Abstract:
Background Meningiomas are associated with the highest postoperative rate of venous thromboembolic events (VTE) among all intracranial tumors. The aim of this study is to compare two entirely different VTE prophylaxis regimens in 724 consecutive patients undergoing meningioma surgery. Methods Two cohorts at a single institution treated with different regimens to prevent VTE were reviewed retrospectively. Cohort A (n = 482; 314 females, mean age 57 years, range: 11–87 years) received our institutional regimen during the years 1999–2006, consisting of low-molecular-weight heparin (LMWH) and compression stockings. For cohort B (n = 242; 163 females, mean age 56.8 years, range: 16–90 years), during the years 2008–2010, the management included intraoperative 10°–20° leg elevation with intermittent pneumatic compression (IPC), heparin and LMWH administration. We compared the incidence of the endpoints pulmonary embolism (PE), deep venous thrombosis (DVT), hemorrhage and death, taking into account several known associated risk factors. Results For all endpoints, we observed a more favorable outcome with the new regimen. The difference in incidence of PEs (cohort A: 38/482, 8%; cohort B: 6/242, 2.5%) reached statistical significance (p = 0.002). In general, patients with skull base meningiomas had a higher risk for PE (OR 2.77). Regarding VTE prophylaxis, an adjusted subgroup analysis suggests that the new regimen is particularly beneficial for patients with skull base meningiomas. Conclusions We recommend perioperative prophylaxis using a management composed of intraoperative leg-elevation, IPC, early heparin administration and LMWH to reduce the risk for PE.

Abstract:
We show that any Banach space contains a continuum of non isomorphic subspaces or a minimal subspace. We define an ergodic Banach space $X$ as a space such that $E_0$ Borel reduces to isomorphism on the set of subspaces of $X$, and show that every Banach space is either ergodic or contains a subspace with an unconditional basis $ which is complementably universal for the family of its block-subspaces. We also use our methods to get uniformity results; for example, in combination with a result of B. Maurey, V. Milman and N. Tomczak-Jaegermann, we show that an unconditional basis of a Banach space, of which every block-subspace is complemented, must be asymptotically $c_0$ or $l_p$.

Abstract:
We prove three new dichotomies for Banach spaces \`a la W.T. Gowers' dichotomies. The three dichotomies characterise respectively the spaces having no minimal subspaces, having no subsequentially minimal basic sequences, and having no subspaces crudely finitely representable in all of their subspaces. We subsequently use these results to make progress on Gowers' program of classifying Banach spaces by finding characteristic spaces present in every space. Also, the results are used to embed any partial order of size $\aleph_1$ into the subspaces of any space without a minimal subspace ordered by isomorphic embeddability.

Abstract:
A display of a topological group G on a Banach space X is a topological isomorphism of G with the isometry group Isom(X,||.||) for some equivalent norm ||.|| on X, where the latter group is equipped with the strong operator topology. Displays of Polish groups on separable real spaces are studied. It is proved that any closed subgroup of the infinite symmetric group S_\infty containing a non-trivial central involution admits a display on any of the classical spaces c0, C([0,1]), lp and Lp for 1 <=p <\infty. Also, for any Polsih group G, there exists a separable space X on which {-1,1} x G has a display.

Abstract:
We investigate questions of maximal symmetry in Banach spaces and the structure of certain bounded non-unitarisable groups on Hilbert space. In particular, we provide structural information about bounded groups with an essentially unique invariant complemented subspace. This is subsequently combined with rigidity results for the unitary representation of ${\rm Aut}(T)$ on $\ell_2(T)$, where $T$ is the countably infinite regular tree, to describe the possible bounded subgroups of ${\rm GL}(\mathcal H)$ extending a well-known non-unitarisable representation of $\mathbb F_\infty$. As a related result, we also show that a transitive norm on a separable Banach space must be strictly convex.

Abstract:
We study problems of maximal symmetry in Banach spaces. This is done by providing an analysis of the structure of small subgroups of the general linear group GL(X), where X is a separable reflexive Banach space. In particular, we provide the first known example of a Banach space X without any equivalent maximal norm, or equivalently such that GL(X) contains no maximal bounded subgroup. Moreover, this space X may be chosen to be super-reflexive.

Abstract:
We analyse several examples of separable Banach spaces, some of them new, and relate them to several dichotomies obtained in the previous paper Banach spaces without minimal subspaces, by classifying them according to which side of the dichotomies they fall. This paper may be seen as a more empirical continuation of Banach spaces without minimal subspaces, in which our stress is on the study of examples for the new classes of Banach spaces considered in that work.

Abstract:
If a Banach space has an unconditional basis it either contains a continuum of non isomorphic subspaces or is isomorphic to its square and hyperplanes and satisfies other regularity properties. An HI Banach space contains a continuum of non isomorphic subspaces.

Abstract:
Few-layer graphene is a layered carbon material with covalent bonding in the layers and weak van der Waals interactions between the layers. The interlayer energy is more than two orders of magnitude smaller than the intralayer one, which hinders the description of the static and dynamic properties within parameter-free electron band structure models. We overcome this difficulty by introducing two sets of matrix elements - one set for the covalent bonds in the graphene layers and another one for the van der Waals interactions between adjacent graphene layers in a tight-binding model of the band structure. Both sets of matrix elements are derived from an ab-initio study on carbon dimers. The matrix elements are then applied in the calculation of the phonon dispersion of graphite and few-layer graphene with AB and ABC layer stacking. The results for AB stacking agree well with the available experimental data, which justifies the application of the matrix elements to other layered carbon structures with van der Waals interactions such as few-layer graphene nanoribbons, multiwall carbon nanotubes, and carbon onions.

Abstract:
We consider a normalized basis in a Banach space with the following property: any normalized block sequence of the basis has a subsequence equivalent to the basis. We show that under uniformity or other natural assumptions, a basis with this property is equivalent to the unit vector basis of $c_0$ or $\ell_p$. We also address an analogous problem for spreading models.