Principal Nested Spheres for Time Warped Functional Data Analysis

There are often two important types of variation in functional data: the horizontal (or phase) variation and the vertical (or amplitude) variation. These two types of variation have been appropriately separated and modeled through a domain warping method (or curve registration) based on the Fisher Rao metric. This paper focuses on the analysis of the horizontal variation, captured by the domain warping functions. The square-root velocity function representation transforms the manifold of the warping functions to a Hilbert sphere. Motivated by recent results on manifold analogs of principal component analysis, we propose to analyze the horizontal variation via a Principal Nested Spheres approach. Compared with earlier approaches, such as approximating tangent plane principal component analysis, this is seen to be the most efficient and interpretable approach to decompose the horizontal variation in some examples

Supergravity approach to tachyon condensation on the brane-antibrane system

We study the tachyon condensation on the D-brane--antiD-brane system from the supergravity point of view. The non-supersymmetric supergravity solutions with symmetry ISO($p,1$) $\times$ SO($9-p$) are known to be characterized by three parameters. By interpreting this solution as coincident $N$ D$p$-branes and ${\bar N}$ ${\bar {\rm D}}p$-branes we give, for the first time, an explicit representation of the three parameters of supergravity solutions in terms of $N, \bar N$ and the tachyon vev. We demonstrate that the solution and the corresponding ADM mass capture all the required properties and give a correct description of the tachyon condensation advocated by Sen on the D-brane--antiD-brane system.Comment: 9 page

The origin of biological macromolecules on the earth. The hypothesis of inorganic template

Studies about the origin of life are reviewed. The nonrandom organization of organelles is discussed from a structural and functional point of view. After postulating that the origin of biomacromolecules was not a random event, the paper develops the hypothesis that polypeptides and polynucleotides were formed on an inorganic template. Only information-containing structures can pass natural selection and develop through evolution

Flat lens without optical axis: Theory of imaging

We derive a general theory for imaging by a flat lens without optical axis. We show that the condition for imaging requires a material having elliptic dispersion relations with negative group refraction, equivalent to an effective anisotropic refractive index n(theta). Imaging can be achieved with both negative (n0) refractive indices. The Veselago-Pendry lens is a special case with isotropic negative refractive index of n(theta)=-1. Realizations of the imaging conditions using anisotropic media and inhomogeneous media, particularly photonic crystals, are discussed. Numerical examples of imaging and requirements for sub-wavelength imaging are also presented.Comment: 5 pages, 4 figure