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.

Q: 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.

A: Spectral learning of dynamic systems from nonequilibrium data∗
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Q: Language learning is thought to be a highly complex process. One of the hurdles in learning a language is to learn the rules of syntax of the language. Rules of syntax are often ordered in that before one rule can applied one must apply another. It has been thought that to learn the order of n rules one must go through all n! permutations. Thus to learn the order of 27 rules would require 27! steps or 1.08889x10 steps. This number is much greater than the number of seconds since the beginning of the universe! In an insightful analysis the linguist Block ([Block 86], pp. 62-63, p.238) showed that with the assumption of transitivity this vast number of learning steps reduces to a mere 377 steps. We present a mathematical analysis of the complexity of Block’s algorithm. The algorithm has a complexity of order n given n rules. In addition, we improve Block’s results exponentially, by introducing an algorithm that has complexity of order less than n log n.

A: On the complexity of learning a language: An improvement of Block’s algorithm
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Q: Transcription of broadcast news is an interesting and challenging application for large-vocabulary continuous speech recognition (LVCSR). We present in detail the structure of a manually segmented and annotated corpus including over 160 hours of German broadcast news, and propose it as an evaluation framework of LVCSR systems. We show our own experimental results on the corpus, achieved with a state-of-the-art LVCSR decoder, measuring the effect of different feature sets and decoding parameters, and thereby demonstrate that real-time decoding of our test set is feasible on a desktop PC at 9.2 % word error rate.

A:
A Broadcast News Corpus for Evaluation and Tuning of German LVCSR Systems
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