The eigenvalue problem for the ∞-Bilaplacian

We consider the problem of finding and describing minimisers of the Rayleigh quotient Λ∞:=infu∈W2,∞(Ω)∖{0}∥Δu∥L∞(Ω)∥u∥L∞(Ω), Λ∞:=infu∈W2,∞(Ω)∖{0}‖Δu‖L∞(Ω)‖u‖L∞(Ω), where Ω⊆RnΩ⊆Rn is a bounded C1,1C1,1 domain and W2,∞(Ω)W2,∞(Ω) is a class of weakly twice differentiable functions satisfying either u=0u=0 on ∂Ω∂Ω or u=|Du|=0u=|Du|=0 on ∂Ω∂Ω . Our first main result, obtained through approximation by LpLp -problems as p→∞p→∞ , is the existence of a minimiser u∞∈W2,∞(Ω)u∞∈W2,∞(Ω) satisfying {Δu∞∈Λ∞Sgn(f∞)Δf∞=μ∞ a.e. in Ω, in D′(Ω), {Δu∞∈Λ∞Sgn(f∞) a.e. in Ω,Δf∞=μ∞ in D′(Ω), for some f∞∈L1(Ω)∩BVloc(Ω)f∞∈L1(Ω)∩BVloc(Ω) and a measure μ∞∈M(Ω)μ∞∈M(Ω) , for either choice of boundary conditions. Here Sgn is the multi-valued sign function. We also study the dependence of the eigenvalue Λ∞Λ∞ on the domain, establishing the validity of a Faber–Krahn type inequality: among all C1,1C1,1 domains with fixed measure, the ball is a strict minimiser of Ω↦Λ∞(Ω)Ω↦Λ∞(Ω) . This result is shown to hold true for either choice of boundary conditions and in every dimension

Open issues in mucopolysaccharidosis type I-hurler

Mucopolysaccharidosis I-Hurler (MPS I-H) is the most severe form of a metabolic genetic disease caused by mutations of IDUA gene encoding the lysosomal α-L-iduronidase enzyme. MPS I-H is a rare, life-threatening disease, evolving in multisystem morbidity including progressive neurological disease, upper airway obstruction, skeletal deformity and cardiomyopathy. Allogeneic hematopoietic stem cell transplantation (HSCT) is currently the gold standard for the treatment of MPS I-H in patients diagnosed and treated before 2-2.5 years of age, having a high rate of success. Beyond the child's age, other factors influence the probability of treatment success, including the selection of patients, of graft source and the donor type employed. Enzyme replacement therapy (ERT) with human recombinant laronidase has also been demonstrated to be effective in ameliorating the clinical conditions of pre-transplant MPS I-H patients and in improving HSCT outcome, by peri-transplant co-administration. Nevertheless the long-term clinical outcome even after successful HSCT varies considerably, with a persisting residual disease burden. Other strategies must then be considered to improve the outcome of these patients: one is to pursue early pre-symptomatic diagnosis through newborn screening and another one is the identification of novel treatments. In this perspective, even though newborn screening can be envisaged as a future attractive perspective, presently the best path to be pursued embraces an improved awareness of signs and symptoms of the disorder by primary care providers and pediatricians, in order for the patients' timely referral to a qualified reference center. Furthermore, sensitive new biochemical markers must be identified to better define the clinical severity of the disease at birth, to support clinical judgement during the follow-up and to compare the effects of the different therapies. A prolonged neuropsychological follow-up of post-transplant cognitive development of children and residual disease burden is needed. In this perspective, the reference center must guarantee a multidisciplinary follow-up with an expert team. Diagnostic and interventional protocols of reference centers should be standardized whenever possible to allow comparison of clinical data and evaluation of results. This review will focus on all these critical issues related to the management of MPS I-H

Proteomic profile of maternal-aged blastocoel fluid suggests a novel role for ubiquitin system in blastocyst quality

Purpose: The etiology of maternal aging, a common cause of female factor infertility and a rate-limiting step in vitro fertilization (IVF) success, remains still unclear. Proteomic changes responsible for the impaired successful pregnancy outcome after IVF with aged blastocysts have not been yet evaluated. The objective of this prospective study was to employ proteomic techniques and bioinformatic tools to enlight differences at the protein level in blastocoel fluid of aged and younger woman. Methods: Protein composition of human blastocoel fluid isolated by micromanipulation from 46 blastocysts of women aged <37 years (group A) and 29 of women aged 6537 years (group B) have been identified by a shotgun proteomic approach based on high-resolution nano-liquid chromatography electrospray-ionization-tandem mass spectrometry (nLC-ESI-MS/MS) using label free for the relative quantification of their expression levels. Results: The proteomic analysis leads to the identification and quantification of 148 proteins; 132 and 116 proteins were identified in groups A and B, respectively. Interestingly, the identified proteins are mainly involved in processes aimed at fine tuning embryo implantation and development. Among the 100 proteins commonly expressed in both groups, 17 proteins are upregulated and 44 downregulated in group B compared to group A. Overall, the analysis identified 33 proteins, which were increased or present only in B while 76 were decreased in B or present only in A. Conclusions: Data revealed that maternal aging mainly affects blastocyst survival and implantation through unbalancing the equilibrium of the ubiquitin system known to play a crucial role in fine-tuning several aspects required to ensure successful pregnancy outcome

Analyticity and criticality results for the eigenvalues of the biharmonic operator

We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove that balls are always critical domains under volume constraint.Comment: To appear on the proceedings of the conference "Geometric Properties for Parabolic and Elliptic PDE's - 4th Italian-Japanese Workshop" held in Palinuro (Italy), May 25-29, 201

Phase field approach to optimal packing problems and related Cheeger clusters

In a fixed domain of $\Bbb{R}^N$ we study the asymptotic behaviour of optimal clusters associated to $\alpha$-Cheeger constants and natural energies like the sum or maximum: we prove that, as the parameter $\alpha$ converges to the "critical" value $\Big (\frac{N-1}{N}\Big ) _+$, optimal Cheeger clusters converge to solutions of different packing problems for balls, depending on the energy under consideration. As well, we propose an efficient phase field approach based on a multiphase Gamma convergence result of Modica-Mortola type, in order to compute $\alpha$-Cheeger constants, optimal clusters and, as a consequence of the asymptotic result, optimal packings. Numerical experiments are carried over in two and three space dimensions

Registro de objetores de conciencia: implicancias de los derechos a la igualdad y a la protección de datos personales

El artículo analiza la constitucionalidad de una de las medidas reglamentarias del derecho a la objeción de conciencia: los registros de objetores de conciencia. Para ello, toma en cuenta las exigencias que plantean los principios de razonabilidad e igualdad, considerando bajo este último aspecto la denominada discriminación indirecta y la igualdad en el acceso a los cargos públicos. Asimismo, la cuestión también es abordada desde las disposiciones de la Ley argentina Nº 25.326, de protección de datos personales.This article discusses the constitutionality of one of the regulatory measures upon the right to conscientious objection: the registration of conscientious objectors. To this end, the requirements posed by the principles of reasonableness and equality are taken into account, considering under the latter the so–called indirect discrimination and equal access to public office. Moreover, the issue is also tackled considering the provisions of argentinian Personal Data Protection Law, Nº 25.326

Bempedoic acid in the management of lipid disorders and cardiovascular risk. 2023 position paper of the International Lipid Expert Panel (ILEP)

Cardiovascular disease (CVD) is a chronic non-communicable disease (NCD) and the predominant cause of morbidity and mortality worldwide. Substantial reductions in the CVD prevalence have been achieved in recent years by the attenuation of risk factors (particularly hypertension and dyslipidaemias) in primary and secondary prevention. Despite the remarkable success of lipid lowering treatments, and of statins in particular, in reducing the risk of CVD, there is still an unmet clinical need for the attainment of guideline lipid-targets in even 2/3 of patients. Bempedoic acid, the first in-class inhibitor of ATP-citrate lyase presents a new approach to lipid-lowering therapy. By reducing the endogenous production of cholesterol, upstream of the rate-limiting enzyme HMG-CoA-reductase, i.e., the target of statins, bempedoic acid reduces circulating plasma concentrations of low-density lipoprotein cholesterol (LDL-C), and major adverse CVD events (MACE). Bempedoic acid has the potential to contribute to the reduction of CVD risk not only as monotherapy, but even further as part of a lipid-lowering combination therapy with ezetimibe, reducing LDL-C cholesterol up to 40%. This position paper of the International Lipid Expert Panel (ILEP) summarises the recent evidence around the efficacy and safety of bempedoic acid and presents practical recommendations for its use, which complement the 'lower-is-better-for-longer' approach to lipid management, which is applied across international guidelines for the management of CVD risk. Practical evidence-based guidance is provided relating to the use of bempedoic acid in atherosclerotic CVD, familial hypercholesterolaemia, and statin intolerance. Although there are still no sufficient data avilable for the role of bempedoic acid in the primary prevention of CVD, its favourable effects on plasma glucose and inflammatory markers makes this drug a rational choice in the patient-centred care of specific groups of primary prevention

Intestinal PPARγ signalling is required for sympathetic nervous system activation in response to caloric restriction.

Nuclear receptor PPARγ has been proven to affect metabolism in multiple tissues, and has received considerable attention for its involvement in colon cancer and inflammatory disease. However, its role in intestinal metabolism has been largely ignored. To investigate this potential aspect of PPARγ function, we submitted intestinal epithelium-specific PPARγ knockout mice (iePPARγKO) to a two-week period of 25% caloric restriction (CR), following which iePPARγKO mice retained more fat than their wild type littermates. In attempting to explain this discrepancy, we analysed the liver, skeletal muscle, intestinal lipid trafficking, and the microbiome, none of which appeared to contribute to the adiposity phenotype. Interestingly, under conditions of CR, iePPARγKO mice failed to activate their sympathetic nervous system (SNS) and increase CR-specific locomotor activity. These KO mice also manifested a defective control of their body temperature, which was overly reduced. Furthermore, the white adipose tissue of iePPARγKO CR mice showed lower levels of both hormone-sensitive lipase, and its phosphorylated form. This would result from impaired SNS signalling and possibly cause reduced lipolysis. We conclude that intestinal epithelium PPARγ plays an essential role in increasing SNS activity under CR conditions, thereby contributing to energy mobilization during metabolically stressful episodes

Impact of long-term elosulfase alfa treatment on respiratory function in patients with Morquio A syndrome

OBJECTIVE: To present long-term respiratory function outcomes from an open-label, multi-center, phase 3 extension study (MOR-005) of elosulfase alfa enzyme replacement therapy (ERT) in patients with Morquio A syndrome. METHODS: In part 1 of MOR-005, patients initially randomized to ERT in the 24-week pivotal study (MOR-004) remained on their regimen (2.0 mg/kg/week or every other week); placebo patients were re-randomized to one of the two regimens. During part 2, all patients received elosulfase alfa 2.0 mg/kg/week. Respiratory function was one of the efficacy endpoints evaluated in MOR-005. Change from MOR-004 baseline to 120 weeks of treatment for the combined population was determined and compared with results from untreated patients from a Morquio A natural history study (MorCAP). RESULTS: Maximum voluntary ventilation (MVV) improved up to week 72 and then stabilized; forced vital capacity (FVC) and forced expiratory volume in 1 s (FEV1) increased continuously over 120 weeks. Mean increases in the modified per-protocol population was 9.2 % for FVC, 8.8 % for FEV1, and 6.1 % for MVV after 120 weeks. All patients ≤14 years showed respiratory improvements, presumably in part related to growth; however, these were greater in treated patients. For those >14 years, treated patients showed improvements, while deterioration occurred in untreated. Altogether, the improvements were significantly greater (P < 0.05) in treated patients. CONCLUSIONS: Long-term ERT is associated with sustained improvements in respiratory function in Morquio A. In younger patients (≤14 years), some improvement may be ascribed to growth. In older patients, other mechanisms, e.g., decreased glycosaminoglycan storage, are likely involved