In this paper, we study Jackiw-Rebbi model, in which a massless fermion is coupled to the kink of λφ 4 theory through a Yukawa interaction. In the original Jackiw-Rebbi model, the soliton is prescribed. However, we are interested in the back-reaction of the fermion on the soliton besides the effect of the soliton on the fermion. Also, as a particular example, we consider a minimal supersymmetric kink model in (1 + 1) dimensions. In this case, the bosonic self-coupling, λ, and the Yukawa coupling between fermion and soliton, g, have a specific relation, g = √ λ/2. As the set of coupled equations of motion of the system is not analytically solvable, we use a numerical method to solve it self-consistently. We obtain the bound energy spectrum, bound states of the system and the corresponding shape of the soliton using a relaxation method, except for the zero mode fermionic state and threshold energies which are analytically solvable. With the aid of these results, we are able to show how the soliton is affected in general and supersymmetric cases. The results we obtain are consistent with the ones in the literature, considering the soliton as background.

Collective or group intelligence is manifested in the fact that a team of cooperating agents can solve problems more efficiently than when those agents work in isolation. Although cooperation is, in general, a successful problem solving strategy, it is not clear whether it merely speeds up the time to find the solution, or whether it alters qualitatively the statistical signature of the search for the solution. Here we review and offer insights on two agent-based models of distributed cooperative problem-solving systems, whose task is to solve a cryptarithmetic puzzle. The first model is the imitative learning search in which the agents exchange information on the quality of their partial solutions to the puzzle and imitate the most successful agent in the group. This scenario predicts a very poor performance in the case imitation is too frequent or the group is too large, a phenomenon akin to Groupthink of social psychology. The second model is the blackboard organization in which agents read and post hints on a public blackboard. This brainstorming scenario performs the best when there is a stringent limit to the amount of information that is exhibited on the board. Both cooperative scenarios produce a substantial speed up of the time to solve the puzzle as compared with the situation where the agents work in isolation. The statistical signature of the search, however, is the same as that of the independent search.

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The so-called size-complexity rule claims the existence of a positive correlation between organism size and number of cell types.In this spirit, here we address the relationship between organism size and number of potential tasks that can be performed.The modeling relies on the assumption that the states of the cells within the aggregates are such that the maximum fitness is realized, but also relies on the existence of tradeoffs among the distinct functions. For group sizes larger than the number of potential tasks, fitness maximization is attained when all cells in group specialize in a given task. Under this scenario, the number of potential tasks equals the number of cell types. We have found that the morphology and the topology of aggregates, as well as the developmental mode, strongly influence the dynamics of body formation. Particularly, it has been observed that more compact structures, such as sphere-like structures, are more likely to follow the claim of the size-complexity rule, whereas more fragile structures such as linear chains, which are more vulnerable to drastic changes due to division mechanisms, can, in a broad scenario, violate the size-complexity rule. K E Y W O R D S :Complexity, division of labor, evolutionary theory.