Complexity of Problems of Commutative Grammars

We consider commutative regular and context-free grammars, or, in other words, Parikh images of regular and context-free languages. By using linear algebra and a branching analog of the classic Euler theorem, we show that, under an assumption that the terminal alphabet is fixed, the membership problem for regular grammars (given v in binary and a regular commutative grammar G, does G generate v?) is P, and that the equivalence problem for context free grammars (do G_1 and G_2 generate the same language?) is in $\mathrm{\Pi_2^P}$

Using the Expectation Maximization Algorithm with Heterogeneous Mixture Components for the Analysis of Spectrometry Data

Coupling a multi-capillary column (MCC) with an ion mobility (IM) spectrometer (IMS) opened a multitude of new application areas for gas analysis, especially in a medical context, as volatile organic compounds (VOCs) in exhaled breath can hint at a person's state of health. To obtain a potential diagnosis from a raw MCC/IMS measurement, several computational steps are necessary, which so far have required manual interaction, e.g., human evaluation of discovered peaks. We have recently proposed an automated pipeline for this task that does not require human intervention during the analysis. Nevertheless, there is a need for improved methods for each computational step. In comparison to gas chromatography / mass spectrometry (GC/MS) data, MCC/IMS data is easier and less expensive to obtain, but peaks are more diffuse and there is a higher noise level. MCC/IMS measurements can be described as samples of mixture models (i.e., of convex combinations) of two-dimensional probability distributions. So we use the expectation-maximization (EM) algorithm to deconvolute mixtures in order to develop methods that improve data processing in three computational steps: denoising, baseline correction and peak clustering. A common theme of these methods is that mixture components within one model are not homogeneous (e.g., all Gaussian), but of different types. Evaluation shows that the novel methods outperform the existing ones. We provide Python software implementing all three methods and make our evaluation data available at http://www.rahmannlab.de/research/ims

Sarasota Performing Arts Research Coalition Community Report

Presents findings from a 2002 Urban Institute survey of Sarasota residents' perceptions of and attitudes toward the performing arts

Washington, D.C. Performing Arts Research Coalition Community Report

Presents findings from a 2002 Urban Institute survey of Washington-area residents' perceptions of and attitudes toward the performing arts

A note on first-order spectra with binary relations

The spectrum of a first-order sentence is the set of the cardinalities of its finite models. In this paper, we consider the spectra of sentences over binary relations that use at least three variables. We show that for every such sentence $\Phi$, there is a sentence $\Phi'$ that uses the same number of variables, but only one symmetric binary relation, such that its spectrum is linearly proportional to the spectrum of $\Phi$. Moreover, the models of $\Phi'$ are all bipartite graphs. As a corollary, we obtain that to settle Asser's conjecture, i.e., whether the class of spectra is closed under complement, it is sufficient to consider only sentences using only three variables whose models are restricted to undirected bipartite graphs

Seattle Performing Arts Research Coalition Community Report 2002

Presents findings from a 2002 Urban Institute survey of Seattle residents' perceptions of and attitudes toward the performing arts

Washington, D.C. Performing Arts Research Coalition Community Report

Presents findings from a 2002 Urban Institute survey of Washington-area residents' perceptions of and attitudes toward the performing arts