Consider a d-type (d<∞) Galton–Watson branching process, conditioned on the event that there are at least k≥2 individuals in the nth generation, pick k individuals at random from the nth generation and trace their lines of descent backward in time till they meet. In this paper, the limit behaviors of the distributions of the generation number of the most recent common ancestor of any k chosen individuals and of the whole population are studied for both critical and subcritical cases. Also, we investigate the limit distribution of the joint distribution of the generation number and their types.

In a Galton-Watson branching process that is not extinct by the nth generation and has at least two individuals, pick two individuals at random by simple random sampling without replacement. Trace their lines of descent back in time till they meet. Call that generation Xn a pairwise coalescence time. Similarly, let Yn denote the coalescence time for the whole population of the nth generation conditioned on the event that it is not extinct. In this paper the distributions of Xn and Yn, and their limit behaviors as n → ∞ are discussed for both the critical and subcritical cases.

To determine the long-term results in patients with critical aortic stenosis who survive initial intervention, and to identify factors which predict prognosis, we studied patients who underwent intervention between 1979 and 1992 for critical aortic stenosis treated within the first three months of life. Patients with a hypoplastic left ventricle or mitral stenosis who were not considered for a biventricular repair were excluded. Follow-up examination included cross-sectional and Doppler echocardiography. All initial and subsequent patient data were reviewed. Of the 64 patients with critical aortic stenosis, 41 (64%) survived more than one month after initial intervention (surgical valvotomy in 39, balloon valvoplasty in two). These survivors constitute the study group. Mild or moderate residual aortic stenosis or regurgitation without further intervention was found in 28 patients at a median duration of 3.1 years (range 0.2–15.0 years). A poor result with re-intervention (n=6) or death (n=7) occurred in 13 patients. The diameter of the aortic valve at presentation was smaller (p<0.02) in patients with a poor result (median 5.5; range 5–15 mm), than in those with a satisfactory result (median 8.0; range 5–10 mm). Significant residual aortic stenosis was present from the time of initial intervention in nine of the 13 patients (69%) with a poor result. No difference was found in the incidence of a duct-dependent systemic circulation, associated cardiac lesions, mechanical ventilation, acidosis or the use of inotropes preoperatively between patients with a satisfactory or a poor late outcome. Of patients with critical aortic stenosis, 64% survived for more than a month after initial intervention. A small aortic valvar diameter at presentation ( 6 mm) and residual stenosis after initial intervention were important determinants of long-term prognosis.

Some critically ill patients have dramatic recollections of the intensive care unit (ICU), whereas 23–50% have little or no recollection of their ICU stay. In addition, cognitive impairments are common following critical illness and ICU treatment. Little is known regarding the relationship between cognitive sequelae and ICU recall. We assessed recall of the ICU and its relationship to cognitive functioning at hospital discharge and 1 and 2 years after discharge in 70 consecutive acute respiratory distress syndrome (ARDS) patients. Seventeen patients (24%) had no recall of the ICU. Patients without ICU recall had increased rates of cognitive sequelae at hospital discharge and 1-year follow-up compared with the ICU recall group. Patients without ICU recall had a greater magnitude of cognitive impairments at hospital discharge, but not at 1- or 2-year follow-up. Profile analysis showed significant group differences in general intellectual functioning, executive function, processing speed, and spatial skills at hospital discharge, but not at 1- or 2-year follow-up. Estimated premorbid intelligence scores were inversely related to the magnitude of cognitive sequelae, suggesting greater “cognitive reserve” in patients with fewer cognitive decrements. (JINS, 2007, 13, 595–605.)

This paper is concerned with the critical nonlinear Gross–Pitaevskii equation, which describes the attractive Bose–Einstein condensate under a magnetic trap. We derive a sharp threshold between the global existence and the blowing-up of the system. Furthermore, we answer the question: how small are the initial data, such that the system has global solutions for the nonlinear critical power $p=1+(4/N)$?