Anti-commutative Groebner-Shirshov basis of a free Lie algebra

One of the natural ways to prove that the Hall words (Philip Hall, 1933) consist of a basis of a free Lie algebra is a direct construction: to start with a linear space spanned by Hall words, to define the Lie product of Hall words, and then to check that the product yields the Lie identities (Marshall Hall, 1950). Here we suggest another way using the Composition-Diamond lemma for free anti-commutative (non-associative) algebras (A.I. Shirshov, 1962)

Analysis of the response of planar polarization interferometer to molecular layer formation: fibrinogen adsorption on silicon nitride surface

The most sensitive optical method of interferometry was exploited for determination of changes in the refractive index following the adsorption of biological molecules onto the solid surface. Instead of having two waveguiding arms (the main and the reference) in traditional Mach-Zhender interferometer, two ortogonal TM and TE modes propagating through the SiO2-Si3N4-SiO2 waveguide structure were employed in planar polarization interferometer (PPI). Multiperiodic PPI response was, therefore, formed due to the phase shift between TM and TE modes. A matrix simulation procedure was developed in order to investigate the influence of both the refractive index and molecular layer thickness on the PPI response. Nonspecifical binding of fibrinogen to silicon nitride surface was studied as a model object for PPI testing. The results obtained are in good agreement with the known information about fibrinogen adsorption on the different surfaces. An attempt to introduce the concept of 'surface molecular concentration and molecular polariziability' instead of 'molecular layer thickness and refractivity' was undertaken. (C) 2001 Elsevier Science B.V. All rights reserved

Flood early warning system: design, implementation and computational modules

AbstractWe present a prototype of the flood early warning system (EWS) developed within the UrbanFlood FP7 project. The system monitors sensor networks installed in flood defenses (dikes, dams, embankments, etc.), detects sensor signal abnormalities, calculates dike failure probability, and simulates possible scenarios of dike breaching and flood propagation. All the relevant information and simulation results are fed into an interactive decision support system that helps dike managers and city authorities to make informed decisions in case of emergency and in routine dike quality assessment. In addition to that, a Virtual Dike computational module has been developed for advanced research into dike stability and failure mechanisms, and for training the artificial intelligence module on signal parameters induced by dike instabilities. This paper describes the UrbanFlood EWS generic design and functionality, the computational workflow, the individual modules, their integration via the Common Information Space middleware, and the first results of EWS monitoring and performance benchmarks