Semi-discrete error estimates and implementation of a mixed method for the Stefan problem

We analyze a dual formulation and finite element method for simulating the Stefan problem with surface tension (originally presented in [C.B. Davis and S.W. Walker, Int. Free Bound. 17 (2015) 427–464]). The method uses a mixed form of the heat equation in the solid and liquid (bulk) domains, and imposes a weak formulation of the interface motion law (on the solid-liquid interface) as a constraint. The computational method uses a conforming mesh approach to accurately capture the jump conditions across the interface. Preliminary error estimates are derived, under reduced regularity assumptions, for the difference between the time semi-discrete solution and the fully discrete solution over one time step. Moreover, details of the implementation are discussed including mesh generation issues. Several simulations of interface growth (in two dimensions) are presented to illustrate the method

Amyloid beta peptides in plasma in early diagnosis of Alzheimer's disease: A multicenter study with multiplexing

We measured concentrations of Abeta peptides 1-42 and 1-40, and their ratio in plasma of patients carefully categorized clinically and neurochemically as having AD or other dementias with a newly commercially available multiplexing assay, characterized by reasonable laboratory performance (intra-assay imprecision in the range of 1.3-3.8% for Abeta1-42, and 1.8-4.1% for Abeta1-40, inter-assay imprecision for Abeta1-42, Abeta1-40, and Abeta1-42/Abeta1-40 concentration ratio in the range of 2.3-11.5%, 2.2-10.4% and 4.2-9.7%, respectively). Patients with AD or mild cognitive impairment of AD type (MCI-AD) whose clinical diagnosis was supported with CSF biomarkers (n=193) had significantly lower Abeta1-42 plasma concentrations (p<0.007), and Abeta1-42/1-40 ratios (p<0.003) compared to patients with other dementias and MCI of other types (n=64). No significant differences between persons with MCI of AD type and patients with early AD were observed, or between MCI of other types versus patients with early dementia of other types. Our findings reconfirm the hypothesis that alterations of biomarker concentrations occur early in a preclinical AD stage and that these alterations are also reflected in plasma