B.1 Scientific and technological objectives of the project and state of the art

Systems composed of a large number of heterogeneous agents that interact exchanging information often display very complex behaviour that cannot deduced in a simple way by studying the behaviour of the single agent.

Sometimes this behaviour corresponds to the movement of the system in an appropriate abstract configuration space (as, for example, in neural networks); in other cases the system takes different shapes in a two- or three-dimensional space, and we can observe the formation and evolution of characteristic and complex patterns.

This second possibility, where the configurations of the system may be interpreted geometrically, is very interesting, because it allows a graphic representation of the evolution of the system, which can be extremely useful to identify some of the relevant characteristics.

Most of the studies performed up to now have been restricted to systems living in a two-dimensional space. Studying two-dimensional objects brings a large amount of simplifications, both in data taking, visual representation and model building. However, it misses the richness of three-dimensional geometry. Some studies of three-dimensional systems have been done, but quite often the resulting patterns had a rather simple geometric shape.

The aim of the present research is to study a three-dimensional system of complex pattern formation, with the aim of getting a strong insight into many different aspects that are relevant also in more complex situation where the components move in a high dimensional configuration space. Examples of the themes we would like to explore are the mechanisms of decision-making, how information propagates among different agents, up to the level where collective decisions on the evolution of the system are taken.

We believe that a very sound approach to these questions consists in choosing a real phenomenon that is interesting per se, to gather experimental data on its behaviour, to extract characteristic features, to model the system and to compare the results with experiments. This approach, in which experiments, modelization and theory go together, has the advantage of producing a solid concrete experimentally tested knowledge, that can be applied to similar, but not identical, phenomena. Moreover the study of real phenomena often leads to surprises, in that one discovers that new unforeseen mechanisms are needed to explain the experimental behaviour.

With these motivations we have started to try to identify a real problem that should be the subject of this research. We have used the following criteria:

a) The problem should be very interesting also not only because of its interdisciplinary

connections, but also from point of view of the original discipline. Moreover there

should be rather similar problems where the same approach could be used.

b) Highly nontrivial three-dimensional patterns should be formed during the evolution of

the system.

c) It should be possible to gather data not only on the behaviour of the systems as whole,

but also on the behaviour of the single agent. In such a way we will gather very

detailed information and it will greatly help us in the correct choice of the model.

Group animal movements look very promising in these respects, and thus we have decided to concentrate our attentions on the flocking behaviour of starlings, which satisfies all criteria mentioned above. More precisely, we want to study the reasons of particular forms of swarming in order to understand the collective movement of the swarm and its shape in relation to the behaviour of the individuals of the group. We will focus on flocks of starlings and the knowledge we plan to gather can be used to compare their behaviour with that of other birds and of other classes of vertebrates (e.g. schools of fish and groups of primates.)

The behaviour of flocks of moving individuals is a crucial problem in Ethology. It has been studied in relation to the physiological and motivational factors that may regulate animal displacement in space, such as in homing, navigation, and migration. However, the precise decision-making of individuals in a flock, the inter-individual distance among individuals and the cohesive relationship between moving troops need further investigation.

StarFlAG aims at making substantial progresses in this problem, using an interdisciplinary approach where competences from different fields are used. At this end we plan:

a) to obtain very precise and accurate data;

b) to learn in details how to model the movements of a flock;

c) to understand the biological meaning of these movements.

We also have the ambitious plan to try and use the insight that we will obtain in this research in a different field, where there are problems that share some characteristic with the present one. Collective movements are a common phenomenon also in human behaviour, and they are particularly relevant in economics. In fact, we think that is worthwhile to explore the possibility of using the models built for the description of flocking, to describe economic herding behaviours. In this way we hope to get new tools to understand the reasons (elements,

assumptions) of social events, e.g. fashions, social dominance, minorities dominance in choices. In other words, we will have new material for studying how preference functions/dynamic interactions or else can be developed, emphasizing the importance of group externalities, network effects, leading to endogenous economic phase changes.

It is now clear that collective frenzy can sometimes override the rationality needed to make markets efficient, and it leads to persistent anomalies in prices (bubbles and crashes). Indeed these phenomena may be at the heart of the so-called volatility clustering effect in financial markets. It would be extremely interesting to disentangle the various sources of this excess volatility, in particular to understand the contribution of collective effects (herding or feedback) onto the price. This could suggest ways, for the regulators, to act on the organization of markets in order to reduce these spurious effects and tame, to some extent, the variability of these markets.

Although the analogy with starling flocks is loose, it is clear that models of complex collective dynamics are important to understand the behaviour of economic agents, in financial markets but also in more general situations. A recurrent theme is the competition between individual opinions (or motion directions) and the influence of the group. If the influence of the group is sufficiently strong, rapid changes of the collective opinion (motion direction) can appear. This can be detrimental in some cases (crashes, group panics) or favourable (rapid adaptation to a changing environment). Data illustrating these effects can be found both in financial markets, but also in the way new technologies, progressively or discontinuously, invade the markets.

It is evident that this last part of the project is rather risky, however the results of this highly interdisciplinary effort could be very interesting: it is also possible that at the end we will find out that the best model for describing flocking of starlings must use, reversely, some concepts and tools already developed in economics.

Flocking of birds has been the subject of speculations and investigations for many years.Most studies have concentrated on the improvement of feeding rate and on the avoidance ofpredation as the prime advantages of being in a group. Flocks size and positional effects onvigilance (mainly antipredatory) have been studied on a variety of animal species including

several bird species(Elgar 1989; Beauchamp 2003) Flock size, positional effects and intra-specific aggression in European starlings have also been studied (Keys & Dugatkin 1990).

In the literature, differences have been reported in the amount of time spent in surveillance according to the position of an individual within a flock, with birds occupying central positions spending less time vigilant and more time feeding than peripheral birds. An inverse relationship between the proportion of time spent vigilant and flock sizes has been found in many flocking species suggesting that flocking serves a dual function of defence against predation and permitting more efficient feeding (Feare 1984). However, very little information is available on the evolutionary meaning of large starling flocks, particularly at the peak of their wintering season when they congregate in roosts of up to hundreds or thousands of individuals and precise attempt to describe the “rules� and “algorithms� governing their social behaviour in their aerial manoeuvres is are still rather limited.

It is well known, actually, that flock sizes increase as the birds prepare to roost in the evening and close to the roost, where flocks from the surrounding feeding areas coalesce. The number of starlings in a flock, as well as inter-individual distances, are subject to variation. The spacing between birds within flocks is greater in the small spring and summer aggregation, than in the large flocks encountered in winter (Bekoff 1995). A starting hypothesis is that flock size and shape has to exert a great attraction effect during the early wintering phase, when a high number of inexperienced birds, at their first migratory experience, have to cope with the difficulty of selecting both a safe roosting site for spending the winter night and information about foraging site where to find sufficient food to survive.

The observation of movements of flocks of large numbers of starlings show the presence of very interesting patterns that evolve in very short times. This effect is particularly evident and it is part of every-day life (flocks of a hundred to thousands of migratory birds can be often easily observed in urban area, performing rather complex evolutions, especially at sunset). In order to characterize experimentally these movements in a quantitative and qualitative way, it is necessary to get information both on the overall shape and on the movement of the single individuals. We would like to stress that although the movements are in a three-dimensional space, single images give us information only on two-dimensional projections and not too much is known on the three dimensional structure of flocks. Furthermore, we want to evaluate changes in size and shape of flocks of birds in relation to local atmospheric conditions.

Although some information can be obtained from the analysis of two-dimensional pictures, it is imperative to arrive at a three-dimensional reconstruction of the flocks. The StarFlAG project will make full use of modern technology (image processing techniques and computers) to gather truly three-dimensional (3D) data on very large groups, with a high resolution both in space and time. We will use simultaneously three different high-resolution digital cameras with high repetition speed in order to gather information from different angles. Special software will be developed to identify birds in the pictures, to reconstruct their orientation, and velocity and to take care of eventual superposition of different birds on the picture. A second software layer will be dedicated the reconstruction of the three dimensional images. Three different cameras will be used to avoid ambiguities in identifying the same birds in two pictures taken form different angle and the high resolution of the cameras is crucial to get precise three dimensional data. These high-resolution data will be complemented with those of a video camera.

The identification of the single individual position and velocity is a crucial component to reconstruct the three-dimensional structure of the flock. In this respect, it is crucial to identify the corresponding individuals in different image sequences. The knowledge of space and time dependence of the velocity and the single bird acceleration would be crucial to reconstruct the shape of the velocity and of the acceleration field and it would be a crucial step in finding out the control mechanisms of these very fast movements.

In parallel, we will try to develop models to explain how the behaviour of the single animal gives rise to such complex patterns. A close feedback with the experimental data will be crucial in inspiring the models and to discriminate possible differences among them. Once, appropriate models for describing the flocking behaviour of starling have been constructed, we want to understand in detail the mechanism that leads to a coordinated change of direction and possible phase transitions in the shape of the flock. It is difficult to forecast the structure of the model in the absence of experimental data on the movements. At the present stage it seems reasonable to suppose that a model where individuals use mostly the information on the nearest individual could be a viable one. Individuals at the border and in particular the one in the front of the flock may play a special role that should be adequately modelled.

In the past, the ubiquity of collective motion phenomena and the fascination they easily exert have triggered a number of interesting modelling efforts. However, typically such studies aimed at understanding particular situations, and thus have focused on a possibly exhaustive description/determination of all interactions in the system. This has led to detailed data and complicated “realistic� models. These models cannot be treated analytically and even their numerical exploration remains limited to rather small groups. A good example for this kind of approach is the very interesting work of F. Heppner and U. Grenader (1990), who proposed a system of stochastic differential equations with 15 parameters to describe and interpret the strong synchronization within limited-size flocks of birds during turning and landing.

Independently “minimal� models, aiming at capturing the essential, universal features of collective motion phenomena occurring in large groups, have appeared. Such an approach has been taken by the following three different communities: computer animations (for the movie industry), and somewhat later, statistical physicists and biologists.

Computer animators have quickly succeeded in pinpointing the essential ingredients necessary for the emergence of collective and cohesive motion of “boids� (the contraction of “bird-oid�), that they use to name the abstract points moving in a virtual space. Perhaps the first widely known flocking simulation was published by C. Reynolds (1987) who was mainly motivated by the visual appearance of a few dozens of coordinatedly flying objects, among them imaginary birds and starships (he subsequently received an Academy Award for his visualization work).

Biologists (Huth 1992) used a similar approach for schools of fish. These were partly made in 3D (Parrish, Vischido et al. 2002, Couzin, Krause et al. 2003) and in some cases they also included a more realistic representation of body size and shape (Kunz and Hemelrijk 2003). Whereas interesting emergent phenomena have been detected regarding population size, number of influential neighbours, density variations in the school and school form, these models are confined to schools of up to about 100 individuals.

Physicists have reached similar models, but with their own preoccupations, different from the search for realism and efficiency characterizing computer animators. Using the powerful transversal concepts of statistical physics, physicists have obtained interesting general results on the emergence of collective motion in arbitrarily-large groups (see, e.g., Vicsek et. al., 1995), but the connection with real-world situations has been largely lacking, due mostly to the limited nature of the knowledge gathered by biologists and the difficulty of gathering data for very large groups. One of the few sources of experimental data is the effort made, some years ago, to detect and analyse large schools of pelagic fishes in 3D. An EU-funded project, “AVITIS� (FAIR PL96 1717), has led to the use of multibeam sonar to roughly estimate the size, shape and structure of fish schools. This method, though, remains limited in resolution (space and time), and the spirit of the AVITIS project was not of fundamental nature, i.e. not aiming at understanding the emergence of complex collective behaviour, but rather to be of direct applicability to the fishing industry.

Using the language of economic theory we could say that we aim to understand the macro-model and the micro-behaviour inducing it. In many problems studied by economists this goal is very important because it is a crucial step to find appropriate regulation procedures.

In economics the relations between the macro-model and the micro-behaviour is well-studied. It has been usually modelled through externalities in agents utility/profit functions. Positive externalities lead to cooperative behaviour (and/or networks, etc), while competing behaviour happens under negative externalities (differentiation of brands, markets etc). The emergence of coalitions/groups lead to unexpected “dense� sets of choices among symmetric agents (Shy 2001, N. Economides 1994-2004). An extensive branch of game theory deals with social conformity under bounded rationality of differently ranked agents. Differences can be due to “better information� or “status symbol/superstar�, leading to imitation effects (R. Selten, M. Wooders 2001-2003). External signals able to induce “direction� on the market are typically “advertising� in the product market and “news� on the financial markets. Some degree of convergence in the “collective� actions implies that actions and events with low prior probabilities happen with likelihood much greater than expected (the so called “fat tails� in the probability distributions (Mantegna-Stanley 1996, Cont, Potters, Bouchaud 1997).

Regulations have a crucial role in economics. The social aim of regulation is to break coordination leading to dominance of one side of the market with respect to the other. On the product market, this is increasingly monitored by antitrust policies, also on advertising. On financial markets, despite intentions, we notice that derivative volumes, strongly enhancing “direction�, are often concentrated in few hands and that symmetric risk management rules (like institutional values at risk, stop losses, etc) enhance “direction�, worsening free market effects. Moreover, often the “interpretation� of signals is “coordinated� by information networks.

Micro-behaviour, regulations and macro-models will play an essential role in our project and we aim to get a better insight on their mutual influence in concrete complex problems. Our goal is to investigate how the new tools, both theoretical and numerical, developed to simulate birds flocking, can be used to help us to describe and interpret the collective economical phenomena. This will be done by developing the appropriate tools of analysis and models that will be compared with the appropriate economical data. Our goal in this context is to increase our ability in designing and predicting the effects of new efficient regulatory rules.

At a qualitative level we could say that “flocking� phenomena occur in economy and finance. For example people tend to follow others in the hope of making a better deal as they typically assume that others might be better informed. In these cases flocking is in the "action space" instead of ordinary space as in the case of birds, but still there are important analogies including the constraint of acting simultaneously within a short time in reaction to both the actual behavioural pattern of neighbours and to a changing global trend. Moreover Internet-based trading technologies spread low-cost desktop access to continuous auction and dealer markets to more and more trend-following individuals. Mixing in on-line access for algorithmically-based artificially-intelligent traders raises the potential for blindingly-fast volatility, since these silicon traders can react in a infinitesimal fraction of the response time of humans who have dominated the markets up to now.

The rules governing the physical steering of birds and those determining the flocking behaviour of traders are likely to be both different and overlapping. The possible analogies are expected to be mutually beneficial when the corresponding agent-based models are constructed.

B.2 Relevance to the objectives of NEST

StarFlAG is highly interdisciplinary project that aims at innovating the techniques for studying group animal movements by using both sophisticated techniques for recording the data and all tools developed for modeling complex systems composed by a large number of interacting heterogeneous agents. It aims at having a high impact not only on the specific problem addressed (flocking of starlings) but to develop techniques that can be used also in distant areas. We plan to investigate if the results we will find may be used to give us insight into a rather far away problem, i.e. herding in economics.

The problems we will study are relevant for biology and for social sciences; our approach tries to of bridge the gap between the physical sciences and these others disciplines in an effective manner. StarFlAG has a practical, problem-solving, approach, grounded in observation and experimental data: its first objective is data taking. At the same time the study of the flocking movements will be tackled from a complexity-inspired approach, taking into account issues such as emergence of collective behaviour.

The teams are highly interdisciplinary, bringing together competences from many areas of applications. If the approach will be successful, we plan to further generalize the results. The teams have the necessary competencies to do so.

StarFlAG addresses a “well-posed problem� that has been chosen in a way promising significant scientific advance at the frontiers of knowledge and the interface between disciplines. The problem is also methodologically tractable given the current state of knowledge. Also the more speculative part of the project, where one tries to use the progresses done in studying the collective movements of animals in the framework of collective social phenomena, is such that significant steps can be taken in the time allowed for the project.

The StarFlAG project objective matches the objectives of the NEST activity.

• Understanding the mechanisms of complex flocking behavior of starlings is a task that is of great importance for the scientific discipline of Ethology. The techniques and the theoretical framework required for reaching this goal will be developed in this project.
• This project implements the transfer of models and of statistical mechanics tools to the study of three-dimensional animal movements and eventually to the modelling techniques of economics.
• It will play an important role in coordinating and consolidating the community of people working on modelling animal movements and to construct a bridge among people working in this discipline and economists interested in collective effects in the social domain.