Applications of combinatorics to statics—a second survey

AbstractSome recent results are presented, concerning the algorithmic aspects of 2-dimensional generic rigidity, and 1-story buildings as tensegrity frameworks. Most of these results were obtained after the completion of the first survey (Recski, 1984) for a ‘Winter School’ organized by the late Professor Z. Frolík. Results in Sections 3 and 4 of the first survey are used throughout

Applications of combinatorics to statics—rigidity of grids

AbstractThe infinitesimal rigidity (or briefly rigidity) of a bar-and-joint framework (in any dimension) can be formulated as a rank condition of the so-called rigidity matrix. If there are n joints in the framework then the size of this matrix is O(n), so the time complexity of determining its rank is O(n3). But in special cases we can work with graph and matroid theoretical models from which very fast and effective algorithms can be obtained. At first the case of planar square grids will be presented where they can be made rigid with diagonal rods and cables in the squares, and with long rods and cables which may be placed between any two joints of the grid. Then we will consider the one- and multi-story buildings, and finally some other results and algorithms

Structure Learning in Weighted Languages

We present Minimum Description Length techniques for learning the structure of weighted languages. MDL is already widely used both for segmentation and classification tasks, and here we show it can be used to formalize further important tools in the descriptive linguists ’ toolbox, including the distinction between accidental and systematic gaps in the data, the detection of ambiguity, the selective discarding of data, and the merging of categories

NP alignment in bilingual corpora

We created a simple gold standard for English-Hungarian NP-level alignment, Orwell’s 1984, (since this already exists in manually verified POS-tagged format in many languages thanks to the Multex and MultexEast project) by manually verifying the automaticaly generated NP chunking (we used the yamcha, mallet and hunchunk taggers) and manually aligning the maximal NPs and PPs. The maximum NP chunking problem is much harder than base NP chunking, with F-measure in the.7 range (as opposed to over.94 for base NPs). Since the results are highly impacted by the quality of the NP chunking, we tested our alignment algorithms both with real world (machine obtained) chunkings, where results are in the.35 range for the baseline algorithm which propagates GIZA++ word alignments to the NP level, and on idealized (manually obtained) chunkings, where the baseline reaches.4 and our current system reaches.64. 1