TASK DEFINITION: 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.
PROBLEM: The First-Order Variable Elimination (FOVE) algorithm allows exact inference to be applied directly to probabilistic relational models, and has proven to be vastly superior to the application of standard inference methods on a grounded propositional model. Still, FOVE operators can be applied under restricted conditions, often forcing one to resort to propositional inference. This paper aims to extend the applicability of FOVE by providing two new model conversion operators: the first and the primary is joint formula conversion and the second is just-different counting conversion. These new operations allow efficient inference methods to be applied directly on relational models, where no existing efficient method could be applied hitherto. In addition, aided by these capabilities, we show how to adapt FOVE to provide exact solutions to Maximum Expected Utility (MEU) queries over relational models for decision under uncertainty. Experimental evaluations show our algorithms to provide significant speedup over the alternatives.

SOLUTION: Extended Lifted Inference with Joint Formulas

PROBLEM: There are many complex combinatorial problems which involve searching for an undirected graph satisfying given constraints. Such problems are often highly challenging because of the large number of isomorphic representations of their solutions. This paper introduces effective and compact, complete symmetry breaking constraints for small graph search. Enumerating with these symmetry breaks generates all and only non-isomorphic solutions. For small search problems, with up to 10 vertices, we compute instance independent symmetry breaking constraints. For small search problems with a larger number of vertices we demonstrate the computation of instance dependent constraints which are complete. We illustrate the application of complete symmetry breaking constraints to extend two known sequences from the OEIS related to graph enumeration.

SOLUTION: Breaking Symmetries in Graph Search with Canonizing Sets

PROBLEM: 1 Ranks, processes and flat grammar ....................................................................................... 2 2 The Rank-Interpretation Architecture for Multilinear Grammars ......................................... 6 2.1 Outline of the Rank-Interpretation Architecture framework .............................................. 6 2.2 A preliminary note on linearity and hierarchy at the phrasal rank ..................................... 7 2.3 Characterisation of the Rank-Interpretation Architecture .................................................. 9 2.3.1 Background ..................................................................................................................... 9 2.3.2 Formal summary ........................................................................................................... 10 2.3.3 Contrast with traditional views of language architecture .............................................. 11 2.3.4 Search for sui generis properties of ranks ..................................................................... 11 2.4 Procedural perspectives on the rank hierarchy ................................................................. 12 3 The discourse rank .............................................................................................................. 15 3.1 The primacy of discourse patterning ................................................................................ 15 3.2 Intonation of an adjacency pair ........................................................................................ 16 3.3 Chanted 'call' intonation .................................................................................................. 18 4 The utterance or text rank ................................................................................................... 20 5 The phrase rank ................................................................................................................... 22 5.1 Characteristics of phrasal structure .................................................................................. 22 5.2 Linear sequences, iteration: regular and subregular grammars ........................................ 23 5.3 A note on long-distance and cross-serial dependencies ................................................... 26 5.4 Prosodic-phonetic interpretation at the phrasal rank ........................................................ 27 6 The word rank ..................................................................................................................... 30 6.1 Flat words ......................................................................................................................... 30 6.2 Flat derivations ................................................................................................................. 30 6.3 Flat compounds ................................................................................................................ 31 6.4 Prosodic-phonetic interpretation at the word rank ........................................................... 31 7 Summary and conclusion .................................................................................................... 33 7.1 From Duality to Multilinear Grammar and Rank Interpretation Architecture ................. 33 7.2 Generalisation to stochastic flat linear models ................................................................. 34 7.3 Future work ...................................................................................................................... 35 8 References ........................................................................................................................... 36

SOLUTION:
Multilinear Grammar: Ranks and Interpretations