# Issues in data expansion in understanding criticality in biological systems

## TL;DR

This paper develops an analytical method for expanding neural data sets to assess criticality in biological systems, revealing limitations in current data analysis approaches and questioning the universality of critical behavior.

## Contribution

It introduces a new analytical approach for data expansion in neural systems and demonstrates its implications for understanding criticality in biological data.

## Key findings

- Expanding data sets analytically can alter perceived critical temperatures.
- Not all experimental data are suitable for criticality analysis.
- Computational analysis may give misleading indications of criticality.

## Abstract

At the point of a second order phase transition also termed as a critical point, systems display long range order and their macroscopic behaviors are independent of the microscopic details making up the system. Due to these properties, it has long been speculated that biological systems that show similar behavior despite having very different microscopics, may be operating near a critical point. Recent methods in neuroscience are making it possible to explore whether criticality exists in neural networks. Despite being large in size, many data sets are still only a minute sample of the neural system and methods towards expanding these data sets have to be considered in order to study the existence of criticality. In this work we develop an analytical method of expanding a dataset to the large N limit so that statements about the critical nature of the data set could be made. We also show using a particular dataset analyzed computationally in literature that expanding data sets keeping the moments of the original data set need not lead to unique values of the critical temperature when the large N limit is considered analytically, despite the mirage of them appearing to do so when analyzed computationally. This suggests that not all available data sets from experiments are amenable for understanding the critically of the underlying system.