Controlling edge dynamics in complex networks

The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the last decade, with considerable advances in the description of their structural and dynamical properties. However, much less effort has been devoted to studying the controllability of the dynamics taking place on them. Here we introduce and evaluate a dynamical process defined on the edges of a network, and demonstrate that the controllability properties of this process significantly differ from simple nodal dynamics. Evaluation of real-world networks indicates that most of them are more controllable than their randomized counterparts. We also find that transcriptional regulatory networks are particularly easy to control. Analytic calculations show that networks with scale-free degree distributions have better controllability properties than uncorrelated networks, and positively correlated in- and out-degrees enhance the controllability of the proposed dynamics.Comment: Preprint. 24 pages, 4 figures, 2 tables. Source code available at http://github.com/ntamas/netctr

Hierarchical self-organization of non-cooperating individuals

Hierarchy is one of the most conspicuous features of numerous natural, technological and social systems. The underlying structures are typically complex and their most relevant organizational principle is the ordering of the ties among the units they are made of according to a network displaying hierarchical features. In spite of the abundant presence of hierarchy no quantitative theoretical interpretation of the origins of a multi-level, knowledge-based social network exists. Here we introduce an approach which is capable of reproducing the emergence of a multi-levelled network structure based on the plausible assumption that the individuals (representing the nodes of the network) can make the right estimate about the state of their changing environment to a varying degree. Our model accounts for a fundamental feature of knowledge-based organizations: the less capable individuals tend to follow those who are better at solving the problems they all face. We find that relatively simple rules lead to hierarchical self-organization and the specific structures we obtain possess the two, perhaps most important features of complex systems: a simultaneous presence of adaptability and stability. In addition, the performance (success score) of the emerging networks is significantly higher than the average expected score of the individuals without letting them copy the decisions of the others. The results of our calculations are in agreement with a related experiment and can be useful from the point of designing the optimal conditions for constructing a given complex social structure as well as understanding the hierarchical organization of such biological structures of major importance as the regulatory pathways or the dynamics of neural networks.Comment: Supplementary videos are to be found at http://hal.elte.hu/~nepusz/research/supplementary/hierarchy

Complexity: The bigger picture

If a concept is not well defined, there are grounds for its abuse. This is particularly true of complexity, an inherently interdisciplinary concept that has penetrated very different fields of intellectual activity from physics to linguistics, but with no underlying, unified theory. Complexity has become a popular buzzword used in the hope of gaining attention or funding -- institutes and research networks associated with complex systems grow like mushrooms. Why and how did it happen that this vague notion has become a central motif in modern science? Is it only a fashion, a kind of sociological phenomenon, or is it a sign of a changing paradigm of our perception of the laws of nature and of the approaches required to understand them? Because virtually every real system is inherently extremely complicated, to say that a system is complex is almost an empty statement - couldn't an Institute of Complex Systems just as well be called an Institute for Almost Everything? Despite these valid concerns, the world is indeed made of many highly interconnected parts over many scales, whose interactions result in a complex behaviour needing separate interpretation for each level. This realization forces us to appreciate that new features emerge as one goes from one scale to another, so it follows that the science of complexity is about revealing the principles governing the ways by which these new properties appear.Comment: Concepts essay, published in Nature http://www.nature.com/nature/journal/v418/n6894/full/418131a.htm

Modeling the emergence of modular leadership hierarchy during the collective motion of herds made of harems

Gregarious animals need to make collective decisions in order to keep their cohesiveness. Several species of them live in multilevel societies, and form herds composed of smaller communities. We present a model for the development of a leadership hierarchy in a herd consisting of loosely connected sub-groups (e.g. harems) by combining self organization and social dynamics. It starts from unfamiliar individuals without relationships and reproduces the emergence of a hierarchical and modular leadership network that promotes an effective spreading of the decisions from more capable individuals to the others, and thus gives rise to a beneficial collective decision. Our results stemming from the model are in a good agreement with our observations of a Przewalski horse herd (Hortob\'agy, Hungary). We find that the harem-leader to harem-member ratio observed in Przewalski horses corresponds to an optimal network in this approach regarding common success, and that the observed and modeled harem size distributions are close to a lognormal.Comment: 18 pages, 7 figures, J. Stat. Phys. (2014

Collective motion of organisms in three dimensions

We study a model of flocking in order to describe the transitions during the collective motion of organisms in three dimensions (e.g., birds). In this model the particles representing the organisms are self-propelled, i.e., they move with the same absolute velocity. In addition, the particles locally interact by choosing at each time step the average direction of motion of their neighbors and the effects of fluctuations are taken into account as well. We present the first results for large scale flocking in the presence of noise in three dimensions. We show that depending on the control parameters both disordered and long-range ordered phases can be observed. The corresponding phase diagram has a number of features which are qualitatively different from those typical for the analogous equilibrium models.Comment: 3 pages, 4 figure

Anomalous segregation dynamics of self-propelled particles

A number of novel experimental and theoretical results have recently been obtained on active soft matter, demonstrating the various interesting universal and anomalous features of this kind of driven systems. Here we consider a fundamental but still unexplored aspect of the patterns arising in the system of actively moving units, i.e., their segregation taking place when two kinds of them with different adhesive properties are present. The process of segregation is studied by a model made of self-propelled particles such that the particles have a tendency to adhere only to those which are of the same kind. The calculations corresponding to the related differential equations can be made in parallel, thus a powerful GPU card allows large scale simulations. We find that the segregation kinetics is very different from the non-driven counterparts and is described by the new scaling exponents $z\simeq 1$ and $z\simeq 0.8$ for the 1:1 and the non-equal ratio of the two constituents, respectively. Our results are in agreement with a recent observation of segregating tissue cells \emph{in vitro}

Collective decision making in cohesive flocks

Most of us must have been fascinated by the eye catching displays of collectively moving animals. Schools of fish can move in a rather orderly fashion and then change direction amazingly abruptly. There are a huge number of further examples both from the living and the non-living world for phenomena during which the many interacting, permanently moving units seem to arrive at a common behavioural pattern taking place in a short time. As a paradigm of this type of phenomena we consider the problem of how birds arrive at a decision resulting in their synchronized landing. We introduce a simple model to interpret this process. Collective motion prior to landing is modelled using a simple self-propelled particle (SPP) system with a new kind of boundary condition, while the tendency and the sudden propagation of the intention of landing is introduced through rules analogous to the random field Ising model in an external field. We show that our approach is capable of capturing the most relevant features of collective decision making in a system of units with a variance of individual intentions and being under an increasing level of pressure to switch states. We find that as a function of the few parameters of our model the collective switching from the flying to the landing state is indeed much sharper than the distribution of the individual landing intentions. The transition is accompanied by a number of interesting features discussed in this report

Az embrionális érhálózat önszerveződése = Self-organization of the embryonic vascular network

Kutatásaink az önszervezően, sok hasonló sejt kölcsönhatása révén létrejövő biológiai rendszerek, ezen belül elsősorban az embriófejlődés során kialakuló érhálózat és extracelluláris mátrix (ECM) tulajdonságainak vizsgálatára irányultak. A kutatómunka szerves része volt a sejtek viselkedésének megfigyelését lehetővé tevő mikroszkópos és statisztikai elemzés technikák kidolgozása is. Bevezettünk, és madárembriókon végzett kísérletekkel alátámasztottuk a fejlődő szöveteknek egy olyan képét, amelyben a szövet deformációira szuperponálódik a szövetbe ágyazott sejtek aktív (és korrelálatlanabb) mozgása. Megmutattuk, hogy a kezdeti érhálózat -- számos korábbi elképzeléssel ellentétben -- egy, az axonnövekedéshez nagyon hasonló sejtinvázióval történik. Sejttenyészetek in vitro viselkedésének analizálásával rámutattunk, hogy a lineáris szegmensek kialakításának egyik fontos mozgatóeleme a sejtek megváltozott mozgása erősen anizotróp környezetben. Ezekre az emprikus megfigyeléseinkre alapozva felállítottuk a vaszkulogenezis egy új elméleti modelljét. Feltérképeztük a korai embriogenezist jellemző szövetmozgásokat madárembriókban. Megmutattuk, hogy a gasztruláció folyamatát kísérő szövetmozgások jól leírhatók egy olyan tovaterjedő mintázatként, ami az embrió mindkét oldalán egy-egy, ellentétes irányban forgó örvényt tartalmaz. Mint a szövetalkotás egyik fő lépését, elemeztük a sejt-ECM kölcsönhatások szerepét a mintázatképzésben. | The research investigated self-organization phenomena in multicellular systems, especially the formation of blood vessel network during embryogenesis. Improvements in automatic microscopy techniques as well as image processing algorithms were also integral part of the research. Based on experimental analysis of delepoing bird embryos we introduced a mechanicl framwork desribing embryonic tissues, where cell autonomous motion is superimposed upon large-scale (convective) tissue movements. We showed that the early vascular network forms through a multicellular sprouting proess, somewhat reminescent to axon growth. Using in vitro cell cultures we showed that the formation of linear segment is a consequence of altered cell behavior in anisotropic environments. Based on these observations, we created a new theoretical model for vasculogenesis. We also mapped the large-scale tissue movements during embryogenesis. In bird embryos tissue movements during gastrulation form a travelling wave-like pattern containing a vortex on either side of the embryo. As a crucial step during tissue formation, we analyzed cell motion-mediated patterning of the extracellular matrix