Relating Fisher Information to Order Parameters
Critical phenomena and phase transitions have been reported in a very broad range of systems, ranging from physical to biological to computational. Phase transitions have been vigorously studied for many decades, producing fundamental scientific and technological results. We study phase transitions and relevant order parameters via statistical estimation theory using the Fisher information matrix. The assumptions that we make limit our analysis to order parameters representable as a negative derivative of thermodynamic potential over some thermodynamic variable. Nevertheless, the resulting representation is sufficiently general and explicitly relates elements of the Fisher information matrix to the rate of change in the corresponding order parameters. The obtained relationships allow us to identify, in particular, second-order phase transitions via diver- gences of individual elements of the Fisher information matrix. See [PLOW11] for more.
Phase Transitions in Least-Effort Communications
Zipf’s law states that given a body of natural language text, the most frequent word will occur approximately twice as often as the second most frequent word, three times as often as the third most frequent word, etc.
We critically examine a specific model that attempts to explain emergence of these power laws in human language. The model is based on the principle of least effort in communications — specifically, the overall effort is balanced between the speaker effort and listener effort, with some trade-off. By explicitly solving a continuous optimisation problem, our results contrast Zipf’s law found by heuristic search (that attained only local minima) in the vicinity of the transition between referentially useless systems and indexical reference systems, with an inverse-factorial (sub-logarithmic) law found at the transition that corresponds to global minima. The inverse-factorial law (i.e., not a power law) is observed to be the most representative frequency distribution among optimal solutions. Check [PAOP10] for details. In an earlier study, we also aimed to reproduce the results found by heuristic search.
Inverse Steering Behaviors
Steering behaviors are a set of reactive algorithms used for navigating autonomous agents in their environment. Combinations of steering behaviors can be used to create complex, interesting and lifelike movement. However, special care has to be given to their arbitration. If done the wrong way, the arbitration can lead to suboptimal, undesired, or even catastrophic results in certain situations. We solve these problems by introducing inverse steering behaviours (ISBs) for controlling physical agents. Inverse steering behaviors change the original concept of steering behaviours and facilitate improved arbitration between different options by using cost based heuristics. Inverse steering behaviours have commercial applications in video games, but also in the Pathfinder Emergency Egress Simulator. The work has been published as chapter in a book on Game Programming [AMO06].