A random binary search tree grown from the uniformly random permutation of [n] is studied. We analyze the exact and asymptotic counts of vertices by rank, the distance from the set of leaves. The asymptotic fraction ck of vertices of a fixed rank k ≥ 0 is shown to decay exponentially with k. We prove that the ranks of the uniformly random, fixed size sample of vertices are asymptotically independent, each having the distribution {ck}. Notoriously hard to compute, the exact fractions ck have been determined for k ≤ 3 only. We present a shortcut enabling us to compute c4 and c5 as well; both are ratios of enormous integers, the denominator of c5 being 274 digits long. Prompted by the data, we prove that, in sharp contrast, the largest prime divisor of the denominator of ck is at most 2k+1 + 1. We conjecture that, in fact, the prime divisors of every denominator for k > 1 form a single interval, from 2 to the largest prime not exceeding 2k+1 + 1.

The 26 December 2004 Tsunami resulted in a death toll of >270,000 persons, making it the most lethal tsunami in recorded history. This article presents performance data observations and the lessons learned by a civilian team dispatched by the Australian government to “provide clinical and surgical functions and to make public health assessments”. The team, prepared and equipped for deployment four days after the event, arrived at its destination 13 days after the Tsunami. Aspiration pneumonia, tetanus, and extensive soft tissue wounds of the lower extremities were the prominent injuries encountered. Surgical techniques had to be adapted to work in the austere environment. The lessons learned included: (1) the importance of team member selection; (2) strategies for self-sufficiency; (3) personnel readiness and health considerations; (4) face-to-face handover; (5) coordination and liaison; (6) the characteristics of injuries; (7) the importance of protocols for patient discharge and hospital staffing; and (8) requirements for interpreter services.

Whereas disaster medical relief teams will be required in the future, the composition and equipment needs will differ according to the nature of the disaster. National teams should be on standby for international response.

To an arbitrary intersection of exceptional varieties of an embedded resolution we associate a finite number of congruences between naturally occurring multiplicities. This theory generalizes previous results concerning just one exceptional variety. Moreover we describe precise equalities which imply the congruences and we give some applications on the poles of Igusa‘s local zeta function.