Pin structures on vector bundles are the natural generalization of Spin structures to the case of nonoriented bundles. Spin(n) is the central Z/2Z extension (or double cover) of SO(n) and Pin−(n) and Pin(n) are two different central extensions of O(n), although they are topologically the same. The obstruction to putting a Spin structure on a bundle ξ (= R → E → B) is w2(ξ) H(B;Z/2Z); for Pin it...

40 is a near branch, an analogous argument again shows that Pin(b) is q's lower-right quadrant. Thus, q is the closest connection between p, Pin(a) and Pin(b). Except for redundancies and pruning of sub-optimal trees, BB-SORT-C searches over all possible ways to construct a Steiner tree sequentially, such that each sink is added by a closest connection to some edge in the current tree. Thus, we...

PURPOSE The purpose of this study was to evaluate the accuracy of a 3.5-mm-diameter anterior cruciate ligament (ACL) tibial retrograde socket drilling pin versus a standard, 2.4-mm drill-tipped guide pin. A secondary purpose was to evaluate surgeon precision in identifying the true (anatomic) center of the ACL tibial footprint using arthroscopic visualization. METHODS Six matched pairs of cad...

A simple, but not widely known, mathematical fact concerning the coverings of the full Lorentz group sheds light on parity and time reversal transformations of fermions. Whereas there is, up to an isomorphism, only one Spin group which double covers the orientation preserving Lorentz group, there are two essentially different groups, called Pin groups, which cover the full Lorentz group. Pin(1,...

OBJECTIVES To validate with an independent study that simple atrophy/postatrophic hyperplastic lesions (proliferative inflammatory atrophy [PIA]) often merge directly with high-grade prostatic intraepithelial neoplasia (PIN). METHODS Using radical prostatectomies (n =14), all high-grade PIN and adenocarcinoma lesions were identified. We examined the two-dimensional topographic relationship be...

This paper presents a new pseudo pin assignment algorithm for crosstalk noise control in multi-layer gridless general area routing. It also tends to minimize the number of vias needed in detailed routing. Our approach consists of two steps: coarse pseudo pin assignment and detailed pseudo pin assignment. Coarse pseudo pin assignment uses the crosstalk noise constraints to estimate the spacing r...

PURPOSE To conduct a prospective randomised controlled study to compare the stability and risk of nerve injury between fractures treated by medial-lateral pin fixation and those treated by 2-lateral pin fixation. METHODS Patients with displaced supracondylar fractures admitted between May 2000 and December 2001 were recruited into the study. They were randomised to treatment either with media...