In this paper we study the problem of predictability in partially observable discrete event systems, i.e., the question whether an observer can predict the occurrence of a fault. We extend the definition of predictability to consider the time interval where the fault will occur: the @math -predictability does not only specify that the fault will be predicted before it occurs, but also that the predictor will be able to predict that its occurrence will occur in @math to @math observations from now. We also provide a quadratic algorithm that decides predictability of the system.
Predictability as presented in this paper was introduced by Genc and Lafortune @cite_13 . Their approach was however only Boolean: they addressed the question can the fault be predicted before it occurs?'' They presented an exponential space algorithm using a structure similar to our optimal predictor. They also announced the existence of a polytime algorithm, similar to the twin plant used for diagnosability and formally presented in an extension of their work @cite_3 .
@cite_13 @cite_3
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In recent years scholars have built maps of science by connecting the academic fields that cite each other, are cited together, or that cite a similar literature. But since scholars cannot always publish in the fields they cite, or that cite them, these science maps are only rough proxies for the potential of a scholar, organization, or country, to enter a new academic field. Here we use a large dataset of scholarly publications disambiguated at the individual level to create a map of science-or research space-where links connect pairs of fields based on the probability that an individual has published in both of them. We find that the research space is a significantly more accurate predictor of the fields that individuals and organizations will enter in the future than citation based science maps. At the country level, however, the research space and citations based science maps are equally accurate. These findings show that data on career trajectories-the set of fields that individuals have previously published in-provide more accurate predictors of future research output for more focalized units-such as individuals or organizations-than citation based science maps. In this work, we address the problem of joint modeling of text and citations in the topic modeling framework. We present two different models called the Pairwise-Link-LDA and the Link-PLSA-LDA models. The Pairwise-Link-LDA model combines the ideas of LDA [4] and Mixed Membership Block Stochastic Models [1] and allows modeling arbitrary link structure. However, the model is computationally expensive, since it involves modeling the presence or absence of a citation (link) between every pair of documents. The second model solves this problem by assuming that the link structure is a bipartite graph. As the name indicates, Link-PLSA-LDA model combines the LDA and PLSA models into a single graphical model. Our experiments on a subset of Citeseer data show that both these models are able to predict unseen data better than the baseline model of Erosheva and Lafferty [8], by capturing the notion of topical similarity between the contents of the cited and citing documents. Our experiments on two different data sets on the link prediction task show that the Link-PLSA-LDA model performs the best on the citation prediction task, while also remaining highly scalable. In addition, we also present some interesting visualizations generated by each of the models.