We study the Monadic Second Order (MSO) Hierarchy over colourings of the discrete plane, and draw links between classes of formula and classes of subshifts. We give a characterization of existential MSO in terms of projections of tilings, and of universal sentences in terms of combinations of “pattern counting” subshifts. Conversely, we characterise logic fragments corresponding to various clas...

We investigate the back-and-forth types which isomorphism types. The main result is that the indecomposable isomorphism types which arise at the finite levels of the back-and-forth hierarchy are the same the finitary isomorphism types in Heindorff.

the question of essentials or principles of quranic exegesis is among major discussions of quranic sciences. essentials of exegesis, i.e., definite beliefs accepted by the commentator, play some role in the process of one’s commentary, as acceptance or otherwise of such principles may cause specific approach to the commentary creating different interpretations of same verses. there are so many ...

Martins D, et al. BMJ Case Rep 2017. doi:10.1136/bcr-2017-221360 Description This beautiful angiogram was obtained from an asymptomatic healthy 14-year-old male. Undergoing cardiovascular evaluation for sport practice, he had a normal physical examination except for a grade II low frequency murmur. Serial otherwise unremarkable ECGs revealed frequent monomorphic ventricular ectopy, which increa...

While the back-and-forth method has been often attributed to Cantor, it turns out that in the original proof of the characterisation of countable linear dense orders, themapping is constructed in a single direction. Cameron has called this method Forth and has shown that it can fail to build an automorphism for some homogeneous structures. We give in this paper a characterisation of those homog...

We use a two-state ratchet model to study the cooperative bidirectional motion of molecular motors on cytoskeletal tracks with randomly alternating polarities. Our model is based on a previously proposed model [Badoual, Proc. Natl. Acad. Sci. U.S.A. 99, 6696 (2002)] for collective motor dynamics and, in addition, takes into account the cooperativity effect arising from the elastic tension that ...