Supine or prone—A continued story

A Success Story . . . to be continued

Transcendence of Sturmian or Morphic Continued Fractions

We prove, using a theorem of W. Schmidt, that if the sequence of partial quotients of the continued fraction expansion of a positive irrational real number takes only two values, and begins with arbitrary long blocks which are ''almost squares,'' then this number is either quadratic or transcendental. This result applies in particular to real numbers whose partial quotients form a Sturmian (or ...

Automatic Continued Fractions Are Transcendental or Quadratic

We establish new combinatorial transcendence criteria for continued fraction expansions. Let α = [0; a1, a2, . . .] be an algebraic number of degree at least three. One of our criteria implies that the sequence of partial quotients (a`)`≥1 of α is not ‘too simple’ (in a suitable sense) and cannot be generated by a finite automaton. Résumé. Nous établissons de nouveaux critères combinatoires de ...

Minor malformations: neonatal or anthropological story?

Minor malformations (mM) are mild physical deformities that with their incidence, number and evolution may be external indicators of hidden, more serious disorders. Most often these are recognized by the neonatologists. First studies done some forty years ago showed an average incidence of 15% in the general population of newborns and about 50% in children with major malformations (MM). A study...

Plant Breeding: A Success Story to be Continued Thanks to the Advances in Genomics

Conventional plant breeding mostly relies upon the generation of new genetic combinations by sexual hybridization and the subsequent application of selection methods on phenotypically evaluated individuals and populations. This approach has been extremely efficient in providing a continuous supply of improved cultivars that have resulted in a dramatic increase of yield in most major crops. Thes...