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

Clinical outcomes in a subpopulation of adults with Morquio A syndrome: results from a long-term extension study of elosulfase alfa

Background: This post hoc subanalysis examined outcomes in adult patients with Morquio A (mucopolysaccharidosis IVA) who received enzyme replacement therapy (ERT) with elosulfase alfa over a 120-weeks period. Patients ≥18 years of age evaluated in an open-label, long-term extension study of elosulfase alfa (modified per protocol [MPP], n = 32; intent-to-treat [ITT], n = 37; MOR-005; NCT01415427) were compared with the ≥18-year-old untreated population with 2-years follow-up from a Morquio A natural history study (n = 10; MorCAP; NCT00787995). The MOR-005 MPP population excluded patients who underwent orthopedic surgical procedures or were noncompliant with study protocol (defined as missing ≥20% of ERT infusions). No MorCAP patients underwent orthopedic surgical procedures during the relevant time period. Endurance was assessed by the 6-min walk test (6MWT) and 3-min stair climb test (3MSCT). Activities of daily living (ADLs) were assessed by the MPS Health Assessment Questionnaire (MPS HAQ). / Results: Least squares (LS) mean (SE) 6MWT distances increased by 34.9 (11.7) m (MPP) and 30.5 (10.8) m (ITT) by week 120; LS mean (SE) change in 3MSCT at week 120 was 6.7 (1.8) stairs/min (MPP) and 5.9 (1.7) stairs/min (ITT). MorCAP patients showed no improvement in 6MWT distance or 3MSCT over a similar period of time. Pulmonary function measures remained unchanged in both MOR-005 and MorCAP adults. All MPS HAQ domain scores improved in MOR-005 adults, whereas MorCAP adults had unchanged caregiver assistance and mobility outcomes and worsened self-care outcomes. / Conclusions: Long-term ERT in adult patients with Morquio A was associated with increased endurance and improvement in performance of ADLs. / Trial registration: Trial Registration NCT01415427. Name of registry: Long-Term Efficacy and Safety Extension Study of BMN 110 in Patients With Mucopolysaccharidosis IVA (Morquio A Syndrome). Registered 8 August 2011, retrospectively registered

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

Early respiratory viral infections in infants with cystic fibrosis

This article is made available for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.Background Viral infections contribute to morbidity in cystic fibrosis (CF), but the impact of respiratory viruses on the development of airway disease is poorly understood. Methods Infants with CF identified by newborn screening were enrolled prior to 4 months of age to participate in a prospective observational study at 4 centers. Clinical data were collected at clinic visits and weekly phone calls. Multiplex PCR assays were performed on nasopharyngeal swabs to detect respiratory viruses during routine visits and when symptomatic. Participants underwent bronchoscopy with bronchoalveolar lavage (BAL) and a subset underwent pulmonary function testing. We present findings through 8.5 months of life. Results Seventy infants were enrolled, mean age 3.1 ± 0.8 months. Rhinovirus was the most prevalent virus (66%), followed by parainfluenza (19%), and coronavirus (16%). Participants had a median of 1.5 viral positive swabs (range 0–10). Past viral infection was associated with elevated neutrophil concentrations and bacterial isolates in BAL fluid, including recovery of classic CF bacterial pathogens. When antibiotics were prescribed for respiratory-related indications, viruses were identified in 52% of those instances. Conclusions Early viral infections were associated with greater neutrophilic inflammation and bacterial pathogens. Early viral infections appear to contribute to initiation of lower airway inflammation in infants with CF. Antibiotics were commonly prescribed in the setting of a viral infection. Future investigations examining longitudinal relationships between viral infections, airway microbiome, and antibiotic use will allow us to elucidate the interplay between these factors in young children with CF

Modal analysis of holey fiber mode-selective couplers

Mode Division Multiplexing is currently investigated as a possible way to increase fiber system capacity. With this approach, different modes of the same fiber carry distinct information. One of the problems to be solved in these systems concerns coupling/decoupling of the various modes to/from the same fiber. In this presentation, the mode features of a mode mux/demux based on holey fibers are investigated, with particular emphasis on optimal device design. Some preliminary experimental results will also be presented

The prescribed mean curvature equation in weakly regular domains

We show that the characterization of existence and uniqueness up to vertical translations of solutions to the prescribed mean curvature equation, originally proved by Giusti in the smooth case, holds true for domains satisfying very mild regularity assumptions. Our results apply in particular to the non-parametric solutions of the capillary problem for perfectly wetting fluids in zero gravity. Among the essential tools used in the proofs, we mention a \textit{generalized Gauss-Green theorem} based on the construction of the weak normal trace of a vector field with bounded divergence, in the spirit of classical results due to Anzellotti, and a \textit{weak Young's law} for $(\Lambda,r_{0})$-minimizers of the perimeter.Comment: 23 pages, 1 figure --- The results on the weak normal trace of vector fields have been now extended and moved in a self-contained paper available at: arXiv:1708.0139

Long-term endurance and safety of elosulfase alfa enzyme replacement therapy in patients with Morquio A syndrome

Long-term efficacy and safety of elosulfase alfa enzyme replacement therapy were evaluated in Morquio A patients over 96weeks (reaching 120weeks in total from pre-treatment baseline) in an open-label, multi-center, phase III extension study. During this extension of a 24-week placebo-controlled phase III study, all patients initially received 2.0mg/kg elosulfase alfa either weekly or every other week, prior to establishment of 2.0mg/kg/week as the recommended dose, at which point all patients received weekly treatment. Efficacy measures were compared to baseline of the initial 24-week study, enabling analyses of changes over 120weeks. In addition to performing analyses for the entire intent-to-treat (ITT) population (N=173), analyses were also performed for a modified per-protocol (MPP) population (N=124), which excluded patients who had orthopedic surgery during the extension study or were non-compliant with the study protocol (as determined by ≥20% missed infusions). Six-minute walk test (6MWT) was the primary efficacy measure; three-minute stair climb test (3MSCT) and normalized urine keratan sulfate (uKS) were secondary efficacy measures. Mean (SE) change from baseline to Week 120 in 6MWT distance was 32.0 (11.3)m and 39.9 (10.1)m for patients receiving elosulfase alfa at 2.0mg/kg/week throughout the study (N=56) and 15.1 (7.1)m and 31.7 (6.8)m in all patients combined, regardless of dosing regimen, for the ITT and MPP populations, respectively. Further analyses revealed that durability of 6MWT improvements was not impacted by baseline 6MWT distance, use of a walking aid, or age. Mean (SE) change at Week 120 in the 3MSCT was 5.5 (1.9) and 6.7 (2.0)stairs/min for patients receiving elosulfase alfa at 2.0mg/kg/week throughout the study and 4.3 (1.2) and 6.8 (1.3)stairs/min in all patients combined, regardless of dosing regimen, for the ITT and MPP populations, respectively Across all patients, mean (SE) change at Week 120 in normalized uKS was -59.4 (1.8)% and -62.3 (1.8)% in the ITT and MPP populations, respectively. In the absence of a placebo group, significance of the sustained improvements could not be evaluated directly. However, to provide context for interpretation of results, comparisons were performed with untreated patients from a Morquio A natural history study. In contrast to the results of the extension study, the untreated patients experienced constant uKS levels and a gradual decline in endurance test results over a similar period of time. Differences from the untreated natural history study patients were significant for 6MWT, 3MSCT, and uKS outcomes for the cohort of patients receiving optimal dosing throughout the study and for all cohorts pooled together, for both ITT and MPP populations (P<0.05). Safety findings were consistent with those of the initial 24-week study, with no new safety signals identified

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