José Halloy. Université Libre de Bruxelles (ULB) International Solvay Institutes for Physics and Chemistry

Transcription

1 José Halloy Université Libre de Bruxelles (ULB) Centre for Nonlinear Phenomena and Complex Systems Department of Social Ecology International Solvay Institutes for Physics and Chemistry

2 Outline of this presentation * Introduction on emergent behaviour - general concepts - examples in animal populations * Natural vs artificial complex systems * Methodology, framework & toolbox * Putting artificial complex systems at work non-exhaustive suggestion list

3 * Classically, problem-solving is based on the "Knowledge" of a central unit which must take the decisions and collect all necessary information. * However an alternative method is extensively used in nature: the method of collective behaviour. In such systems, consisting of a large number of events, the problems are collectively self-solved in real time through the simple behaviour of the units, which interact with each other and with the environment. * Imperfect information, randomness and amplifying communication play a key role.

4 Natural complex systems * Dynamical systems with a large number of events, it does not mean a large number of agents * Descriptions based on models with a limited number of parameters are possible * The size of the population plays an important role * The characteristics of communication play an important role (all to all, next neighbours, etc) * Privileged linked between some agents also may play an important role * The possibility to suppress resources may play an important positive role * Noise and randomness is a positive ingredient to find optimal solutions * Biological systems are not fully self-organised complex systems, they present a mix between centralised and distributed management * Well known experimental and theoretical examples are found in animal societies which are conceptually closer to artificial systems than to their bio-molecular level! Actually, a limited number of simple generic rules are at work in biological systems (from the cellular level to animal societies) and produce optimal emergent collective patterns for resources and work allocation, synchronisation or de-synchronisation without external pacemaker, clustering and sorting

5 Concepts * Emergent behaviour and self-organisation By emergent behaviour we mean a collective behaviour that is not explicitly programmed in each individual but emerge at the level of the group from the numerous interactions between these individuals that only follow local rules (no global map, no global representation). * Randomness Individual actions include a level of intrinsic randomness. An action is never certain but has an intrinsic probability of occurring. The behaviour of each individual becomes then less predictable. The predictability of a system depends also on the level of description and the type of measures done. Randomness and fluctuations play an important role in allowing the system to find optimal solutions. In some cases, there is even an optimal level of noise that contributes to the discovery of optimal solutions. This noise is either at the level of the individuals or the interactions. It can be controlled in artificial systems and modulated in living systems. * Predictability The global outcome of population presenting emergent behaviour is certain in well characterised systems. For instance, the result of emergent collective foraging in ant colonies is certain and efficient. Ants do bring food home or they simply die! Because often the system present multiple possible states coexisting for the same conditions, the specific solutions that accomplish the global behaviour at the level of the group are statistically predictable. For instance the optimal solution to solve a problem is chosen in 85% of the cases while a less optimal solution is selected in 15% of the cases. Nevertheless, the problem is solved in 100% of the cases! The discussion is then shifted towards knowing if 15% of suboptimal behaviour is acceptable and not if the global outcome is predictable. * Evolution and emergent behaviour We think that emergent behaviour is not an equivalent of evolution or even a necessity for evolution to take place. Emergent behaviour does not produce, in itself, new and unexpected behaviour.

6 Self-organised populations * Action and decision are simultaneous and mixed: through the action decisions are taken * Only limited cognitive capabilities of agents are needed to collect and treat information * Tasks or resources allocation between agents is flexible and autonomous * Agents can be unpredictable and no there is no need for a perfect knowledge * Alternative to predict all the needs of an agent population at anytime

7 Natural vs artificial complex systems * It is not a question of biological relevance but about appropriate context of use. * The first point is rather obvious, emergent behaviours appear most useful in real persistent populations of individuals that have to cooperate. * Some applications of the so called ant algorithms do not really fall into this category. Indeed, the population is just momentarily and artificially created to solve the problem like when solving an optimisation problem with an ant algorithm. The problem is solved a priori and then the solution is implemented in a centralised manner. Even if this approach might be interesting, we think that it is somehow diverging from the core logic of emergent behaviour. It is not a question of biological relevance but about appropriate context of use * Emergent behaviour is very useful when the decision has to be taken while action takes place. * It means for example, that there is no possibility to stop the system, to make an optimisation computation and to start it again. When ants are looking for the best source of food with the shortest path they find the optimal solution by working out, by walking the computation (in the literal meaning of the word walk!) and not by stopping solving an optimisation problem and then implementing it. This implies that it takes some time before an optimal solution is found, during this time the colony explore and make use of all available possibilities.

8 Natural examples of emergence * Spatial pattern formation - nest building - trail network - aggregation patterns * Collective choice - food source - settlement place - strategies selection * Regulation of activity * Synchronization or de-synchronization of activity * Social differentiation & division of labour

9 Termites Macrotermes michaelseni (Sjöstedt) J.S. Turner. Cimbebasia 16: (2000).

10 Nest Casting and Digging Dynamics volume excavated (cm3) workers 50 workers 100 workers time (day) * The form of the building is variable in terms of shape and number of galleries * There is regulation i.e. excavated volume per individual is constant * The global structure is preserved (rooms, galleries, etc.)

11 Others examples in vertebrates

12 Example at the cellular level Life cycle of social amoebas (Dictyostelium discoideum) transition from solitary state to multi-cellular organism Lauzeral, Halloy & Goldbeter, Proc Natl Acad Sci U S A. 1997

13 MECHANISMS Local knowledge of the units: complexity/diversity of collective responses without being explicitly coded at the individual level. Parsimony of decision-rules & Simple information transfer Multiple events modify the characteristics of the system & provide new stimuli for further interactions.

14 A large number of scripts are associated to the competition (in space and/or time) of behavioural positive feed-back Negative feed-back is often a by-product of the exhaustion of the resources. Collective choices / Patterns

15 Methodology, framework & toolbox * Experiments at the laboratory (significant number of repetitions!) * Theoretical Tools from dynamical systems theory * Models based on differential equations (ODE, PDE) * Model based on stochastic equations * Stochastic computer simulation or agents based simulations * Numerical experiments - computer simulations Experimental & theoretical results Validated models Predictions

16 Putting artificial complex systems at work non-exhaustive suggestion list * Networks of collaborative computers * Networks of collaborative sensors * Populations of collaborative robots * Network of collaborative transport * Network of collaborative computerised human beings

17 Natural vs artificial complex systems * We need to identify artificial systems (groups of machines and software) where the known rules from natural systems can be applied to produce robust, optimal and autonomous behaviours * We need to translate, mutatis mutandis, those rules into practical algorithms. It also corresponds to the transition from different level of description like for example, from physiology to behaviour or from hardware to software. * We need to pinpoint where the balance between fully distributed and centralized control lies as a function of the task the system is accomplishing or the artificial system has to be designed for. * We need to close the strong cultural gap in methodologies between complex systems science and engineering (model building, computer simulations, experiments, framework, etc.) Engineering complex systems. The emergent properties of complex systems are far removed from the traditional preoccupation of engineers with design and purpose (Nature 427,29 January 2004)

18 Collective choice between two equivalent shelters Experimental setup

19 N = 50 Repartition:50%-50% X1 N S Repartition:95%-5% 2 S S 1 1 S S Sc N 85 Total carrying capacity= 2S

20 Two identical shelters S >>N (No crowding effect) larvae Cockroach: Blatella germanica Fration of experiments larvae Fraction shelter 1 (Rivault & Cloarec, 1998; Rivault et al, 1999; Amé et al, 2004)

21 FRACTION OF EXPERIMENTS S 100 S 55 S N=

22 . Collective response not observed S = 30 Fraction in one shelter Surplus 70 N

23 Three identical shelters S >>N= 50 (No crowding effect) X w = 6/X 2nd = 6/X 3rth 48 >>X = X 2nd 3rth X w <# of individuals> RANK

24 . S=30 100% Fration in 1 shelter % 50% 33% 33% 33% N

25 Aggregation choice between 2 different shelters 21 experiments Number of experiments T= 60 min A n = 20 T = 120 min B Proportion of cockroaches under the shelter B

26 FRACTION OF EXPERIMENTS Two strains (10-10) β> Fraction Shelter 1 (Rivault et al, 1999)

27 Collective choice between 2 different shelters Mean number of individuals under shelters n = 8 light shelter dark shelter Winner: light shelter light shelter dark shelter n = Time (min) Winner: dark shelter

28 Dynamical systems framework mean field ODE model for 2 identical shelters dx 1 dt x 1 =μ 1 S N x x x θ n k x 1 dx 2 dt x 2 =μ 1 S N x x x θ n k x 2 x 1 x 2 x e =N

29 Dynamical systems framework mean field ODE model: only 6 parameters (5) dx 1 dt dx 2 dt x 1 =μ 1 x 2 =μ 1 θ S N x x x n k x 1 θ S N x x x n k x 2 x 1 x 2 x e =N x 1 =x 2

30 Mean field ODE model Bifurcation diagrams for varying S with 3 or 4 shelters

31 Mean field ODE model Bifurcation diagrams for varying N with 3 or 4 shelters x 1 =x 2 =x 3 x 1 =x 2 =x 3 =x 4

32 Optimal response of the group Benefit/Individual B=x x 1 x S x S x 2 (1-x/S) 1 (benefit of being together) (cost of crowding) S>Population 0,8 0,6 0,4 0,2 S<Population (see also Dussutour et al, 2004) % Population in the left shelter

33 Specifications of the Insbot * Behavioural programs (exploratory walk, probabilities of actions, etc.) * Detection of obstacles * Identification of insects ( counting neighbours) * Identifications of Insbots ( counting neighbours) * Detection of the shelters and their quality (light intensity, ) Prediction of the behavioural patterns of the Insbot * If specifications are fulfilled ;-) * Using the solutions of the model and some computer simulations -> We can forecast the global outcome in a given experimental setup -> We can estimate the parameters range to obtain desired pattern -> We can add features to the robot to produce new patterns or add supplementary emergent behaviours (or not emergent even centralised!)