Research in Physics at Institute of Biocomputation and Physics of Complex Systems (BIFI) is aimed at breaking the barriers that have artificially separated traditional disciplines in an attempt to create new lands where far-reaching scientific and technological innovation can emerge. This is the real purpose of the **Science of Complex Systems**; a discipline based on the holistic principle that considers the properties of a system cannot be well understood by analyzing in depth its constituent parts as if they were isolated.

The recent explosion of the activity in the modeling of complex systems, propelled by the unprecedented amount of data and information from different fields such as genetics, proteomic studies, Internet traffic, or records of social networks users, not only has provided a deep understanding of systems behavior, but has also led to the discovery of common properties shared by these seemingly disparate systems.

Spurred by former discoveries, this cross-disciplinary research field has developed a growing set of methods, tools and techniques of an impressive explanatory power, many of them inspired by the analysis of Statistical Physics of equilibrium and non-equilibrium systems in addition to other methodological ingredients coming from Quantum Mechanics, Dynamical Systems, Computational Physics, etc.

The interest of Physics towards Complex Systems Science is twofold. On the one hand, physicists play a pivotal role in the application of physical methods and tools to describe and understand novel emergent collective phenomena in biological, social and technological systems. The other motivating challenge is the need of reformulating the current physical methods in order to tackle those novel physical phenomena that are frequently found in complex systems.

The Area of Physics at BIFI is divided into 5 research lines:

**Spin Glasses****Complex Systems and Networks****Statistical-physics modeling of biomolecules****Molecular Dynamics and Electronic Structure****Nonlinear Models and Complexity**

- Spin Glasses
- Complex Systems

and Networks (COSNET Lab) - Statistical-physics modeling

of biomolecules - Molecular dynamics

and electronic structure - Nonlinear Models

and Complexity

Spin Glasses

**Head of the Research Line:**

Alfonso Tarancón Lafita

**Researchers:**

Andrés Cruz Flor

Luis Antonio Fernández Pérez

Victor Martín Mayor

Juan Jesús Ruíz Lorenzo

David Íñiguez

David Yllanes

Raquel Álvarez Baños

José Miguel Gil Narvión

Antonio Gordillo Guerrero

Andrea Maiorano

Jorge Monforte García

Sergio Pérez Gaviro

Beatriz Seoane

Marco Baity-Jesi

Spin glasses are magnetic alloys that have one salient feature: their properties are never stable as time goes by. When you cool a spin glass below its critical temperature, its properties keep changing for years (although the change is slower as the spin-glass ages). The phenomenon of Aging is not peculiar of spin glasses: many other systems of great industrial relevance (polymers, structural glasses, etc.) suffer it. Aging is important issue: for instance, if the resistance of the materials of the wings of your airplane changes with time, you may be worried. Spin glasses are regarded by scientists as a particularly system simple model to study Aging. However, in spite of their simplicity (as compared with polymers, for instance), spin glasses are still quite a headache for physicists!

We study two kinds of spin glasses: Heisenberg (where the spins are three-dimensional vectors) and Ising (uniaxial spins). We perform both critical-point and low-temperature studies, in and out of equilibrium, using large-scale computing clusters and custom-built computers. In particular, the Janus computer has allowed us to investigate the dynamics for eleven orders of magnitude, from picoseconds to a tenth of a second.

**1.- Phase transitions in disordered systems: the example of the random-field Ising model in four dimensions.** Nikolaos G. Fytas, Victor Martin-Mayor, Marco Picco, Nicolas Sourlas. Phys. Rev. Lett. 116, 227201 (2016).

**2.- Universal critical behavior of the 2d Ising spin glass**. L.A. Fernandez, E. Marinari, V. Martin-Mayor, G. Parisi, J.J. Ruiz-Lorenzo. Phys. Rev. B 94, 024402 (2016).

**3.- Soft Modes, Localization and Two-Level Systems in Spin Glasses**. Marco Baity-Jesi, Victor Martin-Mayor, Giorgio Parisi, Sergio Perez-Gaviro. Phys. Rev. Lett. 115, 267205 (2015).

**4.- The three dimensional Ising spin glass in an external magnetic field: the role of the silent majority**. Janus Collaboration: M. Baity-Jesi, R. A. Banos, A. Cruz, L. A. Fernandez, J. M. Gil-Narvion, A. Gordillo-Guerrero, D. Iniguez, A. Maiorano, F. Mantovani, E. Marinari, V. Martin-Mayor, J. Monforte-Garcia, A. Munoz Sudupe, D. Navarro, G. Parisi, S. Perez-Gaviro, M. Pivanti, F. Ricci-Tersenghi, J.J. Ruiz-Lorenzo, S.F. Schifano, B. Seoane, A. Tarancon, R. Tripiccione, D. Yllanes. J. Stat. Mech. (2014) P05014.

**5.- Universality in the three-dimensional random-field Ising model**. Nikolaos G. Fytas, Victor Martin-Mayor. Phys. Rev. Lett. 110, 227201 (2013).

**6.- Comment on “Evidence of Non-Mean-Field-Like Low-Temperature Behavior in the Edwards-Anderson Spin-Glass Model”**. A. Billoire, L.A. Fernandez, A. Maiorano, E. Marinari, V. Martin-Mayor, G. Parisi, F. Ricci-Tersenghi, J.J. Ruiz-Lorenzo, D. Yllanes. Phys. Rev. Lett. 110, 219701 (2013).

**7.- Thermodynamic glass transition in a spin glass without time-reversal symmetry.** Janus Collaboration: R. A. Baños, A. Cruz, L.A. Fernandez, J. M. Gil-Narvion, A. Gordillo-Guerrero, M. Guidetti, D. Iñiguez, A. Maiorano, E. Marinari, V. Martin-Mayor, J. Monforte-Garcia, A. Muñoz Sudupe, D. Navarro, G. Parisi, S. Perez-Gaviro, J. J. Ruiz-Lorenzo, S.F. Schifano, B. Seoane, A. Tarancon, P. Tellez, R. Tripiccione, D. Yllanes. Proc. Natl. Acad. Sci. USA (2012) 109, 6452-6456-

**8. – The three dimensional Heisenberg spin glass under a weak random anisotropy V.** Martin-Mayor, S. Perez-Gaviro. Rev. B 84, 024419 (2011).

**9. – Static versus dynamic heterogeneities in the D = 3 Edwards-Anderson-Ising spin glass.** Janus Collaboration: R. Alvarez Banos, A. Cruz, L.A. Fernandez, J. M. Gil-Narvion, A. Gordillo-Guerrero, M. Guidetti, A. Maiorano, F. Mantovani, E. Marinari, V. Martin-Mayor, J. Monforte-Garcia, A. Munoz Sudupe, D. Navarro, G. Parisi, S. Perez-Gaviro, J. J. Ruiz-Lorenzo, S.F. Schifano, B. Seoane, A. Tarancon, R. Tripiccione, D. Yllanes. Phys. Rev. Lett. 105, 177202 (2010).

**10. – Nature of the spin-glass phase at experimental length scales.** Janus Collaboration: R. Alvarez Banos, A. Cruz, L.A. Fernandez, J. M. Gil-Narvion, A. Gordillo-Guerrero, M. Guidetti, A. Maiorano, F. Mantovani, E. Marinari, V. Martin-Mayor, J. Monforte-Garcia, A. Munoz Sudupe, D. Navarro, G. Parisi, S. Perez-Gaviro, J. J. Ruiz-Lorenzo, S.F. Schifano, B. Seoane, A. Tarancon, R. Tripiccione, D. Yllanes. J. Stat. Mech. (2010) P06026.

**11. – Critical Behavior of Three-Dimensional Disordered Potts Models with Many States.** R. Alvarez Banos, A. Cruz, L. A. Fernandez, A. Gordillo-Guerrero, J.M. Gil-Narvion, M. Guidetti, A. Maiorano, F. Mantovani, E. Marinari, V. Martin-Mayor, J. Monforte-Garcia, A. Munoz Sudupe, D. Navarro, G. Parisi, S. Perez-Gaviro, J. J. Ruiz-Lorenzo, B. Seoane, S. F. Schifano, A. Tarancon, R. Tripiccione, D. Yllanes. J. Stat. Mech. (2010) P05002.

**12. – Phase transition in the three dimensional Heisenberg spin glass: Finite-size scaling analysis.** L.A. Fernandez, V. Martin-Mayor, S. Perez-Gaviro, A. Tarancon, A.P. Young. Phys. Rev. B 80, 024422 (2009).

**13. – Nonequilibrium spin glass dynamics from picoseconds to 0.1 seconds**. F. Belletti, M. Cotallo, A. Cruz, L.A. Fernandez, A. Gordillo-Guerrero, M. Guidetti, A. Maiorano, F. Mantovani, E. Marinari, V. Martin-Mayor, A. Munoz Sudupe, D. Navarro, G. Parisi, S. Perez-Gaviro, J.J. Ruiz-Lorenzo, S.F. Schifano, D. Sciretti, A. Tarancon, R. Tripiccione, J.L. Velasco, D. Yllanes. Phys. Rev. Lett. 101 (2008) 157201.

**14. – The spin glass transition of the three dimensional Heisenberg spin glass**. I. Campos, M. Cotallo-Aban, V. Martin-Mayor, S. Perez-Gaviro, A. Tarancon. Phys. Rev. Lett. 97, 217204 (2006).

**1.- FIS2015-65078-C2-2-P: COMPUTACIÓN AVANZADA EN MATERIALES Y REDES COMPLEJAS.** IP: David Iñiguez. Plan Nacional MINECO. 01/01/16

**2.- Cloudflow / CFD DESIGN OF BIOMASS BOILERS IN THE CLOUD.** IP: David Iñiguez. Proyecto Europeo H2020. 01/02/15

**3.- E24/3 BIOCOMPUTACIÓN Y FÍSICA DE SISTEMAS COMPLEJOS.** IP: David Iñiguez. Grupos Reconocidos DGA. 01/01/15

**4.- EGI ENGAGE / Engaging the EGI Community towards an Open Science Commons.** IP:David Iñiguez. Proyecto Europeo H2020. 01/03/15

**5.- CONVENIO DE COLABORACIÓN ENTRE EL GOBIERNO DE ARAGÓN, Y LA UNIVERSIDAD DE ZARAGOZA (BIFI) PARA EL SOPORTE DEL NODO DE ARAGÓN DE LA RED ESPAÑOLA DE SUPERCOMPUTACIÓN (RES) PARA 2014.** IP: Alfonso Tarancón. Soporte a Nodo ICTS de la RES. 01/01/14

**6.- E24/3 BIOCOMPUTACION Y FISICA DE SISTEMAS COMPLEJOS.** IP. David Iñiguez. Grupos Reconocidos DGA. 01/01/14

**7.- FCT-14-8712. ACTIVIDADES DE DIVULGACIÓN CIENTÍFICA 2014 UCC+i (UNIVERSIDAD DE ZARAGOZA).** IP: Vicerrectorado Investigacion. FECYT. 01/10/14

**8.- Fortissimo / Factories of the Future Resources, Technology, Infrastructure and Services for Simulation and Modelling.** IP: David Iñiguez. Proyecto Europeo H2020. 01/09/14

**9 – CloudSME / Cloud based Simulation platform for Manufacturing and Engineering.** IP: Alfonso Tarancón. Proyecto Europeo H2020. 01/07/13

**10.- DESARROLLO Y PUESTA EN SERVICIO DEL PROYECTO ARAGÓN OPEN SOCIALDATA.** IP: David Iñiguez. Proyecto de Transferencia . 13/09/13

- Enzo Marinari,
*U. La Sapienza* - Antonio Muñoz Sudupe,
*U. Complutense Madrid* - Denis Navarro,
*U. Zaragoza* - Giorgio Parisi,
*U. La Sapienza* - Sebastiano Fabio Schifano,
*U. Ferrara, INFN* - Federico Ricci Tersenghi,
*U. La Sapienza, INFN* - Raffaele Tripiccione,
*U. Ferrara, INFN* - Peter Young,
*University of Santa Cruz, California (USA).*

Complex Systems

and Networks (COSNET Lab)

and Networks (COSNET Lab)

**Head of the Research Line:**

Professor Yamir Moreno

**Researchers:**

Yamir Moreno *(Group Leader)*

Sandro Meloni *(Researcher)*

Carlos Gracia-Lázaro *(Researcher)*

Emanuele Cozzo *(Postdoctoral researcher)*

Sergio Arregui *(PhD Student)*

Alberto Aleta *(PhD Student)*

Felipe M. Cardoso *(PhD Student)*

Pablo Piedrahita *(PhD 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

Jesús Gómez-Gardeñes

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.

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 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 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.

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.

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 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 benefits 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.

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.

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?**

**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.

**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.- Host mobility drives pathogen competition in spatially structured populations.** C. Poletto, S. Meloni, V. Colizza, Y. Moreno and A. Vespignani. PLoS Computational Biology 9 (8): e1003169 (2013).

**5.- The role of hidden influentials in the diffusion of online information cascades.** R. A Baños, J. Borge-Holthoefer and Y. Moreno. EPJ Data Science 2:6 (2013).

**6.- 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).

**7.- 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).

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

**9.- 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).

**10.- 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).

**11.- 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).

**12.- 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).

**13.- 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).

**14.- 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).

**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.

- 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)*

The content of this Website is protected by Copyright © law

*The reproduction of these texts is strictly prohibited. They may only be used for scientific dissemination and citing always the original source.

Statistical-physics modeling

of biomolecules

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, *Associate professor UZ*

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.

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: we deal with protein design as an optimization process, at fixed backbone, over the choice of the amino acids and their rotamers to be arranged in the protein sequence. Our results suggests that it is important to account for the entropy to design optimal sequences. We are interested in developing the method further, using different force fields for the energy of the rotamers.

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.

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.

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.

**1.- 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).

**2.- 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.

**3.- 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.

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

**5.- 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).

**6.- 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).

**7.- 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).

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

**9.- 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).

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

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

**12.- 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.

**13.- 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).

**14.- 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.**
15.- 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.

**1.- 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.

**2.- 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.

**3.- 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.

**4.- (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.

**5.- 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.

**6.- 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.

**7.- 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.

**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.*

**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).* - Alessandro Fiasconaro
*(ICMA 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

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)*

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)*

Jorge Alberto Jover Galtier *(Departamento de Física Teórica, Facultad de Ciencias)*

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:

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.

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.

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.

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.

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.

**1. Conductance of 1D quantum wires with anomalous electron-wavefunction localization.** Ilias Amanatidis, Ioannis Kleftogiannis, Fernando Falceto, Victor A. Gopar. Phys. Rev. B 85, 235450 (2012).

**2. Ehrenfest dynamics is purity non-preserving: A necessary ingredient for decoherence.** J. L. Alonso, J. Clemente-Gallardo,J. C. Cuchí, P. Echenique, F. Falceto. Journal of Chemical Physics 137, 054106, 2012.

**3. Non-adiabatic effects within a single thermally averaged potential energy surface: Thermal expansion and reaction rates of small molecules.** J. L. Alonso, A. Castro, J. Clemente-Gallardo, P. Echenique, J. J. Mazo, V. Polo, A. Rubio and D. Zueco. Journal of Chemical Physics 137, 22A533, 2012.

**4. Conductance through disordered graphene nanoribbons: Standard and anomalous electron localization.** Ioannis Kleftogiannis, Ilias Amanatidis, Victor A. Gopar. Phys. Rev. B 88, 205414 (2013).

**5. Comment on “Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction” [J. Chem. Phys. 137, 22A530 (2012)].** J. L. Alonso J. Clemente-Gallardo P. Echenique-Robba and J. A. Jover-Galtier. J. Chem. Phys. 139, 087101, 2013.

**6. Beyond Anderson Localization in 1D: Anomalous Localization of Microwaves in Random Waveguides.** A. A. Fernandez-Marin, J. A. Mendez-Bermudez, J. Carbonell, F. Cervera, J. Sanchez-Dehesa, and Victor A. Gopar. Phys. Rev. Lett., 113, 233901 (2014).

**7. Optimal control of high-harmonic generation by intense few-cycle pulses.** Solanpaa, J.; Budagosky, J. A.; Shvetsov-Shilovski, N. I.; et al. Physical Review A 90, 053402. 2014.

**8. Nonextensive thermodynamic functions in the Schrödinger-Gibbs ensemble.** J. L. Alonso, A. Castro, J. Clemente-Gallardo, J. C. Cuchí, P. Echenique-Robba, J. G. Esteve and F. Falceto. Phys. Rev. E 91 022137, 2015 .

**9. NH Activation of Ammonia by [{M(-OMe)(cod)}2] (M = Ir, Rh) Complexes: A DFT Study.** Vélez, E.; Betoré M. P.; Casado, M. A.; Polo, V. Organometallics, 2015, 34, 3959–3966.

**10. Solvent-Free Iridium-Catalyzed Reactivity of CO2 with Secondary Amines and Hydrosilanes.** Julian, A.; Polo, V.; Jaseer, E. A.; Fernandez-Alvarez, F. J.; Oro, L. A. ChemCatChem 2015, 7, 3895–3902.

**11. Enhancing and controlling single-atom high-harmonic generation spectra: a time-dependent density-functional scheme.** A. Castro, A. Rubio, and E. K. U. Gross. Eur. Phys. J. B 88, 191 (2015).

**12. Oxidative Addition of the N–H Bond of Ammonia to Iridium Bis(phosphane) Complexes: A Combined Experimental and Theoretical Study.** Betoré, M. P.; Casado, M. A.; García-Orduña, P.; Lahoz, F. J.; Polo, V.; Oro, L. A. Organometallic, 2016, 35, 720-731.

**13. Alkoxycarbonylation of α,β-Unsaturated Amides Catalyzed by Palladium (II) Complexes: A DFT Study of the Mechanism.** Suleiman, R. K..; Polo, V.; El Ali, B. RSC Advances, 2016, 6, 8440-8448.

**14. Theoretical shaping of femtosecond laser pulses for molecular photo-dissociation with control techniques based on Ehrenfest’s dynamics and time-dependent density-functional theory.** Alberto Castro. ChemPhysChem 17, 1439 (2016).

**15. Tailored pump-probe transient spectroscopy with time-dependent density-functional theory: controlling absorption spectra.** Jessica Walkenhorst, Umberto De Giovannini,1, Alberto Castro, and Angel Rubio. Eur. Phys. J. B 89, 128 (2016).

**1.- FP7-NMP-2011-SMALL-5**: Dynamics and control in nanostructures for magnetic recording and energy applications, 7th framework programme, EU

**2.- 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

**3.- 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

**4.- CTQ2012-35665** DISEÑO DE CATALIZADORES ORGANOMETÁLICOS PARA LA ACTIVACIÓN Y FUNCIONALIZACIÓN DE AMONIACO: ESTUDIOS COMPUTACIONALES Y EXPERIMENTALES., IP. Víctor Polo, (2013-2015), 80730€

**5.- 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€

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

Nonlinear Models

and Complexity

and Complexity

**Head of the Research Line:**

Ricardo López-Ruiz

**Researchers:**

López-Ruiz, Ricardo *(University of Zaragoza)*

López, José Luis *(Public University of Navarra)*

Pellicer-Lostao, Carmen *(University of Zaragoza)*

Sañudo, Jaime *(University of Extremadura)*

The science of complex systems is developed from theoretical questions that cross the majority of scientific disciplines. It also responds to a necessity of modern science: the growing number of diverse agents and sophisticated data interacting on several scales demands new models and new strategies to tackle the complexity of the real world.

The natural systems formed by many interacting entities, from the cell to the ecological, social and economic systems as the usual artificial systems which surround us in our everyday life, are motive of inspiration of new models and new ways of thinking and interpretation that deserve attention to be explored and investigated. The emergent properties that are observed at a macroscopic level cannot be guessed from intrinsic properties of the microscopic components, and in general they often result from processes of development and adaptation, where local and global interactions determine the evolution of their dynamics.

The science of complex systems proposes the need to understand and control the increasing complexity we see in the natural and social systems. Understanding complex systems through modeling is doubly constrained by the usual rules of science: the models must provide a reconstruction of the observed data while being as simple as possible. Explanation can be supported on the basis of theoretical advances of the past century but reconstruction involves more than one level of emergence that implies to think the system as a set of entities considered themselves complex. This new science involves biological and human systems and it contributes to reconcile science with social needs. Then it has a great potential to produce important changes in many aspects of human life, from health to business, from structured public administration to networked private organizations.

Our team brings together researchers from different disciplines working on different aspects and problems of complex systems. Specifically, we are concerned with the calculation of complexity indicators in classical and quantum systems, and also our interest extends to the study of different nonlinear models with applications in ecological, economic and communication systems, always looking for elegant (i.e. simple and relevant) explanations and answers.

**CALCULATION OF COMPLEXITY INDICATORS**

**1.- A Statistical Measure of Complexity**, Chapter in the book CONCEPTS AND RECENT ADVANCES IN GENERALIZED INFORMATION MEASURES AND STATISTICS, Kowalski, Rossignoli & Curado (Eds.), Ch. 7, Bentham Science Books, pp. 147-168, 1st Edition in 2013.

**2.- Special Issue on Statistical Chaos and Complexity**, Collection of 14 articles by 36 researchers published in the International Journal of Applied Mathematics and Statistics (IJAMAS), vol. 26, num. 2, pp. 1-179, 2012.

**3.- Statistical Complexity and Fisher-Shannon Information: Applications**, Chapter in the book STATISTICAL COMPLEXITY, K.D. Sen (Ed.), Ch. 4, pp. 65-127, Springer Books, 1st Edition in September 2011.

**4.- Complexity and Stochastic Synchronization in Coupled Map Lattices and Cellular Automata**, Chapter in the open access book STOCHASTIC CONTROL, C. Myers (Ed.), Ch. 4, pp. 59-79, InTech Books, 1st Edition in September 2010.

**ECONOMIC, ECOLOGICAL AND COMMUNICATION MODELS**

**5.- Complex Systems with Trivial Dynamics**, Contributed Talk to ECCS’12, European Conference on Complex Systems 2012, Proceedings of the ECCS’12, Gilbert, Kirkilionis & Nicolis Eds., Part I, pp. 57-65, Springer Proceedings in Complexity, XVII, 2013.

**6.- Geometrical Derivation of Equilibrium Distributions in some Stochastic Systems**, Chapter in the open access book STOCHASTIC MODELING AND CONTROL, I.G. Ivanov (Ed.), Ch. 4, pp. 63-80, InTech Books, 1st Edition in November 2012.

**7.- Notions of Chaotic Cryptography: Sketch of a Chaos based Cryptosystem**, Chapter in the open access book APPLIED CRYPTOGRAPHY AND NETWORK SECURITY J. Sen (Ed.), Ch. 12, pp. 267-294, InTech Books, 1st Edition in Mars 2012.

**8.- Logistic Models for Symbiosis, Predator-Prey and Competition**, Chapter in the ENCYCLOPEDIA OF NETWORKED AND VIRTUAL ORGANIZATION, vol. II, pp. 838-847, 1st Edition in Mars 2008.

**NONLINEAR OSCILLATORS AND APPLICATIONS**

**9.- The Bistable Brain: A Neuronal Model with Symbiotic Interactions**, Chapter in the book SYMBIOSIS: EVOLUTION, BIOLOGY AND ECOLOGICAL EFFECTS, A.F. Camisao & C.C. Pedroso (Ed.), Ch.10, Nova (Biology) Books, pp. 235-254, 1st Edition in December 2012.

**10.- The Limit Cycles of Liénard Equations in the Weakly Nonlinear Regime**, Far East Journal of Dynamical Systems, vol. 11, pp. 277-296 (2009).

**11.- Complex Patterns on the Plane: Different Types of Basin Fractalization in a Two-Dimensional Mapping**, International Journal of Bifurcation and Chaos, TUTORIAL, vol. 13, pp. 287-310, 2003.

**12.- The Limit Cycles of Liénard Equations in the Strongly Nonlinear Regime**, Chaos, Solitons and Fractals, vol. 11, pp. 747-756 (2000).

**1.- Proyecto Teórico MCYT-FIS2009-13364-C02-01: “Acercamiento computacional a la complejidad en redes, proteínas y sistemas de muchos agentes”.**

**2.- Proyecto Teórico MCYT-FIS2006-12781-C02-01: “Complejidad en proteínas, redes y sistemas de muchos agentes”.**

**3.- Proyecto Teórico MCYT- FIS2004-05073-C04-01:”Caracterización-análisis de fenómenos cooperativos en sistemas complejos ideales y reales”.**

- Danièle Fournier-Prunaret
*(INSA, Toulouse, France)*visited us in December 2003 and 2004. - Stefano Boccaletti
*(INOA, Florence, Italy)*visited us in December 2003 and November 2004. - Mario Chávez
*(Hôpital Salpêtrière, Paris, France)*visited us in November 2004. - Juan R. Sánchez
*(UNMdP, Mar del Plata, Argentina)*visited us in September 2005. - Javier González-Estévez
*(UNET, San Cristóbal, Venezuela)*visited us in June 2006, September 2007 and 2010. - Alberto Robledo
*(UNAM, Mexico DF, Mexico)*visited us in May 2008 and October 2009. - Osvaldo Rosso
*(UBA, Buenos Aires, Argentina)*visited us in June 2008. - Xavier Calbet
*(EUMETSAT, Darmstadt, Germany)*visited us in July 2009. - Elyas Shivanian
*(IKIU, Qazvin, Iran)*visited us in July-December 2010. - Mario Natiello
*(LU, Lund, Sweden)*visited us in September 2011.