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: 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.

A: Soft Constraints of Difference and Equality
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Q: This paper proposes and experimentally validates a Bayesian network model of a range finder adapted to dynamic environments. All modeling assumptions are rigorously explained, and all model parameters have a physical interpretation. This approach results in a transparent and intuitive model. With respect to the state of the art beam model this paper: (i) proposes a different functional form for the probability of range measurements caused by unmodeled objects, (ii) intuitively explains the discontinuity encountered in the state of the art beam model, and (iii) reduces the number of model parameters, while maintaining the same representational power for experimental data. The proposed beam model is called RBBM, short for Rigorously Bayesian Beam Model. A maximum likelihood and a variational Bayesian estimator (both based on expectation-maximization) are proposed to learn the model parameters. Furthermore, the RBBM is extended to a full scan model in two steps: first, to a full scan model for static environments and next, to a full scan model for general, dynamic environments. The full scan model accounts for the dependency between beams and adapts to the local sample density when using a particle filter. In contrast to Gaussian-based state of the art models, the proposed full scan model uses a sample-based approximation. This sample-based approximation enables handling dynamic environments and capturing multimodality, which occurs even in simple static environments.

A: A Rigorously Bayesian Beam Model and an Adaptive Full Scan Model for Range Finders in Dynamic Environments
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Q: Phrases play an important role in natural language understanding and machine translation (Sag et al., 2002; Villavicencio et al., 2005). However, it is difficult to integrate them into current neural machine translation (NMT) which reads and generates sentences word by word. In this work, we propose a method to translate phrases in NMT by integrating a phrase memory storing target phrases from a phrase-based statistical machine translation (SMT) system into the encoder-decoder architecture of NMT. At each decoding step, the phrase memory is first re-written by the SMT model, which dynamically generates relevant target phrases with contextual information provided by the NMT model. Then the proposed model reads the phrase memory to make probability estimations for all phrases in the phrase memory. If phrase generation is carried on, the NMT decoder selects an appropriate phrase from the memory to perform phrase translation and updates its decoding state by consuming the words in the selected phrase. Otherwise, the NMT decoder generates a word from the vocabulary as the general NMT decoder does. Experiment results on the ChineseEnglish translation show that the proposed model achieves significant improvements over the baseline on various test sets.

A:
Translating Phrases in Neural Machine Translation
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