Strict BV relaxed area of Sobolev maps into the circle: the high dimension case

We deal with the relaxed area functional in the strict $BV$-convergence of non-smooth maps defined in domains of generic dimension and taking values into the unit circle. In case of Sobolev maps, a complete explicit formula is obtained. Our proof is based on tools from Geometric Measure Theory and Cartesian currents. We then discuss the possible extension to the wider class of maps with bounded variation. Finally, we show a counterexample to the locality property in case of both dimension and codimension larger than two

Relaxed area of graphs of piecewise Lipschitz maps in the strict BV-convergence

We compute the relaxed Cartesian area in the strict BV-convergence on a class of piecewise Lipschitz maps from the plane to the plane, having jump made of several curves allowed to meet at a finite number of junction points. We show that the domain of this relaxed area is strictly contained in the domain of the classical L1-relaxed area

An evaluation of morphological and functional multi-parametric MRI sequences in classifying non-muscle and muscle invasive bladder cancer

Objectives: Our goal is to determine the ability of multi-parametric magnetic resonance imaging (mpMRI) to differentiate muscle invasive bladder cancer (MIBC) from non-muscle invasive bladder cancer (NMIBC). Methods: Patients underwent mpMRI before tumour resection. Four MRI sets, i.e. T2-weighted (T2W) + perfusion-weighted imaging (PWI), T2W plus diffusion-weighted imaging (DWI), T2W + DWI + PWI, and T2W + DWI + PWI + dif-fusion tensor imaging (DTI) were interpreted qualitatively by two radiologists, blinded to histology results. PWI, DWI and DTI were also analysed quantitatively. Accuracy was determined using histopathology as the reference standard. Results: A total of 82 tumours were analysed. Ninety-six percent of T1-labeled tumours by the T2W + DWI + PWI image set were confirmed to be NMIBC at histopathology. Overall accuracy of the complete mpMRI protocol was 94% in differentiating NMIBC from MIBC. PWI, DWI and DTI quantitative parameters were shown to be significantly different in cancerous versus non-cancerous areas within the bladder wall in T2-labelled lesions. Conclusions: MpMRI with DWI and DTI appears a reliable staging tool for bladder cancer. If our data are validated, then mpMRI could precede cystoscopic resection to allow a faster recognition of MIBC and accelerated treatment pathways. Key Points: • A critical step in BCa staging is to differentiate NMIBC from MIBC. • Morphological and functional sequences are reliable techniques in differentiating NMIBC from MIBC. • Diffusion tensor imaging could be an additional tool in BCa staging

The relaxed area of S1-valued singular maps in the strict BV-convergence

3nononeGiven a bounded open set Ω ⊂ R2, we study the relaxation of the nonparametric area functional in the strict topology in BV (Ω; R2), and compute it for vortex-type maps, and more generally for maps in W1,1(Ω; S1) having a finite number of topological singularities. We also extend the analysis to some specific piecewise constant maps in BV (Ω; S1), including the symmetric triple junction map.Giovanni Bellettini, Simone Carano, Riccardo ScalaBellettini, Giovanni; Carano, Simone; Scala, Riccard

The effect of paliperidone palmitate long-acting injectable (PP-LAI) on "non-core" symptoms of schizophrenia. a retrospective, collaborative, multicenter study in the "real world" everyday clinical practice

Background. Schizophrenia is frequently complicated by the occurrence of depressive symptoms, anhedonia, obsessions and compulsions, suicidal ideation, and substance abuse, that causes exacerbations and remissions and, in several cases, sustained morbidity and disability. Aim. The present study aimed to evaluate the effect of paliperidone palmitate once-monthly long-acting injection (PP-LAI) mainly on "non-core" symptoms in persons with recent diagnosis schizophrenia, during a follow-up period of almost 12 months (T1) in the context of the "real world" everyday clinical practice. Results. Concerning core symptoms of schizophrenia, PP-LAI was effective in reducing all symptoms at T1 as measured by Positive and Negative Syndrome Scale (PANSS), including depressive symptoms, and increased the functioning. Moreover, concerning the non-core symptoms of schizophrenia, PP-LAI treatment was effective in reducing scores of anhedonia, suicidal ideation and obsessive-compulsive symptoms at T1. However, the levels of alexithymia remained relatively stable, even if reduced. Discussion. The present retrospective, multicenter, non-sponsored, collaborative study showed that early PP-LAI treatment was effective in improving almost all the core dimensions and "non-core" symptoms of schizophrenia, and this may have positive repercussions on both functioning and quality of life. Conclusions. PP-LAI treatment should be offered earlier as possible and was effective on "non-core" symptoms of schizophrenia at follow-up, but had a little effect on alexithymia. However, study' limitations must be considered and future researches are needed to confirm these interesting findings