Predictability: a way to characterize complexity

Ja n 20 01 Predictability : a way to characterize Complexity

Predictability, Complexity, and Learning

We define predictive information I(pred)(T) as the mutual information between the past and the future of a time series. Three qualitatively different behaviors are found in the limit of large observation times T:I(pred)(T) can remain finite, grow logarithmically, or grow as a fractional power law. If the time series allows us to learn a model with a finite number of parameters, then I(pred)(T) ...

A NEW WAY TO EXTEND FUZZY IMPLICATIONS

The main purpose of this paper is to use a new way to extend fuzzy implications $I$ from a generalized sublattice $M$ to a bounded lattice $L$, such that the extended implications preserve many of the considered properties of fuzzy implications on $M$.Furthermore, as a special case, we investigate the extension of $(S,N)-$implications. Results indicate that the extended implications preserve ma...

Membrane reactors: A way to increase efficiency

Spatial complexity enhances predictability in food webs

The prediction of an ecosystem's response to an environmental disturbance or the artificial control of ecosystems is a challenging task in ecology. Ecological theory predicts that disturbances frequently result in unexpected responses between interacting species due to the many indirect interactions within a complex community. However, such indeterminacy appears to be unusual in nature. Here us...