163,303 research outputs found
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() SO() are known to be characterized by three
parameters. By interpreting this solution as coincident D-branes and
-branes we give, for the first time, an explicit
representation of the three parameters of supergravity solutions in terms of
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
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