Information Geometry of Spatially Periodic Stochastic Systems

Periodic Solutions of Spatially Periodic, Even Hamiltonian Systems

Spatially periodic stochastic system with infinite globally coupled oscillators.

In this paper we study a spatially periodic stochastic system with infinite globally coupled oscillators driven by a constant force F. With two typical models we show that when F=0 there is a nonequilibrium transition between the state with zero mean field (s=0) and the state with nonzero mean field (s not equal 0). For model I, the transition is not a phase transition, while for the model II i...

Stochastic Analysis of Periodic Real-Time Systems

This paper describes a stochastic analysis method for general periodic real-time systems. The proposed method accurately computes the response time distribution of each task in the system, thus making it possible to determine the deadline miss probability of individual tasks, even for systems with maximum utilization factor greater than one. The method uniformly covers both fixed-priority sched...

Information geometry on complexity and stochastic interaction

Stochastic Reasoning, Free Energy, and Information Geometry

Belief propagation (BP) is a universal method of stochastic reasoning. It gives exact inference for stochastic models with tree interactions and works surprisingly well even if the models have loopy interactions. Its performance has been analyzed separately in many fields, such as AI, statistical physics, information theory, and information geometry. This article gives a unified framework for u...