When Can Matrix Query Languages Discern Matrices?

We investigate when two graphs, represented by their adjacency matrices, can be distinguished by means of sentences formed in MATLANG, a matrix query language which supports a number of elementary linear algebra operators. When undirected graphs are concerned, and hence the adjacency matrices are real and symmetric, precise characterisations are in place when two graphs (i.e., their adjacency matrices) can be distinguished. Turning to directed graphs, one has to deal with asymmetric adjacency matrices. This complicates matters. Indeed, it requires to understand the more general problem of when two arbitrary matrices can be distinguished in MATLANG. We provide characterisations of the distinguishing power of MATLANG on real and complex matrices, and on adjacency matrices of directed graphs in particular. The proof techniques are a combination of insights from the symmetric matrix case and results from linear algebra and linear control theory

Continuity and change in the treatment of frightening subject matter: contemporary retellings of classical mythology for children in the Low Countries

Ever since its origins, children's literature has dealt with frightening subject matter. The forms of such frightening fiction for children are, however, continuously changing. Retellings of classical mythology are a case in point as myths contain subjects that might be considered a threat to the romantic notion of the innocent child. As such, a focus upon the way authors deal with sex, death and violence in retellings of classical mythology reveals how the paradoxical impulses that govern the act of retelling that is, a desire for preserving and challenging cultural tradition alter under the influence of society's changing ideas about children and their literature. This paper concentrates on the rich and vivid tradition of retelling classical myths in the Low Countries. Shifts in the choice of pretext and in the age of the intended audience reveal a change of attitude towards frightening subjects in classical myths during the last decades. A closer look at retellings of the creation myths, dealing with sexual and lethal violence between parents and children, and the subject of death in the myth of Orpheus shows how the retellings of frightening myths range from unequivocal presentations as cautionary tales to demanding narratives generating unfixed meanings

Coordinate-free interpretations of the optimal costs for LQ-problems subject to implicit systems

Control Systems;operations research

Colloidal Flying Carpets

DNA plays a special role in polymer science not just because of the highly selective recognition of complementary single DNA strands but also because bacteria can express DNA chains that are very long yet perfectly monodisperse. The latter reason makes long DNA molecules widely used as model systems in polymer science. Here, we report the unusual self-assembly that takes place in systems of colloids coated with very long double-stranded DNA. In particular, we find that colloids coated with such long DNA can assemble into unique floating crystalline monolayers. Floating colloidal structures have potentially interesting applications as such ordered structures can be assembled in one location and then deposited somewhere else. This would open the way to the assembly of multi-component, layered colloidal crystals.Comment: submitted to PR

Making Queries Tractable on Big Data with Preprocessing

A query class is traditionally considered tractable if there exists a polynomial-time (PTIME) algorithm to answer its queries. When it comes to big data, however, PTIME al-gorithms often become infeasible in practice. A traditional and effective approach to coping with this is to preprocess data off-line, so that queries in the class can be subsequently evaluated on the data efficiently. This paper aims to pro-vide a formal foundation for this approach in terms of com-putational complexity. (1) We propose a set of Π-tractable queries, denoted by ΠT0Q, to characterize classes of queries that can be answered in parallel poly-logarithmic time (NC) after PTIME preprocessing. (2) We show that several natu-ral query classes are Π-tractable and are feasible on big data. (3) We also study a set ΠTQ of query classes that can be ef-fectively converted to Π-tractable queries by re-factorizing its data and queries for preprocessing. We introduce a form of NC reductions to characterize such conversions. (4) We show that a natural query class is complete for ΠTQ. (5) We also show that ΠT0Q ⊂ P unless P = NC, i.e., the set ΠT0Q of all Π-tractable queries is properly contained in the set P of all PTIME queries. Nonetheless, ΠTQ = P, i.e., all PTIME query classes can be made Π-tractable via proper re-factorizations. This work is a step towards understanding the tractability of queries in the context of big data. 1