24,779 research outputs found
Imaging with parallel ray-rotation sheets
A ray-rotation sheet consists of miniaturized optical components that
function - ray optically - as a homogeneous medium that rotates the local
direction of transmitted light rays around the sheet normal by an arbitrary
angle [A. C. Hamilton et al., arXiv:0809.2646 (2008)]. Here we show that two or
more parallel ray-rotation sheets perform imaging between two planes. The image
is unscaled and un-rotated. No other planes are imaged. When seen through
parallel ray-rotation sheets, planes that are not imaged appear rotated,
whereby the rotation angle changes with the ratio between the observer's and
the object plane's distance from the sheets.Comment: 8 pages, 6 figure
How Correlations Influence Lasso Prediction
We study how correlations in the design matrix influence Lasso prediction.
First, we argue that the higher the correlations are, the smaller the optimal
tuning parameter is. This implies in particular that the standard tuning
parameters, that do not depend on the design matrix, are not favorable.
Furthermore, we argue that Lasso prediction works well for any degree of
correlations if suitable tuning parameters are chosen. We study these two
subjects theoretically as well as with simulations
Strong-coupling scales and the graph structure of multi-gravity theories
In this paper we consider how the strong-coupling scale, or perturbative
cutoff, in a multi-gravity theory depends upon the presence and structure of
interactions between the different fields. This can elegantly be rephrased in
terms of the size and structure of the `theory graph' which depicts the
interactions in a given theory. We show that the question can be answered in
terms of the properties of various graph-theoretical matrices, affording an
efficient way to estimate and place bounds on the strong-coupling scale of a
given theory. In light of this we also consider the problem of relating a given
theory graph to a discretised higher dimensional theory, a la dimensional
deconstruction.Comment: 23 pages, 7 figures; v2: additional references included, and minor
typos corrected; version published in JHE
Lewis acid catalyzed transfer hydromethallylation for the construction of quaternary carbon centers
The design and gramâscale synthesis of a cyclohexaâ1,4âdieneâbased surrogate of isobutene gas is reported. Using the highly electronâdeficient Lewis acid B(C6F5)3, application of this surrogate in the hydromethallylation of electronârich styrene derivatives provided sterically congested quaternary carbon centers. The reaction proceeds by C(sp3)âC(sp3) bond formation at a tertiary carbenium ion that is generated by alkene protonation. The possibility of two concurrent mechanisms is proposed on the basis of mechanistic experiments using a deuterated surrogate.TU Berlin, Open-Access-Mittel - 201
The decoupling limit of Multi-Gravity: Multi-Galileons, Dualities and More
In this paper we investigate the decoupling limit of a particular class of
multi-gravity theories, i.e. of theories of interacting spin-2 fields. We
explicitly compute the interactions of helicity-0 modes in this limit, showing
that they take on the form of multi-Galileons and dual forms. In the process we
extend the recently discovered Galileon dualities, deriving a set of new
multi-Galileon dualities. These are also intrinsically connected to healthy,
but higher-derivative, multi-scalar field theories akin to `beyond Horndeski'
models.Comment: 41 pages, 2 figure
Semiclassical analysis for the Kramers-Fokker-Planck equation
We study some accurate semiclassical resolvent estimates for operators that
are neither selfadjoint nor elliptic, and applications to the Cauchy problem.
In particular we get a precise description of the spectrum near the imaginary
axis and precise resolvent estimates inside the pseudo-spectrum. We apply our
results to the Kramers-Fokker-Planck operator
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