Solutions to nonlocal evolution equations governed by non-autonomous forms and demicontinuous nonlinearities

We deal with the existence of solutions having L2 regularity for a class of non autonomous evolution equations. Associated with the equation, a general non local condition is studied. The technique we used combines a finite dimensional reduction together with the Leray-Schauder continuation principle. This approach permits to consider a wide class of nonlinear terms by allowing demicontinuity assumptions on the nonlinearity

Some Results on the Approximation of Solutions of Variational Inequalities for Multivalued Maps on Banach Spaces

AbstractMultivalued $$*$$ ∗ -nonexpansive mappings are studied in Banach spaces. The demiclosedness principle is established. Here we focus on the problem of solving a variational inequality which is defined on the set of fixed points of a multivalued $$*$$ ∗ -nonexpansive mapping. For this purpose, we introduce two algorithms approximating the unique solution of the variational inequality

Regularity, comparison principles and symmetry results for the vectorial p-Laplacian

We prove some regularity results for solutions to vectorial $p$-Laplace equations -{\boldsymbol \Delta}_p{\boldsymbol u}=-\operatorname{\bf div}(|D{\boldsymbol u}|^{p-2}D{\boldsymbol u}) = {\boldsymbol f}(x,{\boldsymbol u})\,\, \mbox{ in $\Omega$}\,. More precisely we address the issue of second order estimates. As a consequence of our regularity results we deduce a weighted Sobolev inequality that leads to weak comparison principles. Furthermore we prove a strong comparison principle that holds where solutions are smooth, going back to a technique due to McNabb and Serrin. As a corollary we run over the moving plane technique to deduce symmetry and monotonicity results for the solutions

On solving variational inequalities defined on fixed point sets of multivalued mappings in Banach spaces

AbstractWe are concerned with the problem of solving variational inequalities which are defined on the set of fixed points of a multivalued nonexpansive mapping in a reflexive Banach space. Both implicit and explicit approaches are studied. Strong convergence of the implicit method is proved if the space satisfies Opial's condition and has a duality map weakly continuous at zero, and the strong convergence of the explicit method is proved if the space has a weakly continuous duality map. An essential assumption on the multivalued nonexpansive mapping is that the mapping be single valued on its nonempty set of fixed points

On the role of the coefficients in the strong convergence of a general type Mann iterative scheme

Let H be a Hilbert space. Let $(W_{n})_{n\in\mathbb{N}}$ be a suitable family of mappings. Let S be a nonexpansive mapping and D be a strongly monotone operator. We study the convergence of the general scheme $x_{n+1}=W_{n}(\alpha_{n}Sx_{n}+(1-\alpha_{n})(I-\mu_{n}D)x_{n})$ in dependence on the coefficients $(\alpha_{n})_{n\in\mathbb{N}}$ , $(\mu_{n})_{n\in\mathbb{N}}$

new technological advancements for interventional oncology

From the discovery of X-rays in 1895, radiology has always been the most technological specialty of medicine, evolving from purely diagnostic to high-tech interventional

On some Mann's type iterative algorithms

AbstractFirst we present some interesting variants of Mann's method. In the last section, we show that many existing results in the literature are concrete realizations of our general scheme under varying assumptions on the coefficients

Percutaneous radiofrequency ablation of HCC: reduced ablation duration and increased ablation size using single, internally cooled electrodes with an optimized pulsing algorithm

Purpose To assess the use of optimized radiofrequency (RF) to achieve larger, spherical ablation volumes with short application duration for hepatocellular carcinoma (HCC). Materials and methods Twenty-two patients (M:F = 17:5, median age 69.6 year, range 63–88) with 28 HCCs due to HCV + liver cirrhosis underwent RFA. 20/28 (71.4%) were tumors ≤3cm diameter, and 8/28 (28.6%) ranged from 3.2 to 4.2 cm. RF was applied using up to 2500mA via an optimized pulsing algorithm with real-time ultrasound monitoring to detect hyperechogenic changes. Single insertions of an internally cooled electrode were performed using exposed tips of 2 or 3 cm for 13 HCCs and 4 cm for 15 HCCs. All patients were followed-up for a minimum of 5 years with contrast-enhanced computed tomography (CECT). Results Technical success was achieved without adverse events in all cases. The mean ablation time was 8.5 ± 2.6 min. In 21/28 (75%), ablation duration ranged from 3 to 9 min, with 12 min duration applied in only 7/28 (25%). Mean coagulation diameters were 2.4 ± 0.14, 3.3 ± 0.62, and 4.4 ± 1.0, for 2, 3 and 4 cm electrodes, respectively (p 3 cm tumors developed local progression. One patient had multifocal disease with no local progression. Conclusion Efficient delivery of RF energy can considerably decrease the ablation time in many instances while achieving larger, relatively spherical, and reproducible areas of ablation with extremely low rates of local tumor progression and adverse events

A novel software platform for volumetric assessment of ablation completeness

Purpose: To retrospectively evaluate the accuracy of a novel software platform for assessing completeness of percutaneous thermal ablations. Materials & methods: Ninety hepatocellular carcinomas (HCCs) in 50 patients receiving percutaneous ultrasound-guided microwave ablation (MWA) that resulted in apparent technical success at 24-h post-ablation computed tomography (CT) and with ≥1-year imaging follow-up were randomly selected from a 320 HCC ablation database (2010–2016). Using a novel volumetric registration software, pre-ablation CT volumes of the HCCs without and with the addition of a 5 mm safety margin, and corresponding post-ablation necrosis volumes were segmented, co-registered and overlapped. These were compared to visual side-by-side inspection of axial images. Results: At 1-year follow-up, CT showed absence of local tumor progression (LTP) in 69/90 (76.7%) cases and LTP in 21/90 (23.3%). For HCCs classified by the software as "incomplete tumor treatments", LTP developed in 13/17 (76.5%) and all 13 (100%) of these LTPs occurred exactly where residual non-ablated tumor was identified by retrospective software analysis. HCCs classified as "complete ablation with <100% 5 mm ablative margins" had LTP in 8/49 (16.3%), while none of 24 HCCs with "complete ablation including 100% 5 mm ablative margins" had LTP. Differences in LTP between both partially ablated HCCs vs completely ablated HCCs, and ablated HCCs with <100% vs with 100% 5 mm margins were statistically significant (p < .0001 and p = .036, respectively). Thus, 13/21 (61.9%) incomplete tumor treatments could have been detected immediately, were the software available at the time of ablation. Conclusions: A novel software platform for volumetric assessment of ablation completeness may increase the detection of incompletely ablated tumors, thereby holding the potential to avoid subsequent recurrences

Candidate biomarkers from the integration of methylation and gene expression in discordant autistic sibling pairs

While the genetics of autism spectrum disorders (ASD) has been intensively studied, resulting in the identification of over 100 putative risk genes, the epigenetics of ASD has received less attention, and results have been inconsistent across studies. We aimed to investigate the contribution of DNA methylation (DNAm) to the risk of ASD and identify candidate biomarkers arising from the interaction of epigenetic mechanisms with genotype, gene expression, and cellular proportions. We performed DNAm differential analysis using whole blood samples from 75 discordant sibling pairs of the Italian Autism Network collection and estimated their cellular composition. We studied the correlation between DNAm and gene expression accounting for the potential effects of different genotypes on DNAm. We showed that the proportion of NK cells was significantly reduced in ASD siblings suggesting an imbalance in their immune system. We identified differentially methylated regions (DMRs) involved in neurogenesis and synaptic organization. Among candidate loci for ASD, we detected a DMR mapping to CLEC11A (neighboring SHANK1) where DNAm and gene expression were significantly and negatively correlated, independently from genotype effects. As reported in previous studies, we confirmed the involvement of immune functions in the pathophysiology of ASD. Notwithstanding the complexity of the disorder, suitable biomarkers such as CLEC11A and its neighbor SHANK1 can be discovered using integrative analyses even with peripheral tissues