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.

Input: Consider Input: Well-established automatic analyses of texts mainly consider frequencies of linguistic units, e.g. letters, words and bigrams, while methods based on cooccurrence networks consider the structure of texts regardless of the nodes label (i.e. the words semantics). In this paper, we reconcile these distinct viewpoints by introducing a generalized similarity measure to compare texts which accounts for both the network structure of texts and the role of individual words in the networks. We use the similarity measure for authorship attribution of three collections of books, each composed of 8 authors and 10 books per author. High accuracy rates were obtained with typical values from 90% to 98.75%, much higher than with the traditional the TF-IDF approach for the same collections. These accuracies are also higher than taking only the topology of networks into account. We conclude that the different properties of specific words on the macroscopic scale structure of a whole text are as relevant as their frequency of appearance; conversely, considering the identity of nodes brings further knowledge about a piece of text represented as a network.

Output: On the role of words in the network structure of texts: application to authorship attribution


Input: Consider Input: In many combinatorial problems one may need to model the diversity or similarity of sets of assignments. For example, one may wish to maximise or minimise the number of distinct values in a solution. To formulate problems of this type we can use soft variants of the well known AllDifferent and AllEqual constraints. We present a taxonomy of six soft global constraints, generated by combining the two latter ones and the two standard cost functions, which are either maximised or minimised. We characterise the complexity of achieving arc and bounds consistency on these constraints, resolving those cases for which NP-hardness was neither proven nor disproven. In particular, we explore in depth the constraint ensuring that at least k pairs of variables have a common value. We show that achieving arc consistency is NP-hard, however bounds consistency can be achieved in polynomial time through dynamic programming. Moreover, we show that the maximum number of pairs of equal variables can be approximated by a factor of 12 with a linear time greedy algorithm. Finally, we provide a fixed parameter tractable algorithm with respect to the number of values appearing in more than two distinct domains. Interestingly, this taxonomy shows that enforcing equality is harder than enforcing difference.

Output: Soft Constraints of Difference and Equality


Input: Consider Input: Knowledge representation is a popular research field in IT. As mathematical knowledge is most formalized, its representation is important and interesting. Mathematical knowledge consists of various mathematical theories. In this paper we consider a deductive system that derives mathematical notions, axioms and theorems. All these notions, axioms and theorems can be considered a small mathematical theory. This theory will be represented as a semantic net. We start with the signature <Set; > where Set is the support set, is the membership predicate. Using the MathSem program we build the signature <Set;  where is set intersection,  is set union, -is the Cartesian product of sets, and is the subset relation.


Output: Building the Signature of Set Theory Using the MathSem Program