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.

UNIT VECTOR FIELDS ON ANTIPODALLY PUNCTURED SPHERES: BIG INDEX, BIG VOLUME

We establish in this paper a lower bound for the volume of a unit vector field (v) over right arrow defined ou S(n) \ {+/-x}, n = 2,3. This lower bound is related to the sum of the absolute values of the indices of (v) over right arrow at x and -x.