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Computing on Functions Using Randomized Vector Representations [article]

E. Paxon Frady, Denis Kleyko, Christopher J. Kymn, Bruno A. Olshausen, Friedrich T. Sommer
2021 arXiv   pre-print
In VFAs, vectors can represent individual data points as well as elements of a function space (a reproducing kernel Hilbert space).  ...  of data points and fulfills the kernel properties for inducing a VFA.  ...  Vectors can represent individual data points as well as elements of a function space that is well-defined as a reproducing kernel Hilbert space.  ... 
arXiv:2109.03429v1 fatcat:dwsu2n5qkfcp7mpeh5bhhsosyu

Adaptive Regularization With the Structure Tensor

Virginia Estellers, Stefano Soatto, Xavier Bresson
2015 IEEE Transactions on Image Processing  
Based on this observation, we propose a variational model for image reconstruction that employs a regularization functional adapted to the local geometry of image by means of its structure tensor.  ...  Our method extends naturally to non-local regularization, where it exploits the local self-similarity of natural images to improve nonlocal TV [2] and diffusion operators [3] .  ...  Non-Local Regularization Non-local TV and Dirichlet regularizers are variational extensions of the NL-means filter [33] for image denoising.  ... 
doi:10.1109/tip.2015.2409562 pmid:25769155 fatcat:cvhexgfl65bn3nbxds7ztac55e

Field space parametrization in quantum gravity and the identification of a unitary conformal field theory at the heart of 2D Asymptotic Safety [article]

Andreas Nink
2017 arXiv   pre-print
The last part concerns the reconstruction of the functional integral out of a given effective theory, where we reconstruct the bare action for an Einstein--Hilbert-type effective average action and for  ...  To this end, we show that the 2D limit of the Einstein--Hilbert action at a nontrivial fixed point becomes Polyakov's induced gravity action which describes a conformal field theory.  ...  Euclidean vs.  ... 
arXiv:1701.08344v1 fatcat:4tz4xx2e3rffda7kyyqmjs3rn4

Long-range electrostatic contribution to the electron-phonon couplings and mobilities of two-dimensional materials [article]

Samuel Poncé, Miquel Royo, Massimiliano Stengel, Nicola Marzari, Marco Gibertini
2022 arXiv   pre-print
Assessing the intrinsic phonon-limited carrier mobility is thus of paramount importance to identify promising candidates for next-generation devices.  ...  We study a wide selection of relevant monolayers ranging from SnS$_2$ to MoS$_2$, graphene, BN, InSe, and phosphorene, showing the importance of the current strategy to fully account for the peculiar nature  ...  obtained from the above all-space kernel by means of the Fourier transforms described in Appendix A.  ... 
arXiv:2207.10190v1 fatcat:5fvrmxncjjfenhxo7ylvoes5xi

Completely Positive, Simple, and Possibly Highly Accurate Approximation of the Redfield Equation

Dragomir Davidović
2020 Quantum  
In the second step, we swap out an arithmetic mean of the spectral density with a geometric one, in these gains and losses, thereby restoring complete positivity.  ...  , the images in Fig. 1 (a) and (d) display the geometric mean g(ω, ω ) = γ(ω)γ(ω ) and the detuning function magnitude versus system frequencies, respectively.  ...  Figure 2 : 2 a) Ratio of the tracenorms of two kernels versus coarse-graining time. Black-full curve is the ratio between the detuning-function and the geometric mean SD.  ... 
doi:10.22331/q-2020-09-21-326 doaj:ee30c48c3ca34cf89af24ad48f263e45 fatcat:teufmuvwx5bpvhyglilkzuu5gq

Completely Positive, Simple, and Possibly Highly Accurate Approximation of the Redfield Equation [article]

Dragomir Davidovic
2020 arXiv   pre-print
In the second step, we swap out an arithmetic mean of the spectral density with a geometric one, in these gains and losses, thereby restoring complete positivity.  ...  , the images in Fig. 1 (a) and (d) display the geometric mean g(ω, ω ) = γ(ω)γ(ω ) and the detuning function magnitude versus system frequencies, respectively.  ...  Figure 2 : 2 a) Ratio of the tracenorms of two kernels versus coarse-graining time. Black-full curve is the ratio between the detuning-function and the geometric mean SD.  ... 
arXiv:2003.09063v4 fatcat:tn5yyvqkbzam3kuwfspidlym44

Continuous Measurement and Stochastic Methods in Quantum Optical Systems [article]

Robert L. Cook
2013 arXiv   pre-print
Through a technique known as projection filtering, we find such a equation for an ensemble of qubits experiencing a diffusive measurement of a collective angular momentum projection, and global rotations  ...  The final topic applies the projection filter to the problem of state reconstruction.  ...  This nonlocal property of a photon wave function has been studied by many authors, with various definitions for a photon's wave function, see [42] for a pertinent discussion.  ... 
arXiv:1301.6193v1 fatcat:k7p4lbcvbffljceokxjdagfvsu

On Quantum Statistical Inference, I [article]

O.E. Barndorff-Nielsen, R.D. Gill, P.E. Jupp
2003 arXiv   pre-print
for supporting a working visit to the University of Pavia.  ...  Acknowledgements We gratefully acknowledge Mathematische Forschungsinstitut Oberwolfach for support through the Research in Pairs programme, and the European Science Foundation's programme on quantum information  ...  This transform is well known from computer-aided tomography, when for instance the data from which an X-ray image must be computed is the collection of one-dimensional images obtained by projecting onto  ... 
arXiv:quant-ph/0307189v2 fatcat:wlqdc5dc2vb4beczeunt4ndqbi

On quantum statistical inference

Ole E. Barndorff-Nielsen, Richard D. Gill, Peter E. Jupp
2003 Journal of The Royal Statistical Society Series B-statistical Methodology  
for supporting a working visit to the University of Pavia.  ...  Acknowledgements We gratefully acknowledge Mathematische Forschungsinstitut Oberwolfach for support through the Research in Pairs programme, and the European Science Foundation's programme on quantum information  ...  This transform is well known from computeraided tomography, when for instance the data from which an X-ray image must be computed is the collection of one-dimensional images obtained by projecting onto  ... 
doi:10.1111/1467-9868.00415 fatcat:jujfsumyknapvksvqkrkjaw3h4

Superposition of gravity waves with different propagation characteristics observed by airborne and space-borne infrared sounders

Isabell Krisch, Manfred Ern, Lars Hoffmann, Peter Preusse, Cornelia Strube, Jörn Ungermann, Wolfgang Woiwode, Martin Riese
2020 Atmospheric Chemistry and Physics  
A complex gravity wave structure consisting of a superposition of multiple wave packets was observed above southern Scandinavia on 28 January 2016 with the Gimballed Limb Observer for Radiance Imaging  ...  The comparison with ERA5 also shows that ray tracing provides reasonable results even for such complex cases with multiple overlapping wave packets.  ...  To identify the best method for the GLORIA measurements, a 2-D fast Fourier transform (FFT) filter, a running mean filter, a Gaussian filter, an SG filter, and a Butterworth filter (BW filter; Butterworth  ... 
doi:10.5194/acp-20-11469-2020 fatcat:rvyshyfhr5gdxalxne4wuf5wsy

Adaptive Quantum Optics with Spatially Entangled Photon Pairs

Hugo Defienne, Matthew Reichert, Jason W. Fleischer
2018 Physical Review Letters  
Light shaping facilitates the preparation and detection of optical states and underlies many applications in communications, computing, and imaging.  ...  We show that patterns of phase modulation for classical laser light can also shape higher orders of spatial coherence, allowing deterministic tailoring of high-dimensional quantum entanglement.  ...  (b) A noise reduction process can be used on the conditional images by using a low-pass frequency filter.  ... 
doi:10.1103/physrevlett.121.233601 fatcat:lhveug44efc53hquxa5enkzsi4

A combined local and global motion estimation and compensation method for cardiac CT

Qiulin Tang, Beshan Chiang, Akinola Akinyemi, Alexander Zamyatin, Bibo Shi, Satoru Nakanishi, Bruce R. Whiting, Christoph Hoeschen
2014 Medical Imaging 2014: Physics of Medical Imaging  
The HSIC-based metrics computes the distance between two distributions in a reproducing kernel Hilbert space (RKHS), meaning that by using a kernel, the input vectors are nonlinearly mapped into a different  ...  In this study, we proposed a family of generic, convex and edge-preserving regularization terms based on the nonlocal means(NLM) filter, and evaluated one of them as an example where the potential function  ...  Studies have shown that there is variation in the agreement between operators viewing the same tissue [1] suggesting that a complimentary technique for verification could improve the robustness of the  ... 
doi:10.1117/12.2043492 fatcat:fyzpc5m6jbh7fjohqpdmtzkhte

Quantum Adversarial Machine Learning [article]

Sirui Lu, Lu-Ming Duan, Dong-Ling Deng
2019 arXiv   pre-print
This is explicitly demonstrated with quantum adversarial learning in different scenarios, including classifying real-life images (e.g., handwritten digit images in the dataset MNIST), learning phases of  ...  quantum machine learning systems to adversarial perturbations, which not only reveals a novel perspective in bridging machine learning and quantum physics in theory but also provides valuable guidance for  ...  Another approach, called the quantum kernel [50, 51, 81] , utilizes the quantum Hilbert space as the feature space for data and compute the kernel function via quantum devices.  ... 
arXiv:2001.00030v1 fatcat:p67vurfb3jbdveehdaugibqqpm

Roadmap on transformation optics

Martin McCall, John B Pendry, Vincenzo Galdi, Yun Lai, S A R Horsley, Jensen Li, Jian Zhu, Rhiannon C Mitchell-Thomas, Oscar Quevedo-Teruel, Philippe Tassin, Vincent Ginis, Enrica Martini (+15 others)
2018 Journal of Optics  
By applying transformations to spacetime, rather than just space, it was shown that events rather than objects could be hidden from view; transformation optics had provided a means of effectively redacting  ...  Thus, conventional and nonlocal TO can be viewed as two extremes in the spatial vs. spectral resolution tradeoff.  ...  Example kernels associated with local and nonlocal constitutive relations are given in figures 19 and 20.  ... 
doi:10.1088/2040-8986/aab976 fatcat:sqd2o4trx5epphfogxfyfoemzi

Sparse Modeling for Image and Vision Processing [article]

Julien Mairal, Jean Ponce (Ecole Normale Supérieure)
2014 arXiv   pre-print
The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing.  ...  The authors would like to thank Ori Bryt and Michael Elad for providing the output of their face compression algorithm (see Figure 3 .9).  ...  Julien Mairal would also like to thank Zaid Harchaoui, Florent Perronnin and Adrien Gaidon for useful discussions leading to improvements of this monograph.  ... 
arXiv:1411.3230v2 fatcat:qeqhd2rbvncqtl6ktuj6mda6ia
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