Ordered Tree Decomposition for HRG Rule Extraction

We present algorithms for extracting Hyperedge Replacement Grammar (HRG) rules from a graph along with a vertex order. Our algorithms are based on finding a tree decomposition of smallest width, relative to the vertex order, and then extracting one rule for each node in this structure. The assumption of a fixed order for the vertices of the input graph makes it possible to solve the problem in polynomial time, in contrast to the fact that the problem of finding optimal tree decompositions for a graph is NP-hard. We also present polynomial-time algorithms for parsing based on our HRGs, where the input is a vertex sequence and the output is a graph structure. The intended application of our algorithms is grammar extraction and parsing for semantic representation of natural language. We apply our algorithms to data annotated with Abstract Meaning Representations and report on the characteristics of the resulting grammars.

Intervalidation of Dendrochronology and 14C Dating on a 700-yr Tree-Ring Sequence Originating from the Eastern Carpathians

ABSTRACTWe present a comparative study on a 700-yr sequence of dendrochronologically ordered tree-rings of Pinus cembra originating from Eastern Carpathians for the period AD 1009–1709. This period covers the solar minima of the Little Ice Age. The aim of this study was to assess the accuracy of our radiocarbon (14C) determinations interpreted on the IntCal13 calibration data and to observe any apparent offsets. The 14C measurements on single and double tree-rings were “wiggle-matched” to secure the dendrochronology cross-matching of all the Pinus cembra wood pieces. The results showed a very good agreement between the age datasets for four out of five wood trunks. However, for one of them a new cross-matching was performed after a quality assurance test, establishing an earlier 48-yr position, recommended by wiggle-matching Bayesian statistics and dendrochronological analysis. Following this adjustment, the quantification of the 14C level variability with respect to the IntCal13 calibration curve was obtained by calculating Δ14C for all tree-ring samples. As a final conclusion, an insignificant 14C concentration offset of –0.63 ± 3.76‰ was found for the Romanian samples.

A Fast and Space-Economical Algorithm for the Tree Inclusion Problem

The ordered tree inclusion is an interesting problem, by which the authors will check whether a pattern tree P can be included in a target tree T, where the order of siblings in both P and T is significant. In this chapter, the authors propose an efficient algorithm for this problem. Its time complexity is bounded by O(|T|⋅loghP) with O(|T| + |P|) space being used, where hP represents the height of P. Up to now the best algorithm for this problem needs Θ(|T|⋅|leaves(P)|) time, where leaves(P) stands for the set of the leaves of P.

Controlling Interfacial Flow Instability via Micro Engineered Surfaces Towards Multiscale Channel Fabrication

Hierarchical branched structures exist in nature in diverse forms, functions and scales stretching from micro to very large sizes. Typically effective as heat and mass transfer networks, ordered hierarchal/ multiscale branched/ tree-like networks could be fabricated by controlling a fluid reshaping process in a device called ‘Multiport Hele-Shaw cell’. Control over the instability by employing micro-modified cell plates, containing ‘source-holes’ as ports, rearranges the fluid into ordered tree-like networks. Reshaping is an outcome of ‘Saffman-Taylor interface instability’ induced by the displacement of a high-viscous fluid by a relatively low-viscous one in the cell. A new configuration of ‘source-holes’, is proposed here to control the instability towards shaping of high-viscous fluid into ordered multiscale treelike layouts. The process is lithography-less method of shaping the fluid spontaneously into 3D layouts in a very short interval of time. Fabricated structures are UV-cured and cast into channel-networks in an elastomer PDMS.