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Criticality Maximizes Complexity in Neural Tissue

View Article: PubMed Central - PubMed

ABSTRACT

The analysis of neural systems leverages tools from many different fields. Drawing on techniques from the study of critical phenomena in statistical mechanics, several studies have reported signatures of criticality in neural systems, including power-law distributions, shape collapses, and optimized quantities under tuning. Independently, neural complexity—an information theoretic measure—has been introduced in an effort to quantify the strength of correlations across multiple scales in a neural system. This measure represents an important tool in complex systems research because it allows for the quantification of the complexity of a neural system. In this analysis, we studied the relationships between neural complexity and criticality in neural culture data. We analyzed neural avalanches in 435 recordings from dissociated hippocampal cultures produced from rats, as well as neural avalanches from a cortical branching model. We utilized recently developed maximum likelihood estimation power-law fitting methods that account for doubly truncated power-laws, an automated shape collapse algorithm, and neural complexity and branching ratio calculation methods that account for sub-sampling, all of which are implemented in the freely available Neural Complexity and Criticality MATLAB toolbox. We found evidence that neural systems operate at or near a critical point and that neural complexity is optimized in these neural systems at or near the critical point. Surprisingly, we found evidence that complexity in neural systems is dependent upon avalanche profiles and neuron firing rate, but not precise spiking relationships between neurons. In order to facilitate future research, we made all of the culture data utilized in this analysis freely available online.

No MeSH data available.


Culture data branching ratios were near 1 after sub-sampling correction. The branching ratios of the culture recordings were found to be close to 1 after correcting for sub-sampling using the new method established by Wilting and Priesemann (2016) (Equation 13), with most data sets being slightly sub-critical. The basic branching ratio calculation method (Equation 11) produced branching ratios that were more widely varied and strongly sub-critical. Histogram bin sizes optimized using methods established in Terrell and Scott (1985).
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Figure 9: Culture data branching ratios were near 1 after sub-sampling correction. The branching ratios of the culture recordings were found to be close to 1 after correcting for sub-sampling using the new method established by Wilting and Priesemann (2016) (Equation 13), with most data sets being slightly sub-critical. The basic branching ratio calculation method (Equation 11) produced branching ratios that were more widely varied and strongly sub-critical. Histogram bin sizes optimized using methods established in Terrell and Scott (1985).

Mentions: We calculated the branching ratio for the culture recording data using both the basic method and new method introduced by Wilting and Priesemann (2016) (Figure 9, see Section 2.11). Using the new method, we found most recordings produced branching ratios slightly below 1 (i.e., slightly sub-critical). Using the previous basic method, we found most recordings produced branching ratios that were substantially less than 1 and much more varied. The result that the majority of the data sets produced branching ratios near 1 is strong evidence that the cultures were operating near a critical point.


Criticality Maximizes Complexity in Neural Tissue
Culture data branching ratios were near 1 after sub-sampling correction. The branching ratios of the culture recordings were found to be close to 1 after correcting for sub-sampling using the new method established by Wilting and Priesemann (2016) (Equation 13), with most data sets being slightly sub-critical. The basic branching ratio calculation method (Equation 11) produced branching ratios that were more widely varied and strongly sub-critical. Histogram bin sizes optimized using methods established in Terrell and Scott (1985).
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Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC5037237&req=5

Figure 9: Culture data branching ratios were near 1 after sub-sampling correction. The branching ratios of the culture recordings were found to be close to 1 after correcting for sub-sampling using the new method established by Wilting and Priesemann (2016) (Equation 13), with most data sets being slightly sub-critical. The basic branching ratio calculation method (Equation 11) produced branching ratios that were more widely varied and strongly sub-critical. Histogram bin sizes optimized using methods established in Terrell and Scott (1985).
Mentions: We calculated the branching ratio for the culture recording data using both the basic method and new method introduced by Wilting and Priesemann (2016) (Figure 9, see Section 2.11). Using the new method, we found most recordings produced branching ratios slightly below 1 (i.e., slightly sub-critical). Using the previous basic method, we found most recordings produced branching ratios that were substantially less than 1 and much more varied. The result that the majority of the data sets produced branching ratios near 1 is strong evidence that the cultures were operating near a critical point.

View Article: PubMed Central - PubMed

ABSTRACT

The analysis of neural systems leverages tools from many different fields. Drawing on techniques from the study of critical phenomena in statistical mechanics, several studies have reported signatures of criticality in neural systems, including power-law distributions, shape collapses, and optimized quantities under tuning. Independently, neural complexity—an information theoretic measure—has been introduced in an effort to quantify the strength of correlations across multiple scales in a neural system. This measure represents an important tool in complex systems research because it allows for the quantification of the complexity of a neural system. In this analysis, we studied the relationships between neural complexity and criticality in neural culture data. We analyzed neural avalanches in 435 recordings from dissociated hippocampal cultures produced from rats, as well as neural avalanches from a cortical branching model. We utilized recently developed maximum likelihood estimation power-law fitting methods that account for doubly truncated power-laws, an automated shape collapse algorithm, and neural complexity and branching ratio calculation methods that account for sub-sampling, all of which are implemented in the freely available Neural Complexity and Criticality MATLAB toolbox. We found evidence that neural systems operate at or near a critical point and that neural complexity is optimized in these neural systems at or near the critical point. Surprisingly, we found evidence that complexity in neural systems is dependent upon avalanche profiles and neuron firing rate, but not precise spiking relationships between neurons. In order to facilitate future research, we made all of the culture data utilized in this analysis freely available online.

No MeSH data available.