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A sharp quantitative version of the anisotropic isoperimetric inequality is established, corresponding to a stability estimate for the Wulff shape of a given surface tension energy. This is achieved by exploiting mass transportation theory, especially Gromov’s proof of the isoperimetric inequality and the Brenier-McCann Theorem. A sharp quantitative version of the Brunn-Minkowski inequality for convex sets is proved as a corollary.

Providing stable and clean energy sources is a necessity for the increasing demands of humanity. Energy produced by Deuterium (D) and Tritium (T) fusion reactions, in particular in tokamaks, is a promising path towards that goal. However, there is little experience with plasmas formed by D-T mixtures, since most of the experiments are currently performed in pure D. After more than 20 years, the Joint European Torus (JET) has carried out new D-T experiments with the aim of exploring some of the unique characteristics expected in future fusion reactors, such as the presence of highly energetic ions in low plasma rotation conditions. A new stable, high confinement and impurity-free D-T regime, with reduction of energy losses with respect to D, has been found. Multiscale physics mechanisms critically determine the thermal confinement. These crucial achievements importantly contribute to the establishment of fusion energy generation as an alternative to fossil fuels. The use of clean energy sources is essential for the humankind. Here, authors show new experiments carried out with Deuterium-Tritium fusion reactions. Results show that energy production by such reactions can be more efficient than expected, confirming fusion as an alternative to fossil fuels.

A quantitative sharp form of the classical isoperimetric inequality is proved, thus giving a positive answer to a conjecture by Hall.

Local volume-constrained minimizers in anisotropic capillarity problems develop free boundaries on the walls of their containers. We prove the regularity of the free boundary outside a closed negligible set, showing in particular the validity of Young’s law at almost every point of the free boundary. Our regularity results are not specific to capillarity problems, and actually apply to sets of finite perimeter (and thus to codimension one integer rectifiable currents) arising as minimizers in other variational problems with free boundaries.

The immune response after SARS-CoV-2 vaccine administration appears to be characterized by high inter-individual variation, even in SARS-CoV-2 positive subjects, who could have experienced different post-infection, unresolved conditions. We monitored anti-SARS-CoV-2 IgG levels and kinetics along with circulating biomarkers in a cohort of 175 healthcare workers during early immunization with COVID-19 mRNA-LNP BNT162b2 vaccine, to identify the associated factors. Subjects with a previous SARS-CoV-2 infection were characterized by higher BMI and CRP levels and lower neutrophil count with respect to naïve subjects. Baseline IgG levels resulted associated with CRP independently on BMI and inflammatory diseases. Among 137 subjects undergoing vaccination and monitored after the first and the second dose, three kinetic patterns were identified. The pattern showing a rapid growth was characterized by higher IgG levels at baseline and higher CRP and MCHC levels than negative subjects. Subjects previously exposed to SARS-CoV-2 showed higher levels of CRP, suggesting persistence of unresolved inflammation. These levels are the main determinant of IgG levels at baseline and characterized subjects belonging to the best performing, post-vaccine antibody kinetic pattern.

We consider liquid drops or crystals lying in equilibrium under the action of a potential energy. For small masses, the proximity of the resulting minimizers from the Wulff shape associated to the surface tension is quantitatively controlled in terms of the smallness of the mass and with respect to the natural notions of distance induced by the regularity of the Wulff shape. Stronger results are proved in the two-dimensional case. For instance, it is shown that a planar crystal undergoing the action of a small exterior force field remains convex and admits only small translations parallel to its faces.

Our work targets mapping of pesticides application rates within the European Union at a 250 m spatial resolution. Source data include global estimates of pesticide inputs, high resolution crop maps and pesticide usage reported by EUROSTAT official figures. Previously published global pesticide application rates in PEST-CHEMGRIDS are used as first guess estimates. These are then adjusted using a calibration dataset gathered from pesticide use in agriculture. The estimation of the applied mass by country and crop type is then combined with high resolution crop maps. The procedure explicitly accounts for data quality and uncertainty through a Maximum Likelihood estimation procedure. This data product features detailed spatial distributions of pesticide inputs, facilitating evaluation of pesticide fate and transport, biogeochemical transformations as well as environmental risk assessment.

The isotope dependence of plasma transport will have a significant impact on the performance of future D-T experiments in JET and ITER and eventually on the fusion gain and economics of future reactors. In preparation for future D-T operation on JET, dedicated experiments and comprehensive transport analyses were performed in H, D and H-D mixed plasmas. The analysis of the data has demonstrated an unexpectedly strong and favourable dependence of the global confinement of energy, momentum and particles in ELMy H-mode plasmas on the atomic mass of the main ion species, the energy confinement time scaling as ${\\tau _E}\\sim {A^{0.5}}$ (Maggi et al., Plasma Phys. Control. Fusion, vol. 60, 2018, 014045; JET Team, Nucl. Fusion, vol. 39, 1999, pp. 1227–1244), i.e. opposite to the expectations based only on local gyro-Bohm (GB) scaling, ${\\tau _E}\\sim {A^{ - 0.5}}$, and stronger than in the commonly used H-mode scaling for the energy confinement (Saibene et al., Nucl. Fusion, vol. 39, 1999, 1133; ITER Physics Basis, Nucl. Fusion, vol. 39, 1999, 2175). The scaling of momentum transport and particle confinement with isotope mass is very similar to that of energy transport. Nonlinear local GENE gyrokinetic analysis shows that the observed anti-GB heat flux is accounted for if collisions, E × B shear and plasma dilution with low-Z impurities (9Be) are included in the analysis (E and B are, respectively the electric and magnetic fields). For L-mode plasmas a weaker positive isotope scaling ${\\tau _E}\\sim {A^{0.14}}$ has been found in JET (Maggi et al., Plasma Phys. Control. Fusion, vol. 60, 2018, 014045), similar to ITER97-L scaling (Kaye et al., Nucl. Fusion, vol. 37, 1997, 1303). Flux-driven quasi-linear gyrofluid calculations using JETTO-TGLF in L-mode show that local GB scaling is not followed when stiff transport (as is generally the case for ion temperature gradient modes) is combined with an imposed boundary condition taken from the experiment, in this case predicting no isotope dependence. A dimensionless identity plasma pair in hydrogen and deuterium L-mode plasmas has demonstrated scale invariance, confirming that core transport physics is governed, as expected, by the 4 dimensionless parameters ρ*, ν*, β, q (normalised ion Larmor radius, collisionality, plasma pressure and safety factor) consistently with global quasi-linear gyrokinetic TGLF calculations (Maggi et al., Nucl. Fusion, vol. 59, 2019, 076028). We compare findings in JET with those in different devices and discuss the possible reasons for the different isotope scalings reported from different devices. The diversity of observations suggests that the differences may result not only from differences affecting the core, e.g. heating schemes, but are to a large part due to differences in device-specific edge and wall conditions, pointing to the importance of better understanding and controlling pedestal and edge processes.

Background:After Sars-CoV-2 outbreak, considering its high mortality and diffusiveness, a mass worldwide vaccination campaign was put in place. Some groups of patients were prioritized in this process. Among them, Systemic Lupus Erythematosus (SLE) ones were considered at high risk of death from COVID-19, especially due to the immunosuppressive (Is) drugs administered. Moreover, at vaccines release there was a complete absence of efficacy and safety data in patients with autoimmune diseases, since phase III trials of most vaccines excluded subjects on Is drugs.Objectives:To assess the impact of Is drugs on BNT162b2 mRNA vaccine’s immunogenicity and safety in SLE patients.Methods:This is a prospective real-life study on consecutively enrolled SLE patients conducted between March 2022 and January 2023. Inclusion criteria: age > 18 and < 70 years, SLE diagnosis (according to EULAR/ACR 2019 criteria) prior to SarS-CoV-2 outbreak, vaccination with 3 doses of BNT162b2 vaccine. Exclusion criteria: high disease activity (SLEDAI-2K >10) or ongoing disease flare at inclusion, treatment with Rituximab or intravenous Immunoglobulins in the last 12 or 2 months respectively. Patients were enrolled 7 days after their 3rd vaccine shot (T0) when demographic and clinical data as well as ongoing therapies (Table 1) were collected, along with eventual adverse events. 6 months (T1) and 12 months (T2) after their 3rd dose, humoral and cellular immune responses were evaluated (both qualitatively and quantitatively). The former analysing anti-receptor binding domain (RBD) IgG antibodies (Ab) with an immunoassay analyser and neutralizing (Neu) Ab through a microneutralization assay. The latter was evaluated analysing interferon (IFN)γ release using an enzyme-linked immunosorbent assay after stimulating whole blood with Sars-CoV-2 peptides.Then, patients were divided in two groups based on therapy at vaccination:-Is: patients receiving an Is drug, including prednisone at dosage higher than 5mg/day, regardless of concomitant Hydroxychloroquine (HCQ) therapy-Non-Is: patients not receiving any Is drugs (i.e. HCQ or prednisone (lower than 5mg/day) alone or in combination; patients not receiving any drug for SLE)The two groups were then compared to establish the influence of eventual Is drugs on immune response after a full vaccination cycle.Results:51 patients were enrolled at T0 (Table 1). Comparing the two groups, no differences emerged for either demographic or clinical parameters, apart for a higher number of SarS-CoV-2 infections in the Non-Is group (p<0.0001). Equally, local and systemic adverse events did not differ among the groups and no life-threatening events were registered. Regarding immune response (Table 2), all patients were available at T1 follow-up visit. 47 (92.2%) showed anti-RBD Ab and 25 (49%) Neu Ab; cellular response was detectable in 43 (84.3%) subjects. The only significant difference regarded Neu Ab, which resulted higher in the Non-Is group both qualitatively (p=0.02) and quantitatively (p=0.02). 28 patients (54.9%) returned at T2. Anti-RBD Ab were still present in 26 patients (92.8%), while Neu Ab in 20 (71.4%). Cellular response was detectable in 25 (89.3%) patients. Both for humoral and cellular response, no significant difference was detectable comparing the two groups Is and Non-Is patients. Lastly, a significant correlation was found between anti-RBD Ab and both Neu Ab and cellular response (data not shown) both at T1 (p<0.001 and =0.002, respectively) and T2 (p<0.001 and =0.005, respectively).Conclusion:Anti-SarS-CoV-2 BNT162b2 mRNA vaccine can induce a persistent immune response in SLE patients while being safe and well tolerated. In fact, even in patients on Is therapy, immune response can be retrieved 1 year after its administration – without being influenced by Is therapies at vaccination. Indeed, Is therapy reduced Neu Ab production without otherwise interfering with the other immune response components. Moreover, whilst no life-threatening events were registered, Is therapies were not associated with adverse events onset.REFERENCES:[1] Aiello A. (2021) Int J Infect Dis, 106:338.[2] Tan SY. (2023) Rheumatology (Oxford), 62(5): 1757.Acknowledgements:NIL.Disclosure of Interests:None declared.

Given a smooth, radial, uniformly log-convex density e V on , n ≥ 2, we characterize isoperimetric sets E with respect to weighted perimeter and weighted volume m = ∫ E e V as balls centered at the origin, provided for some (potentially computable) m 0 >0; this affirmatively answers conjecture (Rosales et al. Calc Var Part Differ Equat 31(1):27–46, 2008 , Conjecture 3.12) for such values of the weighted volume parameter. We also prove that the set of weighted volumes such that this characterization holds true is open, thus reducing the proof of the full conjecture to excluding the possibility of bifurcation values of the weighted volume parameter. Finally, we show the validity of the conjecture when V belongs to a C 2 -neighborhood of c | x | 2 ( c > 0).