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

The in vitro antitumor activity of arene-ruthenium(II) curcuminoid complexes improves when decreasing curcumin polarity

The antitumor activity of ruthenium(II) arene (p-cymene, benzene, hexamethylbenzene) derivatives containing modified curcumin ligands (HCurcI=(1E,4Z,6E)-5-hydroxy-1,7-bis(3,4-dimethoxyphenyl)hepta-1,4,6-trien-3- one and HCurcII = (1E,4Z,6E)-5-hydroxy-1,7-bis(4-methoxyphenyl)hepta-1,4,6-trien-3-one) is described. These have been characterized by IR, ESI-MS and NMR spectroscopy. The X-ray crystal structure of HCurcI has been determined and compared with its related Ru complex. Four complexes have been evaluated against five tumor cell lines, whose best activities [IC50 (\u3bcM)] are: breast MCF7, 9.7; ovarian A2780, 9.4; glioblastoma U-87, 9.4; lung carcinoma A549, 13.7 and colon-rectal HCT116, 15.5; they are associated with apoptotic features. These activities are improved when compared to the already known corresponding curcumin complex, (pcymene) Ru(curcuminato)Cl, about twice for the breast and ovarian cancer, 4.7 times stronger in the lung cancer and about 6.6 times stronger in the glioblastoma cell lines. In fact, the less active (p-cymene)Ru(curcuminato)Cl complex only shows similar activity to two novel complexes in the colon cancer cell line. Comparing antitumor activity between these novel complexes and their related curcuminoids, improvement of antiproliferative activity is seen for a complex containing CurcII in A2780, A549 and U87 cell lines, whose IC50 are halved. Therefore, after replacing OH curcumin groupswith OCH3, the obtained species HCurcI and its Ru complexes have increased antitumor activity compared to curcumin and its related complex. In contrast, HCurcII is less cytotoxic than curcumin but its related complex [(p-cymene)Ru(CurcII)Cl] is twice as active as HCurcII in 3 cell lines. Results fromthese novel arene-Ru curcuminoid species suggest that their increased cytotoxicity on tumor cells correlate with increase of curcuminoid lipophilicity

X-ray crystal structures, density functional theory and docking on deacetylase enzyme for antiproliferative activity of hispolon derivatives on HCT116 colon cancer

The antiproliferative action of hispolon derivatives is stronger than that of related curcumin against several tumor cell lines. Hispolon size, smaller than curcumin, fits better than curcumin into the active site of HDAC6, an enzyme involved in deacetylation of lysine residues. HDACs are considered potential targets for tumor drug discovery and hydroxamates are known inhibitors of HDACs. One of them, SAHA (Vorinostat) is used in clinical studies. Investigations into possible mechanisms for hispolon derivatives active against the HCT116 colon tumor cell line are done after examining the structural results obtained from hispolon X-ray crystal structures as well as performing associated computational docking and Density Functional Theory techniques on HDAC6. These studies show preference for the HDAC6 active site by chelating the Zn center, in contrast with other ineffective hispolon derivatives, that establish only a single bond to the metal center. Structure activity relationships make clear that hydrogenation of the hispolon bridge also leads to single bond (non chelate) hispolon-Zn binding, and consistently nullifies the antiproliferative action against HCT116 tumor

Interaction of foam with a porous medium: Theory and calculations

Closed accessA new theory of foam drainage in the presence of a porous support was introduced and accordingly, a mathematical model which combines the foam drainage equation with the equation describing imbibition into the porous substrate was developed. Proposed dimensionless equations were solved using finite element method. Boundary conditions were zero liquid flux on the top of the foam and continuity of flux on foam/substrate interface. It was found that the kinetics of foam drainage depends on three dimensionless numbers. The result indicated that there are two possible scenarios for the interaction of foam with a porous substrate: (i) a rapid imbibition, the liquid volume fraction at the bottom of the foam is a decreasing function of time. In this regime the imbibition into the porous substrate dominates and it is faster as compared with the foam drainage; (ii) a slow imbibition, the liquid volume fraction at the interface experiences a peak point and imbibition into the porous substrate is slower for some time as compared with the foam drainage

Acute heart failure congestion and perfusion status – impact of the clinical classification on in-hospital and long-term outcomes; insights from the ESC-EORP-HFA Heart Failure Long-Term Registry

Aims: Classification of acute heart failure (AHF) patients into four clinical profiles defined by evidence of congestion and perfusion is advocated by the 2016 European Society of Cardiology (ESC)guidelines. Based on the ESC-EORP-HFA Heart Failure Long-Term Registry, we compared differences in baseline characteristics, in-hospital management and outcomes among congestion/perfusion profiles using this classification. Methods and results: We included 7865 AHF patients classified at admission as: ‘dry-warm’ (9.9%), ‘wet-warm’ (69.9%), ‘wet-cold’ (19.8%) and ‘dry-cold’ (0.4%). These groups differed significantly in terms of baseline characteristics, in-hospital management and outcomes. In-hospital mortality was 2.0% in ‘dry-warm’, 3.8% in ‘wet-warm’, 9.1% in ‘dry-cold’ and 12.1% in ‘wet-cold’ patients. Based on clinical classification at admission, the adjusted hazard ratios (95% confidence interval) for 1-year mortality were: ‘wet-warm’ vs. ‘dry-warm’ 1.78 (1.43–2.21) and ‘wet-cold’ vs. ‘wet-warm’ 1.33 (1.19–1.48). For profiles resulting from discharge classification, the adjusted hazard ratios (95% confidence interval) for 1-year mortality were: ‘wet-warm’ vs. ‘dry-warm’ 1.46 (1.31–1.63) and ‘wet-cold’ vs. ‘wet-warm’ 2.20 (1.89–2.56). Among patients discharged alive, 30.9% had residual congestion, and these patients had higher 1-year mortality compared to patients discharged without congestion (28.0 vs. 18.5%). Tricuspid regurgitation, diabetes, anaemia and high New York Heart Association class were independently associated with higher risk of congestion at discharge, while beta-blockers at admission, de novo heart failure, or any cardiovascular procedure during hospitalization were associated with lower risk of residual congestion. Conclusion: Classification based on congestion/perfusion status provides clinically relevant information at hospital admission and discharge. A better understanding of the clinical course of the two entities could play an important role towards the implementation of targeted strategies that may improve outcomes. © 2019 The Authors. European Journal of Heart Failure © 2019 European Society of Cardiolog