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

Telling the collective story? Moroccan-Dutch young adults’ negotiation of a collective identity through storytelling

Researchers taking a social constructionist perspective on identity agree that identities are constructed and negotiated in interaction. However, empirical studies in this field are often based on interviewer–interviewee interaction or focus on interactions with members of a socially dominant out-group. How identities are negotiated in interaction with in-group members remains understudied. In this article we use a narrative approach to study identity negotiation among Moroccan-Dutch young adults, who constitute both an ethnic and a religious (Muslim) minority in the Netherlands. Our analysis focuses on the topics that appear in focus group participants’ stories and on participants’ responses to each other’s stories. We find that Moroccan-Dutch young adults collectively narrate their experiences in Dutch society in terms of discrimination and injustice. Firmly grounded in media discourse and popular wisdom, a collective narrative of a disadvantaged minority identity emerges. However, we also find that this identity is not uncontested. We use the concept of second stories to explain how participants negotiate their collective identity by alternating stories in which the collective experience of deprivation is reaffirmed with stories in which challenging or new evaluations of the collective experience are offered. In particular, participants narrate their personal experiences to challenge recurring evaluations of discrimination and injustice. A new collective narrative emerges from this work of joint storytelling

A Net Energy Analysis of the Global Agriculture, Aquaculture, Fishing and Forestry System

The global agriculture, aquaculture, fishing and forestry (AAFF) energy system is subject to three unsustainable trends: (1) the approaching biophysical limits of AAFF; (2) the role of AAFF as a driver of environmental degradation; and (3) the long-term declining energy efficiency of AAFF due to growing dependence on fossil fuels. In response, we conduct a net energy analysis for the period 1971–2017 and review existing studies to investigate the global AAFF energy system and its vulnerability to the three unsustainable trends from an energetic perspective. We estimate the global AAFF system represents 27.9% of societies energy supply in 2017, with food energy representing 20.8% of societies total energy supply. We find that the net energy-return-on-investment (net EROI) of global AAFF increased from 2.87:1 in 1971 to 4.05:1 in 2017. We suggest that rising net EROI values are being fuelled in part by ‘depleting natures accumulated energy stocks’. We also find that the net energy balance of AAFF increased by 130% in this period, with at the same time a decrease in both the proportion of rural residents and also the proportion of the total population working in AAFF—which decreased from 19.8 to 10.3%. However, this comes at the cost of growing fossil fuel dependency which increased from 43.6 to 62.2%. Given the increasing probability of near-term fossil fuel scarcity, the growing impacts of climate change and environmental degradation, and the approaching biophysical limits of global AAFF, ‘Odum’s hoax’ is likely soon to be revealed

Large-Scale Candidate Gene Analysis of HDL Particle Features

Background: HDL cholesterol (HDL-C) is an established marker of cardiovascular risk with significant genetic determination. However, HDL particles are not homogenous, and refined HDL phenotyping may improve insight into regulation of HDL metabolism. We therefore assessed HDL particles by NMR spectroscopy and conducted a large-scale candidate gene association analysis. Methodology/Principal Findings: We measured plasma HDL-C and determined mean HDL particle size and particle number by NMR spectroscopy in 2024 individuals from 512 British Caucasian families. Genotypes were 49,094 SNPs in >2,100 cardiometabolic candidate genes/loci as represented on the HumanCVD BeadChip version 2. False discovery rates (FDR) were calculated to account for multiple testing. Analyses on classical HDL-C revealed significant associations (FDR<0.05) only for CETP (cholesteryl ester transfer protein; lead SNP rs3764261: p = 5.6*10(-15)) and SGCD (sarcoglycan delta; rs6877118: p = 8.6*10(-6)). In contrast, analysis with HDL mean particle size yielded additional associations in LIPC (hepatic lipase; rs261332: p = 6.1*10(-9)), PLTP (phospholipid transfer protein, rs4810479: p = 1.7*10(-8)) and FBLN5 (fibulin-5; rs2246416: p = 6.2*10(-6)). The associations of SGCD and Fibulin-5 with HDL particle size could not be replicated in PROCARDIS (n = 3,078) and/or the Women's Genome Health Study (n = 23,170). Conclusions: We show that refined HDL phenotyping by NMR spectroscopy can detect known genes of HDL metabolism better than analyses on HDL-C

Apolipoprotein A-II Influences Apolipoprotein E-Linked Cardiovascular Disease Risk in Women with High Levels of HDL Cholesterol and C-Reactive Protein

Background: In a previous report by our group, high levels of apolipoprotein E (apoE) were demonstrated to be associated with risk of incident cardiovascular disease in women with high levels of C-reactive protein (CRP) in the setting of both low (designated as HR1 subjects) and high (designated as HR2 subjects) levels of high-density lipoprotein cholesterol (HDL-C). To assess whether apolipoprotein A-II (apoA-II) plays a role in apoE-associated risk in the two female groups. Methodology/Principal: Outcome event mapping, a graphical data exploratory tool; Cox proportional hazards multivariable regression; and curve-fitting modeling were used to examine apoA-II influence on apoE-associated risk focusing on HDL particles with apolipoprotein A-I (apoA-I) without apoA-II (LpA-I) and HDL particles with both apoA-I and apoA-II (LpA-I:A-II). Results of outcome mappings as a function of apoE levels and the ratio of apoA-II to apoA-I revealed within each of the two populations, a high-risk subgroup characterized in each situation by high levels of apoE and additionally: in HR1, by a low value of the apoA-II/apoA-I ratio; and in HR2, by a moderate value of the apoA-II/apoA-I ratio. Furthermore, derived estimates of LpA-I and LpA-I:A-II levels revealed for high-risk versus remaining subjects: in HR1, higher levels of LpA-I and lower levels of LpA-I:A-II; and in HR2 the reverse, lower levels of LpA-I and higher levels of LpA-I:A-II. Results of multivariable risk modeling as a function of LpA-I and LpA-I:A-II (dichotomized as highest quartile versus combined three lower quartiles) revealed association of risk only for high levels of LpA-I:A-II in the HR2 subgroup (hazard ratio 5.31, 95% CI 1.12-25.17, p = 0.036). Furthermore, high LpA-I: A-II levels interacted with high apoE levels in establishing subgroup risk. Conclusions/Significance: We conclude that apoA-II plays a significant role in apoE-associated risk of incident CVD in women with high levels of HDL-C and CRP

Impact of Systemic Inflammation and Autoimmune Diseases on apoA-I and HDL Plasma Levels and Functions

The cholesterol of high-density lipoproteins (HDLs) and its major proteic component, apoA-I, have been widely investigated as potential predictors of acute cardiovascular (CV) events. In particular, HDL cholesterol levels were shown to be inversely and independently associated with the risk of acute CV diseases in different patient populations, including autoimmune and chronic inflammatory disorders. Some relevant and direct anti-inflammatory activities of HDL have been also recently identified targeting both immune and vascular cell subsets. These studies recently highlighted the improvement of HDL function (instead of circulating levels) as a promising treatment strategy to reduce inflammation and associated CV risk in several diseases, such as systemic lupus erythematosus and rheumatoid arthritis. In these diseases, anti-inflammatory treatments targeting HDL function might improve both disease activity and CV risk. In this narrative review, we will focus on the pathophysiological relevance of HDL and apoA-I levels/functions in different acute and chronic inflammatory pathophysiological conditions