The Ashkenazi Jewish (AJ) population has long been viewed as a genetic isolate, yet it is still unclear how population bottlenecks, admixture, or positive selection contribute to its genetic structure. Here we analyzed a large AJ cohort and found higher linkage disequilibrium (LD) and identity-by-descent relative to Europeans, as expected for an isolate. However, paradoxically we also found hig...

A3 Start with a finite sequence a1, a2, . . . , an of positive integers. If possible, choose two indices j < k such that aj does not divide ak, and replace aj and ak by gcd(aj , ak) and lcm(aj , ak), respectively. Prove that if this process is repeated, it must eventually stop and the final sequence does not depend on the choices made. (Note: gcd means greatest common divisor and lcm means leas...

Cj(S): The total completion time of schedule S. Finally, for convenience, for each order constructed from aj (bj , cj), we simply call it order aj (respectively, bj , cj). Also, we assume that the subscripts of the orders in a schedule are labelled in such a way that, aj (bj , or cj) (j = 1, 2, . . . , n): means that there are (j − 1) orders of type a scheduled before aj (respectively, bj , or ...

Fundamental to optimal diabetes management is good patient self-care and regular follow-up with health professionals. Missed appointment may disrupt the continuity of diabetes care, thereby interfering with regular preventive screening and timely intervention.1 It may also affect care for other patients due to interference with scheduling, poor use of resources and negative impact on doctor-pat...

1. van der Stelt CA, Vermeulen Windsant‐van den Tweel AM, Egberts AC, van den Bemt PM, Leendertse AJ, Hermens WA, et al. The association between potentially inappropriate prescribing and medication‐related hospital admissions in older patients: A nested case control study. Drug Saf 2016;39:79‐87. 2. Hamilton HJ, Gallagher PF, O’Mahony D. Inappropriate prescribing and adverse drug events in olde...

As a major component of the cytoskeleton, microtubules consist of αβ-tubulin heterodimers and have been recognized as attractive targets for cancer chemotherapy. Microtubule-stabilizing agents (MSAs) promote polymerization of tubulin and stabilize the polymer, preventing depolymerization. The molecular mechanisms by which MSAs stabilize microtubules remain elusive. Here we report a 2.05 Å cryst...

Type 1 Gaucher disease (GD), a non-neuronopathic lysosomal storage disorder, results from the deficient activity of acid beta-glucosidase (GBA). Type 1 disease is panethnic but is more prevalent in individuals of Ashkenazi Jewish (AJ) descent. Of the causative GBA mutations, N370S is particularly frequent in the AJ population, (q approximately .03), whereas the 84GG insertion (q approximately ....

Consider rolling a die with k sides, labeled a1, a2, ..., and ak, respectively. Let P(aj) be the ‘probability’ that a particular side aj appears after rolling the die. Before attempting to calculate P(aj), it is necessary to clarify the meaning of the word ‘probability’. In other words, we must specify what the number P(aj) quantifies. In statistics, the concept of ‘probability’ is formally int...