Computing the lower and upper bounds of Laplace eigenvalue problem: by combining conforming and nonconforming finite element methods

This article is devoted to computing the lower and upper bounds of the Laplace eigenvalue problem. By using the special nonconforming finite elements, i.e., enriched Crouzeix-Raviart element and extension $Q_1^{\rm rot}$, we get the lower bound of the eigenvalue. Additionally, we also use conforming finite elements to do the postprocessing to get the upper bound of the eigenvalue. The postprocessing method need only to solve the corresponding source problems and a small eigenvalue problem if higher order postprocessing method is implemented. Thus, we can obtain the lower and upper bounds of the eigenvalues simultaneously by solving eigenvalue problem only once. Some numerical results are also presented to validate our theoretical analysis.Comment: 19 pages, 4 figure

Efficient Recursion Method for Inverting Overlap Matrix

A new O(N) algorithm based on a recursion method, in which the computational effort is proportional to the number of atoms N, is presented for calculating the inverse of an overlap matrix which is needed in electronic structure calculations with the the non-orthogonal localized basis set. This efficient inverting method can be incorporated in several O(N) methods for diagonalization of a generalized secular equation. By studying convergence properties of the 1-norm of an error matrix for diamond and fcc Al, this method is compared to three other O(N) methods (the divide method, Taylor expansion method, and Hotelling's method) with regard to computational accuracy and efficiency within the density functional theory. The test calculations show that the new method is about one-hundred times faster than the divide method in computational time to achieve the same convergence for both diamond and fcc Al, while the Taylor expansion method and Hotelling's method suffer from numerical instabilities in most cases.Comment: 17 pages and 4 figure

Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes

New algorithms for computing of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction, which can be applied to processes with asymptotically coupled and uncoupled finite phase spaces.Comment: 83 page

Sequence Defined Disulfide-Linked Shuttle for Strongly Enhanced Intracellular Protein Delivery

Intracellular protein transduction technology is opening the door for a promising alternative to gene therapy. Techniques have to address all critical steps, like efficient cell uptake, endolysosomal escape, low toxicity, while maintaining full functional activity of the delivered protein. Here, we present the use of a chemically precise, structure defined three-arm cationic oligomer carrier molecule for protein delivery. This carrier of exact and low molecular weight combines good cellular uptake with efficient endosomal escape and low toxicity. The protein cargo is covalently attached by a bioreversible disulfide linkage. Murine 3T3 fibroblasts could be transduced very efficiently with cargo nlsEGFP, which was tagged with a nuclear localization signal. We could show subcellular delivery of the nlsEGFP to the nucleus, confirming cytosolic delivery and expected subsequent subcellular trafficking. Transfection efficiency was concentration-dependent in a directly linear mode and 20-fold higher in comparison with HIV-TAT-nlsEGFP containing a functional TAT transduction domain. Furthermore, β-galactosidase as a model enzyme cargo, modified with the carrier oligomer, was transduced into neuroblastoma cells in enzymatically active form

A new algorithm for computing the Geronimus transformations for large shifts

A monic Jacobi matrix is a tridiagonal matrix which contains the parameters of the three-term recurrence relation satisfied by the sequence of monic polynomials orthogonal with respect to a measure. The basic Geronimus transformation with shift ? transforms the monic Jacobi matrix associated with a measure d? into the monic Jacobi matrix associated with d?/(x????)?+?C?(x????), for some constant C. In this paper we examine the algorithms available to compute this transformation and we propose a more accurate algorithm, estimate its forward errors, and prove that it is forward stable. In particular, we show that for C?=?0 the problem is very ill-conditioned, and we present a new algorithm that uses extended precision

On the characterization of the heterogeneous mechanical response of human brain tissue

The mechanical characterization of brain tissue is a complex task that scientists have tried to accomplish for over 50 years. The results in the literature often differ by orders of magnitude because of the lack of a standard testing protocol. Different testing conditions (including humidity, temperature, strain rate), the methodology adopted, and the variety of the species analysed are all potential sources of discrepancies in the measurements. In this work, we present a rigorous experimental investigation on the mechanical properties of human brain, covering both grey and white matter. The influence of testing conditions is also shown and thoroughly discussed. The material characterization performed is finally adopted to provide inputs to a mathematical formulation suitable for numerical simulations of brain deformation during surgical procedures.</p