Super-resolution community detection for layer-aggregated multilayer networks

Applied network science often involves preprocessing network data before applying a network-analysis method, and there is typically a theoretical disconnect between these steps. For example, it is common to aggregate time-varying network data into windows prior to analysis, and the tradeoffs of this preprocessing are not well understood. Focusing on the problem of detecting small communities in multilayer networks, we study the effects of layer aggregation by developing random-matrix theory for modularity matrices associated with layer-aggregated networks with $N$ nodes and $L$ layers, which are drawn from an ensemble of Erd\H{o}s-R\'enyi networks. We study phase transitions in which eigenvectors localize onto communities (allowing their detection) and which occur for a given community provided its size surpasses a detectability limit $K^*$. When layers are aggregated via a summation, we obtain $K^*\varpropto \mathcal{O}(\sqrt{NL}/T)$, where $T$ is the number of layers across which the community persists. Interestingly, if $T$ is allowed to vary with $L$ then summation-based layer aggregation enhances small-community detection even if the community persists across a vanishing fraction of layers, provided that $T/L$ decays more slowly than $\mathcal{O}(L^{-1/2})$. Moreover, we find that thresholding the summation can in some cases cause $K^*$ to decay exponentially, decreasing by orders of magnitude in a phenomenon we call super-resolution community detection. That is, layer aggregation with thresholding is a nonlinear data filter enabling detection of communities that are otherwise too small to detect. Importantly, different thresholds generally enhance the detectability of communities having different properties, illustrating that community detection can be obscured if one analyzes network data using a single threshold.Comment: 11 pages, 8 figure

Near-bed hydrodynamics and turbulence below a large-scale plunging breaking wave over a mobile barred bed profile

Funded by The research presented in this paper is part of the SINBAD project. Grant Number: STW (12058) and EPSRC (EP/J00507X/1, EP/J005541/1)Peer reviewedPublisher PDFPublisher PD

An Upper Limit on the Mass of the Circumplanetary Disk for DH Tau b

Indexación: Scopus.DH Tau is a young (sim;1 Myr) classical T Tauri star. It is one of the few young PMS stars known to be associated with a planetary mass companion, DH Tau b, orbiting at large separation and detected by direct imaging. DH Tau b is thought to be accreting based on copious Ha emission and exhibits variable Paschen Beta emission. NOEMA observations at 230 GHz allow us to place constraints on the disk dust mass for both DH Tau b and the primary in a regime where the disks will appear optically thin. We estimate a disk dust mass for the primary, DH Tau A of 17.2 ± 1.7 MÅ, which gives a disk to star mass ratio of 0.014 (assuming the usual gas to dust mass ratio of 100 in the disk). We find a conservative disk dust mass upper limit of 0.42M⊕ for DH Tau b, assuming that the disk temperature is dominated by irradiation from DH Tau b itself. Given the environment of the circumplanetary disk, variable illumination from the primary or the equilibrium temperature of the surrounding cloud would lead to even lower disk mass estimates. A MCFOST radiative transfer model, including heating of the circumplanetary disk by DH Tau b and DH Tau A, suggests that a mass-averaged disk temperature of 22 K is more realistic, resulting in a dust disk mass upper limit of 0.09M⊕ for DH Tau b. We place DH Tau b in context with similar objects and discuss the consequences for planet formation models.http://iopscience.iop.org/article/10.3847/1538-3881/aa74cd/met

The inner environment of Z~CMa: High-Contrast Imaging Polarimetry with NaCo

Context. Z\,CMa is a binary composed of an embedded Herbig Be and an FU Ori class star separated by $\sim100$ au. Observational evidence indicate a complex environment in which each star has a circumstellar disk and drives a jet, and the whole system is embedded in a large dusty envelope. Aims. We aim to probe the circumbinary environment of Z\,CMa in the inner 400 au in scattered light. Methods. We use high contrast imaging polarimetry with VLT/NaCo at $H$ and $K_s$ bands. Results. The central binary is resolved in both bands. The polarized images show three bright and complex structures: a common dust envelope, a sharp extended feature previously reported in direct light, and an intriguing bright clump located 0\farcs3 south of the binary, which appears spatially connected to the sharp extended feature. Conclusions.We detect orbital motion when compared to previous observations, and report a new outburst driven by the Herbig star. Our observations reveal the complex inner environment of Z\,CMa with unprecedented detail and contrast.Comment: Accepted for publication in A&A Letter

Super-Resolution Community Detection for Layer-Aggregated Multilayer Networks

Applied network science often involves preprocessing network data before applying a network-analysis method, and there is typically a theoretical disconnect between these steps. For example, it is common to aggregate time-varying network data into windows prior to analysis, and the trade-offs of this preprocessing are not well understood. Focusing on the problem of detecting small communities in multilayer networks, we study the effects of layer aggregation by developing random-matrix theory for modularity matrices associated with layer-aggregated networks with N nodes and L layers, which are drawn from an ensemble of Erdős–Rényi networks with communities planted in subsets of layers. We study phase transitions in which eigenvectors localize onto communities (allowing their detection) and which occur for a given community provided its size surpasses a detectability limit K*. When layers are aggregated via a summation, we obtain K∗∝O(NL/T), where T is the number of layers across which the community persists. Interestingly, if T is allowed to vary with L, then summation-based layer aggregation enhances small-community detection even if the community persists across a vanishing fraction of layers, provided that T/L decays more slowly than (L−1/2). Moreover, we find that thresholding the summation can, in some cases, cause K* to decay exponentially, decreasing by orders of magnitude in a phenomenon we call super-resolution community detection. In other words, layer aggregation with thresholding is a nonlinear data filter enabling detection of communities that are otherwise too small to detect. Importantly, different thresholds generally enhance the detectability of communities having different properties, illustrating that community detection can be obscured if one analyzes network data using a single threshold

Qualitative and quantitative analysis of milk for the detection of adulteration by Laser Induced Breakdown Spectroscopy (LIBS)

The present work focuses on the development of a fast and cost effective method based on Laser Induced Breakdown Spectroscopy (LIBS) to the quality control, traceability and detection of adulteration in milk. Two adulteration cases have been studied; a qualitative analysis for the discrimination between different milk blends and quantification of melamine in adulterated toddler milk powder. Principal Component Analysis (PCA) and neural networks (NN) have been used to analyze LIBS spectra obtaining a correct classification rate of 98% with a 100% of robustness. For the quantification of melamine, two methodologies have been developed; univariate analysis using CN emission band and multivariate calibration NN model obtaining correlation coefficient (R2) values of 0.982 and 0.999 respectively. The results of the use of LIBS technique coupled with chemometric analysis are discussed in terms of its potential use in the food industry to perform the quality control of this dairy product