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

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

A question of scale

If you search for 'collective behaviour' with your web browser most of the texts popping up will be about group activities of humans, including riots, fashion and mass panic. Nevertheless, collective behaviour is also considered to be an important aspect of observed phenomena in atoms and molecules, for example, during spontaneous magnetization. In your web search, you might also find articles on collectively migrating bacteria, insects or birds; or phenomena where groups of organisms or non- living objects synchronize their signals or motion (think of fireflies flashing in unison or people clapping in phase during rhythmic applause).Comment: Concepts essay, published in Nature http://www.nature.com/nature/journal/v411/n6836/full/411421a0.htm

The kinesin walk: a dynamic model with elastically coupled heads

Recently individual two-headed kinesin molecules have been studied in in vitro motility assays revealing a number of their peculiar transport properties. In this paper we propose a simple and robust model for the kinesin stepping process with elastically coupled Brownian heads showing all of these properties. The analytic and numerical treatment of our model results in a very good fit to the experimental data and practically has no free parameters. Changing the values of the parameters in the restricted range allowed by the related experimental estimates has almost no effect on the shape of the curves and results mainly in a variation of the zero load velocity which can be directly fitted to the measured data. In addition, the model is consistent with the measured pathway of the kinesin ATPase.Comment: 6 pages, 3 figure

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

Collective motion of cells: from experiments to models

Swarming or collective motion of living entities is one of the most common and spectacular manifestations of living systems having been extensively studied in recent years. A number of general principles have been established. The interactions at the level of cells are quite different from those among individual animals therefore the study of collective motion of cells is likely to reveal some specific important features which are overviewed in this paper. In addition to presenting the most appealing results from the quickly growing related literature we also deliver a critical discussion of the emerging picture and summarize our present understanding of collective motion at the cellular level. Collective motion of cells plays an essential role in a number of experimental and real-life situations. In most cases the coordinated motion is a helpful aspect of the given phenomenon and results in making a related process more efficient (e.g., embryogenesis or wound healing), while in the case of tumor cell invasion it appears to speed up the progression of the disease. In these mechanisms cells both have to be motile and adhere to one another, the adherence feature being the most specific to this sort of collective behavior. One of the central aims of this review is both presenting the related experimental observations and treating them in the light of a few basic computational models so as to make an interpretation of the phenomena at a quantitative level as well.Comment: 24 pages, 25 figures, 13 reference video link

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