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Symmetric lenses

Martin Hofmann, Benjamin Pierce, Daniel Wagner
2011 SIGPLAN notices  
) tensor products and sums and the non-existence of full categorical products or sums in the category of symmetric lenses.  ...  This formulation generalizes the familiar structure of asymmetric lenses, and it admits a good notion of composition. Second, we explore the algebraic structure of the space of symmetric lenses.  ...  Acknowledgments We are grateful to Nate Foster for productive discussions of many points, especially about the category of lenses, and to both Nate and Alexandre Pilkiewicz for helpful comments on drafts  ... 
doi:10.1145/1925844.1926428 fatcat:j6mir77yojhbvgihl24qwkemeu

Symmetric lenses

Martin Hofmann, Benjamin Pierce, Daniel Wagner
2011 Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '11  
) tensor products and sums and the non-existence of full categorical products or sums in the category of symmetric lenses.  ...  This formulation generalizes the familiar structure of asymmetric lenses, and it admits a good notion of composition. Second, we explore the algebraic structure of the space of symmetric lenses.  ...  Acknowledgments We are grateful to Nate Foster for productive discussions of many points, especially about the category of lenses, and to both Nate and Alexandre Pilkiewicz for helpful comments on drafts  ... 
doi:10.1145/1926385.1926428 dblp:conf/popl/HofmannPW11 fatcat:3jj6xrk6vnepra5j6lzclbhvwe

Synthesizing Symmetric Lenses [article]

Anders Miltner, Solomon Maina, Kathleen Fisher, Benjamin C. Pierce, David Walker, Steve Zdancewic
2019 arXiv   pre-print
"symmetric lenses" proposed by Hofmann et al.  ...  We extend this synthesis algorithm to a broader class of lenses, called simple symmetric lenses, including all bijective lenses, all of the popular category of "asymmetric" lenses, and a subset of the  ...  Symmetric DNF Lenses Symmetric DNF lenses are an intermediate synthesis target for GreedySynth. There are many fewer symmetric DNF lenses than symmetric regular lenses.  ... 
arXiv:1810.11527v2 fatcat:s6gqlpqtyjehbluacmmbwsawce

Symmetric c-Lenses and Symmetric d-Lenses are Not Coextensive

Michael Johnson, François Renaud
2019 International Workshop on Bidirectional Transformations  
This short paper addresses a long standing open question about symmetric lenses, with the result succinctly summarised by the paper's title.  ...  d-lenses which never arise as symmetric c-lenses.  ...  whose morphisms are those symmetric d-lenses.  ... 
dblp:conf/bx/JohnsonR19a fatcat:22loidieffbkrd2uitxz7ti6qm

Universal Updates for Symmetric Lenses

Michael Johnson, Robert D. Rosebrugh
2017 European Joint Conferences on Theory And Practice of Software  
In addition we explore how to characterise the symmetric d-lenses that arise from cospans of c-lenses among all symmetric d-lenses.  ...  This paper begins an analysis of symmetric c-lenses and their relationship to symmetric dlenses and explains why the authors do not expect symmetric c-lenses, that is, equivalence classes of spans of c-lenses  ...  symmetric lenses).  ... 
dblp:conf/etaps/JohnsonR17 fatcat:2z7eni65yne2xp67t6tbw3cmc4

Gravitational lensing by spherically symmetric lenses with angular momentum

M. Sereno, V. F. Cardone
2002 Astronomy and Astrophysics  
Following Sereno (2002a), we discuss the bending of light rays by spherically symmetric lenses with angular momentum.  ...  Summary and discussion We have investigated the effect of dragging of inertial frames in gravitational lensing for spherically symmetric lenses and a general expression for the deflection angle, to the  ...  We discuss spherically symmetric deflectors.  ... 
doi:10.1051/0004-6361:20021356 fatcat:v7fdvdfhk5bv3ppjd5wr67rihy

Symmetric delta lenses and spans of asymmetric delta lenses

Michael Johnson, Robert Rosebrugh
2017 Journal of Object Technology  
Symmetric delta lenses and spans of asymmetric delta lenses.  ...  As part of a project to unify the treatment of symmetric lenses (of various kinds) as equivalence classes of spans of asymmetric lenses (of corresponding kinds), we relate symmetric delta lenses with spans  ...  Symmetric delta lenses A symmetric delta lens (called an "fb-lens" below) is between categories, say X and Y.  ... 
doi:10.5381/jot.2017.16.1.a2 fatcat:zdau6gfdffhghpmtulo6miqpie

Elliptically Symmetric Lenses and Violation of Burke's Theorem [article]

Sun Hong Rhie
2010 arXiv   pre-print
or cluster lenses.  ...  Thus the total parity of the images of a point source lensed by a bounded elliptically symmetric mass is not an invariant in violation of the Burke's theorem.  ...  lenses and elliptically symmetric lenses as a reasonable model for galaxy and cluster lenses; they are represented as points, sticks, and disks.  ... 
arXiv:1006.0782v2 fatcat:r4oc2djhjnegjfffrojhtod7pm

Gravitational Lensing in Spherically Symmetric Spacetimes [article]

Bonita de Swardt, Peter K. S. Dunsby, Chris Clarkson
2010 arXiv   pre-print
We present a framework for studying gravitational lensing in spherically symmetric spacetimes using 1+1+2 covariant methods.  ...  Figure 1 . 1 Lensing geometry in symmetric spacetimes  ...  form of the deflection angle α, for spherically symmetric lensing situations, which is the main result of this paper.  ... 
arXiv:1002.2041v1 fatcat:ptkcgofmhbgexdvyv5uy72wq6y

A diagrammatic approach to symmetric lenses

Bryce Clarke
2021 Electronic Proceedings in Theoretical Computer Science  
In their ongoing research program, Johnson and Rosebrugh have sought to unify the treatment of symmetric lenses with spans of asymmetric lenses.  ...  The central result of this paper is to demonstrate that the bicategory of symmetric lenses is locally adjoint to the bicategory of spans of asymmetric lenses, through constructing an explicit adjoint triple  ...  Symmetric lenses The goal of this section is to introduce the bicategory SymLens of small categories and symmetric lenses.  ... 
doi:10.4204/eptcs.333.6 fatcat:6ng2at4sdbbclasmgnsf7eq64y

Design of spherical symmetric gradient index lenses

Juan C. Miñano, Dejan Grabovičkić, Pablo Benítez, Juan C. González, Asunción Santamaría, Roland Winston, Jeffrey M. Gordon
2012 Nonimaging Optics: Efficient Design for Illumination and Solar Concentration IX  
Spherical symmetric refractive index distributions also known as Gradient Index lenses such as the Maxwell-Fish-Eye (MFE), the Luneburg or the Eaton lenses have always played an important role in Optics  ...  The recent development of the technique called Transformation Optics has renewed the interest in these gradient index lenses.  ...  INTRODUCTION Spherical symmetric lenses made of isotropic gradient index media have always called the attention of optical designers.  ... 
doi:10.1117/12.931505 fatcat:zw5lz22rkzapln5aoo3wgswbgm

APPROACHING THE CRAMÉR–RAO BOUND IN WEAK LENSING WITH PDF SYMMETRIZATION

Jun Zhang, Pengjie Zhang, Wentao Luo
2016 Astrophysical Journal  
Weak lensing statistics is typically measured as weighted sum of shear estimators or their products (shear-shear correlation).  ...  This can be achieved by symmetrizing the PDF of the shear estimator, or the joint PDF of shear estimator pairs (for shear-shear correlation), without any prior knowledge of the PDF.  ...  PDF-SYM IN SHEAR MEASUREMENT Shear Estimator Let us define the intrinsic galaxy surface brightness distribution before lensing as f I ( x I ), the lensed galaxy (before being processed by the PSF) as  ... 
doi:10.3847/1538-4357/834/1/8 fatcat:vxhaf2b26nhnpoonhayvonyx6e

On Gravitational Lensing by Symmetric and Asymmetric Wormholes

K. A. Bronnikov, K. A. Baleevskikh
2019 Gravitation & Cosmology  
We discuss the peculiarities of gravitational lensing by spherically symmetric wormholes if they are not symmetric with respect to their throats.  ...  noticed, in particular, that wormholes always contain the so-called photon spheres, near which the photon deflection angles can be arbitrarily large, but, in general, the throat is such a sphere only for symmetric  ...  To describe gravitational lensing, one can use the general formulas for asymptotically flat static, spherically symmetric space-times, see, e.g., [8, 9] .  ... 
doi:10.1134/s020228931901002x fatcat:ptbel56itbfrdpnxqjc5elacyi

Axially symmetric hollow beams using refractive conical lenses

M. de Angelis, L. Cacciapuoti, G. Pierattini, G.M. Tino
2003 Optics and lasers in engineering  
We explore the possibility of producing several beam shapes with conical or cylindrical geometry using conical lenses.  ...  We have studied the generation of conical, cylindrical and ''bottle'' shaped beams using conical lenses in combination with spherical lenses.  ...  The output beam is symmetrized by an anamorphic prism pair, spatially filtered with a 50 mm diameter pin hole and expanded in order to obtain a beam with a C1:5 mm waist.  ... 
doi:10.1016/s0143-8166(01)00117-8 fatcat:6ufzv5gwkvdzjafyimd7cefldy

Investigation of Nonrotationally Symmetrical Electrostatic Electron Optical Lenses

Romayne F. Whitmer
1956 Journal of Applied Physics  
Also it is of interest to investigate the aberrations of nonrotationally symmetric lenses and to compare these with those obtained with rotationally symmetric lenses.  ...  In general nonrotationally symmetric lenses suffer from first-order distortion and astigmatism.  ... 
doi:10.1063/1.1722488 fatcat:jpm6ppoo6nfxvalajwzesn6n4i
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