How fluids bend: the elastic expansion for higher-dimensional black holes

Hydrodynamics can be consistently formulated on surfaces of arbitrary co-dimension in a background space-time, providing the effective theory describing long-wavelength perturbations of black branes. When the co-dimension is non-zero, the system acquires fluid-elastic properties and constitutes what is called a fluid brane. Applying an effective action approach, the most general form of the free energy quadratic in the extrinsic curvature and extrinsic twist potential of stationary fluid brane configurations is constructed to second order in a derivative expansion. This construction generalizes the Helfrich-Canham bending energy for fluid membranes studied in theoretical biology to the case in which the fluid is rotating. It is found that stationary fluid brane configurations are characterized by a set of 3 elastic response coefficients, 3 hydrodynamic response coefficients and 1 spin response coefficient for co-dimension greater than one. Moreover, the elastic degrees of freedom present in the system are coupled to the hydrodynamic degrees of freedom. For co-dimension-1 surfaces we find a 8 independent parameter family of stationary fluid branes. It is further shown that elastic and spin corrections to (non)-extremal brane effective actions can be accounted for by a multipole expansion of the stress-energy tensor, therefore establishing a relation between the different formalisms of Carter, Capovilla-Guven and Vasilic-Vojinovic and between gravity and the effective description of stationary fluid branes. Finally, it is shown that the Young modulus found in the literature for black branes falls into the class predicted by this approach - a relation which is then used to make a proposal for the second order effective action of stationary blackfolds and to find the corrected horizon angular velocity of thin black rings.

Expression analysis of heat shock protein 90 (HSP90) and Her2 in colon carcinoma.

PURPOSE The molecular chaperone heat shock protein 90 (HSP90) plays an important role in several types of tumors also participating in the modulation of the activity of receptor tyrosine kinases activity such as members of the Her family. We evaluated the significance of HSP90 and Her2 expression in colon cancer. METHODS HSP90 and Her2 expression was determined by immunohistochemistry and by fluorescence in situ hybridization (FISH) on 355 primary resected colon carcinomas. Results were correlated with pathologic features (Union for International Cancer Control (UICC) pTNM category, tumor localisation, tumor differentiation), additional molecular genetic characteristics (BRAF, KRAS mutational status, mismatch repair genes (MMR)), and survival. RESULTS HSP90 immunoreactivity was observed in various degrees. Fifty-one cases (14 %) were positive for Her2 (score 2+ and 3+) with 16/43 cases with Her2 2+ staining pattern showing amplification of Her2 determined by FISH. There was a significant correlation between high HSP90 expression and Her2 overexpression (p = 0.011). High HSP90 expression was associated with earlier tumor stages (p = 0.019), absence of lymph node (p = 0.006), and absence of distant metastases (p = 0.001). Patients with high tumoral HSP90 levels had a better survival (p = 0.032), but this was not independent from other prognostic relevant pathologic parameters. Her2 expression was not associated with any of the investigated histopathological, molecular, or clinical parameters. CONCLUSIONS High HSP90 levels are reflecting lower malignant potential in colon cancer. Her2 positivity can be observed in a small number of cases. Targeting HSP90 and/or Her2 may be an alternative therapeutic approach in colon cancer in a subset of patients.