Consider the random walk on the permutation group obtained when the step distribution is uniform on a given conjugacy class. It is shown that there is a critical time at which two phase transitions occur simultaneously. On the one hand, the random walk slows down abruptly: the acceleration (i.e., the second time derivative of the distance) drops from 0 to −∞ at this time as n → ∞. On the other ...

K 0 form factor at order p 6 of chiral perturbation theory Abstract This paper describes the calculation of the electromagnetic form factor of the K 0 meson at order p 6 of chiral perturbation theory which is the next-to-leading order correction to the well-known p 4 result achieved by Gasser and Leutwyler. On the one hand, at order p 6 the chiral expansion contains 1-and 2-loop diagrams which ...

The regular representation of an essentially finite 2-group G in the 2-category 2Vectk of (Kapranov and Voevodsky) 2-vector spaces is defined and cohomology invariants classifying it computed. It is next shown that all hom-categories in Rep 2Vectk pGq are 2-vector spaces under quite standard assumptions on the field k, and a formula giving the corresponding “intertwining numbers” is obtained wh...

Objective Among the various sacropelvic fixation methods, S2 alar-iliac (S2AI) screw fixation has several advantages compared to conventional iliac wing screw. However, the placement of S2AI screw still remains a challenge. The purpose of this study was to describe a novel technique of free hand S2AI screw insertion using a K-wire and cannulated screw, and to evaluate the accuracy of the techni...

Previous studies have shown that elevating the K+ levels from 0.75% to 2.11% in the diet of stroke-prone spontaneously hypertensive rats significantly retards the development of stroke and increases their lifespan. On the other hand, stroke-resistant spontaneously hypertensive rats fail to develop stroke even if they are fed the low-K+ version of this diet. Since sympathetic nerves surrounding ...

In this paper we give a first set of communication lower bounds for distributed clustering problems, in particular, for k-center, k-median and k-means. When the input is distributed across a large number of machines and the number of clusters k is small, our lower bounds match the current best upper bounds up to a logarithmic factor. We have designed a new composition framework in our proofs fo...