Rawan Ghnemat

Cyrille Bertelle

Gérard H E Duchamp

Modeling Spatial Organization with Swarm Intelligence Processes

Keywords: Swarm intelligence, complex systems, self-organization, ant systems, spatial organization

Urban Dynamics modeling needs to implement spatial organization emergence in order to describe the development of services evolution and their usage within spatial centers. In this paper, we propose an extension of the nest building algorithm with multi-center, multi-criteria and adaptive processes. We combine a decentralized approach based on emergent clustering mixed with spatial constraints or attractions. Typically, this model is suitable to analyse and simulate urban dynamics like the evolution of cultural equipment in urban area.

1 Introduction: From Urban Dynamics to Complex Systems Urban systems have emergent properties based on their spatial development. This spatial development is both the result of some mecanisms from the system behavior and the actor of the system formation by morphogenetic feedback. The goal of this paper is to study some computable mecanisms and algorithms able to model such spatial self-organization processes, taking into account the complexity of the phenomena.

Complex system theory (Le Moigne, 1999) is based on the fact that, for many applicative domains, we can find similar processes linking emergent global behavior and interaction network of constituents. The global behavior is generally not accessible using classical analytical methods.

In classical analytical methods, the global behavior of the system is the description of the equations. Simulations from these formulations consist in obtaining the trajectories of the behavior predefined by the equations.

In complex systems modeling, we have to model the constituents of the system and the interaction network or system which links these constiuents, using a decentralized approach. So the global behavior of the system cannot be understood by the description of each constituent. In complex system modeling, the global Complexity of geographical space with respect of emergent organizations

behavior is an emergent property from the interaction network or systems between its constituents which leads to the creation of a dynamical organization of these constituents. This dynamical and emergent organization retro-acts on its own components. Two kinds of feedbacks allow to describe these phenomenon. The positive feedback means that the emergence increases the organization constitution. the negative feedback means that the emergence has regulator properties which will finally stop the increasing organization constitution and allow the system stabilization.

Another major aspect of complex systems is that they can be considered as open systems. This means that they are crossed by energetical fluxes that make them evolve in a continuous way. From these energetical fluxes, complex systems can evolve through critical states, using bifurcation schema and attractors behaviors. One of the major vector or support of these energetical fluxes is the environment itself where the complex systems and their entities evolve. In many natural and artificial systems, the environement has some spatial effects which interact on the whole complexity of the phenomenon. This spatial environment can be modified by the system but he can also be the catalyst of its own evolution. Understanding and modelling the deep structural effect of the interaction between the systems and its spatial environment is the goal of the study presented in the sequel.

Social and human developments are typical complex systems. Urban development and dynamics are the perfect illustration of systems where spatial emergence, self-organization and structural interaction between the system and its components occur. In figure 1, we concentrate on the emergence of organized systems from geographical systems. The continuous dynamic development of the organization feed-back on the geographical system which contains the organization components and their environment. To analyse or simulate urban dynamics, nowadays, we can use the great amount of geographical databases directly available for computational treatment within Geographical Information Systems. On the organizational level description, the new development of multiagent systems (MAS) allows nowadays to develop suitable models and efficient simulations.

The applications we focuss on in the models that we will propose in the following concerns specifically the multi-center (or multi-organizational) phenomona inside urban development. As an artificial ecosystem, the city development has to deal with many challenges, specifically for sustainable development, mixing economical, social and environmental aspects. The decentralized methodology proposed in the following allows to deal with multi-criteria problems, leading to propose a decision making assistance, based on simulation analysis.

Gentrification phenomena can be modelled using such methodology. It is typically a multi-criteria self-organization processes where appears emergent coming of new population inside urban or territorial areas. This new population firstly attracted by some criteria, brings some other charateristics which are able to modify and feedback over the environment.

Cultural dynamics processes in urban areas are also such complex systems where multi-criteria must be taken into account. A modelling of these dynamics is presented later in this paper.

2 Swarm Intelligence for Spatial self-Organization Decentralized algorithms have been implemented for many years for various purposes. In this family of algorithms, multi-agent systems can be considered as generic methods (Weiss, 1999). Agent-based programming deals with two main categories of agent concepts: cognitive agents and reactive agents. The first category concerns sophisticated entities able to integrate, for example, knowledge bases or communications systems. Generally, efficient computations, based on these cognitive architectures, implement few agents. The second category of agents, based on reactive architectures, is expected to be used inside numerous entity-based systems. The aim of programs using such architectures, is to deal with emergent organizations using specific algorithms called emergent computing algorithms. Swarm Intelligence is the terminology used to point out such reactive agent-based methods where each entity is built with the same basis of behavior, but reacts in autonoumous way. Swarm Optimization methods concern the problems of optimization where the computation of a function extremum is based on the concept of swarm intelligence.

Ant Colony Optimization (ACO) methods [START_REF] Bonabeau | Swam Intelligence, from natural to artificial systems[END_REF]) is a bioinpired method family where the basic entities are virtual ants which cooperate to find the solution of graph-based problems, like network routing problems, for example. Using indirect communications, based on pheromon deposites over the environment (here a graph), the virtual ants react in an elementary way by a probabilistic choice of path weighted with two coefficients, one comes from the problem heuristic and the other represent the pheromon rate deposit by all the ants until now. The feed-back process of the whole system over the entities is modelled by the pheromon action on the ants themselves.

Particule Swarm Optimization (PSO) is a metaheuristic method initially proposed by J. Kennedy and R. Ebenhart [START_REF] Kennedy | Particle Swarm Optimization In Proceedings of IEEE International Conference on Neural Networks[END_REF].This method is initialized with a virtual particle set which can move over the space of solutions corresponding to a specific optimization problem. The method can be considered as an extension of a bird flocking model, like the BOIDS simulation from C.W. Reynolds [START_REF] Reynolds | Flocks, Herds and Schools: a distributed behavioral model In Computer Graphics[END_REF]. In PSO algorithm, each virtual particle moves according to its current velocity, its best previous position and the best position obtained from the particles of its neighborhood. The feed-back process of the whole system over the entities is modelled by the storage of this two best positions as the result of communications between the system entities.

Other swarm optimization methods have been developped like Artificial Immune Systems [START_REF] De Castro | Artificial immune system: a new computational approach[END_REF] which is based on the metaphor of immune system as a collective intelligence process. F. Schweitzer proposes also a generic method based on distributed agents, using approaches of statistical many-particle physics [START_REF] Schweitzer | Brownian Agents and Active Particles[END_REF].

The method proposed in this paper is based on Ant Clustering and Ant Nest Building, allowing to deal with self-organization processes emerging from spatial constraints and attractive areas.

Ant Custering Modeling

Ant clustering algorithms are inspired by the corposes or larvea classification and aggregation that the ants colony are able to do in the real life. The ants are moving inside a closed area and are able to move some material which are randomly put on this area. After a while, and without any kind of centralized coordonation, the ants success to create some material clusters.

The algorithm is based on the following and very simple behavioral rules that each ant implements:

• When an ant is moving without carrying yet material and finds some material, the ant will take the material w.r.t. the probability number:

P p = k 1 k 1 + f 2 (1)
where f is the material density that the ant perceives locally around itself and k 1 is the treshold. It is easy to check that if f << k 1 then P p is near the value 1 and if f >> k 1 then P p is near the value 0.

• When an ant is moving when carrying some material, the probability to deposit reads:

P d = f k 2 + f 2 (2)
where f is still the material density that the ant perceives locally around itself and k 2 is another treshold. It is easy to check that if f << k 2 then P d is near the value 0 and if f >> k 2 then P d is near the value 1.

Spatial constraints using templates

The ant clustering shows some spatial self-organizations but has the specificity of generating clusters at random places. According to the first random move that the ants start to do at the beginning of the algorithm, some material will initiate aggregation and the clustering processus will complete this aggregation from these initial random first aggregations. To simulate some urban dynamics, we need to introduce specific location with respect to city center for example or cultural equipments. The clustering here will represent the people usage of these centers or equipments and we need to introduce an attractive effect by using a pheromon template. This method follows the algorithm known as Ant Nest Building [START_REF] Bonabeau | Swam Intelligence, from natural to artificial systems[END_REF]. In ant colonies, the center corresponds to the position of the queen which needs to build the nest and the ant colony moves around it to protect the nest by various material taken on the ground. The queen emits a pheromon which allows to attract the ants during their building. The ant has to deposit the material carried only if the pheromon quantity perceived belongs to a specific range. We use an attractive fonction called P t , corresponding to a pheromon template and represented by the left top part of the figure 2.

Using this template function, we remplace in the clustering algorithm, the two previous probabilities defined in equation ( 1) and equation ( 2) by

P ′ p = P p (1 -P t ) (3)
P ′ d = P d P t (4)
In figure 2, we show an implementation of this algorithm using the multi-agent platform called Repast (Repast web site, 2009). The java version of this platform includes some packages allowing to interface with geographical database and geographical information systems (GIS). In figure 2, the graphical output windows is made under OpenMap which is a GIS developped in Java. In this figure, the materials moved by the ants are the small grey or blue circles, the ant moving without material are the green circles and the ant carrying material are the red circles.

Adaptive Spatial Organization Feedback Implementation

Complex systems deal not only with emergent organization processus from the interaction of its own entities, but also with the feedback processus of the organization over its own components. In the proposed model, we can take into account such feedback process and we present, in figure 3, an adaptive processus which makes the queen (which describes the organization itself) modify the environment and the clustering processus itself. Following the template function, the queen locally defines around it two zones. The first zone is near itself and it is expected not to find material there. The second zone corresponds to the template maximum and it is expected to find a great concentration of material there. In the simulation, we count in a dynamic way the number of materials in these two zones and when these numbers reach some tresholds, we make evolve the queen by increasing its own size and so increasing the 2 associated zones. After this evolution, the ants have to move some material following the new template function attraction. The low part of the figure shows the evolution of the queen which has evolved 6 times Templates and associated Ant Nest Building Simulation since the simulation beginning. On this figure, we can see the red curves counting the zones density. Each gap in these density curves corresponds to an evolution of the queen.

Multi-Criteria and Multi-Center System Dynamics

The swarm intelligence algorithms described in the previous section, are the direct formalization of natural social insects systems. They can be considered as the first stage of our modeling organization. From these elementary models, we propose to combine different elements and we need to add other processes in order to model more sophisticated phenomena, by the integration of the following aspects: multi-center, multi-criteria and adaptivity extension for multi-criteria.

To introduce the concept of multi-criteria phenomena, we introduce different kinds of pheromones. Each kind of pheromone is represented by a specific color. We introduce the notion of center which is a specific spatial location. On each center, we are able to define many queens. Each queen, belonging to a center, Adaptive queen behavior modelling: according to its surround material spatial perception, the queen evolves is able to emit its own pheromone which is represented by a colored pheromone that is different from the other queen ones belonging to the same center. A queen, associated to a spatial center, describes a specific criterium linked to a colored pheromone. To represent the same criterium on different centers, we describe it by the same colored pheromone on these different spatial locations.

In order to force the ants to deposit their material only near the center, we have introduced the template function. Even if the pheromone function and the template function must have similarities in order to attract and make deposit the material at the same place, we have to separate these two functions. The template function must exhibit a close area of non nul values near the center to link the material to the center. The pheromone function must attract ants with material on the same place but the attraction phenomena has to cover a widest area than the template function, in order to be able to attract materials and ants at some distance from the center. Definition 3.1 A spatial multi-criteria multi-center simulation is described by a set of n p centers, {P i ; 1 ≤ i ≤ n p }, and by a set of n c colors, {c j ; 1 ≤ j ≤ n c }.

For each center P i , we define a c j -colored template function, Φ ij : S → IR, which gives the value of the c j template intensity on each spatial position. For each center P i , we can define a c j -colored pheromone function, f ij : S → IR, which gives the value of the c j pheromone intensity on each spatial position.

Remark 3.2 We can define the c j -colored template function of the P i center by the following radial exponential function

Φ ij (x, y) = α ij exp(-β ij (d((x, y), (x Pi , y Pi )) -r ij ) 2 ) (5)
where α ij is the template amplitude, β ij is the template slope, (x Pi , y Pi ) are the P i center coordinates.

We then define the c j -colored pheromone function for the P i center with a similar formula

f ij (x, y) = a ij exp(-b ij (d((x, y), (x Pi , y Pi )) -r ij ) 2 ) (6)
where a ij is the template amplitude, b ij is the template slope.

We have to remark that the radius r ij is the same in the above two formulas and allows to define the same maximum value position, but the amplitude and slope are differents. The slope of template function has to create close area of maximal value near the center. The slope of the pheromone function must not have maximal area too much close to the center in order to attract ants or materials which are located at some distance from the center. We give in the following some definitions which allow to generalize the ant nest building algorithm for the multi-criteria multi-center simulation. Definition 3.3 A center P i has the dominant color c j if

a ij = max{a ik ; 1 ≤ k ≤ n c }.
Definition 3.4 On each space location Z = (x, y), we define the c j colored pheromone intensity as the function F j (Z) or F j (x, y) defined by the formula:

F j (Z) = F j (x, y) = np i=1 f ij (x, y). (7)
The multi-criteria multi-center model proposed here, implement some spatial objects that are the material and spatial agents (which are the ants). The ants have to carry the material in order to achieve the spatial self-organization simulation. Definition 3.5 A material involved in a spatial multi-criteria multi-center simulation has to include a characteristic color table which corresponds to the only colors that the material is able to perceive and upon which it will be able to react.

Figure 4

Multi-center multi-colored pheromone template represented by radial exponential functions and the associated ant nest building simulation in Repast Definition 3.6 An ant involved in a spatial multi-criteria multi-center simulation and which is carrying a material has to include a characteristic color table which corresponds to the material characteristic color table.

Definition 3.7 Each ant of the simulation which is carrying some material M l , has to implement a decision process which gives, as output, a color pheromone template c j that is used for the material transportation by the ant. This selected color c j is called the ant behavior.

At each simulation step, a carried material M l is associated to a color c j , called the ant behavior in definition 3.7. The ant which is carrying this material will then move by searching in its neighboring position, the one with the highest value of the c j colored pheromone.

To compute the ant behavior, we search the highest value of the colored pheromone on the space position of the ant and to return the color of this highest value.

The ant moves on the neighboring place which has the highest value of colored pheromone defined by its behavior.

Simulation experiments are made using Repast on OpenMap for a specific following configuration, defined by the initial positions of all the components of the system: (i) the centers, (ii) the queens, (iii) the materials and (iv) the ants. For this experiment, on each center, we put 8 queens, each one is associated to a colored pheromone. On figure 5, we show the result of one simulation where ants progressively aggregate the material around the center, following pheromone trails and clustering algorithm. We can observe the formation of material affectation to each center in order to respect the attraction process, according to the material characteristics.

Figure 5

Simulation computation, at the successive steps: iteration 0, iteration 250, iteration 1600.

On figure 6, we make a zoom of the last step of the simulation shown on the figure 5, removing the ant representation. The color of each center corresponds to the colored pheromone of the highest amplitude over the center. The color of each material corresponds to the behavior color of the ant which carries it, according to the definition 3.7. The multi-template modelling can be used to model cultural equipment dynamics as described in the figure 7. On this figure, we associate to each cultural center (cinema, theatre, ...) a set of queens. Each queen will emit its own pheromone template, associated to a specific criterium (according to age, sex, ...). Initially, we put the material in the residential place. Each material has some characteristics, corresponding to the people living in this residential area. The simulations, corresponding to the previous computations, generate self-organization processes as the results of the set of the attractive effect of all the center and all the templates. Developing dynamical simulations over GIS leading to adaptive and intelligent decision processes is nowadays a great challenge. Urban development and management needs decision making processes which have been developed since many years on deterministic global evolution laws (differential models, for example). The spatial dimension within its complexity is not generally considered in such global model and are often unable to understand some self-organized systems development.

The paper develops some specific swarm intelligence algorithms based on ant colonies processes. Using such decentralized methods, we can model complex multicenter and multi-criteria self-organizations. Urban dynamics can have major benefits by the use of such models in order to simulate and analyze the adaptive usage of urban services like cultural centers. The applicative part of these studies are supported by a French regional project (Haute-Normandie) dealing with the study of cultural dynamics over the urban area of Rouen.

The future steps of this study is (i) to analyze the complexity of the results and to give some interpretation of the distribution generated by the simulation. (ii) to introduce adaptive modeling of the urban centers in respect with their usages. That means how these centers could be able to adapt their own services, according to the users which have been attracted by them, but are also carrying other specificities thanks to the complexity of the multi-criteria involved in the original problem. These futures steps are now in progress and need to augment the behavioral design of the centers. The decentralized approaches which are the characteristics of our models allow such complements in the model, increasing the complexity of the simulation.

Figure 1

 1 Figure 1Complexity of geographical space with respect of emergent organizations

Figure 2

 2 Figure 2Templates and associated Ant Nest Building Simulation

Figure 3

 3 Figure 3Adaptive queen behavior modelling: according to its surround material spatial perception, the queen evolves

Figure 4

 4 Figure 4 represents two centers and two colored pheromons. The template function used to represent the pheromone emission corresponds to the function defined in the remark 3.2. On the bottom of the figure, we present the associated simulation in Repast.

Figure 6

 6 Figure 6Simulation: zoom on final step

  Figure 7Cultural Equipment Dynamics Modelling


Rawan Ghnemat
email: rawan.ghnemat@litislab.eu

Cyrille Bertelle
email: cyrille.bertelle@litislab.eu

Gérard H E Duchamp

URBAN DYNAMICS MODELLING USING ANT NEST BUILDING

Keywords: swarm intelligence, complex systems, self-organization, ant systems, spatial organization

Urban dynamics deal with spatial organizations where a great complexity of interactions appears. Social and economic aspects interact and environmental objectives are nowadays a major purpose for sustainable urban development. We propose some generic modelling processes able to face with this complexity, in order to simulate the evolution of the city centers. These organizational centers need a multi-criteria description for their evolution, including feed-back phenomena of them over their environment and components. We propose a swarm intelligence algorithm, using social-insect collective behavior. We combine a decentralized approach, based on emergent clustering mixed with spatial constraints or attractions, as an extension of the ant nest building algorithm with multi-center. Typically, this model is currently used by ourself, to model and analyze cultural equipment dynamics in urban area.

INTRODUCTION

Many natural and artificial systems have emergent properties based on spatial development. This spatial development is both the result of some mecanisms from the system behavior and the actor of the system formation by morphogenetic feedback. Natural ecosystems or social organizations in urban dynamics are typically such emergent spatial organizations. The goal of this paper is to study some computable mecanisms and algorithms able to model such spatial self-organization processes, taking into account the complexity of the phenomena.

In the next section, complex system concepts are defined and their applications to urban dynamics understanding are described, then swarm intelligence algorithms are described as methodologies to implement the complex systems concepts, using distributed computations. The following section proposes some specific swarm intelligence methods based on ant systems in order to model the spatial organizations emergence. Experiments are given, using RePast muti-agent platform mixed with a geographical information system. Complex system theory [START_REF] Le Moigne | La modélisation des systèmes complexes[END_REF] is based on the fact that for many applicative domains, we can find similar processes linking emergent global behavior and interaction network of constituents. The global behavior is generally not accessible using classical analytical methods.

In classical analytical methods, the global behavior of the system is the description of the equations. Simulations from these formulations, consist in obtaining the trajectories of the behavior predefined in the equation formulation.

In complex systems modelling, we have to model the constituents of the system and the interaction network or system which link these constiuents, using a decentralized approach. So the global behavior of the system cannot be understood by the description of each constituent. In complex system modelling, the global behavior is an emergent property from the interaction network or systems between its constituents and lead to the creation of an dynamical organization of these constituents This dynamical and emergent organization retro-acts on its own components. Two kinds of feedback allow to describe these phenomenon. The positive feedback means that the emergence increases the organization constitution. the negative feedback means that the emergence has regulator properties which finally stop the increasing organization constitution and allow the system stabilization.

Another major aspect of complex systems is that they can be considered as open systems. This means that they are crossed by energetical fluxes that make them evolve in a continuous way. From these energetical fluxes, complex systems can evolve through critical states, using bifurcation schema and attractors behaviors. One of the major vector or support of these energetical fluxes is the environment itself where the complex systems and their entities evolve. In many natural and artificial systems, the environement has some spatial effects which interact on the whole complexity of the phenomenon. This spatial environment can be modified by the system but he can also be the catalyst of its own evolution. Understanding and modelling the deep structural effect of the interaction between the systems and its spatial environment is the goal of the study presented in the sequel.

Application to urban dynamics

Social and human developments are typical complex systems. Urban development and dynamics are the perfect illustration of systems where spatial emergence, self-organization and structural interaction between the system and its components occur. In figure 1, we concentrate on the emergence of organizational systems from geographical systems. The continuous dynamic development of the organization feed-back on the geographical system which contains the organization components and their environment. The lower part of this figure explains our analysis methodology. It consists to describe many applicatives problems by dynamical graphs or environments in order to detect organizations over these dynamical environment. For the organization detection, we use swarm intelligence processes. We model the feed-back process of this emergent organization on the system constituents and its environment. To analyse or simulate urban dynamics, nowadays, we can use the great amount of geographical databases directly available for computational treatment within Geographical Information Systems. On the organizational level description, the new development of multiagent systems (MAS) allows nowadays to develop suitable models and efficient simulations.

The applications we focuss on in the models that we will propose in the following concerns specifically the multi-center (or multi-organizational) phenomona inside urban development. As an artificial ecosystems, the city development has to deal with many challenges, specifically for sustainable development, mixing economical, social and environmental aspects. The decentralized methodology proposed in the following allows to deal with multi-criteria problems, leading to propose a decision making assistance, based on simulation analysis.

Cultural dynamics processes in urban can be modelled using such methodology. It is typically a multi-criteria self-organization processes where appears emergent usage oo urban equipment. A modelling of these dynamics is presented latter in this paper.

Swarm Intelligence and Spatial Environment

Decentralized algorithms have been implemented for many years for various purposes. In this algorithm category, multi-agent systems can be considered as generic methods [START_REF]Multiagent Systems[END_REF]. We deal, in this paper, with agents based on reactive architecture and expected to be used inside numerous entity-based systems. The aim of programs using such architectures, is to deal with emergent organizations using specific algorithms called emergent computing algorithms. Swarm Intelligence is the terminology used to point out such reactive agent-based methods where each entity is built with the same basis of behavior, but reacts in autonoumous way.

Based on swarm intelligence concepts, Ant systems (3) propose some bio-inspired method from social insects mecanisms. For exemple, Ant Colony Optimization (ACO) methods is a such method family where the basic entities are virtual ants which cooperate to find the solution of graph-based problems, like network routing problems, for example. Using indirect communications, based on pheromon deposites over the environment (here a graph), the virtual ants react in elementary way by a probabilistic choice of path weighted with two coefficients, one comes from the problem heuristic and the other represent the pheromon rate deposit by all the ants until now. The feed-back process of the whole system over the entities is modelled by the pheromon action on the ants themselves.

Particule Swarm Optimization (PSO) is a metaheuristic method initially proposed by J. Kennedy and R. Ebenhart [START_REF] Kennedy | Particle Swarm Optimization In Proceedings of IEEE International Conference on Neural Networks[END_REF] which is also based on swarm intelligence concepts. This method is initialized with a virtual particle set which can move over the space of solutions corresponding to a specific optimization problem. The method can be considered as an extension of a bird flocking model, like the BOIDS simulation from C.W. Reynolds [START_REF] Reynolds | Flocks, Herds and Schools: a distributed behavioral model In Computer Graphics[END_REF]. In PSO algorithm, each virtual particle moves according to its current velocity, its best previous position and the best position obtained from the particles of its neighborhood. The feed-back process of the whole system over the entities is modelled by the storage of this two best positions as the result of communications between the system entities.

Other swarm optimization methods have been developped like Artificial Immune Systems (4) which is based on the metaphor of immune system as a collective intelligence process. F. Schweitzer proposes also a generic method based on distributed agents, using approaches of statistical many-particle physics [START_REF] Schweitzer | Brownian Agents and Active Particles[END_REF].

The method proposed in this paper is based on Ant systems, allowing to deal with self-organization processes emerging from spatial constraints and attractive areas.

MULTI-CENTER ANT NEST BUILDING TO MODEL EMERGENT SPATIAL ORGANIZA-TIONS

We will describe in this section, the general algorithm which is proposed to model emergent spatial organizations. This algorithm is based on the ant clustering. We introduce pheromon template to spatially control the clustering from local attraction. This method is a decentralized approach which allows to combinate multicenter and multi-criteria problem and we will show how we can apply it to model cultural dynamics in urban areas.

Ant clustering

Ant clustering algorithms are inspired by the corposes or larvea classification and aggregation that the ants colony are able to do in the real life. The ants are moving inside a closed area and are able to move some material which are randomly put on this area. After a while, and without any kind of centralized coordonation, the ants success to create some material clusters.

The algorithm is based on the following and very simple behavioral rules that each ant implements :

• When an ant is moving without carrying yet material and find some material, the ant will take the material respecting the probability number :

P p = k 1 k 1 + f 2 (1)
where f is the material density that the ant perceives locally around itself and k 1 is the treshold. It is easy to check that if f << k 1 then P p is near the value 1 and if f >> k 1 then P p is near the value 0.

• When an ant is moving when carrying some material, the probability to deposite it is computed by :

P d = f k 2 + f 2 (2)
where f is still the material density that the ant perceives locally around itself and k 2 is another treshold. It is easy to check that if f << k 2 then P d is near the value 0 and if f >> k 2 then P d is near the value 1.

Spatial constraints using template

The ant clustering shows some spatial self-organizations but has the specificity to generate clusters at random places. According to the first random moves that the ants start to do in the beginning of the algorithm, some material will initiate aggregation and the clustering processus will complete this aggregation from these initial random first aggregations. To simulate some urban dynamics, we need to introduce specific location with respect to city center for example or cultural equipments. The clustering here will represent the people usage of these centers or equipments and we need to introduce an attractive effect by using a pheromon template. This method follow the algorithm known as Ant Nest Building (3). In ant colonies, the center corresponds to the position of the queen which needs to build the nest and the ant colony moves around it to protect the nest by various material taken on the ground. The queen emits a pheromon which allows to attract the ants during their building. The ant has to deposite the material carried only if the pheromon quantity perceived belongs to a specific range. We use an attractive fonction called P t , corresponding to a pheromon template and represented by the part (a) of the figure 2.

Using this template function, we remplace in the clustering algorithm, the two provious probabilities defined in equation [START_REF] Benenson | Geosimulation -Automata-based modeling of urban phenomena[END_REF] and equation ( 2) by

P ′ d = P d P t (3)
In figure 2, we show an implementation of this algorithm using the multi-agent platform called Repast [START_REF]Repast web site[END_REF].

The java version of this platform includes some packages allowing to interface with geographical database and geographical information systems (GIS). The graphical output windows is made under OpenMap which is a GIS developped in Java. In figure, the materials moved by the ants are the small grey circles, the ant moving without material are the green circles, the ant carrying material are the red circles and the queen location is the yellow circle.

Multi-template modelling

The previous subsection describes one local attractive process characterized by the queen and its pheromon template emission. The advantage of this method is to be able to combine the solutions of multi-center and multi-criteria problems, using interactive processes, each one is represented by a queen and its pheromon template.

On the figure (3), we can see a simulation with two queens and two pheromon templates. It is possible also for each queen to emit many different kinds of pheromons : we called them colored pheromons. Each colored pheromon will attract only the ants associated to its color.

Application to cultural equipment dynamics

The multi-template modelling can be used to model cultural equipment dynamics as described in the figure [START_REF] De Castro | Artificial immune system: a new computational approach[END_REF]. On this figure, we associate to each cultural center (cinema, theatre, ...) a queen. Each queen will emit many pheromon templates, each template is associated to a specific criterium (according to age, sex, ...). Initially, we put the material in the residential place. Each material has some characteristics, corresponding to the people living in this residential area. The simulation shows the self-organization processus as the result of the set

Conclusion and Perspectives

The paper develops some specific swarm intelligence algorithms based on ant colonies processes. Using such decentralized methods, we can model complex multi-center and multi-criteria self-organizations. Urban dynamics are one of the most relevent problems where these approaches can be efficient. These studies are supported by a french regional project (Haute-Normandie) dealing with the study of cultural dynamics over urban area.

Figure 1 :

 1 Figure 1: Spatial organizations Complexity Description and the Conceptual Generic Model Based on Swarm Intelligence

Figure 2 :

 2 Figure 2: Ant nest building with one center using RePast MAS paltform over OpenMap GIS

Figure 3 :

 3 Figure 3: Multi-center ant nest buiding using RePast over OpenMap

Figure 4 :

 4 Figure 4: Cultural Equipment Dynamics Modelling


V Guglielmo-Viret

O Attre ´e

V Blanco-Gros

P Thullier
email: pthullier@yahoo.com

Comparison of electrochemiluminescence assay and ELISA for the detection of Clostridium botulinum type B neurotoxin

Keywords: Botulinum, Electrochemiluminescence, ELISA, Sensitivity, Toxin

We compared the ELISA and electrochemiluminescence (ECL) immunoassay technologies for the detection of botulinum type B neurotoxin (BotNT B), which requires highly sensitive techniques due to its potent biological activity. BotNT B complexes are the naturally secreted form of the toxin, approximately a third of which consists of the neurotoxin itself; they were aliquoted and frozen for this study. Results of both techniques were interpreted with the same standard statistical tests (ANOVA and Tukey). We first compared two commercial assays for BotNT B: the detection limit of the colorimetric ELISA was 1.56 ng/ml BotNT B complexes versus 0.39-0.78 ng/ml in the ECL test. We then used the same monoclonal antibody and the same polyclonal antibody, respectively purified by protein A and protein G chromatography, to optimize an in-house ELISA test and an in-house ECL test, making it possible to directly compare the two technologies without interference due to the properties of the antibodies used in the two tests. The colorimetric in-house ELISA had a detection threshold of 3.12 ng/ml versus the in-house ECL test whose detection threshold was 0.78-1.56 ng/ml. Thus, in both cases, the ECL assay was two to four times more sensitive than the colorimetric ELISA. The ECL assay was also more rapid (2.5 h for the in-house ECL versus 5 h for in-house ELISA with precoated wells). Overall, these elements can be used to compare the qualities of the two technologies, at least for the detection of protein antigens such as toxins.

Introduction

The neurotoxins (NT) produced by Clostridium botulinum (BotNT), a Gram-positive spore-forming bacterium with at least seven serotypes (see [START_REF] Turton | Botulinum and tetanus neurotoxins: structure, function and therapeutic utility[END_REF] for a review), are amongst the most toxic substances known. The thresholds for detection of these toxins and for diagnosis of poisoning must therefore be very low. For this reason, the most sensitive immunological methods have been adapted towards detecting BotNTs, and efforts to improve these methods are continuing in various laboratories. Interest in detection methods for these toxins has clearly been revived with recent bioterrorism threats, while during the same time period, the food industry has greatly reduced the incidence of accidental poisoning from natural sources.

If used as a biological weapon, the toxin could possibly be administered as an aerosol in its most stable form: the complex naturally secreted by C. botulinum (BotNT complexes) and consisting of the NT associated with non-toxic proteins. The diagnosis of contamination based on the detection of such complexes in skin or mucous membrane samples, even before the onset of symptoms, would make it possible to optimize the medical management of contaminated individuals, by enabling the early administration of specific, neutralising antibodies or other therapeutic compounds [START_REF] Robinson | Management of botulism[END_REF].

The standard reference test for detecting C. botulinum neurotoxins is still the mouse assay, but it takes several days to perform and is thus clearly not appropriate for diagnostic purposes during emergency situations. Optimized ELISAs have been developed; they are more rapid, and their sensitivities are similar to those of the mouse test [START_REF] Szilagyi | Development of sensitive colorimetric capture ELISAs for Clostridium botulinum neurotoxin serotypes A and B[END_REF][START_REF] Poli | Development of sensitive colorimetric capture ELISAs for Clostridium botulinum neurotoxin serotypes E and F[END_REF]. Other techniques for detecting botulinum neurotoxin B (BotNT B) have recently been developed, including those based upon the enzymatic properties of the toxin [START_REF] Wictome | Development of in vitro assays for the detection of botulinum toxins in foods[END_REF][START_REF] Anne | Highthroughput fluorogenic assay for determination of botulinum type B neurotoxin protease activity[END_REF][START_REF] Schmidt | Fluorigenic substrates for the protease activities of botulinum neurotoxins, serotypes A, B, and F[END_REF], antibody chips [START_REF] Ligler | Array biosensor for detection of toxins[END_REF], or using the toxin receptor instead of an antibody [START_REF] Ahn-Yoon | Ganglioside-liposome immunoassay for the detection of botulinum toxin[END_REF]. However, these techniques do not have sufficiently low detection thresholds, are not widely available, or are not necessarily applicable to antigens other than BotNT, even though other toxins (such as mycotoxins, staphylococcal enterotoxins, etc.) are also deemed as potential biological weapons [START_REF] Binder | Medical management of biological warfare and bioterrorism: place of the immunoprevention and the immunotherapy[END_REF].

The electrochemiluminescence (ECL) assay on the BioVeris (Witney, UK) (previously known as Origen) apparatus is comparable to a capture ELISA, but it includes proprietary washing and signal amplification steps [START_REF] Gatto-Menking | Sensitive detection of biotoxoids and bacterial spores using an immunomagnetic electrochemiluminescence sensor[END_REF][START_REF] Zu | Electrogenerated chemiluminescence. 66. The role of direct coreactant oxidation in the ruthenium tris(2,2Vbipyridyl/tripropylamine system and the effect of halide ions on the emission intensity[END_REF]. It can detect concentrations of staphylococcal enterotoxin B as low as 1 pg/ml [START_REF] Kijek | Rapid and sensitive immunomagnetic-electrochemiluminescent detection of staphyloccocal enterotoxin B[END_REF], and is therefore of potential value for developing tests adapted to biodefense needs. However, only one published study directly compares the performances of ECL and ELISA, the latter being the bstandardQ immunological technique. The detection thresholds, for TIMP (tissue inhibitor of metalloproteases-1) protein and for a recombinant antibody in this study, were both essentially equivalent at about 1 ng/ml [START_REF] Baker | Rapid monitoring of recombinant protein products: a comparison of current technologies[END_REF], which is less sensitive than previously published results. Nonetheless, these comparisons were linked to commercial tests, and the methods were not described in detail within this article.

In this current study, we first compared commercial ELISA and ECL tests aimed at the detection of BotNT B. Sensitivity is an essential feature of any test intended for the detection of BotNT B; therefore the sensitivity of such commercial tests is likely to have been extensively optimized to reach detection limits. A comparison of these two tests thus gave initial insights on the sensitivity limits of the ELISA and ECL assays. However, comparisons of the two techniques, if they are to be rigorous, should be independent of the antibodies. We therefore developed and compared an ELISA test and an ECL test using the same antibodies directed against BotNT B. The comparisons may provide direct insights on how the sensitivities of these two techniques compare, at least for the detection of BotNT B and perhaps other protein antigens.

Materials and methods

Antigen

BotNT B complexes (lot A043003-01) were purchased from Metabiologics (Madison, WI), and consisted, approximately, of a third of the molecular mass due to the neurotoxin (M. Goodnough, Metabiologics, personal communication). The specific activity of the preparation was 2.2 Â 10 7 mouse LD 50 /mg. Aliquots of the complex (0.5 mg/ml in citrate buffer containing 5% BSA) were stored frozen at À 80 8C, and used immediately after thawing.

The dilution buffer for all samples was PBS, pH 7.5, chosen as a neutral matrix with a pH that allowed the release of the neurotoxin from the complex [START_REF] Ferreira | Comparison of the mouse bioassay and enzyme-linked immunosorbent assay procedures for the detection of type A botulinal toxin in food[END_REF]. PBS is also a standard buffer unlikely to confer a particular advantage for any of the four tests, and was used as the negative control.

Commercial tests

Commercial ELISA

Precoated microtiter plates, biotinylated detection antibody, streptavidin-enzyme conjugate, buffers, and substrates were provided in the kit purchased from Metabiologics. Reagents were stored at 4 8C, and plates at À 20 8C, according to the manufacturer's instructions. The manufacturer indicates that, although its sensitivity may vary, this ELISA can detect approximately 20 pg/ml pure BotNT B. Washing steps utilised an automatic washer (ELx 405; Bio-Tek Instruments, Winooski, VT) and absorbance at 450 nm was measured with a microplate reader (Power-Wave; Bio-Tech Instruments, Winooski, VT). The test was performed strictly according to the manufacturer's instructions.

Commercial ECL assay

This assay was performed on the latest-generation M1R analyser (BioVeris) using the default values for all parameters provided by the manufacturer (bead type 2.8, bead wash level 5, clean type level 2, and detection sequence standard).

The kit purchased from BioVeris includes the capture and detection reagents, as well as the assay diluent. Reagents were stored and the test was performed strictly according to the manufacturer's instructions. The information supplied by BioVeris at www.bioveris.com indicates that this test detects 50-100 pg/ml pure BotNT B.

In-house tests

Antibodies

The monoclonal antibody (anti-BoNT B 2/3; lot 180701) was provided as murine ascitic fluid by the Centre d'e ´tudes du Bouchet (Vert-le-Petit, France) and was purified on a Hi-Trap protein A HP Column (Amersham Pharmacia Biotech, Orsay, France), according to the manufacturer's instructions. The polyclonal anti-BoNT B 60/1 antibody was purchased as an equine-lyophilised serum from the National Institute for Biological Standards and Controls (Herts, UK) and was purified on a Hi-Trap protein G HP Column (Amersham Pharmacia Biotech, Orsay, France), according to the protocol provided by the manufacturer. Due to its specific neutralising properties, this polyclonal antibody is commonly used in the mouse bioassay for serotyping BotNTs. These antibodies are not used in commercial tests.

Labelling of antibodies

A water-soluble biotin with a spacer arm (Biotin-LC-Sulfo-NHS Ester, BioVeris), whose length is 7.4 A ˚, was used to biotinylate the purified B 60/1 and B 2/ 3 antibodies. A biotin-to-antibody molar ratio of 20:1 was chosen and biotinylation was carried out according to the manufacturer's instructions, which included the removal of unconjugated biotin by dialysis (Slidea-lyser, Perbio, Bezons, France).

Antibodies B 60/1 and B 2/3 were then labelled with ruthenium (II) tris-bipyridine, N-hydroxysuccinimide ester (ORI-TAG-NHS, BioVeris). An ORI-TAGto-antibody molar ratio of 8:1 was used and binding was achieved by means of the protocol recommended by the manufacturer, which included the removal of unconjugated ORI-TAG by size exclusion chromatography (Amersham Pharmacia, Orsay, France).

In-house ELISA

In order to optimize our ELISA, the polyclonal antibody was tested as the capture reagent and the monoclonal antibody used for detection, and vice versa. We also compared detection limits using a specific secondary antibody with that using alkaline phosphatase-conjugated streptavidin and a biotinylated antibody. The capture and detection antibodies were used at concentrations of between 0.5 and 20 Ag/ ml. Different saturation (0.5-4.5% BSA or skimmed milk powder) and dilution (blocking agent plus 0.1-1% Tween 20) buffers were tested, together with the conditions (duration and temperature) for coating, incubation, and detection. For further studies, we selected the most sensitive ELISA protocol that could be obtained.

For this ELISA, the B 2/3 antibody (100 Al of a 10 Ag/ml concentration) was used to coat Nunc Maxisorp microtiter plates (Merck Eurolab Polylabo, Strasbourg, France) overnight at 4 8C. Plates were then washed three times in wash buffer (PBS-Tween 0.1%) in an automatic washer and blocked with 1% BSA in PBS for 60 min at 37 8C. Each of the samples was incubated (100 Al/well) for 2 h at 37 8C. The plates were washed and incubated for 2 h at 37 8C with the biotinylated polyclonal anti-BoNT B 60/1 (100 Al) diluted to a final concentration of 4 Ag/ml in PBS-BSA 1%-Tween 0.1%. The plates were then incubated with alkaline phosphatase-conjugated streptavidin (Amersham Pharmacia) diluted 1/1000 in PBS for 30 min at 37 8C and above, and then with the substrate Sigma-Fast pNPP (Sigma, Saint Quentin Fallavier, France), also for 30 min at 37 8C. The absorbance at 405 nm was then measured with a microplate reader.

In-house ECL assay

During the development of our ECL assay, we tested in particular the polyclonal antibody as the capture antibody, using either the ruthenylated monoclonal antibody or monoclonal antibody plus a specific ruthenylated antibody for detection. Alternatively, the monoclonal antibody was tested as a capture reagent and the polyclonal antibody was ruthenylated for detection. Various concentrations of capture antibody (4-20 Ag/ml), primary antibody (0.5-10 Ag/ml), secondary antibody (0.25-8 Ag/ml), and beads (0.5-1.5 mg/ml) were tested. The incubation conditions for the sample were also optimized (1-16 h at room temperature, 4 8C, or 37 8C) and we tested the benefit derived from bead washing steps at various stages. We assessed the value of a dilution step to slow the reaction before reading the results. Various concentrations of Tween 20 (0.1-1%), BSA, or milk powder (0.5-4.5%) were tested to determine the optimized composition for assay buffer (AB). The most sensitive ECL protocol was then chosen.

For this protocol, the biotinylated capture antibodies were first bound to streptavidin-coated paramagnetic beads (DynabeadsR M280 Streptavidin; BioVeris) by incubating equal volumes of beads (1.5 mg/ml in AB) and capture antibody (10 Ag/ml in AB) together, with shaking, for 30 min at 37 8C. AB consisted of sterile PBS, 1% BSA, and 1% Tween 20. Unbound antibodies were removed by washing the beads twice in AB using a magnetic particle collector and the bead suspension was restored to the original volume with AB. We dispensed 50 Al of beads coated with the capture antibody into each assay well (96-well polypropylene plate with deep, round-bottomed wells; Fisher Bioblock Scientific, Illkirch, France). We added 25 Al of ORI-TAG-labelled detection antibody (4 Ag/ml in AB) and 100 Al of sample to each well, and incubated the plates (2 h at room temperature) with shaking (1100 rpm). We then added 225 Al of AB to each well to slow the reaction; the plate was placed in an M1R analyser and the results of the assay reactions were recorded.

Statistics

We made serial 1:2 dilutions of BotNT B complexes to obtain two ranges of six concentrations, previously selected during the optimization steps, one for ELISA (0.78-12.5 ng/ml) and the other for ECL (0.19-3.13 ng/ml). Samples of Bot NT B complexes and negative controls were tested in triplicate to simulate realistic measurement conditions, using the two commercial tests carried out in parallel on the same day. These measurements were then repeated by the same operator everyday for 3 days. Each series of measurements (one test on 1 day) was analysed by ANOVA followed by the Tukey test (SigmaStat 3.0; SPSS Inc., Chicago, IL). The detection limit of each test, for a given day, was the smallest concentration of complexes giving a signal significantly different ( p b 0.05) from the negative control. Our two in-house tests were carried out and analysed in the same conditions.

Results

Commercial tests

The results obtained with the commercial ELISA and ECL tests are presented in Fig. 1 and Table 1.

Results of the commercial ELISA

The standard deviation between triplicate measurements (evaluating reproducibility) was 4% of the mean and that between the nine values obtained over the 3 days of measurement (evaluating repeatability) was 6% of the mean. We checked that straight lines were obtained when the signals obtained with the commercial ELISA were plotted against complex concentration (R 2 of at least 0.99). Gradients of the extrapolated straight lines were between 0.00127 and 0.0148. Statistical tests showed that the significance threshold was 1.56 ng/ml for each of the 3 days, and the signal-to-noise ratio corresponding to this threshold was between 1.20 and 1.22.

Results of the commercial ECL assay

The standard deviation between triplicate measurements (evaluating reproducibility) was 3% of the mean and that for the nine values obtained over the 3 days of measurement (evaluating repeatability) was 7% of the mean. We checked that straight lines were obtained when the signals obtained with the commercial ECL assay were plotted against complex concentration (R 2 of at least 0.98). The gradients of the extrapolated straight lines were between 591 and 865. It should be noted that gradients depend upon the units in which signals are expressed; thus gradients between ELISA and ECL cannot be directly compared on a numerical basis. Statistical tests showed that the detection limit was 0.78 ng/ml for the first 2 days and 0.39 ng/ml for the third day. The signal-to-noise ratio corresponding to this threshold was 1.15-1.34.

Comparison of the commercial tests

The reproducibility of the commercial ELISA was high (S.D. = 4% of the mean) and within the range of values reported by [START_REF] Poli | Development of sensitive colorimetric capture ELISAs for Clostridium botulinum neurotoxin serotypes E and F[END_REF] (2-5%) regarding ELISAs for the detection of BotNT E and F. The repeatability of this ELISA was also high (S.D. = 6% of the mean), although the S.D. value obtained was equivalent to the highest value reported by Poli et al. The reproducibility (S.D. = 5%) and repeatability (S.D. = 8%) of the commercial ECL assay were slightly lower but of the same magnitude as those of the commercial ELISA. A more reproducible ECL assay (S.D. = 3%) was described by [START_REF] Golla | A sensitive, robust high-throughput electrochemiluminescence assay for rat insulin[END_REF], but this test was less reproducible (S.D. = 13%) than ours for low analyte (insulin) concentrations.

The detection limit of the commercial ELISA was 1.56 ng/ml BotNT B complexes and that of the com- The main elements of the comparison between commercial tests are given, including mean reproducibilities and repeatabilities (calculated as the standard deviation for each day and averaged, or on all experimental values, respectively, and expressed as a percentage of the experimental values) plus detection thresholds, signal-to-noise ratios, and linearity characteristics for each day of experiment. mercial ECL test was 0.39-0.78 ng/ml. The betweenday variation in the detection threshold of the ECL assay is linked to the repeatability of the test and its value is probably due to a threshold effect of our dilution factor. The commercial ECL assay therefore appears to be two to four times more sensitive than the commercial ELISA.

In-house tests

The results obtained with the ELISA and ECL tests we developed are presented in Fig. 2 andTable 2.

Results of in-house ELISA

The standard deviation between triplicate measurements (evaluating reproducibility) was 2% of the mean and that between the nine values obtained over 3 days (evaluating repeatability) was 4% of the mean. We checked that straight lines were obtained when the signals obtained with our ELISA were plotted against the complex concentration (R 2 of at least 0.98). The gradients of the extrapolated straight lines were between 0.0029 and 0.0036. Statistical tests showed that the threshold of significance was 3.12 ng/ml for each of the 3 days. The signal-to-noise ratio corresponding to this threshold was between 1.10 and 1.11.

Results of the in-house ECL assay

The standard deviation between triplicate measurements (evaluating reproducibility) was 5% of the mean and that between the nine values obtained over 3 days (evaluating repeatability) was 8% of the mean. We checked that straight lines were obtained when the signals obtained with our ECL assay were plotted against the complex concentration (R 2 of at least 0.97). The gradients of the extrapolated straight lines were between 132 and 202. Statistical tests showed that the threshold of significance was 1.56 ng/ml for the first day and 0.78 for each of the next 2 days. The signal-tonoise ratio corresponding to this threshold was between 1.14 and 1.38.

Comparison of the in-house tests

The reproducibility (S.D. = 2%) and repeatability (S.D. = 4%) of our ELISA were excellent, and were slightly better than those of the commercial ELISA (4% and 6%, respectively). The reproducibility (S.D. = 5%) and repeatability (S.D. = 8%) of our ECL assay were lower than those of our ELISA, but much higher than those for the less reproducible ECL assays (S.D. = 13%) evaluated by [START_REF] Golla | A sensitive, robust high-throughput electrochemiluminescence assay for rat insulin[END_REF].

The detection limit of our ELISA was 3.12 ng/ ml BotNT B complexes. This value is twice that of the commercial ELISA, probably due to the slope of the signal-to-background noise straight line of our ELISA, which was about 25% of that for the commercial ELISA. This may reflect, for example, differences in antibody reactivity, with our antibodies being less reactive than those used in the commercial ELISA. Based on the use of these antibodies, our ELISA appeared to have been correctly optimized.

The detection threshold of our ECL assay was 0.78-1.56 ng/ml. As for the commercial ECL assay, the between-day variability in sensitivity is linked to test repeatability and its value depends on a threshold effect of our dilution factor. The detection threshold for the commercial ECL assay was 0.39-0.78 ng/ml. Our ECL assay was therefore only 50% as sensitive as the commercial ECL assay. This difference appears to be associated with the gradient of the signal-to-noise line for our ECL test, which, like that for our ELISA, was only about a quarter that of the commercial ECL test. Both of these observations suggest that our antibodies are responsible for these differences and our ECL test also appeared to have been correctly optimized.

Our ECL test is therefore two to four times more sensitive than our ELISA.

Discussion

In this work, we could have used either Bot NT B complexes or the neurotoxin itself as antigen. The complexes are more stable than the purified neurotoxin, and can be frozen for long-term storage according to the manufacturer. In addition, the neurotoxin may be denatured in a variable manner during purification [START_REF] Ferreira | Comparison of the mouse bioassay and enzyme-linked immunosorbent assay procedures for the detection of type A botulinal toxin in food[END_REF]. We therefore decided to use complexes as the antigen, which has the significant advantage of corresponding to certain realistic conditions for implementing these tests. Frozen storage in aliquots allowed for a high repeatability of the tests, a key concern in this study, but a loss of antigenicity cannot be excluded.

We compared a commercial ELISA and ECL tests for detecting BotNT B complexes. We then optimized and compared ELISA and ECL in-house assays using the same antibodies. For both comparisons of commercial or in-house tests, the ECL test was less reproducible and less repeatable; however, it was two to four times more sensitive than the ELISA.

Another advantage of the ECL technique is rapidity, as it takes between 1 h (commercial ECL) and 2.5 h (our ECL) to perform this assay versus the ELISA, which takes between 5 h (commercial test) and 18 h (our test). However, using Superblock saturation and storage buffer (Pierce), we were able to block and then freeze our ELISA plates without affecting their sensitivity (data not shown), thereby reducing the total time required to carry out our ELISA to 5 h. This time is still twice as long as the time required to carry out our ECL test.

Comparison of the slopes for the signal-to-noise lines of each in-house test, with its commercial equivalent, suggested that our antibodies were less reactive than those used in the commercial tests. In particular, purification of polyclonal antibody on the basis of affinity to the antigen rather than to protein G may have resulted in a more reactive antibody, and therefore in a more sensitive test [START_REF] Poli | Development of sensitive colorimetric capture ELISAs for Clostridium botulinum neurotoxin serotypes E and F[END_REF]. We chose to purify the antibody based on affinity for protein G because this method is more standardised and more reliable, and the availability of this horse polyclonal antibody is limited. Purification by protein G was possible because we wanted to compare two tests representative of distinct techniques rather than to refine a single test.

The detection threshold of the commercial ELISA, calculated by statistical methods, corresponds to a signal-to-noise ratio of 1.2, which is effectively the ratio above which the BotNT B can be detected according to the manufacturer. The observed detection threshold of the commercial ELISA corresponds to a concentration of 500 pg/ml pure BotNT B, which is higher than the 20 pg/ml expected based on the data supplied by the manufacturer, but consistent with the detection thresholds of other ELISAs for detecting BotNTs (200 pg/ml neurotoxin; see [START_REF] Poli | Development of sensitive colorimetric capture ELISAs for Clostridium botulinum neurotoxin serotypes E and F[END_REF]. Elements linked to the antigen or transport and storage of reagents may account for this difference between the observed and expected sensitivities. For example, non-toxic proteins of the complex may have masked certain neurotoxin epitopes and not all of the toxin may have been released from the complex in the conditions (e.g., matrix) set for the comparison. We also cannot formally exclude the possibility that the complexes were affected by freezing, even though they are more stable than the purified neurotoxin [START_REF] Chen | Biophysical characterization of the stability of the 150-kilodalton botulinum toxin, the nontoxic component, and the 900-kilodalton botulinum toxin complex species[END_REF]. These possibilities do not invalidate the test comparisons carried out with the same antigen batch that was prepared and stored under the same conditions. When utilizing the optimised ELISA to evaluate the specificity of the antibodies, no crossreactivity was observed with BotNT E at a concentration of 100 Ag/ml, and a weak cross-reactivity was observed with BotNT A as it had a limit of detection 300 times higher than BotNT B.

The detection threshold of the commercial ECL test, calculated by statistical tests, corresponds to a signal-to-noise ratio of 1.15-1.34, which is lower than the ratio (2) beyond which BotNT can be affirmed according to the test's manufacturer. It should be noted that although the calculation method recommended by the manufacturer yields detection thresholds for the ECL test that are about four times less favorable than those we calculated, our calculated detection threshold for the commercial ECL test is equivalent to a concentration of 0.13-0.26 ng/ml BotNT B, which is consistent with the thresholds reported by the test manufacturer (0.05-0.1 ng/ml) despite different calculation methods. Maximum BotNT concentrations of 50 ng/ml (commercial ECL test) or 100 ng/ml (in-house ECL test) were utilized and both gave linear responses, with the same variability as the lower doses.

Additional measurement trials were carried out in a single day, on five samples of different BotNT B complex concentrations in bdirtyQ matrices. Varying quantities of BotNT complex were spiked onto expressed swabs (1 ml of PBS per expression of each swab) of mucous membranes or solid surfaces, or in food extracts (as in [START_REF] Ferreira | Detection of preformed type A botulinal toxin in hash brown potatoes by using the mouse bioasssay and a modified ELISA test[END_REF]. Results showed that the ECL test was again twofold more sensitive than the ELISA (data not shown).

Conclusion

In this study, we compared the colorimetric ELISA and the ECL techniques, either represented by two commercial tests, or by two optimized inhouse tests that we developed using the same antibodies in both tests. All tests were aimed at Bot NT B detection. We decided to detect botulinum complexes rather than purified neurotoxin as they are more stable and this situation is more realistic for breal-worldQ scenarios. The complexes were aliquoted and frozen for storage, to ensure a high repeatability of the tests, but a loss of antigenicity can never be excluded. We analysed our results by means of ANOVA and Tukey tests to ensure that we obtained robust results for sensitivity, independent of the calculation methods proposed by certain proponents of the two techniques. Our tests employed protein G-purified antibody that could have been less reactive than an antigen-purified antibody, but this situation did not affect the validity of the comparison and relieved any ethical problems that could have been associated with disclosing the sensitivity values of a bfinalisedQ biodefense assay.

Fig. 1 .

 1 Fig. 1. Commercial ELISA and ECL tests. The data points correspond to the mean (Ferror bars) of three values and the regression lines were plotted. The ELISA data are plotted as closed symbols, and the regression lines for ELISA are plotted as solid lines. The scale for the ELISA data is shown on the left. The ECL data are plotted as open symbols and the extrapolated lines are plotted as dotted lines. The scale for the ECL data is shown on the right.

Fig. 2 .

 2 Fig. 2. In-house ELISA and ECL tests. The data points correspond to the means F error bars. The ELISA data are plotted as closed symbols and the regression lines as solid lines. The scale for the ELISA data is shown on the left. The ECL data are plotted as open symbols and the extrapolated lines as dotted lines. The scale for the ECL data is shown on the right.

V. Guglielmo-Viret et al. / Journal of Immunological Methods 301 (2005) 164-172

Acknowledgements

This work was funded by the DGA (grant no. 00 CO 014). We thank the Centre d'e ´tudes du Bouchet (CEB) for providing antibody B 2/3.


Rawan Ghnemat

Cyrille Bertelle

Gérard H E Duchamp

SWARM INTELLIGENCE ENGINEERING FOR SPATIAL ORGANIZATION MODELLING

Keywords: swarm intelligence, complex systems, self-organization, ant systems, spatial organization

In this paper, we propose a swarm intelligence algorithm to deal with dynamical and spatial organization emergence. The goal is to model and simulate the developement of spatial centers using multi-criteria. We combine a decentralized approach based on emergent clustering mixed with spatial constraints or attractions. We propose an extension of the ant nest building algorithm with multi-center and adaptive process. Typically, this model is suitable to analyse and simulate urban dynamics like gentrification or the dynamics of the cultural equipment in urban area.

INTRODUCTION

Many natural and artificial systems have emergent properties based on spatial development. This spatial development is both the result of some mecanisms from the system behavior and the actor of the system formation by morphogenetic feedback. Natural ecosystems or social organizations in urban dynamics are typically such emergent spatial organizations. The goal of this paper is to study some computable mecanisms and algorithms able to model such spatial self-organization processes, taking into account the complexity of the phenomena.

In section 2, complex system concepts are defined and their applications to urban dynamics understanding are described. Section 3 presents swarm intelligence algorithms as methodologies to implement the complex systems concepts, using distributed computations. Section 4 proposes some specific swarm intelligence methods based on ant systems in order to model the spatial organizations emergence. Ant clustering is presented as the basis of the selforganization process. An algorithm based on the usage of pheromon template is proposed as an extension of this self-organization process, allowing to control some spatial constraints during the self-organization phenomenon. Using multi-template, we propose a general methodology to model multi-criteria spatial self-organization. Experi-ments are given, using repast agent platform mixed with a geographical information system.

MODELLING SPATIAL COMPLEXITY

Complex System Concepts

From Entities to Systems

Complex system theory [START_REF] Le Moigne | La modélisation des systèmes complexes[END_REF] is based on the fact that for many applicative domains, we can find similar processes linking emergent global behavior and interaction network of constituents. The global behavior is generally not accessible using classical analytical methods.

In classical analytical methods, the global behavior of the system is the description of the equations. Simulations from these formulations, consist in obtaining the trajectories of the behavior predefined in the equation formulation.

In complex systems modelling, we have to model the constituents of the system and the interaction network or system which link these constiuents, using a decentralized approach. So the global behavior of the system cannot be understood by the description of each constituent. In complex system modelling, the global behavior is an emergent property from the interaction network or systems between its constituents and lead to the creation of an dynamical organization of these constituents This dynamical and emergent organization retro-acts on its own components. Two kinds of feedback allow to describe these phenomenon. The positive feedback means that the emergence increases the organization constitution. the negative feedback means that the emergence has regulator properties which finally stop the increasing organization constitution and allow the system stabilization.

Spatial emergence from system and environment interaction

Another major aspect of complex systems is that they can be considered as open systems. This means that they are crossed by energetical fluxes that make them evolve in a continuous way. From these energetical fluxes, complex systems can evolve through critical states, using bifurcation schema and attractors behaviors. One of the major vector or support of these energetical fluxes is the environment itself where the complex systems and their entities evolve. In many natural and artificial systems, the environement has some spatial effects which interact on the whole complexity of the phenomenon. This spatial environment can be modified by the system but he can also be the catalyst of its own evolution. Understanding and modelling the deep structural effect of the interaction between the systems and its spatial environment is the goal of the study presented in the sequel.

Application to urban dynamics

Social and human developments are typical complex systems. Urban development and dynamics are the perfect il-lustration of systems where spatial emergence, self-organization and structural interaction between the system and its components occur. In figure 1, we concentrate on the emergence of organizational systems from geographical systems. The continuous dynamic development of the organization feed-back on the geographical system which contains the organization components and their environment. The lower part of this figure explains our analysis methodology. It consists to describe many applicatives problems by dynamical graphs or environments in order to detect organizations over these dynamical environment. For the organization detection, we use swarm intelligence processes. We model the feed-back process of this emergent organization on the system constituents and its environment. To analyse or simulate urban dynamics, nowadays, we can use the great amount of geographical databases directly available for computational treatment within Geographical Information Systems. On the organi-zational level description, the new development of multiagent systems (MAS) allows nowadays to develop suitable models and efficient simulations.

The applications we focuss on in the models that we will propose in the following concerns specifically the multicenter (or multi-organizational) phenomona inside urban development. As an artificial ecosystems, the city development has to deal with many challenges, specifically for sustainable development, mixing economical, social and environmental aspects. The decentralized methodology proposed in the following allows to deal with multi-criteria problems, leading to propose a decision making assistance, based on simulation analysis.

Gentrification phenomena can be modelled using such methodology. It is typically a multi-criteria self-organization processes where appears emergent coming of new population inside urban or territorial areas. This new population firstly attracted by some criteria, brings some other charateristics which are able to modify and feedback over the environment.

Cultural dynamics processes in urban areas are also such complex systems where multi-criteria must be taken into account. A modelling of these dynamics is presented latter in this paper.

SWARM INTELLIGENCE AND SPATIAL ENVIRONMENT

Decentralized algorithms have been implemented for many years for various purposes. In this algorithm category, multi-agent systems can be considered as generic methods [START_REF]Multiagent Systems[END_REF]. Agent-based programming deals with two main categories of agent concepts: cognitive agents and reactive agents. The first category concerns sophisticated entities able to integrate, for example, knowledge basis or communications systems. Generally, efficient computations, based on these cognitive architectures, implement few agents. The second category of agents, based on reactive architecture, is expected to be used inside numerous entity-based systems. The aim of programs using such architectures, is to deal with emergent organizations using specific algorithms called emergent computing algorithms. Swarm Intelligence is the terminology used to point out such reactive agent-based methods where each entity is built with the same basis of behavior, but reacts in autonoumous way. Swarm Optimization methods concern the problems of optimization where the computation of a function extremum is based on the concept of swarm intelligence.

Ant Colony Optimization (ACO) methods [START_REF] Bonabeau | Swam Intelligence, from natural to artificial systems[END_REF] is a bioinpired method family where the basic entities are virtual ants which cooperate to find the solution of graphbased problems, like network routing problems, for example. Using indirect communications, based on pheromon deposites over the environment (here a graph), the virtual ants react in elementary way by a probabilistic choice of path weighted with two coefficients, one comes from the problem heuristic and the other represent the pheromon rate deposit by all the ants until now. The feed-back process of the whole system over the entities is modelled by the pheromon action on the ants themselves.

Particule Swarm Optimization (PSO) is a metaheuristic method initially proposed by J. Kennedy and R. Ebenhart [START_REF] Kennedy | Particle Swarm Optimization In Proceedings of IEEE International Conference on Neural Networks[END_REF].This method is initialized with a virtual particle set which can move over the space of solutions corresponding to a specific optimization problem. The method can be considered as an extension of a bird flocking model, like the BOIDS simulation from C.W. Reynolds [START_REF] Reynolds | Flocks, Herds and Schools: a distributed behavioral model In Computer Graphics[END_REF]. In PSO algorithm, each virtual particle moves according to its current velocity, its best previous position and the best position obtained from the particles of its neighborhood. The feed-back process of the whole system over the entities is modelled by the storage of this two best positions as the result of communications between the system entities.

Other swarm optimization methods have been developped like Artificial Immune Systems [START_REF] De Castro | Artificial immune system: a new computational approach[END_REF] which is based on the metaphor of immune system as a collective intelligence process. F. Schweitzer proposes also a generic method based on distributed agents, using approaches of statistical many-particle physics [START_REF] Schweitzer | Brownian Agents and Active Particles[END_REF].

The method proposed in this paper is based on Ant Clustering and Ant Nest Building, allowing to deal with self-organization processes emerging from spatial constraints and attractive areas.

EMERGENT SPATIAL ORGANIZATIONS OVER COMPLEX BEHAVIORAL CLUSTERING

We will describe in this section, the general algorithm which is proposed to model emergent spatial organizations. This algorithm is based on the ant clustering. We introduce pheromon template to spatially control the clustering from local attraction. This method is a decentralized approach which allows to combinate multi-center and multi-criteria problem and we will show how we can apply it to model cultural dynamics in urban areas. We conclude this section with the description of an adaptive process which lead to model the feedback of the emergent system on its own mecanisms.

Ant clustering

Ant clustering algorithms are inspired by the corposes or larvea classification and aggregation that the ants colony are able to do in the real life. The ants are moving inside a closed area and are able to move some material which are randomly put on this area. After a while, and without any kind of centralized coordonation, the ants success to create some material clusters. The algorithm is based on the following and very simple behavioral rules that each ant implements :

• When an ant is moving without carrying yet material and find some material, the ant will take the material respecting the probability number :

P p = k 1 k 1 + f 2 (1)
where f is the material density that the ant perceives locally around itself and k 1 is the treshold. It is easy to check that if f << k 1 then P p is near the value 1 and if f >> k 1 then P p is near the value 0.

• When an ant is moving when carrying some mate-rial, the probability to deposite it is computed by :

P d = f k 2 + f 2 (2)
where f is still the material density that the ant perceives locally around itself and k 2 is another treshold. It is easy to check that if f << k 2 then P d is near the value 0 and if f >> k 2 then P d is near the value 1.

In figure 2, we show an implementation of this algorithm using the multi-agent platform called Repast [START_REF]Repast web site[END_REF]. The java version of this platform includes some packages allowing to interface with geographical database and geographical information systems (GIS). In figure 2, the graphical output windows is made under OpenMap which is a Figure 3. Templates and associated Ant Nest Building Simulation. On the left, with one queen. On the right with two queen GIS developped in Java. In figure, the materials moved by the ants are the small grey circles, the ant moving without material are the green circles and the ant carrying material are the red circles.

Spatial constraints using template

The ant clustering shows some spatial self-organizations but has the specificity to generate clusters at random places. According to the first random moves that the ants start to do in the beginning of the algorithm, some material will initiate aggregation and the clustering processus will complete this aggregation from these initial random first aggregations. To simulate some urban dynamics, we need to introduce specific location with respect to city center for example or cultural equipments. The clustering here will represent the people usage of these centers or equipments and we need to introduce an attractive effect by using a pheromon template. This method follow the algorithm known as Ant Nest Building [START_REF] Bonabeau | Swam Intelligence, from natural to artificial systems[END_REF]. In ant colonies, the center corresponds to the position of the queen which needs to build the nest and the ant colony moves around it to protect the nest by various material taken on the ground. The queen emits a pheromon which allows to attract the ants during their building. The ant has to deposite the material carried only if the pheromon quantity perceived belongs to a specific range. We use an attractive fonction called P t , corresponding to a pheromon template and represented by the left top part of the figure 3.

Using this template function, we remplace in the clustering algorithm, the two provious probabilities defined in equation ( 1) and equation ( 2) by

P ′ p = P p (1 -P t ) (3)
P ′ d = P d P t (4)

Multi-template modelling

The previous subsection describes one local attractive process characterized by the queen and its pheromon template emission. The advantage of this method is to be able to combine the solutions of multi-center and multi-criteria problems, using interactive processes, each one is represented by a queen and its pheromon template.

On the figure (3), we can see on the left part, a single queen simulation and in the right part, a simulation with two queens and two pheromon templates. It is possible also for each queen to emit many different kinds of pheromons : we called them colored pheromons. Each colored pheromon will attract only the ants associated to its color.

Application to cultural equipment dynamics

The multi-template modelling can be used to model cultural equipment dynamics as described in the figure [START_REF] Bertelle | Genetic algorithms on automata with multiplicities for adaptive agent behaviour in emergent organizations In SCI[END_REF]. On this figure, we associate to each cultural center (cinema, theatre, ...) a queen. Each queen will emit many pheromon templates, each template is associated to a specific criterium (according to age, sex, ...). Initially, we put the material in the residential place. Each material has some characteristics, corresponding to the people living in this residential area. The simulation shows the selforganization processus as the result of the set of the attractive effect of all the center and all the templates.

Adaptive Spatial Organization Feedback Implementation

As explained in the section 2, complex systems deal not only with emergent organization processus from the interaction of its own entities, but also with the feedback processus of the organization over its own components. In the proposed model, we can take into account such feedback process and we present in figure 5, an adaptive processus which makes the queen (which describes the organization itself) modify the environment and the clustering processus itself. Following the template function, the queen locally defines around it two zones. The first zone is near itself and it is expected not to find material there. The second zone corresponds to the template maximum and it is expected to find a great concentration of material there. In the simulation, we count in a dynamical way the number of materials in these two zones and when these numbers reach some tresholds, we make evolve the queen by increasing its own size and so increasing the 2 associated zones. After this evolution, the ants have to move some material following the new template function attraction. The low part of the figure shows the evolution of the queen which has evolved 6 times since the simulation beginning. On this figure, we can see the red curves counting the zones density. Each gap in these density curves correspond to an evolution of the queen.

CONCLUSION AND PERSPECTIVES

The paper develops some specific swarm intelligence algorithms based on ant colonies processes. Using such decentralized methods, we can model complex multi-center and multi-criteria self-organizations. Urban dynamics are one of the most relevent problems where these approaches can be efficient. These studies are supported by a french regional project (Haute-Normandie) dealing with the study of cultural dynamics over urban area.

Figure 1 .

 1 Figure 1. Spatial organizations Complexity Description and the Conceptual Generic Model Based on Swarm Intelligence

  (a) initial step (b) intermediate step

Figure 2 .

 2 Figure 2. Ant Clustering Simulation using Repast on OpenMap

Figure 4 .

 4 Figure 4. Cultural Equipment Dynamics Modelling