Painless Breakups -- Efficient Demixing of Low Rank Matrices

Assume we are given a sum of linear measurements of $s$ different rank-$r$ matrices of the form $y = \sum_{k=1}^{s} \mathcal{A}_k ({X}_k)$. When and under which conditions is it possible to extract (demix) the individual matrices ${X}_k$ from the single measurement vector ${y}$? And can we do the demixing numerically efficiently? We present two computationally efficient algorithms based on hard thresholding to solve this low rank demixing problem. We prove that under suitable conditions these algorithms are guaranteed to converge to the correct solution at a linear rate. We discuss applications in connection with quantum tomography and the Internet-of-Things. Numerical simulations demonstrate empirically the performance of the proposed algorithms

Rapid, Robust, and Reliable Blind Deconvolution via Nonconvex Optimization

We study the question of reconstructing two signals $f$ and $g$ from their convolution $y = f\ast g$. This problem, known as {\em blind deconvolution}, pervades many areas of science and technology, including astronomy, medical imaging, optics, and wireless communications. A key challenge of this intricate non-convex optimization problem is that it might exhibit many local minima. We present an efficient numerical algorithm that is guaranteed to recover the exact solution, when the number of measurements is (up to log-factors) slightly larger than the information-theoretical minimum, and under reasonable conditions on $f$ and $g$. The proposed regularized gradient descent algorithm converges at a geometric rate and is provably robust in the presence of noise. To the best of our knowledge, our algorithm is the first blind deconvolution algorithm that is numerically efficient, robust against noise, and comes with rigorous recovery guarantees under certain subspace conditions. Moreover, numerical experiments do not only provide empirical verification of our theory, but they also demonstrate that our method yields excellent performance even in situations beyond our theoretical framework

Editorial: advances in understanding marine heatwaves and their impacts

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Benthuysen, J. A., Oliver, E. C. J., Chen, K., & Wernberg, T. Editorial: advances in understanding marine heatwaves and their impacts. Frontiers in Marine Science, 7, (2020): 147, doi:10.3389/fmars.2020.00147.Editorial on the Research Topic Advances in Understanding Marine Heatwaves and Their Impacts In recent years, prolonged, extremely warm water events, known as marine heatwaves, have featured prominently around the globe with their disruptive consequences for marine ecosystems. Over the past decade, marine heatwaves have occurred from the open ocean to marginal seas and coastal regions, including the unprecedented 2011 Western Australia marine heatwave (Ningaloo Niño) in the eastern Indian Ocean (e.g., Pearce et al., 2011), the 2012 northwest Atlantic marine heatwave (Chen et al., 2014), the 2012 and 2015 Mediterranean Sea marine heatwaves (Darmaraki et al., 2019), the 2013/14 western South Atlantic (Rodrigues et al., 2019) and 2017 southwestern Atlantic marine heatwave (Manta et al., 2018), the persistent 2014–2016 “Blob” in the North Pacific (Bond et al., 2015; Di Lorenzo and Mantua, 2016), the 2015/16 marine heatwave spanning the southeastern tropical Indian Ocean to the Coral Sea (Benthuysen et al., 2018), and the Tasman Sea marine heatwaves in 2015/16 (Oliver et al., 2017) and 2017/18 (Salinger et al., 2019). These events have set new records for marine heatwave intensity, the temperature anomaly exceeding a climatology, and duration, the sustained period of extreme temperatures. We have witnessed the profound consequences of these thermal disturbances from acute changes to marine life to enduring impacts on species, populations, and communities (Smale et al., 2019). These marine heatwaves have spurred a diversity of research spanning the methodology of identifying and quantifying the events (e.g., Hobday et al., 2016) and their historical trends (Oliver et al., 2018), understanding their physical mechanisms and relationships with climate modes (e.g., Holbrook et al., 2019), climate projections (Frölicher et al., 2018), and understanding the biological impacts for organisms and ecosystem function and services (e.g., Smale et al., 2019). By using sea surface temperature percentiles, temperature anomalies can be quantified based on their local variability and account for the broad range of temperature regimes in different marine environments. For temperatures exceeding a 90th-percentile threshold beyond a period of 5-days, marine heatwaves can be classified into categories based on their intensity (Hobday et al., 2018). While these recent advances have provided the framework for understanding key aspects of marine heatwaves, a challenge lies ahead for effective integration of physical and biological knowledge for prediction of marine heatwaves and their ecological impacts. This Research Topic is motivated by the need to understand the mechanisms for how marine heatwaves develop and the biological responses to thermal stress events. This Research Topic is a collection of 18 research articles and three review articles aimed at advancing our knowledge of marine heatwaves within four themes. These themes include methods for detecting marine heatwaves, understanding their physical mechanisms, seasonal forecasting and climate projections, and ecological impacts.We thank the contributing authors, reviewers, and the editorial staff at Frontiers in Marine Science for their support in producing this issue. We thank the Marine Heatwaves Working Group (http://www.marineheatwaves.org/) for inspiration and discussions. This special issue stemmed from the session on Advances in Understanding Marine Heat Waves and Their Impacts at the 2018 Ocean Sciences meeting (Portland, USA)

A Census of Large-Scale (≥\ge 10 pc), Velocity-Coherent, Dense Filaments in the Northern Galactic Plane: Automated Identification Using Minimum Spanning Tree

Large-scale gaseous filaments with length up to the order of 100 pc are on the upper end of the filamentary hierarchy of the Galactic interstellar medium. Their association with respect to the Galactic structure and their role in Galactic star formation are of great interest from both observational and theoretical point of view. Previous "by-eye" searches, combined together, have started to uncover the Galactic distribution of large filaments, yet inherent bias and small sample size limit conclusive statistical results to be drawn. Here, we present (1) a new, automated method to identify large-scale velocity-coherent dense filaments, and (2) the first statistics and the Galactic distribution of these filaments. We use a customized minimum spanning tree algorithm to identify filaments by connecting voxels in the position-position-velocity space, using the Bolocam Galactic Plane Survey spectroscopic catalog. In the range of $7.^{\circ}5 \le l \le 194^{\circ}$, we have identified 54 large-scale filaments and derived mass ($\sim 10^3 - 10^5 \, M_\odot$), length (10-276 pc), linear mass density (54-8625 $M_\odot \, \rm{pc}^{-1}$), aspect ratio, linearity, velocity gradient, temperature, fragmentation, Galactic location and orientation angle. The filaments concentrate along major spiral arms. They are widely distributed across the Galactic disk, with 50% located within $\pm$20 pc from the Galactic mid-plane and 27% run in the center of spiral arms (aka "bones"). An order of 1% of the molecular ISM is confined in large filaments. Massive star formation is more favorable in large filaments compared to elsewhere. This is the first comprehensive catalog of large filaments useful for a quantitative comparison with spiral structures and numerical simulations.Comment: Accepted to ApJS. 20 pages (in aastex6 compact format), 6 figures, 1 table. See http://www.eso.org/~kwang/MSTpaper for (1) a preprint with full resolution Fig 6, (2) filaments catalog (Table 1) in ASCII format, and (3) a DS9 region file for the coordinates of the filament

A general solution method for moral hazard problems

Principal-agent models are pervasive in theoretical and applied economics, but their analysis has largely been limited to the "first-order approach" (FOA) where incentive compatibility is replaced by a first-order condition. This paper presents a new approach to solving a wide class of principal-agent problems that satisfy the monotone likelihood ratio property but may fail to meet the requirements of the FOA. Our approach solves the problem via tackling a max-min-max formulation over agent actions, alternate best responses by the agent, and contracts

Neuronal microRNA eeregulation in response to Alzheimer's disease Amyloid-β

Normal brain development and function depends on microRNA (miRNA) networks to fine tune the balance between the transcriptome and proteome of the cell. These small non-coding RNA regulators are highly enriched in brain where they play key roles in neuronal development, plasticity and disease. In neurodegenerative disorders such as Alzheimer's disease (AD), brain miRNA profiles are altered; thus miRNA dysfunction could be both a cause and a consequence of disease. Our study dissects the complexity of human AD pathology, and addresses the hypothesis that amyloid-beta (Abeta) itself, a known causative factor of AD, causes neuronal miRNA deregulation, which could contribute to the pathomechanisms of AD. We used sensitive TaqMan low density miRNA arrays (TLDA) on murine primary hippocampal cultures to show that about half of all miRNAs tested were down-regulated in response to Abeta peptides. Time-course assays of neuronal Abeta treatments show that Abeta is in fact a powerful regulator of miRNA levels as the response of certain mature miRNAs is extremely rapid. Bioinformatic analysis predicts that the deregulated miRNAs are likely to affect target genes present in prominent neuronal pathways known to be disrupted in AD. Remarkably, we also found that the miRNA deregulation in hippocampal cultures was paralleled in vivo by a deregulation in the hippocampus of Abeta42-depositing APP23 mice, at the onset of Abeta plaque formation. In addition, the miRNA deregulation in hippocampal cultures and APP23 hippocampus overlaps with those obtained in human AD studies. Taken together, our findings suggest that neuronal miRNA deregulation in response to an insult by Abeta may be an important factor contributing to the cascade of events leading to AD.N.S. is supported by the Human Frontier Science Program. L.I. is supported by the National Health and Medical Research Council (NHMRC) and the Australian Research Council (ARC), and J.G. is supported by grants from the University of Sydney, the National Health and Medical Research Council (NHMRC), the Australian Research Council (ARC), and the J.O. & J.R. Wicking Trust. Postgraduate scholarship support has been provided by the Wenkart Foundation, GlaxoSmithKline and Alzheimer’s Australia

A content-based retrieval system for UAV-like video and associated metadata

In this paper we provide an overview of a content-based retrieval (CBR) system that has been specifically designed for handling UAV video and associated meta-data. Our emphasis in designing this system is on managing large quantities of such information and providing intuitive and efficient access mechanisms to this content, rather than on analysis of the video content. The retrieval unit in our system is termed a "trip". At capture time, each trip consists of an MPEG-1 video stream and a set of time stamped GPS locations. An analysis process automatically selects and associates GPS locations with the video timeline. The indexed trip is then stored in a shared trip repository. The repository forms the backend of a MPEG-211 compliant Web 2.0 application for subsequent querying, browsing, annotation and video playback. The system interface allows users to search/browse across the entire archive of trips and, depending on their access rights, to annotate other users' trips with additional information. Interaction with the CBR system is via a novel interactive map-based interface. This interface supports content access by time, date, region of interest on the map, previously annotated specific locations of interest and combinations of these. To develop such a system and investigate its practical usefulness in real world scenarios, clearly a significant amount of appropriate data is required. In the absence of a large volume of UAV data with which to work, we have simulated UAV-like data using GPS tagged video content captured from moving vehicles

BitPhylogeny: a probabilistic framework for reconstructing intra-tumor phylogenies.

Cancer has long been understood as a somatic evolutionary process, but many details of tumor progression remain elusive. Here, we present BitPhylogenyBitPhylogeny, a probabilistic framework to reconstruct intra-tumor evolutionary pathways. Using a full Bayesian approach, we jointly estimate the number and composition of clones in the sample as well as the most likely tree connecting them. We validate our approach in the controlled setting of a simulation study and compare it against several competing methods. In two case studies, we demonstrate how BitPhylogeny BitPhylogeny reconstructs tumor phylogenies from methylation patterns in colon cancer and from single-cell exomes in myeloproliferative neoplasm.KY and FM would like to acknowledge the support of the University of Cambridge, Cancer Research UK and Hutchison Whampoa Limited.This is the final published version. It first appeared at http://genomebiology.com/2015/16/1/36