Learning SO(3) Equivariant Representations with Spherical CNNs

We address the problem of 3D rotation equivariance in convolutional neural networks. 3D rotations have been a challenging nuisance in 3D classification tasks requiring higher capacity and extended data augmentation in order to tackle it. We model 3D data with multi-valued spherical functions and we propose a novel spherical convolutional network that implements exact convolutions on the sphere by realizing them in the spherical harmonic domain. Resulting filters have local symmetry and are localized by enforcing smooth spectra. We apply a novel pooling on the spectral domain and our operations are independent of the underlying spherical resolution throughout the network. We show that networks with much lower capacity and without requiring data augmentation can exhibit performance comparable to the state of the art in standard retrieval and classification benchmarks.Comment: Camera-ready. Accepted to ECCV'18 as oral presentatio

Reconsidering Linear Transmit Signal Processing in 1-Bit Quantized Multi-User MISO Systems

In this contribution, we investigate a coarsely quantized Multi-User (MU)-Multiple Input Single Output (MISO) downlink communication system, where we assume 1-Bit Digital-to-Analog Converters (DACs) at the Base Station (BS) antennas. First, we analyze the achievable sum rate lower-bound using the Bussgang decomposition. In the presence of the non-linear quanization, our analysis indicates the potential merit of reconsidering traditional signal processing techniques in coarsely quantized systems, i.e., reconsidering transmit covariance matrices whose rank is equal to the rank of the channel. Furthermore, in the second part of this paper, we propose a linear precoder design which achieves the predicted increase in performance compared with a state of the art linear precoder design. Moreover, our linear signal processing algorithm allows for higher-order modulation schemes to be employed

NLTE and LTE Lick indices for red giants from [M/H] 0.0 to -6.0 at SDSS and IDS spectral resolution

We investigate the dependence of the complete system of 22 Lick indices on overall metallicity scaled from solar abundances, [M/H], from the solar value, 0.0, down to the extremely-metal-poor (XMP) value of -6.0, for late-type giant stars (MK luminosity class III, log(g)=2.0) of MK spectral class late-K to late-F (3750 < Teff < 6500 K) of the type that are detected as "fossils" of early galaxy formation in the Galactic halo and in extra-galactic structures. Our investigation is based on synthetic index values, I, derived from atmospheric models and synthetic spectra computed with PHOENIX in LTE and Non-LTE (NLTE), where the synthetic spectra have been convolved to the spectral resolution, R, of both IDS and SDSS (and LAMOST) spectroscopy. We identify nine indices, that we designate "Lick-XMP", that remain both detectable and significantly [M/H]-dependent down to [M/H] values of at least ~-5.0, and down to [M/H] ~ -6.0 in five cases, while also remaining well-behaved . For these nine, we study the dependence of I on NLTE effects, and on spectral resolution. For our LTE I values for spectra of SDSS resolution, we present the fitted polynomial coefficients, C_n, from multi-variate linear regression for I with terms up to third order in the independent variable pairs (Teff, [M/H]), and (V-K, [M/H]), and compare them to the fitted C_n values of Worthey et al. (1994) at IDS spectral resolution.Comment: Accepted for publication in the Astrophysical Journal. Tables 6 and 7 available electronically from the autho

Transmission of natural scene images through a multimode fibre

The optical transport of images through a multimode fibre remains an outstanding challenge with applications ranging from optical communications to neuro-imaging. State of the art approaches either involve measurement and control of the full complex field transmitted through the fibre or, more recently, training of artificial neural networks that however, are typically limited to image classes belong to the same class as the training data set. Here we implement a method that statistically reconstructs the inverse transformation matrix for the fibre. We demonstrate imaging at high frame rates, high resolutions and in full colour of natural scenes, thus demonstrating general-purpose imaging capability. Real-time imaging over long fibre lengths opens alternative routes to exploitation for example for secure communication systems, novel remote imaging devices, quantum state control processing and endoscopy

General relativistic null-cone evolutions with a high-order scheme

We present a high-order scheme for solving the full non-linear Einstein equations on characteristic null hypersurfaces using the framework established by Bondi and Sachs. This formalism allows asymptotically flat spaces to be represented on a finite, compactified grid, and is thus ideal for far-field studies of gravitational radiation. We have designed an algorithm based on 4th-order radial integration and finite differencing, and a spectral representation of angular components. The scheme can offer significantly more accuracy with relatively low computational cost compared to previous methods as a result of the higher-order discretization. Based on a newly implemented code, we show that the new numerical scheme remains stable and is convergent at the expected order of accuracy.Comment: 24 pages, 3 figure