Correlation function for the Grid-Poisson Euclidean matching on a line and on a circle

We compute the two-point correlation function for spin configurations which are obtained by solving the Euclidean matching problem, for one family of points on a grid, and the second family chosen uniformly at random, when the cost depends on a power $p$ of the Euclidean distance. We provide the analytic solution in the thermodynamic limit, in a number of cases ($p>1$ open b.c.\ and $p=2$ periodic b.c., both at criticality), and analyse numerically other parts of the phase diagram.Comment: 34 pages, 10 figure

Mechanical Ventilation Guided by Uncalibrated Esophageal Pressure May Be Potentially Harmful

Esophageal balloon calibration was proposed in acute respiratory failure patients to improve esophageal pressure assessment. In a clinical setting characterized by a high variability of abdominal load and intrathoracic pressure (i.e., pelvic robotic surgery), the authors hypothesized that esophageal balloon calibration could improve esophageal pressure measurements. Accordingly, the authors assessed the impact of esophageal balloon calibration compared to conventional uncalibrated approach during pelvic robotic surgery

Esophageal balloon calibration during Sigh: A physiologic, randomized, cross-over study

PURPOSE: Optimal esophageal balloon filling volume (Vbest) depends on the intrathoracic pressure. During Sigh breath delivered by the ventilator machine, esophageal balloon is surrounded by elevated intrathoracic pressure that might require higher filling volume for accurate measure of tidal changes in esophageal pressure (Pes). The primary aim of our investigation was to evaluate and compare Vbest during volume controlled and pressure support breaths vs. Sigh breath.MATERIALS AND METHODS: Twenty adult patients requiring invasive volume-controlled ventilation (VCV) for hypoxemic acute respiratory failure were enrolled. After the insertion of a naso-gastric catheter equipped with 10ml esophageal balloon, each patient underwent three 30-min trials as follows: VCV, pressure support ventilation (PSV), and PSV+Sigh. Sigh was added to PSV as 35 cmH2O pressure-controlled breath over 4s, once per minute. PSV and PSV+Sigh were randomly applied and, at the end of each step, esophageal balloon calibration was performed.RESULTS: Vbest was higher for Sigh breath (4.5 [3.0-6.8] ml) compared to VCV (1.5 [1.0-2.9] ml, P=0.0004) and PSV tidal breath (1.0 [0.5-2.4] ml, P<0.0001).CONCLUSIONS: During Sigh breath, applying a calibrated approach for Pes assessment, a higher Vbest was required compared to VCV and PSV tidal breath

Diaphragmatic Kinetics Assessment by Tissue Doppler Imaging and Extubation Outcome: An Observational Study

BACKGROUND: The assessment of diaphragmatic kinetics through tissue Doppler imaging (dTDI) was recently proposed as a means to describe diaphragmatic activity in both healthy individuals and intubated patients undergoing weaning from mechanical ventilation. Our primary aim was to investigate whether the diaphragmatic excursion velocity measured with dTDI at the end of a spontaneous breathing trial (SBT) was different in subjects successfully extubated versus those who passed the trial but exhibited extubation failure within 48 h after extubation.METHODS: We enrolled 100 adult subjects, all of whom had successfully passed a 30-min SBT conducted in CPAP of 5 cm H2O. In cases of extubation failure within 48 h after liberation from invasive mechanical ventilation, subjects were re-intubated or supported through noninvasive ventilation. dTDI was performed at the end of the SBT to assess excursion, velocity, and acceleration.RESULTS: Extubation was successful in 79 subjects, whereas it failed in 21 subjects. The median (interquartile range [IQR]) inspiratory peak excursion velocity (3.1 [IQR 2.0-4.3] vs 1.8 [1.3-2.6] cm/s, P < .001), mean velocity (1.6 [IQR 1.2-2.4] vs 1.1 [IQR 0.8-1.4] cm/s, P < .001), and acceleration (8.8 [IQR 5.0-17.8] vs 4.2 [IQR 2.4-8.0] cm/s2, P = .002) were all significantly higher in subjects who failed extubation compared with those who were successfully extubated. Similarly, the median expiratory peak relaxation velocity (2.6 [IQR 1.9-4.5] vs 1.8 [IQR 1.2-2.5] cm/s, P < .001), mean velocity (1.1 [IQR 0.7-1.7] vs 0.9 [IQR 0.6-1.0] cm/s, P = .002), and acceleration (11.2 [IQR 9.1-19.0] vs 7.1 [IQR 4.6-12.0] cm/s2, P = .004) were also higher in the subjects who failed extubation.CONCLUSIONS: In our setting, at the end of SBT, subjects who developed extubation failure within 48 h after extubation experienced a greater diaphragmatic activation compared with subjects who were successfully extubated. (ClinicalTrials.gov registration NCT03962322.)