Stability of the Brascamp-Lieb constant and applications

We prove that the best constant in the general Brascamp-Lieb inequality is a locally bounded function of the underlying linear transformations. As applications we deduce certain very general Fourier restriction, Kakeya-type, and nonlinear variants of the Brascamp-Lieb inequality which have arisen recently in harmonic analysis

The role of the telomere bouquet in controlling spindle pole body composition in fission yeast meiosis

The telomere bouquet is a highly conserved structure specific to meiotic prophase in which the telomeres are gathered to a limited region of the nuclear periphery. In a number of organisms including fission yeast, the bouquet is tethered to the spindle pole body (SPB) or centrosome. The meiosis-specific factors Bqt1/Bqt2 function as a bridge to connect the telomere proteins Taz1/Rap1 to the SPB. Deletion of any of these elements disrupts the bouquet, leading to defective spindle formation and aberrant meiosis (Tomita and Cooper, 2007). The aim of this thesis was to determine the molecular basis for control of the meiotic spindle by the telomere bouquet. We asked the question: how does the meiotic SPB differ in the presence and absence of bouquet function? Using methods to quantify SPB component levels via fluorescence microscopy in live cells, we found that bouquet-defective strains show a slight elevation of the level of Pcp1, an SPB component, but such elevation is not enough to confer bouquet-mutant phenotypes in bouquet-proficient backgrounds. Indeed, our data suggest that in the absence of the bouquet, SPB duplication occurs properly and with normal timing. However, we observed that the separation of the duplicated SPBs is markedly abnormal, as the duplicated SPBs fail to remain apart and at least one of them often becomes dislodged from the nucleus. Moreover, the γ-tubulin complex fails to localise to both spindle poles. Hence, the duplicated SPBs fail to properly recruit the γ-tubulin complex. We thus investigated the molecular mechanism underlying control of γ-tubulin complex recruitment by the bouquet. Our findings allow us to propose a model that explains the different types of spindle defects seen in the absence of the bouquet

VELOCITY-BASED MODELING OF THE THERMAL LOAD FOR A FORMULA SAE’S DISK BRAKE SIMULATION

This paper proposes a methodology for the estimation of a disk brake’s thermal load based on its vehicle’s velocity, where this thermal load serves as an input for a numerical simulation. The load is estimated through a balance between variation in the mechanical energy of the vehicle and the energy dissipated via aerodynamic and rolling drag forces. The RS Racing UFRGS team provided the vehicle’s data and geometry, and the velocity data was taken from a real endurance competition. The thermal load thus calculated is then used as input for a 3D transient finite element model containing the disk and the wheel hub. The results are consistent with what is expected by the RS Racing UFRGS team. Based on the results of the 3D transient model, two more simplified analysis are viable: one in permanent regime, which achieves a temperature distribution within the oscillation presented on the transient model; and also a 2D analysis which can be made by the replacement of the wheel hub with an equivalent global heat transfer coefficient

On the nonlinear Brascamp-Lieb inequality

We prove a nonlinear variant of the general Brascamp-Lieb inequality. Instances of this inequality are quite prevalent in analysis, and we illustrate this with substantial applications in harmonic analysis and partial differential equations. Our proof consists of running an efficient, or "tight", induction on scales argument, which uses the existence of gaussian near-extremisers to the underlying linear Brascamp-Lieb inequality (Lieb's theorem) in a fundamental way. A key ingredient is an effective version of Lieb's theorem, which we establish via a careful analysis of near-minimisers of weighted sums of exponential functions.Comment: 29 pages. This article subsumes the results of arXiv:1801.05214. To appear in the Duke Mathematical Journa

AzeR, a transcriptional regulator that responds to azelaic acid in Pseudomonas nitroreducens

This is the final version. Available on open access from the Microbiology Society via the DOI in this recordAzelaic acid is a dicarboxylic acid that has recently been shown to play a role in plant-bacteria signalling and also occurs naturally in several cereals. Several bacteria have been reported to be able to utilize azelaic acid as a unique source of carbon and energy, including Pseudomonas nitroreducens. In this study, we utilize P. nitroreducens as a model organism to study bacterial degradation of and response to azelaic acid. We report genetic evidence of azelaic acid degradation and the identification of a transcriptional regulator that responds to azelaic acid in P. nitroreducens DSM 9128. Three mutants possessing transposons in genes of an acyl-CoA ligase, an acyl-CoA dehydrogenase and an isocitrate lyase display a deficient ability in growing in azelaic acid. Studies on transcriptional regulation of these genes resulted in the identification of an IclR family repressor that we designated as AzeR, which specifically responds to azelaic acid. A bioinformatics survey reveals that AzeR is confined to a few proteobacterial genera that are likely to be able to degrade and utilize azelaic acid as the sole source of carbon and energy

Struggling with COVID-19 in Adult Inborn Errors of Immunity Patients: A Case Series of Combination Therapy and Multiple Lines of Therapy for Selected Patients

Background: The SARS-CoV-2 infection is now a part of the everyday lives of immunocompromised patients, but the choice of treatment and the time of viral clearance can often be complex, exposing patients to possible complications. The role of the available antiviral and monoclonal therapies is a matter of debate, as are their effectiveness and potential related adverse effects. To date, in the literature, the amount of data on the use of combination therapies and on the multiple lines of anti-SARS-CoV-2 therapy available to the general population and especially to inborn error of immunity (IEI) patients is small. Methods: Here, we report a case series of five adult IEI patients managed as inpatients at three Italian IEI referral centers (Rome, Treviso, and Cagliari) treated with combination therapy or multiple therapeutic lines for SARS-CoV-2 infection, such as monoclonal antibodies (mAbs), antivirals, convalescent plasma (CP), mAbs plus antiviral, and CP combined with antiviral. Results: This study may support the use of combination therapy against SARS-CoV-2 in complicated IEI patients with predominant antibody deficiency and impaired vaccine response

A sharp <i>k</i>-plane Strichartz inequality for the Schrödinger equation

We prove that ‖ X ( | u | 2 ) ‖ L t , ℓ 3 ≤ C ‖ f ‖ L 2 ( R 2 ) 2 , \begin{equation*} \|X(|u|^2)\|_{L^3_{t,\ell }}\leq C\|f\|_{L^2(\mathbb {R}^2)}^2, \end{equation*} where u ( x , t ) u(x,t) is the solution to the linear time-dependent Schrödinger equation on R 2 \mathbb {R}^2 with initial datum f f and X X is the (spatial) X-ray transform on R 2 \mathbb {R}^2 . In particular, we identify the best constant C C and show that a datum f f is an extremiser if and only if it is a gaussian. We also establish bounds of this type in higher dimensions d d , where the X-ray transform is replaced by the k k -plane transform for any 1 ≤ k ≤ d − 1 1\leq k\leq d-1 . In the process we obtain sharp L 2 ( μ ) L^2(\mu ) bounds on Fourier extension operators associated with certain high-dimensional spheres involving measures μ \mu supported on natural “co- k k -planarity” sets.</p