Can coercive formulations lead to fast and accurate solution of the Helmholtz equation?

A new, coercive formulation of the Helmholtz equation was introduced in [Moiola, Spence, SIAM Rev. 2014]. In this paper we investigate $h$-version Galerkin discretisations of this formulation, and the iterative solution of the resulting linear systems. We find that the coercive formulation behaves similarly to the standard formulation in terms of the pollution effect (i.e. to maintain accuracy as $k\to\infty$, $h$ must decrease with $k$ at the same rate as for the standard formulation). We prove $k$-explicit bounds on the number of GMRES iterations required to solve the linear system of the new formulation when it is preconditioned with a prescribed symmetric positive-definite matrix. Even though the number of iterations grows with $k$, these are the first such rigorous bounds on the number of GMRES iterations for a preconditioned formulation of the Helmholtz equation, where the preconditioner is a symmetric positive-definite matrix.Comment: 27 pages, 7 figure

Analysis of the internal electric fields of pristine ice crystals and aggregate snowflakes, and their effect on scattering

The discrete dipole approximation is used to explore the internal electric fields of plane-wave-illuminated ice particles, and analyse their differential scattering cross sections. The results are displayed for monocrystals and aggregates of size parameters x=2 and x=10. We show that the field is relatively uniform for x=2, but for monocrystals of x=10 there is a complex internal structure. For a hexagonal plate, this structure is a combination of two components: a "distorted" plane wave, with wavefronts aligned perpendicular to the incident wave close to the centre of the plate, and curved forward near the particle boundary; and a standing wave, internally reflected around the perimeter. The former is due to the transverse component of the field i.e., the component perpendicular to the incident wave, and the latter is due to the component parallel to the incident direction. Focussing of the field towards the forward side of the particle is observed. As the particle complexity is increased due to aggregation, the field becomes smoother and less focussing is seen. For complex aggregates, the individual monomers act independently of one another, suggesting simplified methods of calculating scattering from such particles. The influence of the internal fields on far-field scattering is explored. It is demonstrated that scattering in the forward and backward directions is dominated by the transverse component. The parallel component contributes to sidescattering, with its influence on total scattering decreasing with particle complexity. We propose that this is due to the inability of complex particles to maintain a standing wave, diminishing much of the sidescattering observed for monocrystals. Comparisons of the far-field scattering properties of complex aggregates using the discrete dipole and Rayleigh-Gans approximations are also presented for x=2 and x=10, along with results obtained using a soft sphere approximation

Implementation of an interior point source in the ultra weak variational formulation through source extraction

The Ultra Weak Variational Formulation (UWVF) is a powerful numerical method for the approximation of acoustic, elastic and electromagnetic waves in the time-harmonic regime. The use of Trefftz-type basis functions incorporates the known wave-like behaviour of the solution in the discrete space, allowing large reductions in the required number of degrees of freedom for a given accuracy, when compared to standard finite element methods. However, the UWVF is not well disposed to the accurate approximation of singular sources in the interior of the computational domain. We propose an adjustment to the UWVF for seismic imaging applications, which we call the Source Extraction UWVF. Differing fields are solved for in subdomains around the source, and matched on the inter-domain boundaries. Numerical results are presented for a domain of constant wavenumber and for a domain of varying sound speed in a model used for seismic imaging

Plane wave discontinuous Galerkin methods: exponential convergence of the hp-version

We consider the two-dimensional Helmholtz equation with constant coefficients on a domain with piecewise analytic boundary, modelling the scattering of acoustic waves at a sound-soft obstacle. Our discretisation relies on the Trefftz-discontinuous Galerkin approach with plane wave basis functions on meshes with very general element shapes, geometrically graded towards domain corners. We prove exponential convergence of the discrete solution in terms of number of unknowns

The amount of preoperative endometrial tissue surface in relation to final endometrial cancer classification

Diagnosis; Endometrial carcinoma; Endometrial samplingDiagnóstico; Carcinoma de endometrio; Muestreo endometrialDiagnòstic; Carcinoma endometrial; Mostreig endometrialObjective To evaluate whether the amount of preoperative endometrial tissue surface is related to the degree of concordance with final low- and high-grade endometrial cancer (EC). In addition, to determine whether discordance is influenced by sampling method and impacts outcome. Methods A retrospective cohort study within the European Network for Individualized Treatment of Endometrial Cancer (ENITEC). Surface of preoperative endometrial tissue samples was digitally calculated using ImageJ. Tumor samples were classified into low-grade (grade 1–2 endometrioid EC (EEC)) and high-grade (grade 3 EEC + non-endometroid EC). Results The study cohort included 573 tumor samples. Overall concordance between pre- and postoperative diagnosis was 60.0%, and 88.8% when classified into low- and high-grade EC. Upgrading (preoperative low-grade, postoperative high-grade EC) was found in 7.8% and downgrading (preoperative high-grade, postoperative low-grade EC) in 26.7%. The median endometrial tissue surface was significantly lower in concordant diagnoses when compared to discordant diagnoses, respectively 18.7 mm2 and 23.5 mm2 (P = 0.022). Sampling method did not influence the concordance in tumor classification. Patients with preoperative high-grade and postoperative low-grade showed significant lower DSS compared to patients with concordant low-grade EC (P = 0.039). Conclusion The amount of preoperative endometrial tissue surface was inversely related to the degree of concordance with final tumor low- and high-grade. Obtaining higher amount of preoperative endometrial tissue surface does not increase the concordance between pre- and postoperative low- and high-grade diagnosis in EC. Awareness of clinically relevant down- and upgrading is crucial to reduce subsequent over- or undertreatment with impact on outcome

Safety and efficacy of natalizumab in children with multiple sclerosis.

OBJECTIVE: To describe the effect of natalizumab in the treatment of subjects with active multiple sclerosis (MS) treated before the age of 18 years. METHODS: Nineteen pediatric subjects with MS (mean age 14.6 +/- 2.2 years, mean number of attacks 5.2 +/- 1.9 during the pretreatment phase of 27.7 +/- 19.7 months, median pretreatment Expanded Disability Status Scale score [EDSS] 2.5, range 1.0-5.0) were treated with natalizumab at the dose of 300 mg every 28 days. After treatment initiation, patients were reassessed clinically every month; brain MRI was performed at baseline and every 6 months. RESULTS: Patients received a median number of 15 infusions (range 6-26). A transient reversible worsening of preexisting symptoms occurred in 1 subject during and following the first infusion. All the patients remained relapse-free during the whole follow-up. The median EDSS decreased from 2.5 to 2.0 at the last visit (p < 0.001). EDSS remained stable in 5 cases, decreased by at least 0.5 point in 6 cases, and decreased by at least 1 point in 8 cases. At baseline, the mean number of gadolinium-enhancing lesions was 4.1 (range 1-20). During the follow-up, no gadolinium-enhancing lesions were detected (p = 0.008); 3 patients developed new T2-visible lesions at month 6 scan but the overall number of T2 lesions remained stable during the subsequent follow-up. Transient and mild side effects occurred in 8 patients. CONCLUSIONS: Natalizumab was well-tolerated in all subjects. A strong suppression of disease activity was observed in all subjects during the follow-up. Classification of evidence: This study provides Class IV evidence that natalizumab, 300 mg IV once every 28 days, decreased EDSS scores in pediatric patients with MS over a mean treatment period of 15.2 months

Immunohistochemical biomarkers are prognostic relevant in addition to the ESMO-ESGO-ESTRO risk classification in endometrial cancer

Endometrial carcinoma; Immunohistochemistry; OutcomeCarcinoma de endometrio; Inmunohistoquímica; ResultadoCarcinoma d'endometri; Immunohistoquímica; ResultatObjective Pre-operative immunohistochemical (IHC) biomarkers are not incorporated in endometrial cancer (EC) risk classification. We aim to investigate the added prognostic relevance of IHC biomarkers to the ESMO-ESGO-ESTRO risk classification and lymph node (LN) status in EC. Methods Retrospective multicenter study within the European Network for Individualized Treatment of Endometrial Cancer (ENITEC), analyzing pre-operative IHC expression of p53, L1 cell-adhesion molecule (L1CAM), estrogen receptor (ER) and progesterone receptor (PR), and relate to ESMO-ESGO-ESTRO risk groups, LN status and outcome. Results A total of 763 EC patients were included with a median follow-up of 5.5-years. Abnormal IHC expression was present for p53 in 112 (14.7%), L1CAM in 79 (10.4%), ER- in 76 (10.0%), and PR- in 138 (18.1%) patients. Abnormal expression of p53/L1CAM/ER/PR was significantly related with higher risk classification groups, and combined associated with the worst outcome within the ‘high and advanced/metastatic’ risk group. In multivariate analysis p53-abn, ER/PR- and ESMO-ESGO-ESTRO ‘high and advanced/metastatic’ were independently associated with reduced disease-specific survival (DSS). Patients with abnormal IHC expression and lymph node metastasis (LNM) had the worst outcome. Patients with LNM and normal IHC expression had comparable outcome with patients without LNM and abnormal IHC expression. Conclusion The use of pre-operative IHC biomarkers has important prognostic relevance in addition to the ESMO-ESGO-ESTRO risk classification and in addition to LN status. For daily clinical practice, p53/L1CAM/ER/PR expression could serve as indicator for surgical staging and refine selective adjuvant treatment by incorporation into the ESMO-ESGO-ESTRO risk classification

Disease-Modifying Therapies and Coronavirus Disease 2019 Severity in Multiple Sclerosis

Objective: This study was undertaken to assess the impact of immunosuppressive and immunomodulatory therapies on the severity of coronavirus disease 2019 (COVID-19) in people with multiple sclerosis (PwMS). Methods: We retrospectively collected data of PwMS with suspected or confirmed COVID-19. All the patients had complete follow-up to death or recovery. Severe COVID-19 was defined by a 3-level variable: mild disease not requiring hospitalization versus pneumonia or hospitalization versus intensive care unit (ICU) admission or death. We evaluated baseline characteristics and MS therapies associated with severe COVID-19 by multivariate and propensity score (PS)-weighted ordinal logistic models. Sensitivity analyses were run to confirm the results. Results: Of 844 PwMS with suspected (n = 565) or confirmed (n = 279) COVID-19, 13 (1.54%) died; 11 of them were in a progressive MS phase, and 8 were without any therapy. Thirty-eight (4.5%) were admitted to an ICU; 99 (11.7%) had radiologically documented pneumonia; 96 (11.4%) were hospitalized. After adjusting for region, age, sex, progressive MS course, Expanded Disability Status Scale, disease duration, body mass index, comorbidities, and recent methylprednisolone use, therapy with an anti-CD20 agent (ocrelizumab or rituximab) was significantly associated (odds ratio [OR] = 2.37, 95% confidence interval [CI] = 1.18–4.74, p = 0.015) with increased risk of severe COVID-19. Recent use (&lt;1 month) of methylprednisolone was also associated with a worse outcome (OR = 5.24, 95% CI = 2.20–12.53, p = 0.001). Results were confirmed by the PS-weighted analysis and by all the sensitivity analyses. Interpretation: This study showed an acceptable level of safety of therapies with a broad array of mechanisms of action. However, some specific elements of risk emerged. These will need to be considered while the COVID-19 pandemic persists. ANN NEUROL 2021