Mobius Sequence in a Girl and Arthrogryposis in her Half-Brother: Distinct Phenotypes Caused By Prenatal Injuries

Mobius sequence is a congenital facial and abducens nerve palsy, frequently associated to abnormalities of extremities. Arthrogryposis multiplex congenital is defined as a congenital fixation of multiple joints seldom of neurogenic origin. Both sequences must have a genetic origin, but usually are sporadic cases related to environmental factors such as drugs exposition and maternal trauma. A 5-year-old girl and a 1-year-old boy were born with Mobius sequence and arthrogryposis multiplex congenital, respectively. During pregnancies, the mother had vaginal bleeding at 7 weeks and used crack (free-based cocaine) in the first trimester, respectively. The girl also has equinovarus talipes and autistic behavior. The boy has arthrogryposis with flexion contractures of the feet and knees. A vascular disruption, due to hemorrhage and cocaine exposure, causing a transient ischemic insult to embryos in a critical period of development may be responsible for distinct phenotypes in these cases.

TRANSITIVE CIRCLE EXCHANGE TRANSFORMATIONS WITH FLIPS

We study the existence of transit we exchange transformations with flips defined on the unit circle S(1). We provide a complete answer to the question of whether there exists a transitive exchange transformation of S(1) defined on a subintervals and having f flips.

Exchange transformations reversing orientation

University of Sao Paulo (USP)

Spin current in the Mobius cyclacene belts

We report on density functional theory studies of the electronic structure and magnetic properties of Mobius-[n]cyclacenes. The geometry of Mobius bands presents a modulation of bond lengths that is needed to accommodate the twist. This modulation takes the form of bond alternation defects analogous to those of solitons in polyacetylene. The ground state of all Mobius bands is a triplet, with a spin density distribution that follows the bond length modulation. A molecular dynamics simulation of the Mobius cyclacene at 300 K shows that the twist travels around the belt inducing a magnetic current. (C) 2009 Elsevier B. V. All rights reserved.

NONSTATIONARY MIXING AND THE UNIQUE ERGODICITY OF ADIC TRANSFORMATIONS

We define topological and measure-theoretic mixing for nonstationary dynamical systems and prove that for a nonstationary subshift of finite type, topological mixing implies the minimality of any adic transformation defined on the edge space, while if the Parry measure sequence is mixing, the adic transformation is uniquely ergodic. We also show this measure theoretic mixing is equivalent to weak ergodicity of the edge matrices in the sense of inhomogeneous Markov chain theory.