Restricted Universality of Power Series

We prove the existence of a power series having radius of convergence0, whose partial sums have universal approximation propertieson any compact set with connected complement that is containedin a finite union of circles centred at 0 and having rationalradii, but do not have such properties on any compact set withnonempty interior. This relates to a theorem of A. I. Seleznev.2000 Mathematics Subject Classification 30B30 (primary), 30B10,30E60 (secondary).     

The balance between side-chain and backbone-driven association in folding of the α-helical influenza A transmembrane peptide

The correct balance between attractive, repulsive and peptide hydrogen bonding interactions must be attained for proteins to fold correctly. To investigate these important contributors, we sought a comparison of the folding between two 25-residues peptides, the influenza A M2 protein transmembrane domain (M2TM) and the 25-Ala (Ala₂₅). M2TM forms a stable α-helix as is shown by circular dichroism (CD) experiments. Molecular dynamics (MD) simulations with adaptive tempering show that M2TM monomer is more dynamic in nature and quickly interconverts between an ensemble of various α-helical structures, and less frequently turns and coils, compared to one α-helix for Ala₂₅. DFT calculations suggest that folding from the extended structure to the α-helical structure is favored for M2TM compared with Ala₂₅. This is due to CH⋯O attractive interactions which favor folding to the M2TM α-helix, and cannot be described accurately with a force field. Using natural bond orbital (NBO) analysis and quantum theory atoms in molecules (QTAIM) calculations, 26 CH⋯O interactions and 22 NH⋯O hydrogen bonds are calculated for M2TM. The calculations show that CH⋯O hydrogen bonds, although individually weaker, have a cumulative effect that cannot be ignored and may contribute as much as half of the total hydrogen bonding energy, when compared to NH⋯O, to the stabilization of the α-helix in M2TM. Further, a strengthening of NH⋯O hydrogen bonding interactions is calculated for M2TM compared to Ala₂₅. Additionally, these weak CH⋯O interactions can dissociate and associate easily leading to the ensemble of folded structures for M2TM observed in folding MD simulations.     

Comparison of PD BLADE with fat saturation (FS), PD FS and T2 3D DESS with water excitation (WE) in detecting articular knee cartilage defects

The purpose of this study, is to compare the sequences: 1) proton density (PD) BLADE (BLADE is a PROPELLER-equivalent implementation of the Siemens Medical System) with fat saturation (FS) coronal (COR), 2) PD FS COR, 3) multi-planar reconstruction (MPR) with 3 mm slice thickness and 4) multi-planar reconstruction (MPR) with 1.5 mm slice thickness, both from the T2 3D-double-echo steady state (DESS) with water excitation (WE) sagittal (SAG), regarding their abilities to identify changes in the femorotibial condyle cartilage in knee MRI examinations. Thirty three consecutive patients with osteoarthritis (18 females, 15 males; mean age 56 years, range 37–71 years), who had been routinely scanned for knee examination using the previously mentioned image acquisition techniques, participated in the study. A quantitative analysis was performed based on the relative contrast (ReCON) measurements, which were taken both on normal tissues as well as on pathologies. Additionally, a qualitative analysis was performed by two radiologists. Motion and pulsatile flow artifacts were evaluated. The PD BLADE FS COR sequence produced images of higher contrast between Menisci and Cartilage, Fluid and Cartilage, Pathologies and Cartilage as well as of the Conspicuousness Superficial Cartilage and it was found to be superior to the other sequences (p < 0.001). The sequences T2 3D DESS 1.5 mm and T2 3D DESS 3 mm were significantly superior to the PD BLADE FS COR and the PD FS COR sequences in the visualization of Bone and Cartilage and the Conspicuousness Deep Surface Cartilage. This pattern of results is also confirmed by the quantitative analysis. PD FS BLADE sequences are ideal for the depiction of the cartilage pathologies compared to the conventional PD FS and T2 3D DESS sequences.     

The concept of material forces in phase transition problems within the level-set framework

The dynamics of a phase transition front in solids using the level set method is examined in this paper. Introducing an implicit representation of singular surfaces, a regularized version of the sharp interface model arises. The interface transforms into a thin transition layer of nonzero thickness where all quantities take inhomogeneous expressions within the body. It is proved that the existence of an inhomogeneous energy of the material predicts inhomogeneity forces that drive the singularity. The driving force is a material force entering the canonical momentum equation (pseudo-momentum) in a natural way. The evolution problem requires a kinetic relation that determines the velocity of the phase transition as a function of the driving force. Here, the kinetic relation is produced by invoking relations that can be considered as the regularized versions of the Rankine–Hugoniot jump conditions. The effectiveness of the method is illustrated in a shape memory alloy bar.