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In the present paper we propose to rewrite a nonsmooth problem subjected to convex constraints as an unconstrained problem. We show that this novel formulation shares the same global and local minima with the original constrained problem. Moreover, the reformulation can be solved with standard nonsmooth optimization methods if we are able to make projections onto the feasible sets. Numerical evidence shows that the proposed formulation compares favorably against state-of-art approaches. Code can be found at https://github.com/jth3galv/dfppm.

The increased survival in Systemic Lupus Erythematosus (SLE) patients implies the development of chronic damage, occurring in up to 50% of cases. Its prevention is a major goal in the SLE management. We aimed at predicting chronic damage in a large monocentric SLE cohort by using neural networks. We enrolled 413 SLE patients (M/F 30/383; mean age ± SD 46.3±11.9 years; mean disease duration ± SD 174.6 ± 112.1 months). Chronic damage was assessed by the SLICC/ACR Damage Index (SDI). We applied Recurrent Neural Networks (RNNs) as a machine-learning model to predict the risk of chronic damage. The clinical data sequences registered for each patient during the follow-up were used for building and testing the RNNs. At the first visit in the Lupus Clinic, 35.8% of patients had an SDI≥1. For the RNN model, two groups of patients were analyzed: patients with SDI = 0 at the baseline, developing damage during the follow-up (N = 38), and patients without damage (SDI = 0). We created a mathematical model with an AUC value of 0.77, able to predict damage development. A threshold value of 0.35 (sensitivity 0.74, specificity 0.76) seemed able to identify patients at risk to develop damage. We applied RNNs to identify a prediction model for SLE chronic damage. The use of the longitudinal data from the Sapienza Lupus Cohort, including laboratory and clinical items, resulted able to construct a mathematical model, potentially identifying patients at risk to develop damage.

Limited evidences are available on biomarkers to recognize Systemic Lupus erythematosus (SLE) patients at risk to develop erosive arthritis. Anti-citrullinated peptide antibodies (ACPA) have been widely investigated and identified in up to 50% of X-ray detected erosive arthritis; conversely, few studies evaluated anti-carbamylated proteins antibodies (anti-CarP). Here, we considered the application of machine learning models to identify relevant factors in the development of ultrasonography (US)-detected erosive damage in a large cohort of SLE patients with joint involvement. We enrolled consecutive SLE patients with arthritis/arthralgia. All patients underwent joint (DAS28, STR) and laboratory assessment (detection of ACPA, anti-CarP, Rheumatoid Factor, SLE-related antibodies). The bone surfaces of metacarpophalangeal and proximal interphalangeal joints were assessed by US: the presence of erosions was registered with a dichotomous value (0/1), obtaining a total score (0-20). Concerning machine learning techniques, we applied and compared Logistic Regression and Decision Trees in conjunction with the feature selection Forward Wrapper method. We enrolled 120 SLE patients [M/F 8/112, median age 47.0 years (IQR 15.0); median disease duration 120.0 months (IQR 156.0)], 73.3% of them referring at least one episode of arthritis. Erosive damage was identified in 25.8% of patients (mean±SD 0.7±1.6), all of them with clinically evident arthritis. We applied Logistic Regression in conjunction with the Forward Wrapper method, obtaining an AUC value of 0.806±0.02. As a result of the learning procedure, we evaluated the relevance of the different factors: this value was higher than 35% for ACPA and anti-CarP. The application of Machine Learning Models allowed to identify factors associated with US-detected erosive bone damage in a large SLE cohort and their relevance in determining this phenotype. Although the scope of this study is limited by the small sample size and its cross-sectional nature, the results suggest the relevance of ACPA and anti-CarP antibodies in the development of erosive damage as also pointed out in other studies.

[This corrects the article DOI: 10.1371/journal.pone.0207926.].

Recent advances in pharmacogenomics have generated a wealth of data of different types whose analysis have helped in the identification of signatures of different cellular sensitivity/resistance responses to hundreds of chemical compounds. Among the different data types, gene expression has proven to be the more successful for the inference of drug response in cancer cell lines. Although effective, the whole transcriptome can introduce noise in the predictive models, since specific mechanisms are required for different drugs and these realistically involve only part of the proteins encoded in the genome. We analyzed the pharmacogenomics data of 961 cell lines tested with 265 anti-cancer drugs and developed different machine learning approaches for dissecting the genome systematically and predict drug responses using both drug-unspecific and drug-specific genes. These methodologies reach better response predictions for the vast majority of the screened drugs using tens to few hundreds genes specific to each drug instead of the whole genome, thus allowing a better understanding and interpretation of drug-specific response mechanisms which are not necessarily restricted to the drug known targets.

Batch Normalization is an essential component of all state-of-the-art neural networks architectures. However, since it introduces many practical issues, much recent research has been devoted to designing normalization-free architectures. In this paper, we show that weights initialization is key to train ResNet-like normalization-free networks. In particular, we propose a slight modification to the summation operation of a block output to the skip-connection branch, so that the whole network is correctly initialized. We show that this modified architecture achieves competitive results on CIFAR-10, CIFAR-100 and ImageNet without further regularization nor algorithmic modifications.