p2 paragraph 1 (fait par téléphone) [Decentralized algorithms have been implemented since many years]--> [Decentralized algorithms have been implemented for many years] p3 [same basis of behavior, but react in autonoumous way.]--> [same basis of behavior, but reacts in an autonoumous way.] [function extramum is based on the concept of the swarm intelligence.]--> [function extremum is based on the concept of swarm intelligence.] [Using indirect communications, based on pheromons deposite]--> [Using indirect communications, based on pheromon deposits] [the virtual ants react in elementary way by]--> [the virtual ants reacts in elementary ways by] [This method is initialized with a virtual particles set]--> [This method is initialized with a virtual particle set] [each virtual particles moves]--> [each virtual particle moves] [for each individual, a set of some arbitrary complex]--> [for each individual, a set of arbitrary complex] p4 [In that way, we are able to build e ective operations]--> [In this way, we are able to build e ective operations] [the properties of the algebraic structures where belong the output data]--> [the properties of the algebraic structures which belong the output data] p5 Definition 2 [Q = fS1; S2    Sng is the finite set of state;]--> [Q = fS1; S2    Sng is the (finite) set of states;] [function over the set of states]--> [function on the set of states] [which associates to each initial state a value of K]--> [which associates to each initial state a value in K] [and to non- initial state a zero value]--> [and to each non- initial state a zero value] [is a function over the set states]--> [is a function on the set of states] [and to non- initial state a zero value]--> [and to each non- initial state a zero value] [The figure 2 describes the linear]--> [Figure 2 describes the linear] [For these probabilistic automata, the sum of the coecients of each matrix lines is equal to 1.]--> [For these probabilistic automata, the sum of the coefficients of each matrix lines is equal to 1 (being the sum of outgonig and loop probability).] p6 Definition 3 [represent the initial and final transitions]--> [represent the initial and final costs] [agent actions, eventually associated to a]--> [agent actions, possibly associated to a] [which is directly induced by the metric of the spatial location]--> [which is directly induced by the metrics of the spatial location] [to de ne such behavioral distance which lead to powerful]--> [to de ne such a behavioral distance which leads to powerful] [multiplicities over the semiring K, we define the evaluation]--> [multiplicities over the semiring K. We define the evaluation] p7 [a semi-distance or pseudometrics]--> [a distance or metrics] [the sequence of all the lines of the matrices from the linear representation]--> [the sequence of all the lines of the matrices of the linear representation] [is created from a two matrices linear representation;]--> [is created from a linear representation of two matrices;] p8 [as the result of the chromosomes crossing]--> [as the result of chromosome crossings] [With a low probability, each matrix lines]--> [With a low probability, each matrix row] < row ; colonne --> column>> p9 [distances de ned on agent set. The rst is the spatial distance associated to the agent spatial location]--> [distances de ned on agent sets. The first is the spatial distance associated with the agent spatial location] Definition 7 [neighbourhood of the agent x, relatively to its spatial location]--> [neighbourhood of the agent x, relative to its spatial location] [behavioral semi-distance]--> [behavioral distance] [These community swarms formation]--> [These community swarm formation] [automata of all the agent which composed these emergent communities.]--> [automata of all agents which compose these emergent communities.] p11 Figure 5 [Two examples of the resultat of the selection operator]--> [Two examples of the result of selection operators]