William Marshall, Jaime Gomez-Ramirez, Giulio Tononi
Abstract
Integrated information (Φ) is a measure of the cause-effect power of a physical system. This paper investigates the relationship between Φ as defined in Integrated Information Theory and state differentiation ([Formula: see text]), the number of, and difference between potential system states. Here we provide theoretical justification of the relationship between Φ and [Formula: see text], then validate the results using a simulation study. First, we show that a physical system in a state with high Φ necessarily has many elements and specifies many causal relationships. Furthermore, if the average value of integrated information across all states is high, the system must also have high differentiation. Next, we explore the use of [Formula: see text] as a proxy for Φ using artificial networks, evolved to have integrated structures. The results show a positive linear relationship between Φ and [Formula: see text] for multiple network sizes and connectivity patterns. Finally we investigate the differentiation evoked by sensory inputs and show that, under certain conditions, it is possible to estimate integrated information without a direct perturbation of its internal elements. In concluding, we discuss the need for further validation on larger networks and explore the potential applications of this work to the empirical study of consciousness, especially concerning the practical estimation of Φ from neuroimaging data.
This research output has an Altmetric Attention Score of 2. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 31 July 2016.
All research outputs
#14,268,650
of 22,881,154 outputs
Outputs from Frontiers in Psychology
#15,165
of 29,979 outputs
Outputs of similar age
#201,364
of 351,559 outputs
Outputs of similar age from Frontiers in Psychology
#254
of 388 outputs
Altmetric has tracked 22,881,154 research outputs across all sources so far. This one is in the 35th percentile – i.e., 35% of other outputs scored the same or lower than it.
So far Altmetric has tracked 29,979 research outputs from this source. They typically receive a lot more attention than average, with a mean Attention Score of 12.5. This one is in the 46th percentile – i.e., 46% of its peers scored the same or lower than it.
Older research outputs will score higher simply because they've had more time to accumulate mentions. To account for age we can compare this Altmetric Attention Score to the 351,559 tracked outputs that were published within six weeks on either side of this one in any source. This one is in the 40th percentile – i.e., 40% of its contemporaries scored the same or lower than it.
We're also able to compare this research output to 388 others from the same source and published within six weeks on either side of this one. This one is in the 31st percentile – i.e., 31% of its contemporaries scored the same or lower than it.
