Abstract. In this paper we present a new notion of curvature for cell complexes. For each p, we define a pth combinatorial curvature function, which assigns a number to each p-cell of the complex. The curvature of a p-cell depends only on the relationships between the cell and its neighbors. In the case that p = 1, the curvature function appears to play the role for cell complexes that Ricci curvature plays for Riemannian manifolds. We begin by deriving a combinatorial analogue of Bochner's theorems, which demonstrate that there are topological restrictions to a space having a cell decomposition with everywhere positive curvature. Much of the rest of this paper is devoted to comparing the properties of the combinatorial Ricci curvature with those of its Riemannian avatar. IntroductionIn this paper we present a new notion of curvature for cell complexes. For each p, we define a pth combinatorial curvature function, which assigns a number to each p-cell of the complex. The curvature of a p-cell depends only on the relationships between the cell and its neighbors. In the case that p = 1, the curvature function appears to play the role for cell complexes that Ricci curvature plays for Riemannian manifolds. We begin by deriving a combinatorial analogue of Bochner's theorems, which demonstrate that there are topological restrictions to a space having a cell decomposition with everywhere positive curvature. Much of the rest of this paper is devoted to comparing the properties of the combinatorial Ricci curvature with those of its Riemannian avatar. The definitions of these curvature functions come from an analysis of the combinatorial Laplace operator acting on p-chains. In the Riemannian setting, Bochner and Weitzenböck showed that the *

In utero exposures to environmental factors may result in persistent epigenetic modifications affecting normal development and susceptibility to chronic diseases in later life. We explored the relationship between exposure of the growing fetus to maternal depression or antidepressants and DNA methylation at two differentially methylated regions (DMRs) of the imprinted Insulin-like Growth Factor 2 (IGF2) gene. Aberrant DNA methylation at the IGF2 and neighboring H19 DMRs has been associated with deregulated IGF2 expression, childhood cancers and several chronic diseases during adulthood. Our study population is comprised of pregnant mothers and their newborns (n = 436), as part of the Newborn Epigenetics Study (NEST). A standardized questionnaire was completed and medical record data were abstracted to ascertain maternal depression and antidepressive drug use. DMR methylation levels in umbilical cord blood leukocytes were quantified using pyrosequencing. From the 436 newborns, laboratory data were obtained for 356 individuals at the IGF2 DMRs, and for 411 individuals at the H19 DMRs; about half of each group was African American or Caucasian. While overall no association between depression and methylation profiles was found, we observed a significant hypermethylation of the H19 DMRs in newborns of African American (n = 177) but not Caucasian (n = 168) mothers who reported the use of antidepressive drugs during pregnancy (β = +6.89, p = 0.01). Of note, our data reveal a race-independent association between smoking during pregnancy and methylation at the IGF2 DMR (+3.05%, p = 0.01). In conclusion, our findings suggest a race-dependent response related to maternal use of antidepressants at one of the IGF2 DMRs in the offspring.

This study examined the association between numbers of benign melanocytic naevi in 7-year-old children in Oxfordshire born in 1988-9 with their mother's arm naevus count, and maternal and child pigmentation factors. We believe this is the first time that the relationship between child and maternal naevus counts has been reported. A high naevus count in the child was associated with male sex (P = 0.009), freckling (P = 0.001) and propensity of the child to burn in the sun (P = 0.05). A low naevus count was observed in red-haired children (P = 0.02). The strongest association of child's naevus count was with a high maternal arm naevus count, independent of the child's pigmentation factors (trend P < 0.0001). Maternal pigmentation factors were not associated with child's naevus count independent of the child's own pigmentation factors. Maternal arm naevus counts may be a better predictor of child naevus count than the child's own pigmentation factors and children. There has not been examination, however, of the relationship between naevus counts in children and those in their parents. We therefore conducted a study of the occurrence of naevi in children aged 7-8 years in Oxfordshire, examining, in addition to sex and pigmentation factors in the child, the relationship of maternal pigmentation factors and maternal naevus counts with naevi in their offspring.

Definition: Leucocyte‐depleted blood components must contain < 5 × 106 leucocytes per unit (red cells) or adult therapeutic dose (platelets). Practical aspects: To achieve residual leucocyte counts of < 5 × 106, leucocyte‐depletion should be carried out under controlled conditions, ideally within 48 h from the collection of the donor unit. The preparation of leucocyte‐depleted blood components should be subject to a quality monitoring programme designed to assure 100% compliance. Indications for leucocyte‐depleted blood components RECOMMENDED Febrile nonhaemolytic transfusion reactions (FNHTRs) 1 To prevent recurrent FNHTRs after red‐cell transfusions, buffy coat‐depleted red‐cell concentrates should be used, if they are available, or alternatively red‐cell concentrates filtered at the bedside. 2 If FNHTRs continue despite these measures, leucocyte‐depleted red‐cell concentrates should be used. 3 To prevent FNHTRs in patients likely to be dependent on long‐term red‐cell support, the use of buffy‐coat‐depleted or bedside filtered red‐cell concentrates should be considered from the outset of transfusion support. 4 The routine use of pooled platelets derived from buffy coats is associated with a low incidence of FNHTRs. The use of platelet concentrates leucocyte‐depleted prior to storage is recommended for patients with reactions despite the use of such components. Bedside filtration of platelet concentrates is not recommended for the prevention of FNHTRs associated with platelet transfusions. Reducing graft rejection after haemopoietic cell transplantation: Patients with severe aplastic anaemia who are potential haemopoietic cell transplant recipients should receive leucocyte‐depleted blood components from the beginning of transfusion support. The same might apply to patients with haemoglobinopathies, but more evidence is required before a definite recommendation can be made. Prevention of transmission of viral infections by blood transfusion: Leucocyte‐depletion of blood components is an effective alternative to the use of CMV‐seronegative blood components for the prevention of transfusion‐transmitted CMV infection to at‐risk patients. Fetal/neonatal transfusions: Leucocyte‐depleted blood components should be used for intrauterine transfusions and for all transfusions to infants below 1 year of age. POSSIBLE Platelet refractoriness: There is currently no convincing evidence that routine leucocyte‐depletion of blood components produces clinical benefits for patients receiving multiple platelet transfusions, although HLA alloimmunization and platelet refractoriness are reduced. Kidney transplants: Pretransplant blood transfusion may confer some benefit to renal transplant recipients, although some patients will become alloimmunized leading to difficulties in the selection of donor kidneys. Consideration should be given to the leucocyte‐depletion of transfusions to renal transplant patients to prevent HLA alloimmunization unless they are part of a deliberate pretransplant immunosuppression protocol. Immunomodulation...