9,338 research outputs found

    Phaseless computational imaging with a radiating metasurface

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    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

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    I give three descriptions of the Mukai flop of type E_6,IE\_{6,I}, 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 AA. The Mukai flop of type E_6,IIE\_{6,II} is also described.Comment: 35

    Configuration types and cubic surfaces

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    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 n≤8n\le8 essentially distinct points of the projective plane. Each type gives rise to a surface XX obtained by blowing up the points. We classify those types such that n=6n=6 and −KX-K_X 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 Z=m1p1+...+m6p6Z=m_1p_1+...+m_6p_6 such that the points pip_i are essentially distinct and −KX-K_X is nef, given only the configuration type of the points p1,...,p6p_1,...,p_6 and the coefficients mim_i.Comment: 14 pages, final versio
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