9,338 research outputs found
Phaseless computational imaging with a radiating metasurface
Computational imaging modalities support a simplification of the active
architectures required in an imaging system and these approaches have been
validated across the electromagnetic spectrum. Recent implementations have
utilized pseudo-orthogonal radiation patterns to illuminate an object of
interest---notably, frequency-diverse metasurfaces have been exploited as fast
and low-cost alternative to conventional coherent imaging systems. However,
accurately measuring the complex-valued signals in the frequency domain can be
burdensome, particularly for sub-centimeter wavelengths. Here, computational
imaging is studied under the relaxed constraint of intensity-only measurements.
A novel 3D imaging system is conceived based on 'phaseless' and compressed
measurements, with benefits from recent advances in the field of phase
retrieval. In this paper, the methodology associated with this novel principle
is described, studied, and experimentally demonstrated in the microwave range.
A comparison of the estimated images from both complex valued and phaseless
measurements are presented, verifying the fidelity of phaseless computational
imaging.Comment: 18 pages, 18 figures, articl
On Mukai flops for Scorza varieties
I give three descriptions of the Mukai flop of type , one in terms
of Jordan algebras, one in terms of projective geometry over the octonions, and
one in terms of O-blow-ups. Each description shows that it is very similar to
certain flops of type . The Mukai flop of type is also
described.Comment: 35
Configuration types and cubic surfaces
This paper is a sequel to the paper \cite{refGH}. We relate the matroid
notion of a combinatorial geometry to a generalization which we call a
configuration type. Configuration types arise when one classifies the Hilbert
functions and graded Betti numbers for fat point subschemes supported at
essentially distinct points of the projective plane. Each type gives
rise to a surface obtained by blowing up the points. We classify those
types such that and is nef. The surfaces obtained are precisely
the desingularizations of the normal cubic surfaces. By classifying
configuration types we recover in all characteristics the classification of
normal cubic surfaces, which is well-known in characteristic 0 \cite{refBW}. As
an application of our classification of configuration types, we obtain a
numerical procedure for determining the Hilbert function and graded Betti
numbers for the ideal of any fat point subscheme such
that the points are essentially distinct and is nef, given only
the configuration type of the points and the coefficients .Comment: 14 pages, final versio
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