Undersampled Critical Branching Processes on Small-World and Random Networks Fail to Reproduce the Statistics of Spike Avalanches

The power-law size distributions obtained experimentally for neuronal avalanches are an important evidence of criticality in the brain. This evidence is supported by the fact that a critical branching process exhibits the same exponent t~3=2. Models at criticality have been employed to mimic avalanche propagation and explain the statistics observed experimentally. However, a crucial aspect of neuronal recordings has been almost completely neglected in the models: undersampling. While in a typical multielectrode array hundreds of neurons are recorded, in the same area of neuronal tissue tens of thousands of neurons can be found. Here we investigate the consequences of undersampling in models with three different topologies (two-dimensional, small-world and random network) and three different dynamical regimes (subcritical, critical and supercritical). We found that undersampling modifies avalanche size distributions, extinguishing the power laws observed in critical systems. Distributions from subcritical systems are also modified, but the shape of the undersampled distributions is more similar to that of a fully sampled system. Undersampled supercritical systems can recover the general characteristics of the fully sampled version, provided that enough neurons are measured. Undersampling in two-dimensional and small-world networks leads to similar effects, while the random network is insensitive to sampling density due to the lack of a well-defined neighborhood. We conjecture that neuronal avalanches recorded from local field potentials avoid undersampling effects due to the nature of this signal, but the same does not hold for spike avalanches. We conclude that undersampled branching-process-like models in these topologies fail to reproduce the statistics of spike avalanches.

Relações interorganizacionais e eficiência coletiva: um estudo de caso no arranjo produtivo local de confecções do Agreste de Pernambuco

This work is a study in the Local Productive Arrangement of confections from Agreste of Pernambuco, as a relevant sector in economic and social aspect. This research has as central aim to understand how the inter-organizational relations influence the collective efficiency of arrangement. The theoretical framework employed highlights the approaches that deal with the benefits of business agglomeration for the develop­ment of firms and regions. It has discussed the approach of small and medium enter­ prises and industrial districts (SCHMITZ, 1997), which introduce the concept of col­ lective efficiency, explaining that only those externalities explained by Marshall (1996) are not sufficient to explain the competitive advantage of enterprises, expand­ing the idea that organizations achieve competitive advantage not acting alone. To examine the influences of relations in the collective efficiency, it has been taken as analytical perspective theory of social networks (GRANOVETTER, 1973, 1985; BURT, 1992; UZZI, 1997) because it has believe that this approach provides subsi­ dies for a structural analysis of social relationships in face the behavior of human ac­tion. By examining the organizations in a social network, you should understand the reason of this establishment of the relationship, their benefits, and as the information flow takes place and density of links between the actors (Powell; SMITH-DOERR, 1994). As for the methods, this study is characterized as a case study, in according to the purposed objectives, in addition to qualitative method. Also, due to recovering of the historical milestones of the arrangement, it is used a sectional approach with longitudinal perspective (VIEIRA, 2004). The primary and secondary data were used in order to understand the evolutionary process of the sector and their inter-actors re­ lationships in the arrangement for the promotion of development, for both, was used the contend and documentary analysis technique, respectively (DELLAGNELO ; SIL­VA, 2005). The approach of social networks has permitted understand that social re­lationships may extend the collective efficiency of the arrangement, and therefore need to develop policies that encourage the legalization of informal companies in ar­rangement, by showing up themselves representative. Thus, the relations estab­ lished in LPA of confections from Agreste of Pernambuco need for more effective mechanisms to broaden the collective efficiency. Therefore, this way as take place has directly benefited only a group of companies that are linked in some way the sup­portive institutions. So we can conclude that the inter-actor relations have limited the collective efficiency of LPA, being stimulated by the institutions in support only to groups of entrepreneurs, even those that produce external relations for all clustered companies