Decay of correlation for random intermittent maps

We study a class of random transformations built over finitely many intermittent maps sharing a common indifferent fixed point. Using a Young-tower technique, we show that the map with the fastest relaxation rate dominates the asymptotics. In particular, we prove that the rate of correlation decay for the annealed dynamics of the random map is the same as the sharp rate of correlation decay for the map with the fastest relaxation rate.Comment: Minor revision, to appear in Nonlinearit

Stochastic perturbations of intermittent maps

This thesis studies statistical properties of intermittent maps. We obtain three new results. First we use an Ulam-type discretization scheme to provide {\em{pointwise}} approximations for invariant densities of interval maps with a neutral fixed point. We prove that the approximate invariant density converges pointwise to the true density at a rate $C^*\cdot\frac{\ln m}{m}$, where $C^*$ is a computable fixed constant and $\frac{1}{m}$ is the mesh size of the discretization. We then study intermittent maps in a random setting. In particular, we study a random map $T$ which consists of intermittent maps $\{\tau_{k}\}_{k=1}^{K}$ and a position dependent probability distribution $\{p_{k,\varepsilon}(x)\}_{k=1}^{K}$. We prove existence of a unique absolutely continuous invariant measure (ACIM) for the random map $T$. Moreover, we show that, as $\varepsilon$ goes to zero, the invariant density of the random system $T$ converges in the $L^{1}$-norm to the invariant density of the deterministic intermittent map $\tau_{1}$. The outcome of Chapter \ref{chapACIM} contains a first result on stochastic stability, in the strong sense, of intermittent maps. Finally, we study the problem of correlation decay of random map built from finitely many intermittent maps with a common neutral fixed point. Using a Young-tower technique, we show that the map with the fastest relaxation rate dominates the asymptotics. In particular, we prove that the rate of correlation decay for the annealed dynamics of the random map is the same as the {\em sharp rate} of correlation decay for the map with the fastest relaxation rate

Rigorous pointwise approximations for invariant densities of non-uniformly expanding maps

We use an Ulam-type discretization scheme to provide pointwise approximations for invariant densities of interval maps with a neutral fixed point. We prove that the approximate invariant density converges pointwise to the true density at a rate C∗⋅(lnm)/m, where C∗ is a computable fixed constant and m−1 is the mesh size of the discretization

DECAY OF CORRELATION FOR RANDOM INTERMITTENT MAPS

Abstract. We study a class of random transformations built over finitely many intermittent maps sharing a common indifferent fixed point. Using a Young-tower technique, we show that the map with the fastest relaxation rate dominates the asymptotics. In particular, we prove that the rate of correlation decay for the annealed dynamics of the random map is the same as the sharp rate of correlation decay for the map with the fastest relaxation rate

Rigorous pointwise approximations for invariant densities of non-uniformly expanding maps

This article was published in the journal Ergodic Theory and Dynamical Systems and the definitive version is available at: http://dx.doi.org/10.1017/etds.2013.91We use an Ulam-type discretization scheme to provide pointwise approximations for invariant densities of interval maps with a neutral fixed point. We prove that the approximate invariant density converges pointwise to the true density at a rate C∗⋅(lnm)/m, where C∗ is a computable fixed constant and m−1 is the mesh size of the discretization

Effective dose of propofol combined with intravenous esketamine for smooth flexible laryngeal mask airway insertion in two distinct age groups of preschool children

Abstract Background There is limited research on the combined use of propofol and esketamine for anesthesia induction during flexible laryngeal mask airway (FLMA) in pediatric patients, and the effective dosage of propofol for FLMA smooth insertion remains unclear. We explored the effective dose of propofol combined with intravenous esketamine for the smooth insertion of FLMA in two distinct age groups of preschool children. Methods This is a prospective, observer-blind, interventional clinical study. Based on age, preschool children scheduled for elective surgery were divided into group A (aged 1–3 years) and group B (aged 3–6 years). Anesthesia induction was started with intravenous administration of esketamine (1.0 mg.kg− 1) followed by propofol administration. The FLMA was inserted 2 min after propofol administration at the target dose. The initial dose of propofol in group A and group B was 3.0 mg.kg− 1 and 2.5 mg.kg− 1, respectively. The target dose of propofol was determined with Dixon’s up-and-down method, and the dosing interval of propofol was 0.5 mg.kg− 1. If there was smooth insertion of FLMA in the previous patient, the target dose of propofol for the next patient was reduced by 0.5 mg.kg− 1; otherwise, it was increased by 0.5 mg.kg− 1. The median 50% effective dose (ED50) for propofol was estimated using Dixon’s up-and-down method and Probit analysis, while the 95% effective dose (ED95) was estimated through Probit analysis. Vital signs and adverse events during induction were recorded. Results Each group included 24 pediatric patients. Using Dixon’s up-and-down method, the ED50 of propofol combined with esketamine for smooth insertion of FLMA in group A was 2.67 mg.kg− 1 (95%CI: 1.63–3.72), which was higher than that in group B (2.10 mg. kg− 1, 95%CI: 1.36–2.84) (p = 0.04). Using Probit analysis, the ED50 of propofol was calculated as 2.44 (95% CI: 1.02–3.15) mg.kg− 1 in group A and 1.93 (95% CI: 1.39–2.32) mg.kg− 1 in group B. The ED95 of propofol was 3.72 (95%CI: 3.07–15.18) mg.kg− 1 in group A and 2.74 (95%CI: 2.34–5.54) mg.kg− 1 in group B. In Group B, one pediatric patient experienced laryngospasm. Conclusion The effective dose of propofol when combined with intravenous esketamine for smooth insertion of FLMA in children aged 1–3 years is 2.67 mg.kg− 1, which is higher than that in children aged 3–6 years (2.10 mg. kg− 1). Trial registration Chinese Clinical Trial Registry Center (Registration Number: ChiCTR2100044317; Registration Date: 2021/03/16