Sharif Digital Repository

Many different scaling laws are observed in financial data. As an example, the distribution of Log-Return of stock prices obey power law, provided relatively short time intervals are considered. In standard statistical physics, scaling laws are observed in critical phenomena, where the system has long-ranged correlations. Within the same context, to arrive at criticality one has to tune some external parameters, such as the temperature. Yet, there are a group of systems that tend towards criticality through their dynamics. Such systems are called self-organised critical systems.There have been proposed many different mechanisms and models to address why power laws are observed in financial... 

Experiments conducted in recent two decades indicated critical behavior in neural activity at different scales. Theoretically occurrences of these critical and power-law behavior can significantly facilitate brain activities correspondent to computation and memory tasks, but attaining the critical point essentially demands externally fine-tuning which has not been established yet. This fine-tuning often lies with placing system at transition point. Recent studies of group showed that a transition from synchronous to asynchronous phase could be achievable by a change in external parameters. At the very transition point, neuronal avalanches statistically demonstrate a power-law behavior which...