This project is structured around three conceptual milestones:
(1) Development of a Science of Complex Systems,
(2) strong transversal component affecting all the scientific objectives proposed, and
(3) interdisciplinarity of the investigated problems.
THE SCIENCE OF COMPLEX SYSTEMS – In the last decades, there has been a steadily increasing interest to transfer methods and concepts belonging to statistical mechanics proper to other scientific areas. In a complementary fashion, the analysis from a global viewpoint of the emerging organization in problems belonging to disciplines external (in principle) to physics, as biology or sociology, has uncovered the parallelisms between collective behaviour in the latter and the formal approaches using in condensed matter physics or complex materials. We are on the way to unifying both the phenomenology observed in those apparently disparate systems and the techniques shared by the study of all of them. In this sense, the groups taking part in this project are well aware of (i) the need to adapt analytical techniques and concepts arising from statistical mechanics to other disciplines and (ii) the advance that can be possibly obtained by understanding the organizational dynamics of systems formed by many interacting agents, in particular those characteristic of biology and sociology, in the language and framework of statistical mechanics at and out-of-equilibrium. These milestones transcend the individual research programme of the groups, but rely on the precise advances they contribute.
TRANSVERSALITY OF OBJECTIVES – The scientific programme of this project is structures in three sublines and ten different objectives. All the suggested tasks involve, completely or partially at least, empirical observations; they require specific models tailored to describe the systems of interest; they have a strong computational component due to their very complex nature; and they develop as far as possible formal and analytical studies. In what follows, we present brief descriptions of the objectives:
(1) Study of quantum effects in static and dynamic properties of molecules and solids. The thermodynamic and kinetic properties of light atoms, especially hydrogen, cannot be properly described without taking into account quantum effects. Our goal is to develop a simulation code able to perform this calculation, and to apply it to the study of the following systems: Water and ice; diffusion of light defects in semiconductors and graphene; phase diagram of neon and the diffusion of hydrogen in a matrix of disordered nano-spheres. Apart from quantum nuclear effects we will study some electronic properties that can only be described through the quantum formalism, among them ultra-small semiconductors, organic structures, and graphene. This objective shares techniques with objectives 2, 3, and 4.
(2) Study of the properties of complex fluids, polymers, and liquid crystals. We will study the structural and thermodynamic properties of some complex fluids and their mixtures. Simulations on dendrimers (nano particles with application in catalysis), drug transport and lubricants will be performed. The smectic phase in polydisperse solutions of platelets will be studied from a theoretical viewpoint; we will develop a hybrid method to study defects in liquid crystals. This objective shares techniques with objectives 1, 3, and 4; its results are of interest for the study of soft biological matter (objective 5); conceptually, it is close to the study of heterogeneous populations (objective 6) here from a static viewpoint.
(3) Study of the behaviour of confined systems and interfaces. Here we will study the properties of non-homogeneous fluids. When a fluid is confined inside a material or in contact with a solid wall, it presents non-homogeneous profiles that try to minimize its free energy. Interfaces also appear when the fluid coexists in two phases (liquid and vapour, for instance). We will focus in the study of phases and phase transitions, and in self-assembly phenomena. Confinement modifies these effects, increasing or inhibiting them in different situations, even changing their very nature (as order in a phase transition). The techniques to be used go from the design of models and their formal analysis to experiments, and include computational simulation that will require developing specific, system-dependent methods. Recently, the UAM and ICMM groups have established the link the CWT and the microscopic level by means of the Intrinsic Sampling Method (ISM), which constitutes an excellent tool to extract relevant information regarding the microscopic structure of interfaces from molecular simulations. The ISM allows for an identification of those particles pertaining to the liquid and those to the vapour phase for each sample configuration along a simulation run. Thus it is possible to define an intrinsic surface separating vapour and liquid phases. In the preceding research program (MOSSNOHO-CM) this methodology was successfully applied to the study of liquid-vapour interfaces in metals, water, and recently water-hydrofobic liquid interfaces. In the present program, the ISM methodology will be a key point to enhance the collaboration among various groups, in order to tackle different problems. We will focus in the study of thermal fluctuations at interfaces (liquid-vapour, liquid-liquid, membranes, etc.). This objective shares techniques with objectives 1, 2, 4, and 5. The presence of non-trivial fluctuations and phase transitions is observed in almost all systems studied in this project, especially in systems tacked in objective 1 (water), 5 (membrane formation), 6 (quasispecies), and 9 (dynamics on complex networks).
(4) Analysis of dynamical features and hydrodynamic description of condensed matter. We will study the dynamics of complex molecules as fluxes, the interface dynamics of a mixture of colloids and polymers in solution, and the forces induced by fluctuations. We will also perform experiments on the vitreous transition in polymers, both confined and non-confined, and on the behaviour of a two-dimensional granular system subject to vibrations. Apart from the clear implication this objective has for objectives 1, 2, and 3 it can produce results of potential application to our understanding of systems studied in objective 5, and systems extended in space or with geometrical restrictions (objectives 6 and 7).
(5) Study of vesicle properties through models involving realistic characteristics of the self-assemly process of amphiphilic aggregates, and of membrane duplication. We intend to formulate coarse-grained models for the molecular constituents of double-layer membranes (including a more realistic description of the solvent), with the goal of studying different features of the self-assembly of amphiphilic aggregates, among them aggregation kinetics, volumetric properties of the fluid and its properties in confinement, adsorption of aggregates on substrates versus the formation of Langmuir monolayers, the influence of composition in mixtures of aggregates, and the properties of simple aggregating processes versus the effects of interaction among vesicles at high volumetric fraction. Some of these processes involve dynamical phase transitions that will require the development of new methods. We expect to integrate the models of membrane deformation with those describing self-assembled filaments, with the eventual goal of characterizing the formation and dynamics of the septal ring. Part of the tasks to be developed in this objective rely on the knowledge provided by the investigation performed in objectives 2, 3, and 4. The study of how environmental and intrinsic conditions affect the final state attained by a population is shared by objectives 6 and 7.
(6) Study of environmental and molecular features responsible for the fast adaptation of quasispecies, with the end of identifying mechanisms inducing extinction. Quasispecies will be described through phenomenological models as well as through explicit populations of sequences. We intend to analyse the effect of different physical environments: explicit space, affecting individual transport; regular and stochastic fluctuations in selection pressures; and the presence of correlations of different character in the genome space. All these analyses are motivated by empirical observations in viral quasispecies, in molecular quasispecies (RNA) and in the distribution of diversity in other natural systems. The relationship between pattern and process is an important aspect of the study of these complex populations, shared by objectives 2, 3, and 5. The relationship with objectives 7 (through the relationship between quasispecies and metapopulations), 8 (topology of the genome space), 9 (dynamics on neutral networks) and 10 (defectors versus cooperators) is even closer.
(7) Development of self-assembly realistic models with the goal of studying the characteristics of ecosystems and predicting its expected evolution under the stress exerted by human activity. One of the most promising tools to study ecosystem construction and the emergence of its complex structure is self-assembly models. A set of species is assembled one by one through a succession of invasions. The ecosystem is thus built up as new species arrive, adopting a conformation resistant to new invasions or extinctions. In cases where ecological niches are different, the symmetry between invading species is broken, such that different clades can be distinguished. An example is mutualistic networks. An open question is how those networks are constructed, in particular, under which selective pressures do they develop the high degree of nestedness observed. The construction of complex ecosystems has parallelisms with the self-organization of complex heterogeneous materials (objective 2) and is constrained by the geometry of the environment (objectives 4 and 5). The organization in metapopulations admits a description formally analogous to that of quasispecies on a neutral network (objective 6 and 9). Cooperative interactions (objective 10) play an important role in the structure of the ecosystem.
(8) Study of topological properties of different complex networks and their implications on processes such as transmission information or the resistance to attack and failure. We will study (i) the topology of neutral networks of RNA viruses, analysing their degree distribution, clustering, degree-degree correlations, and the presence of hierarchical or community organization in the network; (ii) brain connectivity networks from data obtained from electroencephalograms and magnetoencephalograms, where the network is extracted from the signal obtained through electrodes (nodes) measuring the activity in different brain areas, and considering a connection between two such areas when their activity is correlated; (iii) recommendation networks, that is bipartite networks characterized by a large number of nodes (users/papers) and where connections are based on already performed or future buys of users. This objective also includes the development of statistical methods to transform time series into complex networks. Its results are of use to the study of complex molecular populations (objective 2) and other natural populations (objectives 6, 7, and 9), and can be especially relevants to analyse social interactions (objective 10).
(9) Study of dynamical processes of and on complex networks by means of including dynamical systems on each node, and allowing the reorganization of the network structure. This objective focuses on the study of processes taking place in/on a network when its nodes are dynamical systems and, simultaneously, changes in network structure are permitted. We will implement Ising model on small-world and scale-free networks, and our plan is to extend these studies to the antiferromagnetic Ising model. Advancing in the study of biological networks, we plan to analyse the degree of nestedness in mutualistic networks. Finally, we aim at proposing different evolutionary models able to explain the topological features of the different complex networks, studying among others the evolution of the network through genetic algorithms. As has been said, this objective shares tasks, overlaps in its tools or has implications in objectives 3, 6, 7, and 8.
(10) Study of the emergence and sustainability of cooperation in biological systems and social environments. The goal of this objective is to design models adapted to real situations (biological or social) where sustained cooperation, against intuition, is observed. Interactions will be modelled through spatial extended game theory. We will apply analytical techniques and multi agent simulations to study the emerging behaviour, trying to justify the mechanisms inducing cooperation. In the social context, we will carry out experiments on a web platform to identify the trend to cooperate or defect in human groups under controlled conditions. The final aim is to formulate general principles to advance in our understanding of how cooperation emerges in a given situation. Data analysis, the properties of the systems, the acting mechanisms, and the results to be obtained have analogies with the studies proposed in objectives 6, 7, and 8.
INTERDISCIPLINARITY OF SCIENTIFIC OBJECTIVES – While the scientific objectives of this project are heterogeneous, this consortium is relatively homogeneous regarding the background of participating scientists, mostly physicist of condensed matter or complex systems. In the last ten years, the research of some of the groups has approached other scientific fields, with the result that collaborations with groups in other institutions, with specialists in complementary experimental techniques or with different backgrounds has become mandatory. This is the reason that we have a number of external collaborators, which contribute their experience there where our own background becomes insufficient. In this same direction, we highlight the participation of two associated members, Bmat and Innaxis, with interest in the potential applicability of the results derived from this project. GISC-UC3M and UPM collaborate with the group of Jordi Bascompte (field ecology, theoretical biology and evolution) in the Estación Biológica de Doñana, CSIC; CAB maintains regular collaborations with researchers from that center (Ester Lázaro, viral dynamics; Carlos Briones, RNA world) and with the group of Esteban Domingo (evolution of RNA viruses) in the Centro de Biología Molecular “Severo Ochoa” (UAM-CSIC); GICS-UC3M collaborates with an economist hired by the group itself, as well as with Miguel Angel Zavala, from the Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria (INIA). Other collaborators of this group are: Giorgio Cinacchi, University of Bristol, UK; Zhengdong Cheng, Texas A&M University, US; Szabolcs Varga, University of Pannonia, Veszprém, Hungary; István Szalai, University of Pannonia, Veszprém, Hungary; Luis Lafuente, Universidad de Sevilla; Andrew O. Parry, Imperial College London, UK; Rob Beardmore, Imperial College London, UK; and Michael E. Cates, University of Edinburgh, UK. The group URJC has been collaborating in the last years with the company Bmat in optimizing recommendation systems in sociale networks. It has also collaborated with members of Innaxis in characterizing spatially extended networks. Finally, thel group GISC-UCM maintains collaborations with: Chris van der Broeck, Universidad de Hasselt, Belgium; Frank Jülicher, Max Planck Institute for the Physics of Complex Systems, Dresden, Germany; Rodrigo Soto, Universidad de Chile, Chile; Victor A. Malyshev and J. Knoester, University of Groningen, Holland; Cord Müller, University of Bayreuth, Germany; Vittorio Bellani, University of Pavia, Italy; Rudolf Römer, Unirsity of Warwick, UK; Rudolf Hey, Paul Drude Institute, Germany; Pedro Orellana, Universidad Católica del Norte, Chile; Enrique Diez, Universidad de Salamanca, Spain; Ara Sedrakyan, Yerevan Institute of Physics, Armenia; Marcelo Lyra, Universidade Federal de Alagoas, Brasil; and Constantino Tsallis, Centro Brasileiro de Pesquisas Físicas, Brasil.
