Invariants of broken discrete symmetries.

The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.

Development and Characterization of a Porcine Mitral Valve Scaffold for Tissue Engineering.

Decellularized scaffolds represent a promising alternative for mitral valve (MV) replacement. This work developed and characterized a protocol for the decellularization of whole MVs. Porcine MVs were decellularized with 0.5% (w/v) SDS and 0.5% (w/v) SD and sterilized with 0.1% (v/v) PAA. Decellularized samples were seeded with human foreskin fibroblasts and human adipose-derived stem cells to investigate cellular repopulation and infiltration, and with human colony-forming endothelial cells to investigate collagen IV formation. Histology revealed an acellular scaffold with a generally conserved histoarchitecture, but collagen IV loss. Following decellularization, no significant changes were observed in the hydroxyproline content, but there was a significant reduction in the glycosaminoglycan content. SEM/TEM analysis confirmed cellular removal and loss of some extracellular matrix components. Collagen and elastin were generally preserved. The endothelial cells produced newly formed collagen IV on the non-cytotoxic scaffold. The protocol produced acellular scaffolds with generally preserved histoarchitecture, biochemistry, and biomechanics.

Entropic sampling via Wang-Landau random walks in dominant energy subspaces.

Dominant energy subspaces of statistical systems are defined with the help of restrictive conditions on various characteristics of the energy distribution, such as the probability density and the fourth order Binder's cumulant. Our analysis generalizes the ideas of the critical minimum energy subspace (CRMES) technique, applied previously to study the specific heat's finite-size scaling. Here, we illustrate alternatives that are useful for the analysis of further finite-size anomalies and the behavior of the corresponding dominant subspaces is presented for the two-dimensional (2D) Baxter-Wu and the 2D and 3D Ising models. In order to show that a CRMES technique is adequate for the study of magnetic anomalies, we study and test simple methods which provide the means for an accurate determination of the energy-order-parameter (E,M) histograms via Wang-Landau random walks. The 2D Ising model is used as a test case and it is shown that high-level Wang-Landau sampling schemes yield excellent estimates for all magnetic properties. Our estimates compare very well with those of the traditional Metropolis method. The relevant dominant energy subspaces and dominant magnetization subspaces scale as expected with exponents alpha/nu and gamma/nu, respectively. Using the Metropolis method we examine the time evolution of the corresponding dominant magnetization subspaces and we uncover the reasons behind the inadequacy of the Metropolis method to produce a reliable estimation scheme for the tail regime of the order-parameter distribution.