A Grassmann-Rayleigh quotient iteration for computing invariant subspaces

The classical Rayleigh quotient iteration (RQI) allows one to compute a one-dimensional invariant subspace of a symmetric matrix A. Here we propose a generalization of the RQI which computes a p-dimensional invariant subspace of A. Cubic convergence is preserved and the cost per iteration is low compared to other methods proposed in the literature.

A Grassman-Rayleigh quotient iteration for computing invariant subspaces

The classical Rayleigh Quotient Iteration (RQI) computes a 1-dimensional invariant subspace of a symmetric matrix A with cubic convergence. We propose a generalization of the RQI which computes a p-dimensional invariant subspace of A. The geometry of the algorithm on the Grassmann manifold Gr(p,n) is developed to show cubic convergence and to draw connections with recently proposed Newton algorithms on Riemannian manifolds.

α-Synuclein senses lipid packing defects and induces lateral expansion of lipids leading to membrane remodeling.

There is increasing evidence for the involvement of lipid membranes in both the functional and pathological properties of α-synuclein (α-Syn). Despite many investigations to characterize the binding of α-Syn to membranes, there is still a lack of understanding of the binding mode linking the properties of lipid membranes to α-Syn insertion into these dynamic structures. Using a combination of an optical biosensing technique and in situ atomic force microscopy, we show that the binding strength of α-Syn is related to the specificity of the lipid environment (the lipid chemistry and steric properties within a bilayer structure) and to the ability of the membranes to accommodate and remodel upon the interaction of α-Syn with lipid membranes. We show that this interaction results in the insertion of α-Syn into the region of the headgroups, inducing a lateral expansion of lipid molecules that can progress to further bilayer remodeling, such as membrane thinning and expansion of lipids out of the membrane plane. We provide new insights into the affinity of α-Syn for lipid packing defects found in vesicles of high curvature and in planar membranes with cone-shaped lipids and suggest a comprehensive model of the interaction between α-Syn and lipid bilayers. The ability of α-Syn to sense lipid packing defects and to remodel membrane structure supports its proposed role in vesicle trafficking.

UbiDM: A new paradigm for product design and manufacturing via ubiquitous computing technology

Since ubiquitous technology was introduced in the early 1980s, it has rapidly developed, and been applied to various domains mainly for the improvement of human life. In this article, the authors propose that ubiquitous computing technology can be effectively used for the design and manufacturing of a product by proposing a new paradigm, called UbiDM (Design and Manufacture via Ubiquitous Computing Technology). The key aspect of UbiDM is the utilisation of the entire product lifecycle information obtained via ubiquitous computing technology for the design and manufacture of the product. The new paradigm can solve many of the problems that have not been properly handled by previous manufacturing paradigms. Specifically, it will address the concept of UbiDM by the following aspects: (1) why there is a need for UbiDM; (2) the essence of UbiDM; (3) enabling technologies; (4) application area; (5) worldwide RD status; and (6) the societal impacts of UbiDM.