Neural Nearest Neighbors Networks

Non-local methods exploiting the self-similarity of natural signals have been well studied, for example in image analysis and restoration. Existing approaches, however, rely on k-nearest neighbors (KNN) matching in a fixed feature space. The main hurdle in optimizing this feature space w.r.t. application performance is the non-differentiability of the KNN selection rule. To overcome this, we propose a continuous deterministic relaxation of KNN selection that maintains differentiability w.r.t. pairwise distances, but retains the original KNN as the limit of a temperature parameter approaching zero. To exploit our relaxation, we propose the neural nearest neighbors block (N3 block), a novel non-local processing layer that leverages the principle of self-similarity and can be used as building block in modern neural network architectures. We show its effectiveness for the set reasoning task of correspondence classification as well as for image restoration, including image denoising and single image super-resolution, where we outperform strong convolutional neural network (CNN) baselines and recent non-local models that rely on KNN selection in hand-chosen features spaces.Comment: to appear at NIPS*2018, code available at https://github.com/visinf/n3net

Discovery Of Cold, Pristine Gas Possibly Accreting Onto An Overdensity Of Star-Forming Galaxies At Redshift z ~ 1.6

We report the discovery of large amounts of cold (T ~ 10^4 K), chemically young gas in an overdensity of galaxies at redshift z ~ 1.6 in the Great Observatories Origins Deep Survey southern field (GOODS-S). The gas is identified thanks to the ultra-strong Mg II absorption features it imprints in the rest-frame UV spectra of galaxies in the background of the overdensity. There is no evidence that the optically-thick gas is part of any massive galaxy (i.e. M_star > 4x10^9 M_sun), but rather is associated with the overdensity; less massive and fainter galaxies (25.5 < z_850 < 27.5 mag) have too large an impact parameter to be causing ultra-strong absorption systems, based on our knowledge of such systems. The lack of corresponding Fe II absorption features, not detected even in co-added spectra, suggests that the gas is chemically more pristine than the ISM and outflows of star-forming galaxies at similar redshift, including those in the overdensity itself, and comparable to the most metal-poor stars in the Milky Way halo. A crude estimate of the projected covering factor of the high-column density gas (N_H >~ 10^20 cm-2) based on the observed fraction of galaxies with ultra-strong absorbers is C_F ~ 0.04. A broad, continuum absorption profile extending to the red of the interstellar Mg II absorption line by <~ 2000 km/s is possibly detected in two independent co-added spectra of galaxies of the overdensity, consistent with a large-scale infall motion of the gas onto the overdensity and its galaxies. Overall, these findings provides the first tentative evidence of accretion of cold, chemically young gas onto galaxies at high redshift, possibly feeding their star formation activity. The fact that the galaxies are members of a large structure, as opposed to field galaxies, might play a significant role in our ability to detect the accreting gas.Comment: 57 pages, 17 figures, 1 table; accepted for publication by ApJ (Aug 9, 2011); minor modifications to match the accepted versio

A symmetry breaking mechanism for selecting the speed of relativistic solitons

We propose a mechanism for fixing the velocity of relativistic soliton based on the breaking of the Lorentz symmetry of the sine-Gordon (SG) model. The proposal is first elaborated for a molecular chain model, as the simple pendulum limit of a double pendulums chain. It is then generalized to a full class of two-dimensional field theories of the sine-Gordon type. From a phenomenological point of view, the mechanism allows one to select the speed of a SG soliton just by tuning elastic couplings constants and kinematical parameters. From a fundamental, field-theoretical point of view we show that the characterizing features of relativistic SG solitons (existence of conserved topological charges and stability) may be still preserved even if the Lorentz symmetry is broken and a soliton of a given speed is selected.Comment: 23 pages, no figure

The Self-Financing Equation in High Frequency Markets

High Frequency Trading (HFT) represents an ever growing proportion of all financial transactions as most markets have now switched to electronic order book systems. The main goal of the paper is to propose continuous time equations which generalize the self-financing relationships of frictionless markets to electronic markets with limit order books. We use NASDAQ ITCH data to identify significant empirical features such as price impact and recovery, rough paths of inventories and vanishing bid-ask spreads. Starting from these features, we identify microscopic identities holding on the trade clock, and through a diffusion limit argument, derive continuous time equations which provide a macroscopic description of properties of the order book. These equations naturally differentiate between trading via limit and market orders. We give several applications (including hedging European options with limit orders, market maker optimal spread choice, and toxicity indexes) to illustrate their impact and how they can be used to the benefit of Low Frequency Traders (LFTs)

Supersparse Linear Integer Models for Optimized Medical Scoring Systems

Scoring systems are linear classification models that only require users to add, subtract and multiply a few small numbers in order to make a prediction. These models are in widespread use by the medical community, but are difficult to learn from data because they need to be accurate and sparse, have coprime integer coefficients, and satisfy multiple operational constraints. We present a new method for creating data-driven scoring systems called a Supersparse Linear Integer Model (SLIM). SLIM scoring systems are built by solving an integer program that directly encodes measures of accuracy (the 0-1 loss) and sparsity (the $\ell_0$-seminorm) while restricting coefficients to coprime integers. SLIM can seamlessly incorporate a wide range of operational constraints related to accuracy and sparsity, and can produce highly tailored models without parameter tuning. We provide bounds on the testing and training accuracy of SLIM scoring systems, and present a new data reduction technique that can improve scalability by eliminating a portion of the training data beforehand. Our paper includes results from a collaboration with the Massachusetts General Hospital Sleep Laboratory, where SLIM was used to create a highly tailored scoring system for sleep apnea screeningComment: This version reflects our findings on SLIM as of January 2016 (arXiv:1306.5860 and arXiv:1405.4047 are out-of-date). The final published version of this articled is available at http://www.springerlink.co

Selection Rules for Black-Hole Quantum Transitions

We suggest that quantum transitions of black holes comply with selection rules, analogous to those of atomic spectroscopy. In order to identify such rules, we apply Bohr's correspondence principle to the quasinormal ringing frequencies of black holes. In this context, classical ringing frequencies with an asymptotically vanishing real part \omega_R correspond to virtual quanta, and may thus be interpreted as forbidden quantum transitions. With this motivation, we calculate the quasinormal spectrum of neutrino fields in spherically symmetric black-hole spacetimes. It is shown that \omega_R->0 for these resonances, suggesting that the corresponding fermionic transitions are quantum mechanically forbidden.Comment: 4 pages, 2 figure