These are the words the great French mathematician used to describe his initial thoughts when he proved that there is a prime number greater than 11 [11, p. 76]. His final mental image he described as "... a place somehere between the confused mass and the first point". In commenting on this in his fascinating but quirky monograph, he asks "What may be the use of such a strange and cloudy image...

Sound and complete semantics for classical propositional logic can be obtained by interpreting sentences as sets. Replacing sets with commuting dense binary relations produces an interpretation that turns out to be sound but not complete for R. Adding transitivity yields sound and complete semantics for RM, because all normal Sugihara matrices are representable as algebras of binary relations.

AFFILIATIONS: Junyent, chandrasekar, and bringi—Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, Colorado; rutledge, kennedy, brunkow, george, and bowie—Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado CORRESPONDING AUTHOR: Francesc Junyent, Electrical and Computer Engineering, Colorado State University, 209 Campus D...

Since 1979 when threshold schemes were introduced by Blakley (Bla79) and Shamir (Sha79), many papers in this area have been published. These papers are mostly about particular designs and applications of threshold schemes. In this work, we are interested in characterisations of ideal threshold schemes rather than particular constructions. Of course, these characteristic properties do not depend...

not much worried whether they be right or wrong. His desire to be the center of attraction may lead him to do things considered irrational when viewed from other angles. If he is in the upper 10 per cent of his class at school, it might be well to advance him to the next grade, provided he is sufficiently interested to show that he is capable of doing the work. If convenient, the teacher should...

Lucia Melloni,1,* Caspar M. Schwiedrzik,1 Michael Wibral,2 Eugenio Rodriguez,1 and Wolf Singer1 1Max Planck Institute for Brain Research, Department of Neurophysiology, Deutschordenstraße 46, 60528 Frankfurt am Main, Germany 2MEG Unit, Brain Imaging Center, Johann Wolfgang Goethe University, Schleusenweg 2-16, 60528 Frankfurt am Main, Germany *Correspondence: [email protected] DOI 1...