Approximate Hermitian-Yang-Mills structures and semistability for Higgs bundles. II: Higgs sheaves and admissible structures

We study the basic properties of Higgs sheaves over compact K\"ahler manifolds and we establish some results concerning the notion of semistability; in particular, we show that any extension of semistable Higgs sheaves with equal slopes is semistable. Then, we use the flattening theorem to construct a regularization of any torsion-free Higgs sheaf and we show that it is in fact a Higgs bundle. Using this, we prove that any Hermitian metric on a regularization of a torsion-free Higgs sheaf induces an admissible structure on the Higgs sheaf. Finally, using admissible structures we proved some properties of semistable Higgs sheaves.Comment: 18 pages; some typos correcte

Longitudinal investigation of energy expenditure in infants with cystic fibrosis

Objective: To determine when energy expenditure becomes elevated in infants with cystic fibrosis (CF). Design: Longitudinal studies of total energy expenditure (TEE) using doubly labeled water were conducted in infants identified with CF by newborn screening through the first year of life. Setting: Hospital and community based studies in Denver, Colorado, USA and Cambridge, UK. Results: Eight of the 12 infants enrolled had begun enzyme therapy but were clinically asymptomatic. Four of the 12 infants were heterozygous for the delta F508 mutation, however no difference was seen in TEE from the remaining homozygous infants. TEE was compared to control cohorts at 2, 6 and 12 months of age. There was no difference from the control groups in TEE/kg fat free mass (FFM)/day at 2 months. However, by 6 months of age TEE/kg FFM/day in infants with CF exceeded that of age-matched controls by 25% (P < 0.001). This elevation in TEE continued at 12 months of age exceeding that of controls by 30% (P < 0.05). Conclusions: These results indicate that infants with CF have increased energy needs by 6 months of age and that early diagnosis alone does not prevent the development of increased caloric requirements. These findings emphasize the need for close nutritional monitoring to prevent suboptimal growth during infancy in this population. Sponsorship: This research was supported by grant number 5 MO1 RR00069, General Clinical Research Centers Program, National Center for Research Resources, NIH