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

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

Holey fibre mode-selective couplers

Mode-selective coupling in an asymmetric holey fibre coupler is demonstrated both numerically and experimentally for the first time. The coupler's performance is shown to be ultrabroadband, with significant potential existing for the use of such couplers in high bandwidth few-mode fibre networks

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

Molecular characterization of Bifidobacterium longum biovar longum NAL8 plasmids and construction of a novel replicon screening system

In this study, we performed molecular characterization and sequence analysis of three plasmids from the human intestinal isolate Bifidobacterium longum biovar longum NAL8 and developed a novel vector screening system. Plasmids pNAL8H (10 kb) and pNAL8M (4.9 kb) show close sequence similarity to and the same gene organization as the already characterized B. longum plasmids. The B. longum plasmid pNAC1 was identified as being most closely related to pNAL8L (3.5 kb). However, DNA sequence analysis suggested that direct repeat-rich sites could have promoted several recombination events to diversify the two plasmid molecules. We verified the likely rolling circle replication of plasmid pNAL8L and studied the phylogenetic relationship in all the Bifidobacterium plasmids fully sequenced to date based on in silico comparative sequence analysis of their replication proteins and iteron regions. Our transformation experiments confirmed that the ColE1 replication origin from high-copy-number pUC vectors could interfere with the replication apparatus of Bifidobacterium plasmids and give rise to false positive clones. As a result, we developed a system suitable for avoiding possible interference by other functional replication modules on the vector and for screening functional replicons from wild-type plasmids

Boundary and defect CFT: Open problems and applications

A review of Boundary and defect conformal field theory: open problems and applications, following a workshop held at Chicheley Hall, Buckinghamshire, UK, 7–8 Sept. 2017. We attempt to provide a broad, bird’s-eye view of the latest progress in boundary and defect conformal field theory in various sub-fields of theoretical physics, including the renormalization group, integrability, conformal bootstrap, topological field theory, supersymmetry, holographic duality, and more. We also discuss open questions and promising research directions in each of these sub-fields, and combinations thereof

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

Delphi consensus on the current clinical and therapeutic knowledge on Anderson-Fabry disease

BACKGROUND: Management of Anderson-Fabry disease (AFD) is contentious, particularly regarding enzyme replacement therapy (ERT). We report results of a Delphi consensus panel on AFD management. METHODS: A survey to gauge consensus among AFD experts was distributed online and responses were analysed. Statements on: 1) diagnosis; 2) when starting ERT; 3) management of ERT infusion and adverse reactions; and 4) follow-up/monitoring response to therapy and progression of disease were included. Responses without consensus were discussed with an enlarged panel and modified to reach consensus. RESULTS: 15 experts responded to the survey. After plenary discussion among the enlarged panel, consensus was reached on most statements. Key points were the use of a target organ biopsy to show Gb3 deposits in symptomatic women with negative molecular analysis, the need for ERT in symptomatic women and in all patients with persistent signs and symptoms±organ damage. It was agreed to assess vital signs before ERT administration and use a 0.2μL filter on infusion to reduce the risk of adverse reactions, that serum should be drawn prior to the first infusion for anti-agalsidase antibody analysis to have a baseline value if a subsequent adverse reaction appears, and that pre-medication is required in those with prior infusion reactions. Holter ECG monitoring, cardiac and brain MRI, renal parameters, and abdominal ultrasound were considered important for the assessment of disease progression and response at ERT. CONCLUSIONS: This consensus supplies guidance to healthcare providers on best practice in the management of patients with AFD and indicates a need for more guidanc

Two examples of minimal Cheeger sets in the plane

We construct two minimal Cheeger sets in the Euclidean plane, i.e., unique minimizers of the ratio \u201cperimeter over area\u201d among their own measurable subsets. The first one gives a counterexample to the so- called weak regularity property of Cheeger sets, as its perimeter does not coincide with the 1-dimensional Hausdorff measure of its topological boundary. The second one is a kind of porous set, whose boundary is not locally a graph at many of its points, yet it is a weakly regular open set admitting a unique (up to vertical translations) nonparametric solution to the prescribed mean curvature equation, in the extremal case corresponding to the capillarity for perfectly wetting fluids in zero gravity