Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

Qualitative Properties of Magnetic Fields in Scalar Field Cosmology

We study the qualitative properties of the class of spatially homogeneous Bianchi VI_o cosmological models containing a perfect fluid with a linear equation of state, a scalar field with an exponential potential and a uniform cosmic magnetic field, using dynamical systems techniques. We find that all models evolve away from an expanding massless scalar field model in which the matter and the magnetic field are negligible dynamically. We also find that for a particular range of parameter values the models evolve towards the usual power-law inflationary model (with no magnetic field) and, furthermore, we conclude that inflation is not fundamentally affected by the presence of a uniform primordial magnetic field. We investigate the physical properties of the Bianchi I magnetic field models in some detail.Comment: 12 pages, 2 figures in REVTeX format. to appear in Phys. Rev.

Inferential Transitions

This paper provides a naturalistic account of inference. We posit that the core of inference is constituted by bare inferential transitions (BITs), transitions between discursive mental representations guided by rules built into the architecture of cognitive systems. In further developing the concept of BITs, we provide an account of what Boghossian [2014] calls ‘taking’—that is, the appreciation of the rule that guides an inferential transition. We argue that BITs are sufficient for implicit taking, and then, to analyse explicit taking, we posit rich inferential transitions (RITs), which are transitions that the subject is disposed to endorse

Basic principles of stable isotope analysis in humanitarian forensic science.

While the identity of a victim of a localized disaster – such as a train or bus crash – may be established quickly through personal effects, fingerprints, dental records, and a comparison of decedent DNA to family reference specimen DNA, a different scenario presents itself in mass disasters, such as the Asian Tsunami of 2004. In the aftermath of the tsunami, visual appearance was initially used to assign “foreign” or “indigenous” classifications to the remains of thousands of victims. However, this visual identification approach was undermined by the speed with which bodies deteriorated under the hot and humid conditions. Time was spent populating ante-mortem DNA databases for different nationalities, which led to problems when creating a post-mortem DNA database because recovery of viable DNA was compromised due to rapid decomposition. As a consequence, only 1.3% of victims were identified by DNA; in contrast, 61% were identified based on dental examination, although this process took several months and a significant number of deceased from the 2004 Asian Tsunami still remain to be identified

Scaling ozone responses of forest trees to the ecosystem level in a changing climate

Many uncertainties remain regarding how climate change will alter the structure and function of forest ecosystems. At the Aspen FACE experiment in northern Wisconsin, we are attempting to understand how an aspen/birch/maple forest ecosystem responds to long-term exposure to elevated carbon dioxide (CO 2 ) and ozone (O 3 ), alone and in combination, from establishment onward. We examine how O 3 affects the flow of carbon through the ecosystem from the leaf level through to the roots and into the soil micro-organisms in present and future atmospheric CO 2 conditions. We provide evidence of adverse effects of O 3 , with or without co-occurring elevated CO 2 , that cascade through the entire ecosystem impacting complex trophic interactions and food webs on all three species in the study: trembling aspen ( Populus tremuloides Michx . ), paper birch ( Betula papyrifera Marsh), and sugar maple ( Acer saccharum Marsh). Interestingly, the negative effect of O 3 on the growth of sugar maple did not become evident until 3 years into the study. The negative effect of O 3 effect was most noticeable on paper birch trees growing under elevated CO 2 . Our results demonstrate the importance of long-term studies to detect subtle effects of atmospheric change and of the need for studies of interacting stresses whose responses could not be predicted by studies of single factors. In biologically complex forest ecosystems, effects at one scale can be very different from those at another scale. For scaling purposes, then, linking process with canopy level models is essential if O 3 impacts are to be accurately predicted. Finally, we describe how outputs from our long-term multispecies Aspen FACE experiment are being used to develop simple, coupled models to estimate productivity gain/loss from changing O 3 .Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72464/1/j.1365-3040.2005.01362.x.pd

State of the climate in 2013

In 2013, the vast majority of the monitored climate variables reported here maintained trends established in recent decades. ENSO was in a neutral state during the entire year, remaining mostly on the cool side of neutral with modest impacts on regional weather patterns around the world. This follows several years dominated by the effects of either La Niña or El Niño events. According to several independent analyses, 2013 was again among the 10 warmest years on record at the global scale, both at the Earths surface and through the troposphere. Some regions in the Southern Hemisphere had record or near-record high temperatures for the year. Australia observed its hottest year on record, while Argentina and New Zealand reported their second and third hottest years, respectively. In Antarctica, Amundsen-Scott South Pole Station reported its highest annual temperature since records began in 1957. At the opposite pole, the Arctic observed its seventh warmest year since records began in the early 20th century. At 20-m depth, record high temperatures were measured at some permafrost stations on the North Slope of Alaska and in the Brooks Range. In the Northern Hemisphere extratropics, anomalous meridional atmospheric circulation occurred throughout much of the year, leading to marked regional extremes of both temperature and precipitation. Cold temperature anomalies during winter across Eurasia were followed by warm spring temperature anomalies, which were linked to a new record low Eurasian snow cover extent in May. Minimum sea ice extent in the Arctic was the sixth lowest since satellite observations began in 1979. Including 2013, all seven lowest extents on record have occurred in the past seven years. Antarctica, on the other hand, had above-average sea ice extent throughout 2013, with 116 days of new daily high extent records, including a new daily maximum sea ice area of 19.57 million km2 reached on 1 October. ENSO-neutral conditions in the eastern central Pacific Ocean and a negative Pacific decadal oscillation pattern in the North Pacific had the largest impacts on the global sea surface temperature in 2013. The North Pacific reached a historic high temperature in 2013 and on balance the globally-averaged sea surface temperature was among the 10 highest on record. Overall, the salt content in nearsurface ocean waters increased while in intermediate waters it decreased. Global mean sea level continued to rise during 2013, on pace with a trend of 3.2 mm yr-1 over the past two decades. A portion of this trend (0.5 mm yr-1) has been attributed to natural variability associated with the Pacific decadal oscillation as well as to ongoing contributions from the melting of glaciers and ice sheets and ocean warming. Global tropical cyclone frequency during 2013 was slightly above average with a total of 94 storms, although the North Atlantic Basin had its quietest hurricane season since 1994. In the Western North Pacific Basin, Super Typhoon Haiyan, the deadliest tropical cyclone of 2013, had 1-minute sustained winds estimated to be 170 kt (87.5 m s-1) on 7 November, the highest wind speed ever assigned to a tropical cyclone. High storm surge was also associated with Haiyan as it made landfall over the central Philippines, an area where sea level is currently at historic highs, increasing by 200 mm since 1970. In the atmosphere, carbon dioxide, methane, and nitrous oxide all continued to increase in 2013. As in previous years, each of these major greenhouse gases once again reached historic high concentrations. In the Arctic, carbon dioxide and methane increased at the same rate as the global increase. These increases are likely due to export from lower latitudes rather than a consequence of increases in Arctic sources, such as thawing permafrost. At Mauna Loa, Hawaii, for the first time since measurements began in 1958, the daily average mixing ratio of carbon dioxide exceeded 400 ppm on 9 May. The state of these variables, along with dozens of others, and the 2013 climate conditions of regions around the world are discussed in further detail in this 24th edition of the State of the Climate series. © 2014, American Meteorological Society. All rights reserved

Search for gravitational waves from Scorpius X-1 in the second Advanced LIGO observing run with an improved hidden Markov model

We present results from a semicoherent search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1, using a hidden Markov model (HMM) to track spin wandering. This search improves on previous HMM-based searches of LIGO data by using an improved frequency domain matched filter, the J-statistic, and by analyzing data from Advanced LIGO's second observing run. In the frequency range searched, from 60 to 650 Hz, we find no evidence of gravitational radiation. At 194.6 Hz, the most sensitive search frequency, we report an upper limit on gravitational wave strain (at 95% confidence) of h095%=3.47×10-25 when marginalizing over source inclination angle. This is the most sensitive search for Scorpius X-1, to date, that is specifically designed to be robust in the presence of spin wandering. © 2019 American Physical Society