A sharp uniform bound for the distribution of sums of Bernoulli trials

In this note we establish a uniform bound for the distribution of a sum $S_n=X_1+\cdots+X_n$ of independent non-homogeneous Bernoulli trials. Specifically, we prove that $\sigma_n \mathbb{P}(S_n\!=\!j)\leq\eta$ where $\sigma_n$ denotes the standard deviation of $S_n$ and $\eta$ is a universal constant. We compute the best possible constant $\eta\sim 0.4688$ and we show that the bound also holds for limits of sums and differences of Bernoullis, including the Poisson laws which constitute the worst case and attain the bound. We also investigate the optimal bounds for $n$ and $j$ fixed. An application to estimate the rate of convergence of Mann's fixed point iterations is presented.Comment: This paper is a revised version of a previous articl

Binding and uptake of H-ferritin are mediated by human transferrin receptor-1

Ferritin is a spherical molecule composed of 24 subunits of two types, ferritin H chain (FHC) and ferritin L chain (FLC). Ferritin stores iron within cells, but it also circulates and binds specifically and saturably to a variety of cell types. For most cell types, this binding can be mediated by ferritin composed only of FHC (HFt) but not by ferritin composed only of FLC (LFt), indicating that binding of ferritin to cells is mediated by FHC but not FLC. By using expression cloning, we identified human transferrin receptor-1 (TfR1) as an important receptor for HFt with little or no binding to LFt. In vitro, HFt can be precipitated by soluble TfR1, showing that this interaction is not dependent on other proteins. Binding of HFt to TfR1 is partially inhibited by diferric transferrin, but it is hindered little, if at all, by HFE. After binding of HFt to TfR1 on the cell surface, HFt enters both endosomes and lysosomes. TfR1 accounts for most, if not all, of the binding of HFt to mitogen-activated T and B cells, circulating reticulocytes, and all cell lines that we have studied. The demonstration that TfR1 can bind HFt as well as Tf raises the possibility that this dual receptor function may coordinate the processing and use of iron by these iron-binding molecules

GGPS1 Mutation and Atypical Femoral Fractures with Bisphosphonates

Atypical femoral fractures have been associated with long-term bisphosphonate treatment.1,2 However, the underlying mechanisms remain obscure. We studied three sisters who had atypical femoral fractures after receiving various oral bisphosphonates for 6 years. Two of the sisters had a single fracture (at the ages of 64 and 73 years), and one had bilateral fractures (one at the age of 60 years and the other at the age of 61 years). Given the low incidence of atypical femoral fractures in the general population (5.9 per 10,000 person-years),3 we hypothesized that these sisters might have an underlying genetic background that contributed to these fractures

Thyroid disorders are common in first-degree relatives of individuals with type 1 diabetes mellitus

Objective Thyroid diseases are common in individuals with type 1 diabetes mellitus (T1DM) and should be investigated annually in these individuals. The aim of this study was to evaluate the frequency of thyroid diseases in first degree relatives (FDR) of patients with T1DM. Subjects and methods Eighty individuals (40 patients with T1DM and 40 FDR) were interviewed and blood was sampled for thyroid-stimulating hormone (TSH), free thyroxine (FT4) and thyroid peroxidase (TPO) antibodies measurement. Autoantibodies against glutamic acid decarboxylase 65 (GAD65), islet antigen-2 (IA2) and autoantibodies against insulin (AAI) were measured in FDR. Results We found a similar prevalence of thyroid dysfunction in patients with T1DM and their FDR (22.5% vs. 27.5%; p = 0,79). There were no differences in serum TSH levels (p = 0.29), FT4 (p = 0,45), frequency of abnormal TSH (p = 0.28), positive TPO antibodies (p = 0.13), titers of TPO antibodies (in positive cases) between patients with T1DM and their FDR (p = 0.94). Conclusions Thyroid abnormalities seem to be common not only in patients with T1DM but also in their FDR, which suggests that screening strategies for thyroid diseases might also be useful to these individuals