A Fast Active Set Block Coordinate Descent Algorithm for ℓ1\ell_1-regularized least squares

The problem of finding sparse solutions to underdetermined systems of linear equations arises in several applications (e.g. signal and image processing, compressive sensing, statistical inference). A standard tool for dealing with sparse recovery is the $\ell_1$-regularized least-squares approach that has been recently attracting the attention of many researchers. In this paper, we describe an active set estimate (i.e. an estimate of the indices of the zero variables in the optimal solution) for the considered problem that tries to quickly identify as many active variables as possible at a given point, while guaranteeing that some approximate optimality conditions are satisfied. A relevant feature of the estimate is that it gives a significant reduction of the objective function when setting to zero all those variables estimated active. This enables to easily embed it into a given globally converging algorithmic framework. In particular, we include our estimate into a block coordinate descent algorithm for $\ell_1$-regularized least squares, analyze the convergence properties of this new active set method, and prove that its basic version converges with linear rate. Finally, we report some numerical results showing the effectiveness of the approach.Comment: 28 pages, 5 figure

An Active-Set Algorithmic Framework for Non-Convex Optimization Problems over the Simplex

In this paper, we describe a new active-set algorithmic framework for minimizing a non-convex function over the unit simplex. At each iteration, the method makes use of a rule for identifying active variables (i.e., variables that are zero at a stationary point) and specific directions (that we name active-set gradient related directions) satisfying a new "nonorthogonality" type of condition. We prove global convergence to stationary points when using an Armijo line search in the given framework. We further describe three different examples of active-set gradient related directions that guarantee linear convergence rate (under suitable assumptions). Finally, we report numerical experiments showing the effectiveness of the approach.Comment: 29 pages, 3 figure

Scanning integer points with lex-inequalities: A finite cutting plane algorithm for integer programming with linear objective

We consider the integer points in a unimodular cone K ordered by a lexicographic rule defined by a lattice basis. To each integer point x in K we associate a family of inequalities (lex-cuts) that defines the convex hull of the integer points in K that are not lexicographically smaller than x. The family of lex-cuts contains the Chvatal-Gomory cuts, but does not contain and is not contained in the family of split cuts. This provides a finite cutting plane method to solve the integer program min{cx : x \in S \cap Z^n }, where S \subset R^n is a compact set and c \in Z^n . We analyze the number of iterations of our algorithm.Comment: 16 pages, 1 figur

Relax and penalize: a new bilevel approach to mixed-binary hyperparameter optimization

In recent years, bilevel approaches have become very popular to efficiently estimate high-dimensional hyperparameters of machine learning models. However, to date, binary parameters are handled by continuous relaxation and rounding strategies, which could lead to inconsistent solutions. In this context, we tackle the challenging optimization of mixed-binary hyperparameters by resorting to an equivalent continuous bilevel reformulation based on an appropriate penalty term. We propose an algorithmic framework that, under suitable assumptions, is guaranteed to provide mixed-binary solutions. Moreover, the generality of the method allows to safely use existing continuous bilevel solvers within the proposed framework. We evaluate the performance of our approach for a specific machine learning problem, i.e., the estimation of the group-sparsity structure in regression problems. Reported results clearly show that our method outperforms state-of-the-art approaches based on relaxation and roundin

Which comes first? New insights on comorbidity between eating disorders and bipolar disorders.

Abstract Aims : Bipolar disorders (BDs) and eating disorders (EDs) are both common and severe mental illness and present wide areas of symptomatological overlap. The present study aims to focus on the most significant aspects of this comorbidity. Methods This review summarizes epidemiology, aethiopathology, prognostic impact, assessment, treatment of comorbidity between BDs and EDs, and comorbidity between bipolar or eating disorders and other psychiatric disorders. We have reviewed articles published in PubMed/Medline, Scopus, Embase, ScienceDirect from 2005 to 2020 concerning comorbidity between eating and bipolar disorders, and systematic reviews or metanalysis on comorbidities between EDs or BDs and other psychiatric disorders. Results Studies that specifically evaluate the prevalence of EDs in patients with bipolar disorder are more than the studies that investigate the opposite. In BDs, binge eating disorder (BED) represents the most common eating disorder with a prevalence ranging from 8,8% to 28,8%, whereas BN has a prevalence ranging from 4,8% to 10%, and AN from 1% to 7,4%. Instead, in ED patients, prevalence of bipolar disorders ranges from 11,5% to 68.1%. The relationship between EDs and BDs has not been yet investigated enough and consequently has not been totally understood. The presence of EDs has been considered as a marker of clinical severity in patients with bipolar disorders, whereas the presence of bipolar disorder in patients with EDs seems not to have a considerable effect on the age at onset of ED symptoms and on their severity. Comorbidities between EDs or BDs and other psychiatric disorders were also examined. Discussion Given the strong co-occurrence of eating and bipolar disorder, the treatment for one of these should consider that the other one may co-exist, and therefore should focus on both of them. In patients suffering from one of these disorders, the early screening for the other one should be made. As for pharmacological treatment, it is mandatory to consider that pharmacological treatment effective for one of the two disorders could worsen symptoms of the other, for instance many psychotropic medications could cause weight gain. Further studies are needed to reach an early diagnosis through the development of screening tools, and to deepen aspects of this comorbidity that remain still unknown with particular regard to pharmacological treatment and to biopsychological aspects that might be useful in determining the aetiopathology

Lifestyle and dietary factors, iron status and one-carbon metabolism polymorphisms in a sample of Italian women and men attending a Transfusion Medicine Unit: a cross-sectional study

Iron (Fe) status among healthy male and female blood donors, aged 18–65 years, is estimated. General characteristics and lifestyle factors, dietary habits and major one-carbon metabolism-related polymorphisms were also investigated. An explorative cross-sectional study design was used to examine a sample of blood donors attending the Transfusion Medicine Unit of the Verona University Hospital, Italy. From April 2016 to May 2018, 499 subjects were enrolled (255 men, 244 women, 155 of whom of childbearing age). Major clinical characteristics including lifestyle, dietary habits and Fe status were analysed. The MTHFR 677C > T, cSHMT 1420C > T, DHFR 19bp ins/del and RFC1 80G > A polymorphisms were also assayed. Mean plasma concentrations of Fe and ferritin were 16·6 µmol/l (95 % CI 16·0, 17·2) and 33·8 µg/l (95 % CI 31·5, 36·2), respectively. Adequate plasma Fe concentrations (> 10·74 µmol/l) were detected in 84·3 % and adequate ferritin concentrations (20–200 µg/l) was found in 72·5 % of the whole cohort. Among the folate-related polymorphisms analysed, carriers of the DHFR 19bp del/del mutant allele showed lower ferritin concentration when compared with DHFR 19bp ins/del genotypes. In a sample of Italian healthy blood donors, adequate plasma concentrations of Fe and ferritin were reached in a large proportion of subjects. The relationship of Fe status with lifestyle factors and folate-related polymorphisms requires more investigation to clarify further gene–nutrient interactions between folate and Fe metabolism

Citric acid aerospace stainless steel passivation: a green approach

Passivation is a common treatment to maximize the corrosion resistance of stainless steel. Nitric acid is generally used and involves several ecological problems, citric acid could be a promising and environmentally friendly alternative to nitric acid. In this work citric acid has been extracted from lemon waste using and eco- friendly procedure. The stainless steel samples have been treated in both nitric and citric acid (commercial and extracted) and corrosion test have been performed. The results show how citric acid can be used as substitute of nitric acid in passivation treatment

Molecular detection of TP53, Ki-Ras and p16INK4A promoter methylation in plasma of patients with colorectal cancer and its association with prognosis. Results of a 3-year GOIM (Gruppo Oncologico dell'Italia Meridionale) prospective study.

BACKGROUND:Despite the improvement in detection and surgical therapy in the last years, the outcome of patients affected by colorectal carcinoma (CRC) remains limited by metastatic relapse. The aim of this study was to investigate the presence of free tumor DNA in the plasma of CRC patients in order to understand its possible prognostic role. PATIENTS AND METHODS: Ki-Ras, TP53 mutations and p16(INK4A) methylation status were prospectively evaluated in tumor tissues and plasma of 66 CRC patients. RESULTS: In 50 of the 66 primitive tumor cases (76%) at least one significant alteration was identified in Ki-Ras and/or TP53 and/or p16(INK4A) genes. Eighteen of the 50 patients presented the same alteration both in the plasma and in the tumor tissue. At univariate analysis, Ki-Ras mutations proved to be significantly related to quicker relapse (P <0.01), whereas only a trend towards statistical significance (P = 0.083) was observed for the TP53 mutations CONCLUSIONS: Detection of Ki-Ras and TP53 mutation in plasma should be significantly related to disease recurrence. These data suggest that patients with a high risk of recurrence can be identified by means of the analysis of tumor-derived plasma DNA with the use of fairly non-invasive techniques

Depressive Symptoms during Pregnancy. Prevalence and Correlates with Affective Temperaments and Psychosocial Factors

Pregnancy is a unique experience in women's life, requiring a great ability of adaptation and self-reorganization; vulnerable women may be at increased risk of developing depressive symptoms. This study aimed to examine the incidence of depressive symptomatology during pregnancy and to evaluate the role of affective temperament traits and psychosocial risk factors in predicting them. We recruited 193 pregnant women, collected data regarding sociodemographic, family and personal clinical variables, social support and stressful life events and administered the Mood Disorder Questionnaire (MDQ), the Patient Health Questionnaire-9 (PHQ-9), and the Temperament Evaluation of Memphis, Pisa, Paris and San Diego-Autoquestionnaire (TEMPS-A). In our sample, prevalence of depressive symptomatology was 41.45% and prevalence of depression was 9.85% (6.75% mild and 3.10% moderate depression). We have chosen a cutoff &gt;4 on PHQ-9 to identify mild depressive symptoms which may predict subsequent depression. Statistically significant differences between the two groups were found in the following factors: gestational age, occupation, partner, medical conditions, psychiatric disorders, family psychiatric history, stressful life events, and TEMPS-A mean scores. In our sample mean scores on all affective temperaments but the hyperthymic, were significantly lower in the control group. Only depressive and hyperthymic temperaments were found to be, respectively, risk and protective factors for depressive symptomatology. The current study confirms the high prevalence and complex aetiology of depressive symptomatology during pregnancy and suggests that affective temperament assessment seems to be a useful adjunctive instrument to predict depressive symptomatology during pregnancy and postpartum