Basic principles of mixed Virtual Element Methods Brezzi, F.; Falk, Richard S.; Donatella Marini, L.
ESAIM. Mathematical modelling and numerical analysis,
07/2014, Letnik:
48, Številka:
4
Journal Article
Recenzirano
Odprti dostop
The aim of this paper is to give a simple, introductory presentation of the extension of the Virtual Element Method to the discretization of H(div)-conforming vector fields (or, more generally, of (n ...− 1) − Cochains). As we shall see, the methods presented here can be seen as extensions of the so-called BDM family to deal with more general element geometries (such as polygons with an almost arbitrary geometry). For the sake of simplicity, we limit ourselves to the 2-dimensional case, with the aim of making the basic philosophy clear. However, we consider an arbitrary degree of accuracy k (the Virtual Element analogue of dealing with polynomials of arbitrary order in the Finite Element Framework).
Background
Aesthetically pleasing results and fast, uneventful recovery are highly desirable after rejuvenating ablative laser procedures. Wound dressings following ablative laser procedures should ...ideally improve and optimize the wound healing environment.
Objective
The purpose of this comparative split‐face, single‐blinded, prospective observational study was to assess the efficacy and acceptability of two primary wound dressings immediately after a full‐face fractional CO2 laser resurfacing procedure.
Methods
The assessments of an innovative film‐forming dressing called Stratacel (SC) vs spring thermal water + Vaseline (V+) were conducted after a standardized, single‐pass, full‐face ablative fractional CO2 laser skin resurfacing procedure. Clinical parameters, such as haemoglobin – HB; surface temperature – ST; micro‐textural modifications – MT; superficial melanin – M; intrafollicular porphyrins – P, were assessed at different phases of the healing process using standardized, non‐invasive technologies.
Results
Five female volunteers were enrolled in this inpatient, controlled pilot study. Most of the clinical parameters considered, including 3D surface texture analysis, revealed a better performance of SC vs. V+ during the early, more delicate phases of the healing process.
Conclusions
This preliminary study, even if performed on a small number of volunteers, confirmed a definite advantage of the tested semipermeable film‐forming formula (SC) over a more conventional postoperative skin care regime (V+). Clinical results could be explained by a better uniformity of distribution of SC over the micro‐irregularities induced by ablative fractional CO2 laser resurfacing. Its thin, semipermeable film might, in fact, act as an efficient, perfectly biocompatible, full contact, temporary skin barrier, able to protect extremely delicate healing surfaces from potential environmental irritations.
Equivalent projectors for virtual element methods Ahmad, B.; Alsaedi, A.; Brezzi, F. ...
Computers & mathematics with applications (1987),
September 2013, 2013-09-00, 20130901, Letnik:
66, Številka:
3
Journal Article
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In the original virtual element space with degree of accuracy k, projector operators in the H1-seminorm onto polynomials of degree ≤k can be easily computed. On the other hand, projections in the L2 ...norm are available only on polynomials of degree ≤k−2 (directly from the degrees of freedom). Here, we present a variant of the virtual element method that allows the exact computations of the L2 projections on all polynomials of degree ≤k. The interest of this construction is illustrated with some simple examples, including the construction of three-dimensional virtual elements, the treatment of lower-order terms, the treatment of the right-hand side, and the L2 error estimates.
Aesthetically pleasing results and fast, uneventful recovery are highly desirable after rejuvenating ablative laser procedures. Wound dressings following ablative laser procedures should ideally ...improve and optimize the wound healing environment.
The purpose of this comparative split-face, single-blinded, prospective observational study was to assess the efficacy and acceptability of two primary wound dressings immediately after a full-face fractional CO
laser resurfacing procedure.
The assessments of an innovative film-forming dressing called Stratacel (SC) vs spring thermal water + Vaseline (V+) were conducted after a standardized, single-pass, full-face ablative fractional CO
laser skin resurfacing procedure. Clinical parameters, such as haemoglobin - HB; surface temperature - ST; micro-textural modifications - MT; superficial melanin - M; intrafollicular porphyrins - P, were assessed at different phases of the healing process using standardized, non-invasive technologies.
Five female volunteers were enrolled in this inpatient, controlled pilot study. Most of the clinical parameters considered, including 3D surface texture analysis, revealed a better performance of SC vs. V+ during the early, more delicate phases of the healing process.
This preliminary study, even if performed on a small number of volunteers, confirmed a definite advantage of the tested semipermeable film-forming formula (SC) over a more conventional postoperative skin care regime (V+). Clinical results could be explained by a better uniformity of distribution of SC over the micro-irregularities induced by ablative fractional CO
laser resurfacing. Its thin, semipermeable film might, in fact, act as an efficient, perfectly biocompatible, full contact, temporary skin barrier, able to protect extremely delicate healing surfaces from potential environmental irritations.
Crystalline aquifers are layered systems in which the hydrogeological path of waters extends from highly weathered, shallow and porous rocks to poorly weathered, deep and fissured rocks. This varying ...hydrogeological setting influences the water chemistry in different ways. The paper aims to reconstruct the water-rock interaction process in these various environments starting from a solid reactant represented by an average granite rock and several waters from the shallow aquifer. Afterwards, the water-rock interaction processes occurring in the deep environment are reconstructed, varying the geochemical conditions (primary reactants, secondary mineral phases allowed to precipitate, fO2 and fCO2), with a special focus on fluoride (F-). The evolution from the F-poor, Ca-HCO3 facies to the F-rich, Na-HCO3 water type of high pH was simulated using reaction path modelling. The obtained results show that the theoretical evolution trends well reproduce both shallow and deep water samples providing detailed information on the behavior of fluoride and other relevant constituents (i.e., Na, K, Ca, Mg, SiO2). The performed model represents a flexible and powerful tool for environmental research, applicable in other areas hosting F-rich groundwater.
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•Reaction path modelling of granite dissolution in meteoric water•Water composition changes from shallow to deep aquifers based on environmental conditions.•In Ca-HCO3 waters the fluoride content is mainly due to the dissolution of Biotite.•The precipitation of calcite, coupled with the dissolution of fluorite causes an increase in fluoride in the Na- HCO3 waters.
Little is known about mechanisms of resistance to poly(adenosine diphosphate-ribose) polymerase inhibitors (PARPi) and platinum chemotherapy in patients with metastatic breast cancer and BRCA1/2 ...mutations. Further investigation of resistance in clinical cohorts may point to strategies to prevent or overcome treatment failure.
We obtained tumor biopsies from metastatic breast cancer patients with BRCA1/2 deficiency before and after acquired resistance to PARPi or platinum chemotherapy. Whole exome sequencing was carried out on each tumor, germline DNA, and circulating tumor DNA. Tumors underwent RNA sequencing, and immunohistochemical staining for RAD51 foci on tumor sections was carried out for functional assessment of intact homologous recombination (HR).
Pre- and post-resistance tumor samples were sequenced from eight patients (four with BRCA1 and four with BRCA2 mutation; four treated with PARPi and four with platinum). Following disease progression on DNA-damaging therapy, four patients (50%) acquired at least one somatic reversion alteration likely to result in functional BRCA1/2 protein detected by tumor or circulating tumor DNA sequencing. Two patients with germline BRCA1 deficiency acquired genomic alterations anticipated to restore HR through increased DNA end resection: loss of TP53BP1 in one patient and amplification of MRE11A in another. RAD51 foci were acquired post-resistance in all patients with genomic reversion, consistent with reconstitution of HR. All patients whose tumors demonstrated RAD51 foci post-resistance were intrinsically resistant to subsequent lines of DNA-damaging therapy.
Genomic reversion in BRCA1/2 was the most commonly observed mechanism of resistance, occurring in four of eight patients. Novel sequence alterations leading to increased DNA end resection were seen in two patients, and may be targetable for therapeutic benefit. The presence of RAD51 foci by immunohistochemistry was consistent with BRCA1/2 protein functional status from genomic data and predicted response to later DNA-damaging therapy, supporting RAD51 focus formation as a clinically useful biomarker.
•We analyzed mechanisms of resistance to PARP inhibitor/platinum chemotherapy in BRCA1/2-mutant metastatic breast cancer.•Genomic reversion to functional BRCA1/2 protein was identified in one-half of patients.•Up-regulation of DNA end resection was identified as a resistance mechanism in two additional patients.•RAD51 foci assessed by immunohistochemistry correlated with clinical response to PARP inhibitor/platinum.•RAD51 focus staining warrants further exploration as a biomarker for clinical use.
We discuss the application of virtual elements to linear elasticity problems, for both the compressible and the nearly incompressible case. Virtual elements are very close to mimetic finite ...differences (see, for linear elasticity, L. Beirão da Veiga, M2AN Math. Model. Numer. Anal., 44 (2010), pp. 231-250) and in particular to higher order mimetic finite differences. As such, they share the good features of being able to represent in an exact way certain physical properties (conservation, incompressibility, etc.) and of being applicable in very general geometries. The advantage of virtual elements is the ductility that easily allows high order accuracy and high order continuity.
We provide a framework for the analysis of a large class of discontinuous methods for second-order elliptic problems. It allows for the understanding and comparison of most of the discontinuous ...Galerkin methods that have been proposed over the past three decades for the numerical treatment of elliptic problems.
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