Mini-Cog for the diagnosis of Alzheimer's disease dementia and other dementias within a secondary care setting

© 2014 The Cochrane Collaboration. This is the protocol for a review and there is no abstract. The objectives are as follows: To determine the diagnostic accuracy of the Mini-Cog for detecting Alzheimer's disease dementia and related dementias in a secondary care setting. To investigate the heterogeneity of test accuracy in the included studies and potential sources of heterogeneity. These potential sources of heterogeneity will include the baseline prevalence of dementia in study samples, thresholds used to determine positive test results, the type of dementia (Alzheimer's disease dementia or all causes of dementia), and aspects of study design related to study quality. We will also identify gaps in the evidence where further research is required

Grating-assisted superresolution of slow waves in Fourier space

We present a far-field optical technique allowing measurements of the dispersion relation of electromagnetic fields propagating under the light cone in photonic nanostructures. It relies on the use of a one-dimensional grating to probe the evanescent tail of the guided field in combination with a high-numerical-aperture Fourier- space imaging setup. A high-resolution spectroscopy of the far-field emission diagram allows us to accurately and efficiently determine the dispersion curve and the group-index dispersion of planar photonic crystal waveguides operating in the slow-light regime

Transmutations and spectral parameter power series in eigenvalue problems

We give an overview of recent developments in Sturm-Liouville theory concerning operators of transmutation (transformation) and spectral parameter power series (SPPS). The possibility to write down the dispersion (characteristic) equations corresponding to a variety of spectral problems related to Sturm-Liouville equations in an analytic form is an attractive feature of the SPPS method. It is based on a computation of certain systems of recursive integrals. Considered as families of functions these systems are complete in the $L_{2}$-space and result to be the images of the nonnegative integer powers of the independent variable under the action of a corresponding transmutation operator. This recently revealed property of the Delsarte transmutations opens the way to apply the transmutation operator even when its integral kernel is unknown and gives the possibility to obtain further interesting properties concerning the Darboux transformed Schr\"{o}dinger operators. We introduce the systems of recursive integrals and the SPPS approach, explain some of its applications to spectral problems with numerical illustrations, give the definition and basic properties of transmutation operators, introduce a parametrized family of transmutation operators, study their mapping properties and construct the transmutation operators for Darboux transformed Schr\"{o}dinger operators.Comment: 30 pages, 4 figures. arXiv admin note: text overlap with arXiv:1111.444

Pattern selection in the absolutely unstable regime as a nonlinear eigenvalue problem: Taylor vortices in axial flow

A unique pattern selection in the absolutely unstable regime of a driven, nonlinear, open-flow system is analyzed: The spatiotemporal structures of rotationally symmetric vortices that propagate downstream in the annulus of the rotating Taylor-Couette system due to an externally imposed axial through-flow are investigated for two different axial boundary conditions at the in- and outlet. Unlike the stationary patterns in systems without through-flow the spatiotemporal structures of propagating vortices are independent of parameter history, initial conditions, and system's length. They do, however, depend on the axial boundary conditions, the driving rate of the inner cylinder and the through-flow rate. Our analysis of the amplitude equation shows that the pattern selection can be described by a nonlinear eigenvalue problem with the frequency being the eigenvalue. Approaching the border between absolute and convective instability the eigenvalue problem becomes effectively linear and the selection mechanism approaches that one of linear front propagation. PACS:47.54.+r,47.20.Ky,47.32.-y,47.20.FtComment: 15 pages (LateX-file), 8 figures (Postscript

Equivalences between localisations of categories provided by replacements

We give a characterisation of functors whose induced functor on the level of localisations is an equivalence and where the isomorphism inverse is induced by some kind of replacements such as projective resolutions or cofibrant replacements