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.

Uma cidade para pessoas: funcionalidade, racionalidade e emotividade nas relações mobiliário urbano, espaço público e cidadãos

This research investigates how functionality, rationality, and emotionality applied to urban furniture design contribute to the organization, legibility, and qualification of public spaces, according to different layouts, physical and visual qualities of the urban furniture as well as the quality of urban infrastructure that may influence the uses and appropriation of urban spaces by pedestrians, turning those spaces into socially centripetal or centrifugal places. The work consists of two parts. First refers to a bibliographical review concerning two main issues of the investigation: product design and legibility of public space, defining the conceptual and theoretical bases, linked to methodological strategies aimed at systemic planning and integrated management of urban furniture design and legibility of public spaces (sidewalks), that are necessary to define the existing relationships among the user s interface (pedestrians); product (urban artifacts); built environment (sidewalks). The second part refers to the achievement of empirical approach throughout visual analysis of public spaces and the functional and qualitative evaluation of the existing urban furniture in the central neighborhood of Cidade Alta, Natal, RN, according to the theoretical researched concepts and methodological procedures. The results expose the weaknesses and levels of intensity arising from the relations among public space, urban furniture, and users, revealing the need for theoretical and practical approaches which would help the decision-making in planning, designing and integrating innovative, sustainable, and ethical solutions in order to design attractive public spaces that could provide sociability and citizenship throughout integrated public management, city systemic thinking and urban identity. The suggested guidelines at the end of this research will provide the necessary strategies to design suitable urban furniture systems according to aesthetic and practical urban infrastructure and city context, aiming to ease visual and physical conflicts that may negatively interfere with the appropriation of public spaces by the citizens