MSO Queries on Trees: Enumerating Answers under Updates Using Forest Algebras

We describe a framework for maintaining forest algebra representations that are of logarithmic height for unranked trees. Such a representations can be computed in O(n) time and updated in O(log(n)) time. The framework is of potential interest for data structures and algorithms for trees whose complexity depend on the depth of the tree (representation). We provide an exemplary application of the framework to the problem of efficiently enumerating answers to MSO-definable queries over trees which are subject to local updates. We exhibit an algorithm that uses an O(n) preprocessing phase and enumerates answers with O(log(n)) delay between them. When the tree is updated, the algorithm can avoid repeating expensive preprocessing and restart the enumeration phase within O(log(n)) time. Our algorithms and complexity results in the paper are presented in terms of node-selecting tree automata representing the MSO queries

Current and Future Experimental Strategies for Structural Analysis of Trichothecene Mycotoxins-A Prospectus

Fungal toxins, such as those produced by members of the order Hypocreales, have widespread effects on cereal crops, resulting in yield losses and the potential for severe disease and mortality in humans and livestock. Among the most toxic are the trichothecenes. Trichothecenes have various detrimental effects on eukaryotic cells including an interference with protein production and the disruption of nucleic acid synthesis. However, these toxins can have a wide range of toxicity depending on the system. Major differences in the phytotoxicity and cytotoxicity of these mycotoxins are observed for individual members of the class, and variations in toxicity are observed among different species for each individual compound. Furthermore, while diverse toxicological effects are observed throughout the whole cellular system upon trichothecene exposure, the mechanism of toxicity is not well understood. In order to comprehend how these toxins interact with the cell, we must first have an advanced understanding of their structure and dynamics. The structural analysis of trichothecenes was a subject of major interest in the 1980s, and primarily focused on crystallographic and solution-state Nuclear Magnetic Resonance (NMR) spectroscopic studies. Recent advances in structural determination through solution- and solid-state NMR, as well as computation based molecular modeling is leading to a resurgent interest in the structure of these and other mycotoxins, with the focus shifting in the direction of structural dynamics. The purpose of this work is to first provide a brief overview of the structural data available on trichothecenes and a characterization of the methods commonly employed to obtain such information. A summary of the current understanding of the relationship between structure and known function of these compounds is also presented. Finally, a prospectus on the application of new emerging structural methods on these and other related systems is discussed