Craniosynostosis in Pycnodysostosis: Broadening the Spectrum of the Cranial Flat Bone Abnormalities

Pycnodysostosis is a rare autosomal recessive skeletal dysplasia caused by the absence of active cathepsin K, which is a lysosomal cysteine protease that plays a role in degrading the organic matrix of bones, acting in bone resorption and bone remodeling. The disease is primarily characterized by osteosclerosis, bone fragility, short stature, acro-osteolysis, and delayed closure of the cranial sutures. A differing feature, cranial synostosis, has occasionally been described in this disorder. We reviewed six unrelated patients with pycnodysostosis (mean age of 10 years and 4 months) in order to evaluate the presence of craniosynostosis. In addition to the typical findings of the condition, they all presented premature fusion of the corona! suture. Although none of them showed signs of cranial hypertension, one patient had had the craniosynostosis surgically corrected previously. These data suggest that the cranial sutures in pycnodysostosis can display contradictory features: wide cranial sutures, which are commonly described, and craniosynostosis. The clinical impact of this latter finding still remains to be elucidated. Further studies are necessary to address more precisely the role of cathepsin K in suture patency. (C) 2010 Wiley-Liss, Inc.

Robust tori in a double-waved Hamiltonian model

A Hamiltonian system perturbed by two waves with particular wave numbers can present robust tori, which are barriers created by the vanishing of the perturbed Hamiltonian at some defined positions. When robust tori exist, any trajectory in phase space passing close to them is blocked by emergent invariant curves that prevent the chaotic transport. Our results indicate that the considered particular solution for the two waves Hamiltonian model shows plenty of robust tori blocking radial transport. (C) 2010 Elsevier B.V. All rights reserved.

The non-twist standard map with robust tori

The non-twist standard map occurs frequently in many fields of science specially in modelling the dynamics of the magnetic field lines in tokamaks. Robust tori, dynamical barriers that impede the radial transport among different regions of the phase space, are introduced in the non-twist standard map in a conservative fashion. The resulting non-twist standard map with robust tori is an improved model to study transport barriers in plasmas confined in tokamaks.

Tunneling among rotation tori

We consider an integrable Hamiltonian system generated by the resonant normal form in order to study a particular mechanism of tunneling. We isolated near doublets of energy corresponding to rotation tori of the classical dynamics counterpart and the degeneracies breakdown is attributed to rotation-rotation tunneling. (C) 2008 Elsevier B.V. All rights reserved.

Tori embedded in R(3) with dense principal lines

In this paper are given examples of tori T(2) embedded in R(3) with all their principal lines dense. These examples are obtained by stereographic projection of deformations of the Clifford torus in S(3). (C) 2008 Elsevier Masson SAS. All rights reserved.