitative prediction of protein folding behaviors from a simple statistical model. Bruscolini, P.; Naganathan, A. N. J. Am. Chem. Soc. 133 – 14, pp. 5372 – 5379. 2011.

16.- Influence of direct motor-motor interaction in models for cargo transport by a single team of motors. S. Bouzat, F. Falo. Physical Biology 7, 046009 (2010).

17.- Computational Protein Design with Side-Chain Conformational Entropy. Sciretti, D.; Bruscolini,P.; Pelizzola,A.; Pretti,M.; Jaramillo,A. Proteins. Structure Function and Bioinformatics 74 – 1, pp. 176 – 191. 2009.

18.- Exploring the free energy landscape: From dynamics to networks and back. D. Prada-Gracia, J. Gómez-Gardeñes, P. Echenique, F. Falo. PLoS Computational Biology 5(6): e1000415. (2009) 9 pages.

Main research projects

1.-FIS2017-87519-P: Abordando la complejidad de Sistemas Sociotécnicos, Biológicos y Naturales National Project. Founding Agency: AGENCIA ESTATAL DE INVESTIGACIÓN PIs: Yamir Moreno Vega and Fernando Falo. Star-end date: 1-1-18/31-12-20.

2.- CTQ2016-78895-R PROPIEDADES DE NUEVOS SISTEMAS NANOESTRUCTURADOS DE IMPORTANCIA TECNOLOGICA, MINECO. PLAZO DE EJECUCIÓN: DEL 30/12/2016 AL 29/12/2019. PI1: RAMON GONZALEZ RUBIO; PI2: ANTONIO REY GAYO. UCM.

3.- E36_17R : Grupo de Investigación: Física Estadística y No Lineal. Regional Project. Founding Agency: DIPUTACIÓN GENERAL DE ARAGÓN. PI. Juan José Mazo. 2018-2020. Start-end date: 1-1-17/ 31-12-19

4.- E30-17R : Grupo de Investigación: Supercomputación y Física de Sistemas Complejos y Biológicos (COMPHYS). Founding Agency: DIPUTACIÓN GENERAL DE ARAGÓN. PI. David Iñiguez Dieste. 2018-2020. Start-end date: 1-1-17/ 31-12-19

5.- FIS2014-55867-P: SocioBioTec: “FÍSICA ESTADÍSTICA Y NO LINEAL APLICADA A SISTEMAS SOCIALES, BIOLÓGICOS Y TECNOLÓGICOS.”
National Project. PI: Juan José Mazo Torres. Funding agency: MINECO. MINISTERIO DE ECONOMIA Y COMPETITIVIDAD. Start-end date: 01/01/2015 – 31/12/2017.

6.- FIS2011-25167: Redes, Biofísica y Ciencia No Lineal. National Project. PI: Juan José Mazo Torres. Funding agency: Ministerio de Ciencia e Innovación. Start-end date: 1-1-2012 / 31-7-2015.

7.- FIS2009-13364-C02-01. “ACERCAMIENTO COMPUTACIONAL A LA COMPLEJIDAD EN REDES,PROTEINAS, Y SISTEMAS DE MUCHOS AGENTES”. Ámbito geográfico: Nacional. PI: Pierpaolo Bruscolini. Funding agency: MINISTERIO DE CIENCIA E INNOVACION. Start-end date: 01/01/2010 – 31/12/2012.

8.- (FIS2008-01240).Dinámica y Estructura de Sistemas Complejos. Ámbito geográfico: Nacional. PI: Juan José Mazo Torres. Funding agency: MINISTERIO DE CIENCIA E INNOVACION. Start-end date: 2009-2011.

9.- FIS2006-12781-C02-01 “COMPLEJIDAD EN PROTEÍNAS, REDES Y SISTEMAS DE MUCHOS AGENTES”. Ámbito geográfico: Nacional. PI: Pierpaolo Bruscolini. Funding agency: MINISTERIO DE EDUCACION Y CIENCIA. Start-end date: 01/10/2006 – 30/09/2009.

10.- FIS2009-13364-C02-02 “Modelos físicos para la simulación de tránsitos conformacionales en proteínas”. National Project. PI: Antonio Rey Gayo. Funding agency:Ministerio de Ciencia e Innovación. Proyecto Start-end date: 2010- 2013.

11.- S2009/PPQ-1551: “Química a alta presión, QUIMAPRES”. Regional Project. PI: Antonio Rey Gayo (at the UCM-SIMPOL group). Valentín García Baonza (coordinator). Funding agency: Comunidad de Madrid. Start-end date: 2010 – 2013.

Collaborators

Bruscolini’s group:

• Alessandro Pelizzola, Dept of Physics, Politecnico di Torino (Italy).
• Antonio Rey, Dept. of Chemistry, UCM, Madrid (Spain).
• Laura Itzhaki, Dept. of Pharmacy, Cambridge University (UK).
• Javier Sancho Sanz, BIFI, Universidad de Zaragoza (Spain).
• Ramón Hurtado, BIFI, Universidad de Zaragoza (Spain).
• Milagros Medina, BIFI, Universidad de Zaragoza (Spain).
• Fernando Falo Fornies, BIFI, Universidad de Zaragoza (Spain).
• Sergio Perez Gaviro, BIFI, Centro Universitario de la Defensa, Zaragoza, Spain.
• Mauro Magnani, University of Urbino, (Italy)

Rey’s Group

• Patrícia F.N. Faísca (University of Lisbon, Portugal).
• Valentín García Baonza (UCM, Dept. Química Física I).
• Pierpaolo Bruscolini (UZ y BIFI).
• Manuel Ángel Ramos (UCM, Dept. Matemática Aplicada).

Falo’s Group

• Sebastián Bouzat, CEA Bariloche, Argentina).
• Juan José Mazo (ICMA and Universidad de Zaragoza).
• Jesús Gómez-Gardeñes (BIFI and University of Zaragoza).
• María del Carmen Morón (ICMA and University of Zaragoza).
• Jesús Bergues (Universidad San Jorge, Zaragoza).
• Pierpaolo Bruscolini (UZ y BIFI).
• Ricardo Arías González. Instituto de Nanociencia de Madrid (IMDEA).
• Anabel Lostao. Instituto de Nanociencia de Aragón.

Molecular dynamics and electronic structure

Head of the Research Line:

Jesús Clemente-Gallardo

Researchers: Permanent members

José Luis Alonso Buj (Departamento de Física Teórica, Facultad de Ciencias)
Alberto Castro Barrigón (ARAID, Edificio I+D)
Jesús Clemente Gallardo (Departamento de Física Teórica, Edificio I+D)
Fernando Falceto Blecua (Departamento de Física Teórica, Facultad de Ciencias)
Jorge Alberto Jover Galtier (CUD)
Víctor Gopar (Departamento de Física Teórica, Facultad de Ciencias)
Víctor Polo Ortiz (Departamento de Química Física, Facultad de Ciencias)

Researchers: PhD students

Adrián Gómez Pueyo (Departamento de Física Teórica, Edificio I+D)

SUMMARY OF THE RESEARCH LINE

In our group, we are mainly concerned with the application of theoretical and computational tools to the study of the behavior of biological and solid state systems. Most of our methods are based on quantum mechanics and in the tools required to combine it efficiently with classical mechanical methods. We deal with many different aspects, from the most theoretical to the most applied. The following are our main lines of work:

A.- Hybrid quantum-classical models: non-adiabatic dynamics of molecular systems

Quantum Mechanics admits a description in terms of tensorial objects defined on the space of physical states. It has been proved very helpful to describe important magnitudes such as the entanglement or the purity of a given system, while being formally analogous to the tensorial description of a classical mechanical system. Both formalisms admit Hamiltonian descriptions for the most common dynamical situations, and this fact allows a straightforward generalization to statistical systems with that type of dynamics for the microstates.

When describing molecular systems, it is common to approximate some degrees of freedom (usually those corresponding to the nuclei) and describe them as classical objects, but there are some degrees of freedom (usually part or the electronic system) which must be described as quantum objects. The tensorial description allows us to combine them in a hybrid quantum-classical description which can be made to maintain several mathematical properties and this provides us with a mathematically rigorous description of the corresponding statistical system. With these tools a firm theoretical background can be constructed to enlarge traditional adiabatic methods such as those based on the Ehrenfest formalism in order to include properties such as decoherence of the electronic dynamics.

Nonetheless, several properties of the resulting models are not fully understood yet. We are studying the main properties of the equilibrium distributions of hybrid systems, in particular in the thermodynamic limit. We are also studying their dynamical properties, in particular what concerns the decoherence of the electronic states. And finally, we are trying to understand ab initio how to model the interaction of a hybrid system with an environment by incorporating stochastic effects in the hybrid dynamics.

B.- Foundations and applications of time-dependent density-functional theory

Density-functional methods have become the most successful techniques for electronic structure calculations; the time-dependent variant is the choice for spectroscopic studies that involve excited electronic states. We develop algorithms and code for the application of these theoretical tools and we belong to the team of developers of the code Octopus (http://www.tddft.org/programs/octopus/)

From the code we also consider relevant applications in Physics, mostly centered on molecules and nanostructures, with focus on the irradiation of the systems with large intensity lasers, and the non-linear phenomena triggered by these usually ultra-short pulses.

C.-Analysis of chemical phenomena using DFT

In this research line, theoretical studies at the DFT level are carried out for molecular systems of interest in the fields of material science and catalysis. Working together with experimental groups of inorganic and physical chemistry, theoretical calculations are nowadays a fundamental tool for the understanding of chemical concepts. Hence, important questions regarding reaction mechanisms, spectroscopic properties or molecular orbital analysis are elucidated from first principles. The theoretical results not only provide a detailed explanation of the obtained results but serve as a guide for the rational design of new molecular species with desired properties.

D.- Quantum optimal control theory

The properties and the microscopic structure of matter can be modified at the electronic level with external knobs: most notably with ultra-fast custom-shaped intense laser pulses, but also through the modification of variables such as temperature, pressure, doping, presence of external static electric or magnetic fields, etc. We propose the use of first-principles electronic structure techniques (for example, time-dependent density-functional theory, TDDFT) in connection with control theories, to design materials, or prepare states of matter, with optimal values of selected properties. The rapidly evolving capabilities of advanced laser sources (pulse durations, intensities, shaping freedom) has triggered intense research in quantum optimal control theory and other control schemes – yet few studies have directly addressed the fast, attosecond scale movement of electrons with an ab initio technique such as TDDFT, that also promises the capacity of dealing with large systems. TDDFT offers the possibility of dealing with highly non-linear response of atomic and molecular systems, even though its accuracy and reliability are permanently improving, and still require theoretical and methodological advances.

E.- Wave transport phenomena in complex systems.

Transport of quantum and classical waves through complex systems has attracted a lot of interest from both fundamental and practical interests. For instance, transport of quantum waves, or matter waves, such as electrons and photons are at the forefront of research in condensed matter. This has been motivated by the creation of new materials such as graphene and topological insulators.

In this research line we investigate the effects of the presence of disorder such as impurities on different quantities related to the quantum transport of electrons through small samples made of graphene, topological insulator materials, and normal metals. The presence of disorder gives a random character to the transport electronic properties of the materials. Thus, in this research line we are particularly interested in studying the statistical properties of quantities, such as the conductance, shot noise, concurrence, etc.

Regarding classical waves, it turns out that many phenomena that one can observe in quantum waves (electrons) can be also seen in classical (macroscopic) systems such as microwave waveguides. This is a signature of the universality of the wave phenomena that we study. Therefore, our theoretical framework has been applied to studied the transmission of electromagnetic waves, and other quantities, in experimental microwave setups.

Relevant publications

1. A. Fernandez-Marin, J. A. Mendez-Bermudez, J. Carbonell, F. Cervera, J. Sanchez-Dehesa, and Victor A. Gopar, Beyond Anderson Localization in 1D: Anomalous Localization of Microwaves in Random Waveguides. Phys. Rev. Lett., 113, 233901 (2014).
2. L. Alonso, A. Castro, J. Clemente-Gallardo, J. C. Cuchí, P. Echenique-Robba, J. G. Esteve and F. Falceto, Nonextensive thermodynamic functions in the Schrödinger-Gibbs ensemble , Phys. Rev. E 91 022137, 2015
3. Vélez, E.; Betoré M. P.; Casado, M. A.; Polo, V., NH Activation of Ammonia by [{M(-OMe)(cod)}2] (M = Ir, Rh) Complexes: A DFT Study, Organometallics,34, 3959–3966 (2015)
4. Castro, A. Rubio, and E. K. U. Gross, Enhancing and controlling single-atom high-harmonic generation spectra: a time-dependent density-functional scheme, Eur. Phys. J. B 88, 191 (2015).
5. Betoré, M. P.; Casado, M. A.; García-Orduña, P.; Lahoz, F. J.; Polo, V.; Oro, L. A. Oxidative Addition of the N–H Bond of Ammonia to Iridium Bis(phosphane) Complexes: A Combined Experimental and Theoretical Study, Organometallic, 2016, 35, 720-731.
6. Suleiman, R. K..; Polo, V.; El Ali, B., Alkoxycarbonylation of α,β-Unsaturated Amides Catalyzed by Palladium (II) Complexes: A DFT Study of the Mechanism, RSC Advances, 2016, 6, 8440-8448.
7. Alberto Castro, Theoretical shaping of femtosecond laser pulses for molecular photo-dissociation with control techniques based on Ehrenfest’s dynamics and time-dependent density-functional theory, ChemPhysChem 17, 1439 (2016).
8. Jessica Walkenhorst, Umberto De Giovannini,1, Alberto Castro, and Angel Rubio, Tailored pump-probe transient spectroscopy with time-dependent density-functional theory: controlling absorption spectra, Eur. Phys. J. B 89, 128 (2016).
9. Adrián Gómez Pueyo, Jorge A. Budagosky, and Alberto Castro, Optimal control with nonadiabatic molecular dynamics: Application to the Coulomb explosion of Sodium clusters, Phys. Rev. A 94, 063421 (2016).
10. A. Mendez-Bermudez, J. A. Martinez-Mendoza, V. A. Gopar, and I. Varga, Lloyd-model generalization: Conductance fluctuations in one-dimensional disordered systems, Physical Review E, 93, 012135 (2016).
11. David Kammerlander, Alberto Castro, and Miguel A.L. Marques, Optimization of the ionization time of an atom with tailored laser pulses: a theoretical study, Eur. Phys. J. B 90, 91 (2017).
12. Ilias Amanatidis, Ioannis Kleftogiannis, Fernando Falceto and Victor A. Gopar,, Coherent wave transmission in quasi-one-dimensional systems with Lévy disorder,
    Physical Review E, 96, 062141 (2017).
13. F. Cariñena, J. Clemente-Gallardo, J. A. Jover-Galtier and G. Marmo, Tensorial dynamics on the space of quantum states, J. Phys. A: Math. Theor. , 50, 365301, (2017)
14. L. Alonso, P. Bruscolini, A. Castro, J. Clemente-Gallardo, J. C. Cuchí, and J. A. Jover-Galtier, Ehrenfest statistical dynamics in chemistry: study of decoherence effects, J. Chem. Theor. Comp. 18, 3975 (2018).
15. Gómez Pueyo, M. A. L. Marques, A. Rubio, and A. Castro, Propagators for the time-dependent Kohn-Sham equations: multistep, Runge-Kutta, exponential Runge-Kutta, and commutator free Magnus methods, J. Chem. Theor. Comp. 14, 3040 (2018).
16. J. L. Alonso, Filiberto Ares, and José Luis Brun.Unraveling the Landau’s consistence criterium and the meaning of interpenetration in the “Two-Fluid” Model. The European Physical Journal B. Volume 91 – Issue 10, 226 (2018)

Main research projects

• FP7-NMP-2011-SMALL-5: Dynamics and control in nanostructures for magnetic recording and energy applications, 7^th framework programme, EU
• FIS2013-46159-C3-2-P. TEORÍA DE SISTEMAS HÍBRIDOS CLÁSICO-CUÁNTICOS: EQUILIBRIO, DINÁMICA Y CONTROL., 01/07/2014-31/12/2017, 45980€, IP: Alberto Castro
• FIS2014-61301-EXP: “Una ruta nueva en la bsqueda del funcional exacto de la teorı́a de funcionales de la densidad” (. Entidad financiadora: Ministerio de Economiı́a y Competitividad. Investigador principal: Alberto Castro. Financiación: 35000€ Duración del proyecto: 09/2015 – 08/2017
• CTQ2012-35665 DISEÑO DE CATALIZADORES ORGANOMETÁLICOS PARA LA ACTIVACIÓN Y FUNCIONALIZACIÓN DE AMONIACO: ESTUDIOS COMPUTACIONALES Y EXPERIMENTALES., IP. Víctor Polo, (2013-2015), 80730€
• CTQ2015-67366-P: ACTIVACIÓN DE NH3 Y CO2 POR COMPLEJOS DE RODIO E IRIDIO Y SU APLICACIÓN EN EL DESARROLLO DE PROCESOS CATALÍTICOS PARA LA SÍNTESIS DE COMPUESTOS DE ALTO VALOR AÑADIDO, IP Víctor Polo – Miguel Angel Casado (2016-2018), 112651€
• FIS2017-82426-P: OPTIMIZACIÓN Y MODELOS MICROSCÓPICOS DESDE PRIMEROS PRINCIPIOS. IP: Alberto Castro, 42350€

Collaborators

• Juan Carlos Cuchí, Universidad de Lérida, Spain
• Ángel Rubio, Universidad del Pais Vasco, Spain

Theoretical and Applied Modeling of Complex Systems (GOTHAM)

Head of research line:

Jesús Gómez Gardeñes

Researchers:

Prof. Jesús Gómez Gardeñes
Prof. Luis Mario Floría
Dr. Alessio Cardillo
David Soriano-Paños

SUMARY OF THE RESEARCH LINE

The research of the group of Theoretical and Applied Modeling of Complex Systems (GOTHAM) relies on the use of tools from Statistical Physics, Nonlinear Dynamics and Network Science for the modeling and understanding of the functioning of Complex Systems such as the brain, societies, ecosystems, etc. To this aim, we elaborate models that attempt to capture the essential microscopic interactions that shape the relationships between the fundamental components of these systems (such as neurons, humans, species, etc.) and that give rise to emergent collective behaviors (such as cognition or neurological disorders, the emergence of consensus or epidemic states, biodiversity or mass extinctions, etc).

The nature of our research is truly interdisciplinary and multiscale, given the different nature of the systems addressed and the different levels of complexity which they belong to. However, the statistical physics approach allows us to disengage the essential aspects that, once incorporated into models, help us to reproduce the phenomenology observed in experiments and field work. This way, our models aim at going beyond purely theoretical aspects so that, based on the available data, we are able to reproduce real observations and to make quantitative predictions.
Our activity is therefore favored by the increase and improvements achieved in the capture of biological and social data. A field, data science, whose advance must go hand in hand with our understanding about the mechanisms and laws that govern the patterns and behaviors observed in real datasets. This is, in a nutshell, our mission in GOTHAM.

RECENT ACTIVITY

Our recent activity focuses on these research lines:

a) Social systems and mobility: In this area we study the different patterns of interaction between individuals that determine human behavior in society. From our tendency to cooperate despite the individual costs that this implies, to even our way of moving in our daily life. The study of our behavior yields relevant information about how individual behavior and, above all, our interactions, influence the functioning of our society at different levels.

Social network of proximity interactions in two hunter gatherer populations. NATURE HUMAN BEHAVIOUR 1, 43 (2017).

Some of the problems tackled recently in this line are:
• The study of mobility in large cities through complex multilayer networks to detect segregation as a function of the socioeconomic status of their individuals [ROYAL SOCIETY OPEN SCIENCE 3, 150654 (2016)].
• The evolution and transmission of culture in hunter-gatherer populations through complex multilayer networks [NATURE HUMAN BEHAVIOR 1, 43 (2017)].
• The detection of cooperative phenotypes in humans through the use of game theory for the analysis of human decisions when facing social dilemmas [SCIENCE ADVANCES 2, e1600451 (2016)].

Networks of daily commutes in the city of Medellín (Colombia) for three different socioeconomic classes. ROYAL SOCIETY OPEN SCIENCE 3, 150654 (2016).

b) Epidemiology: Historically, the usual way to characterize the evolution of an epidemic process is the formulation of compartmental models. Originally, these models were analyzed under mean-field hypothesis. However, at the beginning of the current century, epidemic models were adapted to take into account that the interaction between agents was described as a complex network, thus leaving behind the previous hypotheses. These theories supposed a great advance, allowing to estimate precisely the influence of the architecture of interactions in the epidemiological threshold.

MIR (Mobility-Interaction-Return ) metapopulation model for recurrent mobility. PHYSICAL REVIEW X 8, 031039 (2018).

Despite the advances achieved thanks to the incorporation of complex networks to shape the interactions within epidemic models, the need to understand the emergence of epidemic outbreaks at local, national and global scales (such as SARS in 2003, the H1N1 virus in 2009 or more recently the Chikungunya and Zika) continues to demand an improvement of the models and, in particular, of the way in which we incorporate interaction patterns between agents. One improvement is the addition of agents mobility through metapopulation models. Starting from the use of complex metapopulations, during the last decade models have been progresively refined in order to capture the influence of realistic mobility patterns.

(Left) Network of daily commutes in the city of Santiago de Cali (Colombia). (Right) Spatio-temporal evolution of the epidemic across this city. NATURE PHYSICS 14, 391 (2018).

Recently [NATURE PHYSICS 14, 391 (2018) and PHYSICAL REVIEW X 8, 031039 (2018)], our group has proposed a theoretical model, Movement-Interaction-Return, which allows to quantify the influence of recurrent mobility patterns in the propagation of simple epidemics in real metapopulations based on demographic data and the observed patterns of daily commutes. This model is able to reproduce with great precision the results obtained by numerical simulations based on Monte Carlo algorithms, both for the incidence of an epidemic and for the value of the epidemiological threshold. The use of this type of metapopulation frameworks concentrates our activity in the field of epidemics, combining theoretical modeling and the use of real data on mobility, demography and epidemic incidence.

c) Ecología: In this line we intend to address the study of interaction networks in the field of ecology. A correct approach must tackle the problem by considering the different types of relationships between species that appear in an ecosystem (e.g., facilitation, competition, predation, mutualism, etc.). However, most studies on the structure and dynamics of ecological networks focus on a single type of interaction so that the description of the systems is incomplete. Our general objective in this line is to develop theoretical frameworks that accommodate different types of interaction under the same formalism. This way, aspects such as the stability of ecological balances or the emergence of biodiversity can be analyzed in full.

Different plant-plant interaction networks from various semiarid systems. These networks contain positive and negative interactions among vegetal species. JOURNAL OF ECOLOGY 106, 1443 (2018).

Our recent work in this line has focused on the coexistence of positive (facilitation) and negative (competition) interactions between plant species. To this aim, the balance between these interactions was studied through complex signed networks elaborated from data collected in semi-arid regions [ECOGRAPHY 40, 733-741 (2017)]. Through the structural analysis of these networks it was found that the balance between interactions of different sign is closely related to different aspects of interest for the environmental management of the ecosystems they represent [JOURNAL OF ECOLOGY 106, 1443 (2018)].

d) Explosive Phase Transitions. Our goal in this line is to explain how collective phenomena (such as epidemics, synchronization, social consensus, etc.) appear as phase transitions. In particular, it is especially interesting to determine the conditions under which these transitions pass from being soft, so that changes in the system appear progressively as the interaction between the elements of the system increases, to explosive, that is, giving rise to collective phenomena in an abrupt form once exceeded a “critical” value of the coupling between units.

Emergency of explosive transitions in social contagion processes. SCIENTIFIC REPORTS 6, 19767 (2016).

Explosive transitions, apart from being attractive from the theoretical point of view, are of special interest as they describe scenarios in which the system under study passes suddenly to an excited state without any type of early warning. In this sense, the sudden activation of collective states may entail extremely harmful consequences in the case of epidemics or synchronized states (e.g. epilepsy). Therefore, it is in these two areas where we focus our research on explosive phase transitions.

RELEVANT PUBLICATIONS

1.- Critical regimes driven by recurrent mobility patterns of reaction-diffusion processes in networks.  J. Gómez-Gardeñes, D. Soriano-Paños & A. Arenas
NATURE PHYSICS 14, 391-395 (2018);
2.- Spreading processes in multiplex metapopulations containing different mobility networks. D. Soriano-Paños, L . Lotero A. Arenas & J. Gómez-Gardeñes
PHYSICAL REVIEW X 8, 031039 (2018);
3. Multiplex decomposition of non-Markovian dynamics and the hidden layer reconstruction problem. L. Lacasa, I.P. Mariño, J. Miguez, V. Nicosia, E. Roldán, A. Lisica, S. W. Grill & J. Gómez-Gardeñes
PHYSICAL REVIEW X 8, 031038 (2018);
4. The structure of plant spatial association networks increases plant diversity in global drylands. H. Saiz, J. Gómez-Gardeñes, J.P. Borda & F. Maestre
JOURNAL OF ECOLOGY 106, 1443 (2018);
5. Epidemics on plants: Modeling long-range dispersal on spatially embedded networks. J.H. Arias-Castro, J. Gómez-Gardeñes, S. Meloni & E. Estrada
JOURNAL OF THEORETICAL BIOLOGY 453, 1-13 (2018);
6. Interplay between cost and benefits triggers nontrivial vaccination uptake. B. Steinegger, A. Cardillo, P. De los Rios, J. Gómez-Gardeñes, & A. Arenas
PHYSICAL REVIEW E 97, 032308 (2018)
7. Graph analysis of cell clusters forming vascular networks. A.P Alves, O.N. Mesquita, J. Gómez-Gardeñes & U. Agero
ROYAL SOCIETY OPEN SCIENCE 5, 171592 (2018);
8. Characterization of hunter-gatherer networks and implications for cumulative culture. A.B. Migliano, A.E. Page, J. Gómez-Gardeñes, G.D. Salali, S. Viguier, M. Dyble, J. Thompson, N. Chaudhary, D. Smith, R. Mace, M. G. Thomas, V. Latora & L. Vinicius
NATURE HUMAN BEHAVIOUR 1, 43 (2017);
9. Optimizing Diffusion in Multiplexes by Maximizing Layer Dissimilarity. A.B. Serrano, J. Gómez-Gardeñes & R.F.S. Andrade
PHYSICAL REVIEW E 95, 052312 (2017);
10. Evidence of Structural Balance in Spatial Ecological Networks. H. Saiz, J. Gómez-Gardeñes, P. Nuche, A. Girón, Y. Pueyo & C.L. Alados
ECOGRAPHY 40, 733-741 (2017);
11. Synchronization in Networks with Multiple Interaction Layers. C.I. Del Genio, J. Gómez-Gardeñes, I. Bonamassa & S. Boccaletti
SCIENCE ADVANCES 2, e1601679 (2016);
12. Rich do not rise early: Spatio-temporal patterns in the Mobility Networks of different Socio-economic classes. L. Lotero, R.G. Hurtado, L.M. Floría & J. Gómez-Gardeñes
ROYAL SOCIETY OPEN SCIENCE 3, 150654 (2016);
13. Synchronization unveils the organizaton of Ecological networks with Positive and Negative interactions. A. Girón, H. Saiz, F.S. Bacelar, R.F.S. Andrade & J. Gómez-Gardeñes
CHAOS 26, 065302 (2016);
14. Humans display a reduced set of consistent Behavioral Phenotypes in Dyadic Games. J. Poncela, M. Gutiérrez, C. Gracia-Lázaro, J. Vicens, J. Gómez-Gardeñes, J. Perelló, Y. Moreno, J. Duch & A. Sánchez
SCIENCE ADVANCES 2, e1600451 (2016);
15. Network Bipartivity and the Transportation Efficiency of European Passenger Airlines. J. Gómez-Gardeñes & E. Estrada
PHYSICA D 323, 57-63 (2016);
16. Amplitude dynamics favors synchronization in complex networks. L.V. Gambuzza, J. Gómez-Gardeñes & M. Frasca
SCIENTIFIC REPORTS 6, 24915 (2016);
17. Explosive Contagions in Networks. J. Gómez-Gardeñes, L. Lotero, S. Taraskin, & F. Pérez-Reche
SCIENTIFIC REPORTS 6, 19767 (2016);

MAIN RESEARCH PROJECTS

1.- FIS2017-87519-P: TAPLEX: Abordando la complejidad de Sistemas Sociotécnicos, Biológicos y Naturales. National Project. PI: Y. Moreno – F. Falo. Funding agency: MINECO. MINISTERIO DE ECONOMIA Y COMPETITIVIDAD. Start-end date: 01/01/2018 – 31/12/2020.
2.-FIS2015-71582-C2: ESTUDIO DE TRANSICIONES DINÁMICAS EN REDES. National Project. PI: Alex Arenas. Funding agency: MINECO. MINISTERIO DE ECONOMIA Y COMPETITIVIDAD. Start-end date: 01/01/2016 – 31/12/2018.
3.- FIS2014-55867-P: SocioBioTec: FÍSICA ESTADÍSTICA Y NO LINEAL APLICADA A SISTEMAS SOCIALES, BIOLÓGICOS Y TECNOLÓGICOS. National Project. PI: Juan José Mazo Torres. Funding agency: MINECO. MINISTERIO DE ECONOMIA Y COMPETITIVIDAD. Start-end date: 01/01/2015 – 31/12/2017.
4.- 313788/2013-8: Dynamics and Structure of Complex Systems. National Project. PI: J. Gómez Gardeñes – R.F.S. Andrade. Funding agency: CNPq (Brazil) – Science Without Borders program. Start-end date: 01/01/2014 – 31/12/2016.
5.- FIS2012-38266-C02-01: Análisis multiescala de sitemas complejos: estructura y dinámica. National Project. PI: Alex Arenas. Funding agency: MINECO. MINISTERIO DE ECONOMIA Y COMPETITIVIDAD. Start-end date: 01/01/2013 – 31/12/2015.
6.- FIS2011-25167: Redes, Biofísica y Ciencia No Lineal. National Project. PI: Juan José Mazo Torres. Funding agency: Ministerio de Ciencia e Innovación. Start-end date: 1-1-2012 / 31-7-2015.
7.- FIS2011-14539-E: NAVEGACION CUANTICA EN REDES DE INFORMACION. National Project. PI: Jesús Gómez Gardeñes. Funding agency: Ministerio de Ciencia e Innovación. Start-end date: 1-3-2012 / 28-2-2014.

Collaborators

• Alex Arenas, University Rovira i Virgili. Tarragona (Spain).
• Heliana Arias, Universidad del Valle, Cali (Colombia).
• Albert Diaz Guilera, University of Barcelona, Barcelona (Spain).
• Jordi Duch, University Rovira i Virgili. Tarragona (Spain).
• Ernesto Estrada, Strathclyde University, Glasgow (UK).
• Mattia Frasca, Università di Catania (Italy).
• Lucas Lacasa, Queen Mary University of London, London (UK).
• Vito Latora, Queen Mary University of London, London (UK).
• Laura Lotero, Universidad Pontificia Bolivariana, Medellín (Colombia).
• Sandro Meloni, IFISC, Palma de Mallorca (Spain).
• Andrea B. Migliano, University College of London, London (UK).
• Francisco J. Pérez-Reche, University of Aberdeen, Aberdeen (UK).
• Miguel Romance, Universidad Rey Juan Carlos (Spain).
• Hugo Saiz, Universidad Rey Juan Carlos (Spain).
• Jordi Soriano, University of Barcelona, Barcelona (Spain).