Dilogarithm Identities in Conformal Field Theory and Group Homology

Recently, Rogers' dilogarithm identities have attracted much attention in the setting of conformal field theory as well as lattice model calculations. One of the connecting threads is an identity of Richmond-Szekeres that appeared in the computation of central charges in conformal field theory. We show that the Richmond-Szekeres identity and its extension by Kirillov-Reshetikhin can be interpreted as a lift of a generator of the third integral homology of a finite cyclic subgroup sitting inside the projective special linear group of all $2 \times 2$ real matrices viewed as a {\it discrete} group. This connection allows us to clarify a few of the assertions and conjectures stated in the work of Nahm-Recknagel-Terhoven concerning the role of algebraic $K$-theory and Thurston's program on hyperbolic 3-manifolds. Specifically, it is not related to hyperbolic 3-manifolds as suggested but is more appropriately related to the group manifold of the universal covering group of the projective special linear group of all $2 \times 2$ real matrices viewed as a topological group. This also resolves the weaker version of the conjecture as formulated by Kirillov. We end with the summary of a number of open conjectures on the mathematical side.Comment: 20 pages, 2 figures not include

Diffusion of gold nanoclusters on graphite

We present a detailed molecular-dynamics study of the diffusion and coalescence of large (249-atom) gold clusters on graphite surfaces. The diffusivity of monoclusters is found to be comparable to that for single adatoms. Likewise, and even more important, cluster dimers are also found to diffuse at a rate which is comparable to that for adatoms and monoclusters. As a consequence, large islands formed by cluster aggregation are also expected to be mobile. Using kinetic Monte Carlo simulations, and assuming a proper scaling law for the dependence on size of the diffusivity of large clusters, we find that islands consisting of as many as 100 monoclusters should exhibit significant mobility. This result has profound implications for the morphology of cluster-assembled materials

"Axillary recurrences after sentinel lymph node biopsy: A multicentre analysis and follow-up of sentinel lymph node negative breast cancer patients"

Item does not contain fulltextINTRODUCTION: The objective of this study was to conduct a multicentre data analysis to identify prognostic factors for developing an axillary recurrence (AR) after negative sentinel lymph node biopsy (SLNB) in a large cohort of breast cancer patients with long follow-up. PATIENTS AND METHODS: The prospective databases from different hospitals of clinically node negative breast cancer patients operated on between, 2000 and 2002 were analyzed. SLNB was performed and pathological analysis done by local pathologists according to national guidelines. Adjuvant treatment was given according to contemporary guidelines. Multivariate analysis was performed using all available variables, a p-value of <0,05 was considered to be significant. RESULTS: A total of 929 patients who did not undergo axillary lymph node dissection were identified. After a median follow up of 77 (range 1-106) months, fifteen patients developed an isolated AR (AR rate 1,6%). Multivariate analysis showed that young age (p = 0.007) and the absence of radiotherapy (p = 0.010) significantly increased the risk of developing an AR. Distant metastasis free survival (DMFS) was significantly worse for patients with an AR compared to all other breast cancer patients (p < 0,0001). CONCLUSION: Even after long-term follow up, the risk of developing an AR after a negative SLN in breast cancer is low. Young age and absence of radiation therapy are highly significant factors for developing an axillary recurrence. DMFS is worse for AR patients compared to patients initially diagnosed with N0 or N1 disease