Kernel Approximation on Manifolds II: The L∞L_{\infty}-norm of the L2L_2-projector

This article addresses two topics of significant mathematical and practical interest in the theory of kernel approximation: the existence of local and stable bases and the L_p--boundedness of the least squares operator. The latter is an analogue of the classical problem in univariate spline theory, known there as the "de Boor conjecture". A corollary of this work is that for appropriate kernels the least squares projector provides universal near-best approximations for functions f\in L_p, 1\le p\le \infty.Comment: 25 pages; minor revision; new proof of Lemma 3.9; accepted for publication in SIAM J. on Math. Ana

Temperature-driven single-valley Dirac fermions in HgTe quantum wells

We report on temperature-dependent magnetospectroscopy of two HgTe/CdHgTe quantum wells below and above the critical well thickness $d_c$. Our results, obtained in magnetic fields up to 16 T and temperature range from 2 K to 150 K, clearly indicate a change of the band-gap energy with temperature. The quantum well wider than $d_c$ evidences a temperature-driven transition from topological insulator to semiconductor phases. At the critical temperature of 90 K, the merging of inter- and intra-band transitions in weak magnetic fields clearly specifies the formation of gapless state, revealing the appearance of single-valley massless Dirac fermions with velocity of $5.6\times10^5$ m$\times$s$^{-1}$. For both quantum wells, the energies extracted from experimental data are in good agreement with calculations on the basis of the 8-band Kane Hamiltonian with temperature-dependent parameters.Comment: 5 pages, 3 figures and Supplemental Materials (4 pages

On the order of summability of the Fourier inversion formula

In this article we show that the order of the point value, in the sense of Łojasiewicz, of a tempered distribution and the order of summability of the pointwise Fourier inversion formula are closely related. Assuming that the order of the point values and certain order of growth at infinity are given for a tempered distribution, we estimate the order of summability of the Fourier inversion formula. For Fourier series, and in other cases, it is shown that if the distribution has a distributional point value of order k, then its Fourier series is e.v. Cesàro summable to the distributional point value of order k+1. Conversely, we also show that if the pointwise Fourier inversion formula is e.v. Cesàro summable of order k, then the distribution is the (k+1)-th derivative of a locally integrable function, and the distribution has a distributional point value of order k+2. We also establish connections between orders of summability and local behavior for other Fourier inversion problems

Airway management in neonates and infants: European Society of Anaesthesiology and Intensive Care and British Journal of Anaesthesia joint guidelines.

Airway management is required during general anaesthesia and is essential for life-threatening conditions such as cardiopulmonary resuscitation. Evidence from recent trials indicates a high incidence of critical events during airway management, especially in neonates or infants. It is important to define the optimal techniques and strategies for airway management in these groups. In this joint European Society of Anaesthesiology and Intensive Care (ESAIC) and British Journal of Anaesthesia (BJA) guideline on airway management in neonates and infants, we present aggregated and evidence-based recommendations to assist clinicians in providing safe and effective medical care. We identified seven main areas of interest for airway management: i) preoperative assessment and preparation; ii) medications; iii) techniques and algorithms; iv) identification and treatment of difficult airways; v) confirmation of tracheal intubation; vi) tracheal extubation, and vii) human factors. Based on these areas, Population, Intervention, Comparison, Outcomes (PICO) questions were derived that guided a structured literature search. GRADE (Grading of Recommendations, Assessment, Development and Evaluation) methodology was used to formulate the recommendations based on those studies included with consideration of their methodological quality (strong '1' or weak '2' recommendation with high 'A', medium 'B' or low 'C' quality of evidence). In summary, we recommend: 1. Use medical history and physical examination to predict difficult airway management (1С). 2. Ensure adequate level of sedation or general anaesthesia during airway management (1B). 3. Administer neuromuscular blocker before tracheal intubation when spontaneous breathing is not necessary (1С). 4. Use a videolaryngoscope with an age-adapted standard blade as first choice for tracheal intubation (1B). 5. Apply apnoeic oxygenation during tracheal intubation in neonates (1B). 6. Consider a supraglottic airway for rescue oxygenation and ventilation when tracheal intubation fails (1B). 7. Limit the number of tracheal intubation attempts (1C). 8. Use a stylet to reinforce and preshape tracheal tubes when hyperangulated videolaryngoscope blades are used and when the larynx is anatomically anterior (1C). 9. Verify intubation is successful with clinical assessment and end-tidal CO2 waveform (1C). 10. Apply high-flow nasal oxygenation, continuous positive airway pressure or nasal intermittent positive pressure ventilation for postextubation respiratory support, when appropriate (1B)

Disruption of the expression of the proprotein convertase PC7 reduces BDNF production and affects learning and memory in mice

PC7 belongs to the proprotein convertase family, whose members are implicated in the cleavage of secretory precursors. The in vivo function of PC7 is unknown. Herein, we find that the precursor proBDNF is processed into mature BDNF in COS-1 cells coexpressing proBDNF with either PC7 or Furin. Conversely, the processing of proBDNF into BDNF is markedly reduced in the absence of either Furin or PC7 in mouse primary hepatocytes. In vivo we observe that BDNF and PC7 mRNAs are colocalized in mouse hippocampus and amygdala and that mature BDNF protein levels are reduced in these brain areas in PC7 KO mice but not in the hippocampus of PC1/3 KO mice. Various behavioral tests reveal that in PC7 KO mice spatial memory is intact and plasticity of responding is mildly abnormal. Episodic and emotional memories are severely impaired, but both are rescued with the tyrosine receptor kinase B agonist 7,8-dihydroxyflavone. Altogether, these results support an in vivo role for PC7 in the regulation of certain types of cognitive performance, in part via proBDNF processing. Because polymorphic variants of human PC7 are being characterized, it will be important in future studies to determine their effects on additional physiological and behavioral processes

Airway Management in the Paediatric Difficult Intubation Registry: A Propensity Score Matched Analysis of Outcomes Over Time

BACKGROUND: The Paediatric Difficult Intubation Collaborative identified multiple attempts and persistence with direct laryngoscopy as risk factors for complications in children with difficult tracheal intubations and subsequently engaged in initiatives to reduce repeated attempts and persistence with direct laryngoscopy in children. We hypothesised these efforts would lead to fewer attempts, fewer direct laryngoscopy attempts and decrease complications. METHODS: Paediatric patients less than 18 years of age with difficult direct laryngoscopy were enrolled in the Paediatric Difficult Intubation Registry. We define patients with difficult direct laryngoscopy as those in whom (1) an attending or consultant obtained a Cormack Lehane Grade 3 or 4 view on direct laryngoscopy, (2) limited mouth opening makes direct laryngoscopy impossible, (3) direct laryngoscopy failed in the preceding 6 months, and (4) direct laryngoscopy was deferred due to perceived risk of harm or poor chance of success. We used a 5:1 propensity score match to compare an early cohort from the initial Paediatric Difficult Intubation Registry analysis (August 6, 2012-January 31, 2015, 785 patients, 13 centres) and a current cohort from the Registry (March 4, 2017-March 31, 2023, 3925 patients, 43 centres). The primary outcome was first attempt success rate between cohorts. Success was defined as confirmed endotracheal intubation and assessed by the treating clinician. Secondary outcomes were eventual success rate, number of attempts at intubation, number of attempts with direct laryngoscopy, the incidence of persistence with direct laryngoscopy, use of supplemental oxygen, all complications, and severe complications. FINDINGS: First-attempt success rate was higher in the current cohort (42% vs 32%, OR 1.5 95% CI 1.3-1.8, p \u3c 0.001). In the current cohort, there were fewer attempts (2.2 current vs 2.7 early, regression coefficient -0.5 95% CI -0.6 to -0.4, p \u3c 0.001), fewer attempts with direct laryngoscopy (0.6 current vs 1.0 early, regression coefficient -0.4 95% CI -0.4 to 0.3, p \u3c 0.001), and reduced persistence with direct laryngoscopy beyond two attempts (7.3% current vs 14.1% early, OR 0.5 95% CI 0.4-0.6, p \u3c 0.001). Overall complication rates were similar between cohorts (19% current vs 20% early). Severe complications decreased to 1.8% in the current cohort from 3.2% in the early cohort (OR 0.55 95% CI 0.35-0.87, p = 0.011). Cardiac arrests decreased to 0.8% in the current cohort from 1.8% in the early cohort. We identified persistence with direct laryngoscopy as a potentially modifiable factor associated with severe complications. INTERPRETATION: In the current cohort, children with difficult tracheal intubations underwent fewer intubation attempts, fewer attempts with direct laryngoscopy, and had a nearly 50% reduction in severe complications. As persistence with direct laryngoscopy continues to be associated with severe complications, efforts to limit direct laryngoscopy and promote rapid transition to advanced techniques may enhance patient safety. FUNDING: None

ADAM2 Interactions with Mouse Eggs and Cell Lines Expressing α4/α9 (ITGA4/ITGA9) Integrins: Implications for Integrin-Based Adhesion and Fertilization

Integrins are heterodimeric cell adhesion molecules, with 18 α (ITGA) and eight β (ITGB) subunits forming 24 heterodimers classified into five families. Certain integrins, especially the α(4)/α(9) (ITGA4/ITGA9) family, interact with members of the ADAM (a disintegrin and metalloprotease) family. ADAM2 is among the better characterized and also of interest because of its role in sperm function. Having shown that ITGA9 on mouse eggs participates in mouse sperm-egg interactions, we sought to characterize ITGA4/ITGA9-ADAM2 interactions.An anti-β(1)/ITGB1 function-blocking antibody that reduces sperm-egg binding significantly inhibited ADAM2 binding to mouse eggs. Analysis of integrin subunit expression indicates that mouse eggs could express at least ten different integrins, five in the RGD-binding family, two in the laminin-binding family, two in the collagen-binding family, and ITGA9-ITGB1. Adhesion assays to characterize ADAM2 interactions with ITGA4/ITGA9 family members produced the surprising result that RPMI 8866 cell adhesion to ADAM2 was inhibited by an anti-ITGA9 antibody, noteworthy because ITGA9 has only been reported to dimerize with ITGB1, and RPMI 8866 cells lack detectable ITGB1. Antibody and siRNA studies demonstrate that ITGB7 is the β subunit contributing to RPMI 8866 adhesion to ADAM2.These data indicate that a novel integrin α-β combination, ITGA9-ITGB7 (α(9)β(7)), in RPMI 8866 cells functions as a binding partner for ADAM2. ITGA9 had previously only been reported to dimerize with ITGB1. Although ITGA9-ITGB7 is unlikely to be a widely expressed integrin and appears to be the result of "compensatory dimerization" occurring in the context of little/no ITGB1 expression, the data indicate that ITGA9-ITGB7 functions as an ADAM binding partner in certain cellular contexts, with implications for mammalian fertilization and integrin function