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Showing 1–26 of 26 results for author: Liang, M

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  1. arXiv:2608.13984  [pdf

    physics.optics

    Multi-quantum-channel mediated tunable single-photon skyrmions from metasurfaces

    Authors: Yan Wang, Zhenyu Guo, Minggui Liang, Shuangchun Wen, Yijie Shen, Hailu Luo

    Abstract: Quantum optical skyrmions, as topologically robust quantum information carriers, hold transformative potential for resilient high-dimensional quantum information networks. However, their practical exploitation was still restricted to a single quantum channel, which precludes the multiplexing essential for practical high-capacity quantum networks. Here, we utilize a metasurface to achieve multi-cha… ▽ More

    Submitted 14 August, 2026; originally announced August 2026.

  2. arXiv:2603.12470  [pdf, ps, other

    physics.space-ph cs.AI

    CLARE: Classification-based Regression for Electron Temperature Prediction

    Authors: Michael Liang, Blake DeHaas, Naomi Maruyama, Xiangning Chu, Takumi Abe, Koh-Ichiro Oyama

    Abstract: Electron temperature (Te) is an important parameter governing space weather in the upper atmosphere, but has historically been underexplored in the space weather machine learning literature. We present CLARE, a machine learning model for predicting electron temperature in the Earth's plasmasphere trained on AKEBONO (EXOS-D) satellite measurements as well as solar and geomagnetic indices. CLARE use… ▽ More

    Submitted 12 March, 2026; originally announced March 2026.

    Comments: 19 pages, 8 figures. Submitted to JGR: Machine Learning and Computation. Research conducted at CU Boulder LASP with support from NASA and JAXA

  3. arXiv:2603.09650  [pdf

    physics.optics

    Toroidal helical pulses

    Authors: Shuai Shi, Hongcheng Zhou, Junjie Shao, Pan Tang, Bing-Zhong Wang, Mu-Sheng Liang, Yanhe Lyu, Boris A. Malomed, Yijie Shen, Ren Wang

    Abstract: Toroidal topologies and helicity are pervasive in nature and hold basic importance in scientific research. In particular, the interplay between these features gives rise to fascinating toroidal helical electromagnetic excitations. Here, we present a theoretical framework and experimental realization to introduce a family of toroidal helical pulses, exploring the intersection of the helicity and pr… ▽ More

    Submitted 14 May, 2026; v1 submitted 10 March, 2026; originally announced March 2026.

    Comments: To be published in Communications Physics

  4. arXiv:2510.24386  [pdf, ps, other

    physics.optics

    Fluorescence intensity correlations enable 3D imaging without sample rotations

    Authors: Robert G. Radloff, Felix F. Zimmermann, Siqi Li, Stephan Kuschel, Anatoli Ulmer, Yanwen Sun, Takahiro Sato, Peihao Sun, Johann Haber, Diling Zhu, Miklós Tegze, Gyula Faigel, Matthew R. Ware, Jordan T. O'Neal, Jumpei Yamada, Taito Osaka, Robert Zierold, Carina Hedrich, Dimitrios Kazazis, Yasin Ekinci, Makina Yabashi, Ichiro Inoue, Andrew Aquila, Meng Liang, Agostino Marinelli , et al. (1 additional authors not shown)

    Abstract: Lensless X-ray imaging provides element-specific nanoscale insights into thick samples beyond the reach of conventional light and electron microscopy. Coherent diffraction imaging (CDI) methods, such as ptychographic tomography, can recover three-dimensional (3D) nanoscale structures but require extensive sample rotation, adding complexity to experiments. X-ray elastic-scattering patterns from a s… ▽ More

    Submitted 29 October, 2025; v1 submitted 28 October, 2025; originally announced October 2025.

  5. arXiv:2509.26357  [pdf, ps, other

    physics.plasm-ph

    Validation of ERMES 20.0 finite element code for MAST Upgrade O-X mode conversion

    Authors: Ruben Otin, Ying Hao Matthew Liang, Thomas Wilson, Simon Freethy, Valerian Hall-Chen

    Abstract: This study presents the validation of the frequency-domain finite element code ERMES 20.0, benchmarked against Finite Difference Time Domain (FDTD) solvers. The simulations focus on Ordinary-Extraordinary (O-X) mode conversion in the Electron Bernstein Wave (EBW) regime of the MAST Upgrade experiment. Validation is performed in terms of mode conversion efficiency and wave propagation characteristi… ▽ More

    Submitted 30 September, 2025; originally announced September 2025.

  6. A Doppler backscattering diagnostic for the EXL-50U spherical tokamak: plasma considerations and preliminary quasioptical design

    Authors: Ying Hao Matthew Liang, Valerian Hongjie Hall-Chen, Terry L. Rhodes, Yumin Wang, Yihang Zhao

    Abstract: The EXL-50U spherical tokamak was built by Energy iNNovation to develop technologies for proton-boron fusion in spherical tokamaks (Liu et al., Phys. Plasmas 2024). We present a conceptual design of the Doppler backscattering (DBS) diagnostic for the EXL-50U spherical tokamak. DBS is a diagnostic capable of measuring plasma turbulence, which is especially important for transport in tokamaks. Start… ▽ More

    Submitted 19 April, 2026; v1 submitted 22 September, 2025; originally announced September 2025.

    Journal ref: Fusion Engineering and Design, Volume 228, July 2026, 115770

  7. arXiv:2508.18927  [pdf, ps, other

    physics.optics

    Robust Circularly Polarized Luminescence via Quasi-Bound States in the Continuum in Intrinsic Chiral Silicon Metasurfaces

    Authors: Xiao-ke Zhu, Yu-Chen Wei, Jose L. Pura, Matthijs Berghuis, Minpeng Liang, Beatriz Castillo López de Larrinzar, Shunsuke Murai, Antonio García-Martín, José A. Sánchez-Gil, Sailing He, Jaime Gómez Rivas

    Abstract: We demonstrate a circularly polarized photoluminescence emission, with dissymmetry factors $g_\mathrm{PL}$ over 0.1, from achiral organic dye molecules by leveraging quasi-bound states in the continuum (quasi-BICs) and surface lattice resonances (SLRs) in intrinsic silicon chiral metasurfaces. We find that the $g_\mathrm{PL}$ associated with the quasi-BIC mode remains robust against variations in… ▽ More

    Submitted 26 August, 2025; originally announced August 2025.

  8. arXiv:2508.00348  [pdf, ps, other

    gr-qc astro-ph.CO astro-ph.IM physics.space-ph

    Toward Efficient and Accurate EMRI Parameter Estimation: A Machine Learning-Enhanced MCMC Framework

    Authors: Bo Liang, Chang Liu, Hanlin Song, Zhenwei Lyu, Minghui Du, Peng Xu, Ziren Luo, Sensen He, Haohao Gu, Tianyu Zhao, Manjia Liang, Yuxiang Xu, Li-e Qiang, Mingming Sun, Wei-Liang Qian

    Abstract: The detection of gravitational waves from extreme-mass-ratio inspirals (EMRIs) in space-based antennas like Taiji and Laser Interferometer Space Antenna promises deep insights into strong-field gravity and black hole physics. However, the complex, highly degenerate, and nonconvex likelihood landscapes characteristic of EMRI parameter spaces pose severe challenges for conventional Markov chain Mont… ▽ More

    Submitted 18 August, 2026; v1 submitted 1 August, 2025; originally announced August 2025.

    Journal ref: Research 9, 1055 (2026)

  9. arXiv:2507.23145  [pdf, ps, other

    physics.optics

    Ray-tracing image simulations of transparent objects with complex shape and inhomogeneous refractive index

    Authors: Armin Kalita, Bryan Oller, Thomas Paula, Alexander Bußmann, Sebastian Marte, Gabriel Blaj, Raymond G. Sierra, Sandra Mous, Kirk A. Larsen, Xinxin Cheng, Matt J. Hayes, Kelsey Banta, Stella Lisova, Peter Nguyen, Serge A. H. Guillet, Divya Thanasekaran, Silke Nelson, Mengning Liang, Stefan Adami, Nikolaus A. Adams, Claudiu A. Stan

    Abstract: Optical images of transparent three-dimensional objects can be different from a replica of the object's cross section in the image plane due to refraction at the surface or in the body of the object. Simulations of the object's image are thus needed for the visualization and validation of physical models. We report ray-tracing image simulations that achieved high physical fidelity, reproducing opt… ▽ More

    Submitted 21 April, 2026; v1 submitted 30 July, 2025; originally announced July 2025.

    Comments: 9 figures, see journal version for high resolution figures and supplementary materials

    Journal ref: Phys. Rev. Fluids, 11, 044908 (2026)

  10. arXiv:2506.19172  [pdf, ps, other

    physics.chem-ph physics.atom-ph physics.optics

    Imaging valence electron rearrangement in a chemical reaction using hard X-ray scattering

    Authors: Ian Gabalski, Alice Green, Philipp Lenzen, Felix Allum, Matthew Bain, Surjendu Bhattacharyya, Mathew A. Britton, Elio G. Champenois, Xinxin Cheng, James P. Cryan, Taran Driver, Ruaridh Forbes, Douglas Garratt, Aaron M. Ghrist, Martin Graßl, Matthias F. Kling, Kirk A. Larsen, Mengning Liang, Ming-Fu Lin, Yusong Liu, Michael P. Minitti, Silke Nelson, Joseph S. Robinson, Philip H. Bucksbaum, Thomas J. A. Wolf , et al. (2 additional authors not shown)

    Abstract: We have observed the signatures of valence electron rearrangement in photoexcited ammonia using ultrafast hard X-ray scattering. Time-resolved X-ray scattering is a powerful tool for imaging structural dynamics in molecules because of the strong scattering from the core electrons localized near each nucleus. Such core-electron contributions generally dominate the differential scattering signal, ma… ▽ More

    Submitted 23 June, 2025; originally announced June 2025.

  11. arXiv:2412.19169  [pdf, other

    astro-ph.IM gr-qc physics.comp-ph

    Accelerating Stochastic Gravitational Wave Backgrounds Parameter Estimation in Pulsar Timing Arrays with Flow Matching

    Authors: Bo Liang, Chang Liu, Tianyu Zhao, Minghui Du, Manjia Liang, Ruijun Shi, Hong Guo, Yuxiang Xu, Li-e Qiang, Peng Xu, Wei-Liang Qian, Ziren Luo

    Abstract: Pulsar timing arrays (PTAs) are essential tools for detecting the stochastic gravitational wave background (SGWB), but their analysis faces significant computational challenges. Traditional methods like Markov-chain Monte Carlo (MCMC) struggle with high-dimensional parameter spaces where noise parameters often dominate, while existing deep learning approaches fail to model the Hellings-Downs (HD)… ▽ More

    Submitted 26 December, 2024; originally announced December 2024.

  12. arXiv:2409.07957  [pdf, other

    physics.comp-ph astro-ph.IM cs.AI

    Rapid Parameter Estimation for Extreme Mass Ratio Inspirals Using Machine Learning

    Authors: Bo Liang, Hong Guo, Tianyu Zhao, He wang, Herik Evangelinelis, Yuxiang Xu, Chang liu, Manjia Liang, Xiaotong Wei, Yong Yuan, Peng Xu, Minghui Du, Wei-Liang Qian, Ziren Luo

    Abstract: Extreme-mass-ratio inspiral (EMRI) signals pose significant challenges in gravitational wave (GW) astronomy owing to their low-frequency nature and highly complex waveforms, which occupy a high-dimensional parameter space with numerous variables. Given their extended inspiral timescales and low signal-to-noise ratios, EMRI signals warrant prolonged observation periods. Parameter estimation becomes… ▽ More

    Submitted 12 September, 2024; originally announced September 2024.

  13. arXiv:2408.10472  [pdf

    physics.optics physics.app-ph

    Hybrid electromagnetic toroidal vortices

    Authors: Ren Wang, Beier Ying, Shuai Shi, Junsong Wang, Bing-Zhong Wang, Musheng Liang, Yijie Shen

    Abstract: The ubiquitous occurrence of toroidal vortices or vortex rings in fluid-dynamic scenarios in nature has garnered significant attention of scientific frontier, whilst, the electromagnetic counterparts of which were only proposed recently with two distinct manifestations: vector toroidal pulses [Nat. Photon. 16, 523 (2022)] and scalar phase toroidal vortices [Nat. Photon. 16, 519 (2022)]. This dicho… ▽ More

    Submitted 19 August, 2024; originally announced August 2024.

  14. arXiv:2402.08891  [pdf

    physics.optics

    Towards a dynamically reconfigurable pixelated reflective display: Focused ion beam for phase-change metapixel structures

    Authors: Daniel T. Yimam, Minpeng Liang, Jianting Ye, Bart J. Kooi

    Abstract: The switching and optical properties of phase-change thin films are actively investigated for future smart optical devices. The possibility of having more than one stable state, the large optical contrast between phases, and the fast and reversible switching are some attractive properties driving the research interest. Optical devices based on phase change alloys are considered the frontier conten… ▽ More

    Submitted 13 February, 2024; originally announced February 2024.

  15. arXiv:2310.18529  [pdf, other

    physics.optics eess.IV

    FPM-INR: Fourier ptychographic microscopy image stack reconstruction using implicit neural representations

    Authors: Haowen Zhou, Brandon Y. Feng, Haiyun Guo, Siyu Lin, Mingshu Liang, Christopher A. Metzler, Changhuei Yang

    Abstract: Image stacks provide invaluable 3D information in various biological and pathological imaging applications. Fourier ptychographic microscopy (FPM) enables reconstructing high-resolution, wide field-of-view image stacks without z-stack scanning, thus significantly accelerating image acquisition. However, existing FPM methods take tens of minutes to reconstruct and gigabytes of memory to store a hig… ▽ More

    Submitted 31 October, 2023; v1 submitted 27 October, 2023; originally announced October 2023.

    Comments: Project Page: https://hwzhou2020.github.io/FPM-INR-Web/

  16. arXiv:2301.12578  [pdf

    physics.optics physics.app-ph

    Structural colors and enhanced resolution at the nanoscale: Local structuring of phase-change materials using focused ion beam

    Authors: Daniel T. Yimam, Minpeng Liang, Jianting Ye, Bart J. Kooi

    Abstract: In the past few years, phase-change materials have become increasingly important in nano-photonics and optoelectronics. The advantages of sizeable optical contrast between phases and the additional degree of freedom from phase switching have been the driving force. From multilevel reflectance to dynamic nanoprinting and structural colors, phase-change materials have achieved outstanding results wi… ▽ More

    Submitted 29 January, 2023; originally announced January 2023.

    Comments: nanophotonics, focused ion beam, nanoprinting, pulsed laser deposition, phase change materials

  17. arXiv:2209.04260  [pdf, other

    astro-ph.HE hep-ex hep-ph physics.space-ph

    Search for relativistic fractionally charged particles in space

    Authors: DAMPE Collaboration, F. Alemanno, C. Altomare, Q. An, P. Azzarello, F. C. T. Barbato, P. Bernardini, X. J. Bi, M. S. Cai, E. Casilli, E. Catanzani, J. Chang, D. Y. Chen, J. L. Chen, Z. F. Chen, M. Y. Cui, T. S. Cui, Y. X. Cui, H. T. Dai, A. De-Benedittis, I. De Mitri, F. de Palma, M. Deliyergiyev, A. Di Giovanni, M. Di Santo , et al. (126 additional authors not shown)

    Abstract: More than a century after the performance of the oil drop experiment, the possible existence of fractionally charged particles FCP still remains unsettled. The search for FCPs is crucial for some extensions of the Standard Model in particle physics. Most of the previously conducted searches for FCPs in cosmic rays were based on experiments underground or at high altitudes. However, there have been… ▽ More

    Submitted 9 September, 2022; originally announced September 2022.

    Comments: 19 pages, 6 figures, accepted by PRD

    Report number: 106, 063026

    Journal ref: Physical Review D 106.6 (2022): 063026

  18. arXiv:2204.13241  [pdf, other

    math.NA physics.atom-ph

    Computational Approaches to Model X-ray Photon Correlation Spectroscopy from Molecular Dynamics

    Authors: Shaswat Mohanty, Christopher B. Cooper, Hui Wang, Mengning Liang, Wei Cai

    Abstract: X-ray photon correlation spectroscopy (XPCS) allows for the resolution of dynamic processes within a material across a wide range of length and time scales. X-ray speckle visibility spectroscopy (XSVS) is a related method that uses a single diffraction pattern to probe ultrafast dynamics. Interpretation of the XPCS and XSVS data in terms of underlying physical processes is necessary to establish t… ▽ More

    Submitted 5 January, 2023; v1 submitted 27 April, 2022; originally announced April 2022.

    Comments: 31 pages, 11 figures, submitted to Modelling and Simulations in Materials Science and Engineering

    Journal ref: Modelling and Simulation in Materials Science and Engineering 30 (2022) 075004

  19. arXiv:2109.09189  [pdf

    cs.LG physics.data-an

    Probabilistic Bearing Fault Diagnosis Using Gaussian Process with Tailored Feature Extraction

    Authors: Mingxuan Liang, Kai Zhou

    Abstract: Rolling bearings are subject to various faults due to its long-time operation under harsh environment, which will lead to unexpected breakdown of machinery system and cause severe accidents. Deep learning methods recently have gained growing interests and extensively applied in the data-driven bearing fault diagnosis. However, current deep learning methods perform the bearing fault diagnosis in th… ▽ More

    Submitted 19 September, 2021; originally announced September 2021.

  20. arXiv:2109.08885  [pdf, other

    cond-mat.quant-gas physics.atom-ph quant-ph

    Realization of Qi-Wu-Zhang model in spin-orbit-coupled ultracold fermions

    Authors: Ming-Cheng Liang, Yu-Dong Wei, Long Zhang, Xu-Jie Wang, Han Zhang, Wen-Wei Wang, Wei Qi, Xiong-Jun Liu, Xibo Zhang

    Abstract: Based on the optical Raman lattice technique, we experimentally realize the Qi-Wu-Zhang model for quantum anomalous Hall phase in ultracold fermions with two-dimensional (2D) spin-orbit (SO) coupling. We develop a novel protocol of pump-probe quench measurement to probe, with minimal heating, the resonant spin flipping on particular quasi-momentum subspace called band-inversion surfaces. With this… ▽ More

    Submitted 20 July, 2022; v1 submitted 18 September, 2021; originally announced September 2021.

    Comments: 7 pages, 4 figures in the main text, and 6 pages, 3 figures in the supplemental material

    Journal ref: Physical Review Research 5, L012006 (2023)

  21. arXiv:2005.05288  [pdf, other

    physics.optics eess.IV eess.SP

    Non-iterative complex wave-field reconstruction based on Kramers-Kronig relations

    Authors: Cheng Shen, An Pan, Mingshu Liang, Changhuei Yang

    Abstract: A new computational imaging method to reconstruct the complex wave-field is reported. Due to the existence of zero frequency component, the measured signal by amplitude modulation of pupil has a spectrum similar to the one of off-axis hologram. The mathematical analogy between them is established in this paper. Based on this observation and analyticity of band-limited signal under any diffraction-… ▽ More

    Submitted 11 May, 2020; originally announced May 2020.

  22. arXiv:1910.13494  [pdf, other

    physics.atm-clus physics.chem-ph

    X-ray diffractive imaging of controlled gas-phase molecules: Toward imaging of dynamics in the molecular frame

    Authors: Thomas Kierspel, Andrew Morgan, Joss Wiese, Terry Mullins, Andy Aquila, Anton Barty, Richard Bean, Rebecca Boll, Sébastien Boutet, Philip Bucksbaum, Henry N. Chapman, Lauge Christensen, Alan Fry, Mark Hunter, Jason E. Koglin, Mengning Liang, Valerio Mariani, Adi Natan, Joseph Robinson, Daniel Rolles, Artem Rudenko, Kirsten Schnorr, Henrik Stapelfeldt, Stephan Stern, Jan Thøgersen , et al. (3 additional authors not shown)

    Abstract: We report experimental results on the diffractive imaging of three-dimensionally aligned 2,5-diiodothiophene molecules. The molecules were aligned by chirped near-infrared laser pulses, and their structure was probed at a photon energy of 9.5 keV ($λ\approx130 \text{pm}$) provided by the Linac Coherent Light Source. Diffracted photons were recorded on the CSPAD detector and a two-dimensional diffr… ▽ More

    Submitted 7 February, 2020; v1 submitted 29 October, 2019; originally announced October 2019.

  23. arXiv:1706.08453  [pdf, other

    astro-ph.IM astro-ph.HE hep-ex physics.ins-det

    The DArk Matter Particle Explorer mission

    Authors: J. Chang, G. Ambrosi, Q. An, R. Asfandiyarov, P. Azzarello, P. Bernardini, B. Bertucci, M. S. Cai, M. Caragiulo, D. Y. Chen, H. F. Chen, J. L. Chen, W. Chen, M. Y. Cui, T. S. Cui, A. D'Amone, A. De Benedittis, I. De Mitri, M. Di Santo, J. N. Dong, T. K. Dong, Y. F. Dong, Z. X. Dong, G. Donvito, D. Droz , et al. (139 additional authors not shown)

    Abstract: The DArk Matter Particle Explorer (DAMPE), one of the four scientific space science missions within the framework of the Strategic Pioneer Program on Space Science of the Chinese Academy of Sciences, is a general purpose high energy cosmic-ray and gamma-ray observatory, which was successfully launched on December 17th, 2015 from the Jiuquan Satellite Launch Center. The DAMPE scientific objectives… ▽ More

    Submitted 14 September, 2017; v1 submitted 26 June, 2017; originally announced June 2017.

    Comments: 45 pages, including 29 figures and 6 tables. Published in Astropart. Phys

    Journal ref: Astropart. Phys. 95 (2017) 6-24

  24. Strongly aligned gas-phase molecules at Free-Electron Lasers

    Authors: Thomas Kierspel, Joss Wiese, Terry Mullins, Joseph Robinson, Andy Aquila, Anton Barty, Richard Bean, Rebecca Boll, Sébastien Boutet, Philip Bucksbaum, Henry N. Chapman, Lauge Christensen, Alan Fry, Mark Hunter, Jason E. Koglin, Mengning Liang, Valerio Mariani, Andrew Morgan, Adi Natan, Vladimir Petrovic, Daniel Rolles, Artem Rudenko, Kirsten Schnorr, Henrik Stapelfeldt, Stephan Stern , et al. (5 additional authors not shown)

    Abstract: We demonstrate a novel experimental implementation to strongly align molecules at full repetition rates of free-electron lasers. We utilized the available in-house laser system at the coherent x-ray imaging beamline at the Linac Coherent Light Source. Chirped laser pulses, i. e., the direct output from the regenerative amplifier of the Ti:Sa chirped pulse amplification laser system, were used to s… ▽ More

    Submitted 17 October, 2015; v1 submitted 11 June, 2015; originally announced June 2015.

    Comments: 10 pages, 5 figures

    Journal ref: J. Phys. B: At. Mol. Opt. Phys. 48 (2015) 204002

  25. arXiv:1402.1997   

    physics.optics

    Experimental study of a terahertz time-domain spectrometer based on photoconductive antenna

    Authors: Jitao Zhang, Wei-Ren Ng, Mingguang Tuo, Min Liang, M. E. Gehm, Hao Xin

    Abstract: We construct a terahertz time-domain spectrometer (THz-TDS) system based on photoconductive antenna (PCA). A 800 nm Ti sapphire femtosecond laser with 80 MHz repetition rate provides the pump and probe laser pulse, which has a 45 fs pulse width (as short as 15 fs is available) and as much as 400 mW power. Two commercial PCAs with 34 um and 6 um gap size are used as the emitter and receiver, respec… ▽ More

    Submitted 7 August, 2014; v1 submitted 9 February, 2014; originally announced February 2014.

    Comments: 13 pages,8 figures. This paper has been withdrawn by the author due to an supplement of a new result

  26. arXiv:1003.0846  [pdf, ps, other

    physics.optics physics.data-an

    Cryptotomography: reconstructing 3D Fourier intensities from randomly oriented single-shot diffraction patterns

    Authors: N. D. Loh, M. Bogan, V. Elser, A. Barty, S. Boutet, S. Bajt, J. Hajdu, T. Ekeberg, F. R. N. C. Maia, J. Schulz, M. M. Seibert, B. Iwan, N. Timneanu, S. Marchesini, I. Schlichting, R. L. Shoeman, L. Lomb, M. Frank, M. Liang, H. N. Chapman

    Abstract: We reconstructed the 3D Fourier intensity distribution of mono-disperse prolate nano-particles using single-shot 2D coherent diffraction patterns collected at DESY's FLASH facility when a bright, coherent, ultrafast X-ray pulse intercepted individual particles of random, unmeasured orientations. This first experimental demonstration of cryptotomography extended the Expansion-Maximization-Compres… ▽ More

    Submitted 5 April, 2010; v1 submitted 3 March, 2010; originally announced March 2010.

    Comments: 4 pages, 4 figures