On the existence threshold for positive solutions of p-laplacian equations with a concave-convex nonlinearity

We study the following boundary value problem with a concave-convex nonlinearity: \begin{equation*} \left\{ \begin{array}{r c l l} -\Delta_p u & = & \Lambda\,u^{q-1}+ u^{r-1} & \textrm{in }\Omega, \\ u & = & 0 & \textrm{on }\partial\Omega. \end{array}\right. \end{equation*} Here $\Omega \subset \mathbb{R}^n$ is a bounded domain and $1<q<p<r<p^*$. It is well known that there exists a number $\Lambda_{q,r}>0$ such that the problem admits at least two positive solutions for $0<\Lambda<\Lambda_{q,r}$, at least one positive solution for $\Lambda=\Lambda_{q,r}$, and no positive solution for $\Lambda > \Lambda_{q,r}$. We show that $$\lim_{q \to p} \Lambda_{q,r} = \lambda_1(p),$$ where $\lambda_1(p)$ is the first eigenvalue of the p-laplacian. It is worth noticing that $\lambda_1(p)$ is the threshold for existence/nonexistence of positive solutions to the above problem in the limit case $q=p$

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

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

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

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

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

The natural history of growth in patients with Hunter syndrome: Data from the Hunter Outcome Survey (HOS)

Hunter syndrome (mucopolysaccharidosis type II) affects growth but the overall impact is poorly understood. This study investigated the natural history of growth and related parameters and their relationship with disease severity (as indicated by cognitive impairment). Natural history data from males followed prospectively in the Hunter Outcome Survey registry and not receiving growth hormone or enzyme replacement therapy, or before treatment start, were analysed (N=676; January 2014). Analysis of first-reported measurements showed short stature by 8years of age; median age-corrected standardized height score (z-score) in patients aged 8-12years was -3.1 (1st, 3rd quartile: -4.3, -1.7; n=68). Analysis of growth velocity using consecutive values found no pubertal growth spurt. Patients had large head circumference at all ages, and above average body weight and body mass index (BMI) during early childhood (median z-score in patients aged 2-4years, weight [n=271]: 1.7 [0.9, 2.4]; BMI [n=249]: 2.0 [1.1, 2.7]). Analysis of repeated measurements over time found greater BMI in those with cognitive impairment than those without, but no difference in height, weight or head circumference. Logistic regression modelling (data from all time points) found that increased BMI was associated with the presence of cognitive impairment (odds ratio [95% CI], 3.329 [2.313-4.791]), as were increased weight (2.365 [1.630-3.433]) and head circumference (1.749 [1.195-2.562]), but not reduced height. Unlike some other MPS disorders, there is no evidence at present for predicting disease severity in patients with Hunter syndrome based on changes in growth characteristics