G-Brownian Motion as Rough Paths and Differential Equations Driven by G-Brownian Motion

The present paper is devoted to the study of sample paths of G-Brownian motion and stochastic differential equations (SDEs) driven by G-Brownian motion from the view of rough path theory. As the starting point, we show that quasi-surely, sample paths of G-Brownian motion can be enhanced to the second level in a canonical way so that they become geometric rough paths of roughness 2 < p < 3. This result enables us to introduce the notion of rough differential equations (RDEs) driven by G-Brownian motion in the pathwise sense under the general framework of rough paths. Next we establish the fundamental relation between SDEs and RDEs driven by G-Brownian motion. As an application, we introduce the notion of SDEs on a differentiable manifold driven by GBrownian motion and construct solutions from the RDE point of view by using pathwise localization technique. This is the starting point of introducing G-Brownian motion on a Riemannian manifold, based on the idea of Eells-Elworthy-Malliavin. The last part of this paper is devoted to such construction for a wide and interesting class of G-functions whose invariant group is the orthogonal group. We also develop the Euler-Maruyama approximation for SDEs driven by G-Brownian motion of independent interest

Successful Versus Failed Transition From Controlled Ventilation to Pressure Support Ventilation in COVID-19 Patients: A Retrospective Cohort Study

Objectives: In patients with COVID-19 respiratory failure, controlled mechanical ventilation (CMV) is often necessary during the acute phases of the disease. Weaning from CMV to pressure support ventilation (PSV) is a key objective when the patient's respiratory functions improve. Limited evidence exists regarding the factors predicting a successful transition to PSV and its impact on patient outcomes. Design: Retrospective observational cohort study. Setting: Twenty-four Italian ICUs from February 2020 to May 2020. Patients: Mechanically ventilated ICU patients with COVID-19-induced respiratory failure. Intervention: The transition period from CMV to PSV was evaluated. We defined it as "failure of assisted breathing" if the patient returned to CMV within the first 72 hours. Measurements and main results: Of 1260 ICU patients screened, 514 were included. Three hundred fifty-seven patients successfully made the transition to PSV, while 157 failed. Pao2/Fio2 ratio before the transition emerged as an independent predictor of a successful shift (odds ratio 1.00; 95% CI, 0.99-1.00; p = 0.003). Patients in the success group displayed a better trend in Pao2/Fio2, Paco2, plateau and peak pressure, and pH level. Subjects in the failure group exhibited higher ICU mortality (hazard ratio 2.08; 95% CI, 1.42-3.06; p &lt; 0.001), an extended ICU length of stay (successful vs. failure 21 +/- 14 vs. 27 +/- 17 d; p &lt; 0.001) and a longer duration of mechanical ventilation (19 +/- 18 vs. 24 +/- 17 d, p = 0.04). Conclusions: Our study emphasizes that the Pao2/Fio2 ratio was the sole independent factor associated with a failed transition from CMV to PSV. The unsuccessful transition was associated with worse outcomes

Stochastic many-particle model for LFP electrodes

In the framework of non-equilibrium thermodynamics, we derive a new model for many-particle electrodes. The model is applied to LiFePO4 (LFP) electrodes consisting of many LFP particles of nanometer size. The phase transition from a lithium-poor to a lithium-rich phase within LFP electrodes is controlled by both different particle sizes and surface fluctuations leading to a system of stochastic differential equations. An explicit relation between battery voltage and current controlled by the thermodynamic state variables is derived. This voltage–current relation reveals that in thin LFP electrodes lithium intercalation from the particle surfaces into the LFP particles is the principal rate-limiting process. There are only two constant kinetic parameters in the model describing the intercalation rate and the fluctuation strength, respectively. The model correctly predicts several features of LFP electrodes, viz. the phase transition, the observed voltage plateaus, hysteresis and the rate-limiting capacity. Moreover we study the impact of both the particle size distribution and the active surface area on the voltage–charge characteristics of the electrode. Finally we carefully discuss the phase transition for varying charging/discharging rates

Omecamtiv mecarbil in chronic heart failure with reduced ejection fraction, GALACTIC‐HF: baseline characteristics and comparison with contemporary clinical trials

Aims: The safety and efficacy of the novel selective cardiac myosin activator, omecamtiv mecarbil, in patients with heart failure with reduced ejection fraction (HFrEF) is tested in the Global Approach to Lowering Adverse Cardiac outcomes Through Improving Contractility in Heart Failure (GALACTIC‐HF) trial. Here we describe the baseline characteristics of participants in GALACTIC‐HF and how these compare with other contemporary trials. Methods and Results: Adults with established HFrEF, New York Heart Association functional class (NYHA) ≥ II, EF ≤35%, elevated natriuretic peptides and either current hospitalization for HF or history of hospitalization/ emergency department visit for HF within a year were randomized to either placebo or omecamtiv mecarbil (pharmacokinetic‐guided dosing: 25, 37.5 or 50 mg bid). 8256 patients [male (79%), non‐white (22%), mean age 65 years] were enrolled with a mean EF 27%, ischemic etiology in 54%, NYHA II 53% and III/IV 47%, and median NT‐proBNP 1971 pg/mL. HF therapies at baseline were among the most effectively employed in contemporary HF trials. GALACTIC‐HF randomized patients representative of recent HF registries and trials with substantial numbers of patients also having characteristics understudied in previous trials including more from North America (n = 1386), enrolled as inpatients (n = 2084), systolic blood pressure &lt; 100 mmHg (n = 1127), estimated glomerular filtration rate &lt; 30 mL/min/1.73 m2 (n = 528), and treated with sacubitril‐valsartan at baseline (n = 1594). Conclusions: GALACTIC‐HF enrolled a well‐treated, high‐risk population from both inpatient and outpatient settings, which will provide a definitive evaluation of the efficacy and safety of this novel therapy, as well as informing its potential future implementation