Global Saturation of Regularization Methods for Inverse Ill-Posed Problems

In this article the concept of saturation of an arbitrary regularization method is formalized based upon the original idea of saturation for spectral regularization methods introduced by A. Neubauer in 1994. Necessary and sufficient conditions for a regularization method to have global saturation are provided. It is shown that for a method to have global saturation the total error must be optimal in two senses, namely as optimal order of convergence over a certain set which at the same time, must be optimal (in a very precise sense) with respect to the error. Finally, two converse results are proved and the theory is applied to find sufficient conditions which ensure the existence of global saturation for spectral methods with classical qualification of finite positive order and for methods with maximal qualification. Finally, several examples of regularization methods possessing global saturation are shown.Comment: 29 page

Structure of the Bacterial Sex F Pilus reveals an assembly of a Stoichiometric Protein-Phospholipid Complex

Conjugative pili are widespread bacterial appendages that play important roles in horizontal gene transfer, in spread of antibiotic resistance genes, and as sites of phage attachment. Among conjugative pili, the F “sex” pilus encoded by the F plasmid is the best functionally characterized, and it is also historically the most important, as the discovery of F-plasmid-mediated conjugation ushered in the era of molecular biology and genetics. Yet, its structure is unknown. Here, we present atomic models of two F family pili, the F and pED208 pili, generated from cryoelectron microscopy reconstructions at 5.0 and 3.6 Å resolution, respectively. These structures reveal that conjugative pili are assemblies of stoichiometric protein-phospholipid units. We further demonstrate that each pilus type binds preferentially to particular phospholipids. These structures provide the molecular basis for F pilus assembly and also shed light on the remarkable properties of conjugative pili in bacterial secretion and phage infection

Effect of a medical food on body mass index and activities of daily living in patients with Alzheimer's disease: secondary analyses from a randomized, controlled trial

Contains fulltext : 97852.pdf (publisher's version ) (Closed access)OBJECTIVES: To investigate the effect of a medical food (Souvenaid) on body mass index (BMI) and functional abilities in patients with mild Alzheimer's disease (AD). DESIGN/SETTING/PARTICIPANTS/INTERVENTION /MEASUREMENTS: These analyses were performed on data from a 12-week, double-blind, randomized, controlled, multicenter, proof-of-concept study with a similarly designed and exploratory 12-week extension period. Patients with mild AD (Mini-Mental State Examination score of 20-26) were randomized to receive either the active product or an iso-caloric control product. While primary outcomes included measures of cognition, the 23-item Alzheimer's Disease Cooperative Study-Activities of Daily Living (ADCS-ADL) scale was included as a secondary outcome. Both ADCS-ADL and BMI were assessed at baseline and Weeks 6, 12 and 24. Data were analyzed using a repeated-measures mixed model. RESULTS: Overall, data suggested an increased BMI in the active versus the control group at Week 24 (ITT: p = 0.07; PP: p = 0.03), but no treatment effect on ADCS-ADL was observed. However, baseline BMI was found to be a significant treatment effect modifier (ITT: p = 0.04; PP: p = 0.05), and an increase in ADCS-ADL was observed at Week 12 in patients with a 'low' baseline BMI (ITT: p = 0.02; PP: p = 0.04). CONCLUSIONS: These data indicate that baseline BMI significantly impacts the effect of Souvenaid on functional abilities. In addition, there was a suggestion that Souvenaid increased BMI

Soluble forms of tau are toxic in Alzheimer's disease

Accumulation of neurofibrillary tangles (NFT), intracellular inclusions of fibrillar forms of tau, is a hallmark of Alzheimer Disease. NFT have been considered causative of neuronal death, however, recent evidence challenges this idea. Other species of tau, such as soluble misfolded, hyperphosphorylated, and mislocalized forms, are now being implicated as toxic. Here we review the data supporting soluble tau as toxic to neurons and synapses in the brain and the implications of these data for development of therapeutic strategies for Alzheimer’s disease and other tauopathies