The Adaptive Sampling Revisited

The problem of estimating the number $n$ of distinct keys of a large collection of $N$ data is well known in computer science. A classical algorithm is the adaptive sampling (AS). $n$ can be estimated by $R.2^D$, where $R$ is the final bucket (cache) size and $D$ is the final depth at the end of the process. Several new interesting questions can be asked about AS (some of them were suggested by P.Flajolet and popularized by J.Lumbroso). The distribution of $W=\log (R2^D/n)$ is known, we rederive this distribution in a simpler way. We provide new results on the moments of $D$ and $W$. We also analyze the final cache size $R$ distribution. We consider colored keys: assume that among the $n$ distinct keys, $n_C$ do have color $C$. We show how to estimate $p=\frac{n_C}{n}$. We also study colored keys with some multiplicity given by some distribution function. We want to estimate mean an variance of this distribution. Finally, we consider the case where neither colors nor multiplicities are known. There we want to estimate the related parameters. An appendix is devoted to the case where the hashing function provides bits with probability different from $1/2$

Cygnus A super-resolved via convex optimisation from VLA data

We leverage the Sparsity Averaging Reweighted Analysis (SARA) approach for interferometric imaging, that is based on convex optimisation, for the super-resolution of Cyg A from observations at the frequencies 8.422GHz and 6.678GHz with the Karl G. Jansky Very Large Array (VLA). The associated average sparsity and positivity priors enable image reconstruction beyond instrumental resolution. An adaptive Preconditioned Primal-Dual algorithmic structure is developed for imaging in the presence of unknown noise levels and calibration errors. We demonstrate the superior performance of the algorithm with respect to the conventional CLEAN-based methods, reflected in super-resolved images with high fidelity. The high resolution features of the recovered images are validated by referring to maps of Cyg A at higher frequencies, more precisely 17.324GHz and 14.252GHz. We also confirm the recent discovery of a radio transient in Cyg A, revealed in the recovered images of the investigated data sets. Our matlab code is available online on GitHub.Comment: 14 pages, 7 figures (3/7 animated figures), accepted for publication in MNRA

Adaptive Filters Revisited - RFI Mitigation in pulsar observations

Pulsar detection and timing experiments are applications where adaptive filters seem eminently suitable tools for radio-frequency-interference (RFI) mitigation. We describe a novel variant which works well in field trials of pulsar observations centred on an observing frequency of 675 MHz, a bandwidth of 64 MHz and with 2-bit sampling. Adaptive filters have generally received bad press for RFI mitigation in radio astronomical observations with their most serious drawback being a spectral echo of the RFI embedded in the filtered signals. Pulsar observations are intrinsically less sensitive to this as they operate in the (pulsar period) time domain. The field trials have allowed us to identify those issues which limit the effectiveness of the adaptive filter. We conclude that adaptive filters can significantly improve pulsar observations in the presence of RFI.Comment: Accepted for publication in Radio Scienc

Robust Covariance Adaptation in Adaptive Importance Sampling

Importance sampling (IS) is a Monte Carlo methodology that allows for approximation of a target distribution using weighted samples generated from another proposal distribution. Adaptive importance sampling (AIS) implements an iterative version of IS which adapts the parameters of the proposal distribution in order to improve estimation of the target. While the adaptation of the location (mean) of the proposals has been largely studied, an important challenge of AIS relates to the difficulty of adapting the scale parameter (covariance matrix). In the case of weight degeneracy, adapting the covariance matrix using the empirical covariance results in a singular matrix, which leads to poor performance in subsequent iterations of the algorithm. In this paper, we propose a novel scheme which exploits recent advances in the IS literature to prevent the so-called weight degeneracy. The method efficiently adapts the covariance matrix of a population of proposal distributions and achieves a significant performance improvement in high-dimensional scenarios. We validate the new method through computer simulations

eXtended Variational Quasicontinuum Methodology for Lattice Networks with Damage and Crack Propagation

Lattice networks with dissipative interactions are often employed to analyze materials with discrete micro- or meso-structures, or for a description of heterogeneous materials which can be modelled discretely. They are, however, computationally prohibitive for engineering-scale applications. The (variational) QuasiContinuum (QC) method is a concurrent multiscale approach that reduces their computational cost by fully resolving the (dissipative) lattice network in small regions of interest while coarsening elsewhere. When applied to damageable lattices, moving crack tips can be captured by adaptive mesh refinement schemes, whereas fully-resolved trails in crack wakes can be removed by mesh coarsening. In order to address crack propagation efficiently and accurately, we develop in this contribution the necessary generalizations of the variational QC methodology. First, a suitable definition of crack paths in discrete systems is introduced, which allows for their geometrical representation in terms of the signed distance function. Second, special function enrichments based on the partition of unity concept are adopted, in order to capture kinematics in the wakes of crack tips. Third, a summation rule that reflects the adopted enrichment functions with sufficient degree of accuracy is developed. Finally, as our standpoint is variational, we discuss implications of the mesh refinement and coarsening from an energy-consistency point of view. All theoretical considerations are demonstrated using two numerical examples for which the resulting reaction forces, energy evolutions, and crack paths are compared to those of the direct numerical simulations.Comment: 36 pages, 23 figures, 1 table, 2 algorithms; small changes after review, paper title change

Coarse-to-Fine: Learning Compact Discriminative Representation for Single-Stage Image Retrieval

Image retrieval targets to find images from a database that are visually similar to the query image. Two-stage methods following retrieve-and-rerank paradigm have achieved excellent performance, but their separate local and global modules are inefficient to real-world applications. To better trade-off retrieval efficiency and accuracy, some approaches fuse global and local feature into a joint representation to perform single-stage image retrieval. However, they are still challenging due to various situations to tackle, $e.g.$, background, occlusion and viewpoint. In this work, we design a Coarse-to-Fine framework to learn Compact Discriminative representation (CFCD) for end-to-end single-stage image retrieval-requiring only image-level labels. Specifically, we first design a novel adaptive softmax-based loss which dynamically tunes its scale and margin within each mini-batch and increases them progressively to strengthen supervision during training and intra-class compactness. Furthermore, we propose a mechanism which attentively selects prominent local descriptors and infuse fine-grained semantic relations into the global representation by a hard negative sampling strategy to optimize inter-class distinctiveness at a global scale. Extensive experimental results have demonstrated the effectiveness of our method, which achieves state-of-the-art single-stage image retrieval performance on benchmarks such as Revisited Oxford and Revisited Paris. Code is available at https://github.com/bassyess/CFCD.Comment: Accepted to ICCV 202

The Core-Collapse Supernova Rate in Arp299 Revisited

We present a study of the CCSN rate in nuclei A and B1 of the luminous infrared galaxy Arp299, based on 11 years of Very Large Array monitoring of their radio emission at 8.4 GHz. Significant variations in the nuclear radio flux density can be used to identify the CCSN activity in the absence of high-resolution very long baseline interferometry observations. In the case of the B1-nucleus, the small variations in its measured diffuse radio emission are below the fluxes expected from radio supernovae, thus making it well-suited to detect RSNe through flux density variability. In fact, we find strong evidence for at least three RSNe this way, which results in a lower limit for the CCSN rate of 0.28 +/- 0.16 per year. In the A-nucleus, we did not detect any significant variability and found a SN detection threshold luminosity which allows only the detection of the most luminous RSNe known. Our method is basically blind to normal CCSN explosions occurring within the A-nucleus, which result in too small variations in the nuclear flux density, remaining diluted by the strong diffuse emission of the nucleus itself. Additionally, we have attempted to find near-infrared counterparts for the earlier reported RSNe in the Arp299 nucleus A, by comparing NIR adaptive optics images from the Gemini-N telescope with contemporaneous observations from the European VLBI Network. However, we were not able to detect NIR counterparts for the reported radio SNe within the innermost regions of nucleus A. While our NIR observations were sensitive to typical CCSNe at 300 mas from the centre of the nucleus A, suffering from extinction up to A_v~15 mag, they were not sensitive to such highly obscured SNe within the innermost nuclear regions where most of the EVN sources were detected. (abridged)Comment: 12 pages, 4 figures and 7 tables. Accepted for publication in MNRA