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...our networks constrained in 2D space percolate. To do so, we measure the size S1 of the giant connected component (GCC) and the size S2 of the second largest component (GCC2) as a function of the age =-=[18,19]-=-. Figure 3B shows that the number of nodes forming such connected components smoothly increases at the same rate along the first days of the network development, up to the DIV 6 when the difference in...

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...works are identified as a single-scale homogeneous population of nodes. This is in agreement with reports on many other biological systems like the neuronal network of the worm Caenorhabditis elegans =-=[24,25]-=-, and suggests the existence of physical costs for the creation of new connections and/or nodes limited capacity [26]. While the number of neighbors (the degree) is a quantity retaining information at...

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...and 7. These ‘‘hubs’’ at the peak days of the culture evolution result from a branching process, allowing each single neuron to reach a larger neighborhood. Thus, at variance with scale-free networks =-=[22,23]-=-, our cultured and clustered networks are identified as a single-scale homogeneous population of nodes. This is in agreement with reports on many other biological systems like the neuronal network of ...

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...and 7. These ‘‘hubs’’ at the peak days of the culture evolution result from a branching process, allowing each single neuron to reach a larger neighborhood. Thus, at variance with scale-free networks =-=[22,23]-=-, our cultured and clustered networks are identified as a single-scale homogeneous population of nodes. This is in agreement with reports on many other biological systems like the neuronal network of ...

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...works are identified as a single-scale homogeneous population of nodes. This is in agreement with reports on many other biological systems like the neuronal network of the worm Caenorhabditis elegans =-=[24,25]-=-, and suggests the existence of physical costs for the creation of new connections and/or nodes limited capacity [26]. While the number of neighbors (the degree) is a quantity retaining information at...

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...rk-wide quantities. For that purpose, we calculated several topological properties of the extracted adjacency matrices (using the Matlab Boost Graph Library package and the Brain Connectivity Toolbox =-=[20]-=-), whose definitions are provided in [5,20]. In particular, we analyzed the clustering coefficient (C), the average shortest path length (L), the local (Eloc) and global (Eglob) efficiency [8], the ne...

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...igurations, which in graph theory are termed smallworld [7], are ubiquitously found in real-world networking systems. Small-world structures have been shown to enhance the system’s overall efficiency =-=[8,9]-=-, while concurrently warranting a good balance between two apparently antagonistic tendencies for segregation and integration in structuring processes, needed for the network’s parallel, and yet synth...

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...igurations, which in graph theory are termed smallworld [7], are ubiquitously found in real-world networking systems. Small-world structures have been shown to enhance the system’s overall efficiency =-=[8,9]-=-, while concurrently warranting a good balance between two apparently antagonistic tendencies for segregation and integration in structuring processes, needed for the network’s parallel, and yet synth...

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...e the attainment of its mature state is not random, being instead governed and characterized by processes eventually leading to configurations which are comparable to many other real complex networks =-=[5]-=-. In particular, networking neurons simultaneously feature a high overall clustering and a relatively short path-length between any pair of them [6]. Such configurations, which in graph theory are ter...

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...gree-degree correlations, i.e. to quantify whether the degrees of two connected nodes are correlated. It is known, indeed, that biological networks feature generally disassortative network structures =-=[27]-=-, that is connections are more likely to be established between high-degree and low-degree nodes. In our system, we used the assortativity coefficient described in the Experimental set-up section. Fig...

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...biological systems like the neuronal network of the worm Caenorhabditis elegans [24,25], and suggests the existence of physical costs for the creation of new connections and/or nodes limited capacity =-=[26]-=-. While the number of neighbors (the degree) is a quantity retaining information at the level of a single node, one can go further to inspect degree-degree correlations, i.e. to quantify whether the d...

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...bly of isolated (cultured) neurons self-organizes to form a complex neural network is a fundamental problem [1–3]. Despite their more limited, and yet laboratory-controllable, repertoire of responses =-=[1,4]-=-, the understanding of such cultures’ organization is, indeed, a basis for the comprehension of the mechanisms involved in their in vivo counterparts, and provide a useful framework for the investigat...

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...n neuronal cultures restricted their attention to functional networks (statistical dependence between nodes activities) and not to the physical connections supporting the functionality of the network =-=[11]-=-. The reason behind this drawback is that the majority of investigations focused on excessively dense cultures, hindering the observation of their fine scale structural connectivity. Although there ar...

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...in vitro cultured neuronal network, and such an evidence actually links to other studies where assortativity was found in simple in vivo neuronal systems, like the C. elegans neural network structure =-=[28]-=-. Spatial-growth model A series of previous studies [15,16] singled out tension along neurites and adhesion to the substrate as the two main factors conditioning the neuronal self-organization into a ...

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...maintained in darkness under controlled temperature (290C) and humidity (70%). The density at which cultures are seeded determines the maturation rate and the spatial organization at the mature state =-=[15,16]-=-. For the purpose of this work, aimed at studying the network evolution into a clustered network, 6 dense cultures of 12 ganglia each (*1,200 neurons) were used and monitored during 18 days in vitro (...

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...a basis for the comprehension of the mechanisms involved in their in vivo counterparts, and provide a useful framework for the investigation of neuronal network development in real biological systems =-=[3]-=-. Some previous studies highlighted the fact that the structuring of a neuronal cultured network before the attainment of its mature state is not random, being instead governed and characterized by pr...

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... are comparable to many other real complex networks [5]. In particular, networking neurons simultaneously feature a high overall clustering and a relatively short path-length between any pair of them =-=[6]-=-. Such configurations, which in graph theory are termed smallworld [7], are ubiquitously found in real-world networking systems. Small-world structures have been shown to enhance the system’s overall ...

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...ies striving to indirectly infer the underlying anatomical connectivity from the functional network, it has been shown that strong functional correlations may exist with no direct physical connection =-=[12]-=-. Only few studies dealt with the physical wiring circuitry. However, on the one hand, only small networks were considered; on the other hand, how the network state evolves during the course of the ma...

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...h information for devising a proper growth model, qualitatively reproducing the set of our experimental evidence. Together with confirming several results of previous works on functional connectivity =-=[13]-=-, or on morphological structuring at a specific stage of the cultures’ evolution [6], we offer a systematic characterization of several topological network’s measures from the very initial until the f...

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...the growth rate decreases and a different mechanism starts shaping the network: tension is generated along the neurites as they stretch between neurons or bifurcation points to form straight segments =-=[17]-=-. The latter process favors neuron migration, giving rise to clusters of neurons, and the fusion of parallel neurites into thicker bundles together with the retraction of those branches which did not ...

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...bly of isolated (cultured) neurons self-organizes to form a complex neural network is a fundamental problem [1–3]. Despite their more limited, and yet laboratory-controllable, repertoire of responses =-=[1,4]-=-, the understanding of such cultures’ organization is, indeed, a basis for the comprehension of the mechanisms involved in their in vivo counterparts, and provide a useful framework for the investigat...

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...maintained in darkness under controlled temperature (290C) and humidity (70%). The density at which cultures are seeded determines the maturation rate and the spatial organization at the mature state =-=[15,16]-=-. For the purpose of this work, aimed at studying the network evolution into a clustered network, 6 dense cultures of 12 ganglia each (*1,200 neurons) were used and monitored during 18 days in vitro (...

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...our networks constrained in 2D space percolate. To do so, we measure the size S1 of the giant connected component (GCC) and the size S2 of the second largest component (GCC2) as a function of the age =-=[18,19]-=-. Figure 3B shows that the number of nodes forming such connected components smoothly increases at the same rate along the first days of the network development, up to the DIV 6 when the difference in...

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...tly warranting a good balance between two apparently antagonistic tendencies for segregation and integration in structuring processes, needed for the network’s parallel, and yet synthetic performance =-=[10]-=-. In this paper, we experimentally investigate the self-organization into a network of an in vitro culture of neurons during the course of development, and explore the changes of the main topological ...

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...der a 12:12 h light:dark cycle from their fifth nymph growth to their early adult stage of development. At this latter stage, we followed the dissection and culturing protocol thoroughly described in =-=[14]-=-. In brief, the frontal ganglia were dissected from anesthetized animals, and enzymatically treated to soften the sheath. Ganglia were then forced to pass through the tip of a 200 ml pipette to mechan...

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...ted values for equivalent random (and lattice) null model networks (see Fig. 4B). In doing so, we follow the approach that was recently used in similar circumstances for the obtainment of null models =-=[21]-=-. According to Watts and Strogatz’s model [7], a small-world network simultaneously exhibits short characteristic path length, like random graphs, and high clustering, like regular lattices. Here, we ...