The adjoint representation inside the exterior algebra of a simple Lie algebra

For a simple complex Lie algebra $\mathfrak g$ we study the space of invariants $A=\left( \bigwedge \mathfrak g^*\otimes\mathfrak g^*\right)^{\mathfrak g}$, (which describes the isotypic component of type $\mathfrak g$ in $\bigwedge \mathfrak g^*$) as a module over the algebra of invariants $\left(\bigwedge \mathfrak g^*\right)^{\mathfrak g}$. As main result we prove that $A$ is a free module, of rank twice the rank of $\mathfrak g$, over the exterior algebra generated by all primitive invariants in $(\bigwedge \mathfrak g^*)^{\mathfrak g}$, with the exception of the one of highest degree.Comment: Final version. More misprints corrected. To appear in Advances in Mathematic

On special covariants in the exterior algebra of a simple Lie algebra

We study the subspace of the exterior algebra of a simple complex Lie algebra linearly spanned by the copies of the little adjoint representation or, in the case of the Lie algebra of traceless matrices, by the copies of the n-th symmetric power of the defining representation. As main result we prove that this subspace is a free module over the subalgebra of the exterior algebra generated by all primitive invariants except the one of highest degree.Comment: Latex file, 11 pages, Final version, appeared in "Rendiconti Lincei - Matematica e Applicazioni

Extreme transport of light in spheroids of tumor cells

Extreme waves are intense and unexpected wavepackets ubiquitous in complex systems. In optics, these rogue waves are promising as robust and noise-resistant beams for probing and manipulating the underlying material. Localizing large optical power is crucial especially in biomedical systems, where, however, extremely intense beams have not yet been observed. We here discover that tumor-cell spheroids manifest optical rogue waves when illuminated by randomly modulated laser beams. The intensity of light transmitted through bio-printed three-dimensional tumor models follows a signature Weibull statistical distribution, where extreme events correspond to spatially-localized optical modes propagating within the cell network. Experiments varying the input beam power and size indicate that the rogue waves have a nonlinear origin. We show that these nonlinear optical filaments form high-transmission channels with enhanced transmission. They deliver large optical power through the tumor spheroid, and can be exploited to achieve a local temperature increase controlled by the input wave shape. Our findings shed light on optical propagation in biological aggregates and demonstrate how nonlinear extreme event formation allows light concentration in deep tissues, paving the way to using rogue waves in biomedical applications, such as light-activated therapies

Peri-implant diseases and systemic inflammation: A preliminary analysis from a cross-sectional survey of patients with hypertension

Background: The aim of this study was to investigate the association between peri-implant diseases and systemic inflammation assessed by serum C-reactive protein (CRP) levels in a sample of patients with hypertension. Methods: A total of 151 participants with hypertension were included in a cross-sectional study. The population was divided into six groups according to their peri-implant and periodontal status (healthy controls, mucositis, peri-implantitis, periodontitis, periodontitis and mucositis, periodontitis, and peri-implantitis). Linear, logistic regression, and correlation analyses were performed. Results: CRP levels were statistically significantly higher in participants with periodontitis alone (median 3.2 mg/L, interquartile range [IQR] 1.8, p = 0.012), combined with mucositis (3.10 mg/L, IQR 2.35, p < 0.001) or peri-implantitis (2.7 mg/L, IQR 2.53, p = 0.002) when compared to the healthy controls (1 mg/L, IQR 1.2). This association was independent of age, sex, smoking status, and adiposity differences. Participants with periodontitis with and without peri-implant diseases had the greatest odds of exhibiting CRP > 3 mg/L (odds ratio = 7.3, 95% confidence interval 1.6-33.9). Conclusions: Peri-implant diseases are associated with systemic inflammation, but the nature of the association should be further investigated

Primary Pulmonary Epithelioid Hemangioendothelioma: A Rare Cause of PET-Negative Pulmonary Nodules

We report here a case of primary pulmonary epithelioid hemangioendothelioma diagnosed in a 67-year-old Caucasian man, presenting with exertion dyspnoea, dry cough, and multiple bilateral pulmonary nodules revealed by computed tomography. At the 18F-fluorodeoxyglucose positron emission tomography, these nodules were negative. The histopathological diagnosis was made on a pulmonary wedge resection (performed during video-thoracoscopic surgery)

Association between subclinical atherosclerosis and oral inflammation: a cross-sectional study

Background: The aim of this cross-sectional study was to investigate the association between carotid intima-media thickness (c-IMT) values and periodontal and peri-implant diseases in a sample of patients with hypertension. Methods: A total of 151 participants with presence of at least one dental implant in function for >5 years were recruited. Anthropometric measurements, 24-h ambulatory blood pressure monitoring, ultrasound assessment of carotid arteries (c-IMT and presence of plaque) were recorded and venous blood samples obtained. An oral examination was performed by calibrated examiners to ascertain prevalence and severity of periodontal and peri-implant diseases. Binomial logistic regression was performed to investigate the potential association between various measures of exposure of dental diseases and predictors of cardiovascular risk (c-IMT > 0.9 mm and presence of plaque or their combination). Results: Diagnosis of periodontitis (OR 6.71, 95% CI: 2.68-16.76, P < 0.001), cumulative mucosal/gingival inflammation (Periodontal Screening and Recording score) (OR 1.25, 95% CI:1.12-1.41, P < 0.001), and mucositis (OR 3.34, 95% CI:1.13-9.85, P < 0.05) were associated with c-IMT > 0.9 mm and/or plaque presence independent of age, sex, smoking, 24 h systolic blood pressure and body mass index differences. No statistically significant results were noted for peri-implantitis. Linear regression models confirmed a positive association of cumulative mucosal/gingival inflammation (β = 0.011, SE 0.002, P < 0.001), diagnosis of periodontitis (β = 0.114, SE 0.020, P < 0.001), and peri-implant diseases (β = 0.011, SE 0.002, P < 0.001) with increased c-IMT values. Conclusions: This study confirms a positive association between mucosal/gingival inflammation and subclinical atherosclerosis assessed by c-IMT values and the presence of carotid plaque in patients with hypertension, independent of traditional cardiovascular risk factors. Future studies are needed to further characterize this relationship

The management of patients with inflammatory bowel disease-associated spondyloarthritis: Italian Group for the Study of Inflammatory Bowel Disease (IG-IBD) and Italian Society of Rheumatology (SIR) recommendations based on a pseudo-Delphi consensus

Spondyloarthritis (SpA) is the most frequent extraintestinal manifestation in patients with inflammatory bowel diseases (IBD). When IBD and spondyloarthritis coexist, musculoskeletal and intestinal disease features should be considered when planning a therapeutic strategy. Treatment options for IBD and SpA have expanded enormously over the last few years, but randomized controlled trials with specific endpoints focused on SpA are not available in the IBD setting. To address this important clinical topic, the Italian Group for the Study of Inflammatory Bowel Disease (IG-IBD) and the Italian Society of Rheumatology (SIR) jointly planned to draw updated therapeutic recommendations for IBD-associated SpA using a pseudo -Delphi method. This document presents the official recommendations of IG-IBD and SIR on the management of IBD-associated SpA in the form of 34 statements and 4 therapeutic algorithms. It is intended to be a reference guide for gastroenterologists and rheumatologists dealing with IBD-associated SpA

Impact of COVID-19 Pandemic on Surgical Breast Cancer Patients Undergoing Neoadjuvant Therapy: A Multicentric Study

Background/Aim: Due to the SARS-CoV-2 pandemic, many scientific committees proposed neoadjuvant therapy (NACT) bridging treatment as a novel strategy and indication. The aim of the study was to evaluate the impact of COVID-19 pandemic on breast cancer patients undergoing NACT. Patients and Methods: All breast cancer patients referred to two Breast Units during COVID-19-pandemic were enrolled. Results: Out of 814 patients, 43(5.3%) were enrolled in the COVID-19-group and compared with 94 (7.9%) similar Pre-COVID-19 patients. We observed a reduction in the number of patients undergoing NACT, p=0.0019. No difference was reported in terms of clinical presentation, indications, and tumor response. In contrast, a higher number of vascular adverse events was reported (6.9% vs. 0% p=0.029). Immediate breast cancer reconstructions following invasive surgery suffered a significant slowdown (5.9% vs. 47.7%, p=0.019). Conclusion: COVID-19 caused a reduction in the number of patients undergoing NACT, with no changes in terms of indications, clinical presentation, and tumor response. Furthermore, there was an increased incidence of vascular events

Use of biologics for the management of Crohn's disease: IG-IBD clinical guidelines based on the GRADE methodology

A cure for Crohn's disease (CD), a chronic inflammatory disease of the gastrointestinal tract of unknown etiology, is not available, so patients require lifelong management to keep inflammation under control. The therapeutic armamentarium has expanded with approval of several biological drugs, including in-fliximab, adalimumab, vedolizumab and ustekinumab - monoclonal antibodies that target different in-flammatory pathways - and darvadstrocel, a suspension of expanded human allogeneic, adipose-derived, mesenchymal stromal cells for the treatment of refractory complex perianal fistula. Notwithstanding ex-isting practice guidelines on medical therapy for CD, the Italian Group for the Study of Inflammatory Bowel Disease felt the need to issue new guidelines focused on the use of biologics for managing the intestinal manifestations of CD and based on the GRADE methodology. This document presents recom-mendations regarding six clinical settings, from the induction to the maintenance of clinical remission, and from optimization and de-escalation of treatments to dealing with perianal CD and post-operative recurrence. The 19 evidence-based statements are supported by information on the quality of the evi-dence, agreement rate among panel members, and panel comments mainly based on evidence from real world studies