Artificial networks that resemble brain networks (in terms of predefined topological features) are useful to investigate the specific characteristics of brain networks. However, the problem of obtaining such artificial networks is difficult given the number of network's components and the topological constraints involved. Structural optimization problems in brain networks can be defined as those that imply the identification of a network topology that satisfy a number of constraints (generally determined by the characteristics of an original neuronal or brain network) and are optimal with respect to a (or set of) measure(s) defined in the space of networks.

In (Sporns_and_Koetter:2004), motifs are used to study the information processing of brain networks. In these networks, structural motifs are identified as a set of brain areas and pathways that can potentially engage in different patterns of interactions. Authors introduce functional motifs to refer to specific combinations of nodes and connections (contained in the structural motifs) that may be recruited or activated in the course of neural information processing.

We use MATEDA to implement the evolution of artificial networks by simultaneoulsy optimizing the number of structural and functional motifs. By rewiring original random networks, a Pareto set approximation of the space of network topologies (subject to constraints on the degree of each vertex) is obtained. The evolved networks are then compared to the original brain networks across different attributes. The code included below shows the Mateda implementation of the evolution of networks that resemble the macaque visual cortex network which together with other Cortical Connectivity Data Sets is available from the Brain Connectivity Toolbox home page We also used the brain connectivity toolbox functions to implement the computation of the number of structural and functional motifs for the artificial networks evolved.

In the code, the learning and sampling steps are used to rewire the networks in the selected population fulfiling that the networks obtained keep the same indegree and outdegree distribution of the original macaque network. The seeding method generates an initial population that satisfies the same topological constraints.

  % For a description of the evolution of artificial brain networks 
  % see (Sporns_and_Koetter:2004) 
 
  global outconfs;
  global outdegree;
 
  load('fve30'); % The original brain network matrix is kept in variable CIJ
  NumbVar = size(CIJ,1)^2;
  Card(1,:) = zeros(1,NumbVar); 
  Card(2,:) = ones(1,NumbVar);  
  
  F = 'MatrixNumberMotifs'; 
  InDegree = sum(CIJ');
  OutDegree = sum(CIJ);
  
  PopSize = 500;  cache  = [1,1,1,1,1];  maxgen =  200;
 
  selparams(1:2) = {0.5,'ParetoRank_ordering'};
  edaparams{1} = {'learning_method','LearnMutationPoints',{PopSize}};
  edaparams{2} = {'sampling_method','SampleMutatedNetworks',{PopSize}};
  edaparams{3} = {'selection_method','truncation_selection',selparams};
  edaparams{4} = {'replacement_method','best_elitism',{'ParetoRank_ordering'}};
  edaparams{5} = {'stop_cond_method','max_gen',{maxgen}}; 
  
  seeding_params{1} = [InDegree];
  seeding_params{2} =  [OutDegree]';
  edaparams{6} = {'seeding_pop_method','seeding_constrained_network',seeding_params};  
  [AllStat,Cache]=RunEDA(PopSize,NumbVar,F,Card,cache,edaparams) 

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