In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Example Input: Observable operator models (OOMs) and related models are one of the most important and powerful tools for modeling and analyzing stochastic systems. They can exactly describe dynamics of finite-rank systems, and be efficiently learned from data by moment based algorithms. Almost all OOM learning algorithms are developed based on the assumption of equilibrium data which is very difficult to guarantee in real life, especially for complex processes with large time scales. In this paper, we derive a nonequilibrium learning algorithm for OOMs, which dismisses this assumption and can effectively extract the equilibrium dynamics of a system from nonequilibrium observation data. In addition, we propose binless OOMs for the application of nonequilibrium learning to continuous-valued systems. In comparison with the other OOMs with continuous observations, binless OOMs can achieve consistent estimation from nonequilibrium data with only linear computational complexity.
Example Output: Spectral learning of dynamic systems from nonequilibrium data∗

Example Input: In this paper we explore a symmetry-based search space reduction technique which can speed up optimal pathfinding on undirected uniform-cost grid maps by up to 38 times. Our technique decomposes grid maps into a set of empty rectangles, removing from each rectangle all interior nodes and possibly some from along the perimeter. We then add a series of macro-edges between selected pairs of remaining perimeter nodes to facilitate provably optimal traversal through each rectangle. We also develop a novel online pruning technique to further speed up search. Our algorithm is fast, memory efficient and retains the same optimality and completeness guarantees as searching on an unmodified grid map.
Example Output: Symmetry-Based Search Space Reduction For Grid Maps

Example Input: In this paper, we introduce a lightweight dynamic epistemic logical framework for automated planning under initial uncertainty. We reduce plan verification and conformant planning to model checking problems of our logic. We show that the model checking problem of the iteration-free fragment is PSPACE-complete. By using two non-standard (but equivalent) semantics, we give novel model checking algorithms to the full language and the iteration-free language.
Example Output:
A Dynamic Epistemic Framework for Conformant Planning