On Three-Dimensional Space Groups

An entirely new and independent enumeration of the crystallographic space groups is given, based on obtaining the groups as fibrations over the plane crystallographic groups, when this is possible. For the 35 ``irreducible'' groups for which it is not, an independent method is used that has the advantage of elucidating their subgroup relationships. Each space group is given a short ``fibrifold name'' which, much like the orbifold names for two-dimensional groups, while being only specified up to isotopy, contains enough information to allow the construction of the group from the name.Comment: 26 pages, 8 figure

The D4D_4 Root System is Not Universally Optimal

We prove that the $D_4$ root system (equivalently, the set of vertices of the regular 24-cell) is not a universally optimal spherical code. We further conjecture that there is no universally optimal spherical code of 24 points in $S^3$, based on numerical computations suggesting that every 5-design consisting of 24 points in $S^3$ is in a 3-parameter family (which we describe explicitly, based on a construction due to Sali) of deformations of the $D_4$ root system.Mathematic

The Mathieu group M-12 and its pseudogroup extension M-13

We study a construction of the Mathieu group M-12 using a game reminiscent of Loyd's "15-puzzle." The elements of M-12 are realized as permutations on 12 of the 13 points of the finite projective plane of order 3. There is a natural extension to a "pseudogroup" M-13 acting on all 13 points, which exhibits a limited form of sextuple transitivity. Another corollary of the construction is a metric, akin to that induced by a Cayley graph, on both M-12 and M-13. We develop these results, and extend them to the double covers and automorphism groups of M-12 and M-13, using the ternary Golay code and 12 x 12 Hadamard matrices. In addition, we use experimental data on the quasi-Cayley metric to gain some insight into the structure of these groups and pseudogroups.Mathematic

The Mathieu group M12 and the M13 game

This is the author's accepted manuscript

Expression and localization of aquaporin water channels in adult pig urinary bladder

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Serial characterisation of monocyte and neutrophil function after lung resection.

OBJECTIVES: The primary aim of this prospective study was to perform a comprehensive serial characterisation of monocyte and neutrophil function, circulating monocyte subsets, and bronchoalveolar lavage (BAL) fluid after lung resection. A secondary aim was to perform a pilot, hypothesis-generating evaluation of whether innate immune parameters were associated with postoperative pneumonia. METHODS: Forty patients undergoing lung resection were studied in detail. Blood monocytes and neutrophils were isolated preoperatively and at 6, 24 and 48 h postoperatively. BAL was performed preoperatively and immediately postoperatively. Monocyte subsets, monocyte responsiveness to lipopolysaccharide (LPS) and neutrophil phagocytic capacity were quantified at all time points. Differential cell count, protein and cytokine concentrations were measured in BAL. Pneumonia evaluation at 72 h was assessed using predefined criteria. RESULTS: After surgery, circulating subsets of classical and intermediate monocytes increased significantly. LPS-induced release of proinflammatory cytokines from monocytes increased significantly and by 48 h a more proinflammatory profile was found. Neutrophil phagocytosis demonstrated a small but significant fall. Factors associated with postoperative pneumonia were: increased release of specific proinflammatory and anti-inflammatory cytokines from monocytes; preoperative neutrophilia; and preoperative BAL cell count. CONCLUSIONS: We conclude that postoperative lung inflammation is associated with specific changes in the cellular innate immune response, a better understanding of which may improve patient selection and prediction of complications in the future