Isometric group actions on Banach spaces and representations vanishing at infinity

Our main result is that the simple Lie group $G=Sp(n,1)$ acts properly isometrically on $L^p(G)$ if $p>4n+2$. To prove this, we introduce property ({\BP}_0^V), for $V$ be a Banach space: a locally compact group $G$ has property ({\BP}_0^V) if every affine isometric action of $G$ on $V$, such that the linear part is a $C_0$-representation of $G$, either has a fixed point or is metrically proper. We prove that solvable groups, connected Lie groups, and linear algebraic groups over a local field of characteristic zero, have property ({\BP}_0^V). As a consequence for unitary representations, we characterize those groups in the latter classes for which the first cohomology with respect to the left regular representation on $L^2(G)$ is non-zero; and we characterize uniform lattices in those groups for which the first $L^2$-Betti number is non-zero.Comment: 28 page

On twisted Fourier analysis and convergence of Fourier series on discrete groups

We study norm convergence and summability of Fourier series in the setting of reduced twisted group $C^*$-algebras of discrete groups. For amenable groups, F{\o}lner nets give the key to Fej\'er summation. We show that Abel-Poisson summation holds for a large class of groups, including e.g. all Coxeter groups and all Gromov hyperbolic groups. As a tool in our presentation, we introduce notions of polynomial and subexponential H-growth for countable groups w.r.t. proper scale functions, usually chosen as length functions. These coincide with the classical notions of growth in the case of amenable groups.Comment: 35 pages; abridged, revised and update

Nonlinear spectral calculus and super-expanders

Nonlinear spectral gaps with respect to uniformly convex normed spaces are shown to satisfy a spectral calculus inequality that establishes their decay along Cesaro averages. Nonlinear spectral gaps of graphs are also shown to behave sub-multiplicatively under zigzag products. These results yield a combinatorial construction of super-expanders, i.e., a sequence of 3-regular graphs that does not admit a coarse embedding into any uniformly convex normed space.Comment: Typos fixed based on referee comments. Some of the results of this paper were announced in arXiv:0910.2041. The corresponding parts of arXiv:0910.2041 are subsumed by the current pape

Property (T) and rigidity for actions on Banach spaces

We study property (T) and the fixed point property for actions on $L^p$ and other Banach spaces. We show that property (T) holds when $L^2$ is replaced by $L^p$ (and even a subspace/quotient of $L^p$), and that in fact it is independent of $1\leq p<\infty$. We show that the fixed point property for $L^p$ follows from property (T) when 1. For simple Lie groups and their lattices, we prove that the fixed point property for $L^p$ holds for any $1< p<\infty$ if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive Banach spaces.Comment: Many minor improvement

Towards ensemble asteroseismology of the young open clusters Chi Persei and NGC 6910

As a result of the variability survey in Chi Persei and NGC6910, the number of Beta Cep stars that are members of these two open clusters is increased to twenty stars, nine in NGC6910 and eleven in Chi Persei. We compare pulsational properties, in particular the frequency spectra, of Beta Cep stars in both clusters and explain the differences in terms of the global parameters of the clusters. We also indicate that the more complicated pattern of the variability among B type stars in Chi Persei is very likely caused by higher rotational velocities of stars in this cluster. We conclude that the sample of pulsating stars in the two open clusters constitutes a very good starting point for the ensemble asteroseismology of Beta Cep-type stars and maybe also for other B-type pulsators.Comment: 4 pages, Astronomische Nachrichten, HELAS IV Conference, Arecife, Lanzarote, Feb 2010, submitte

The chromatin landscape of primary synovial sarcoma organoids is linked to specific epigenetic mechanisms and dependencies.

Synovial sarcoma (SyS) is an aggressive mesenchymal malignancy invariably associated with the chromosomal translocation t(X:18; p11:q11), which results in the in-frame fusion of the BAF complex gene SS18 to one of three SSX genes. Fusion of SS18 to SSX generates an aberrant transcriptional regulator, which, in permissive cells, drives tumor development by initiating major chromatin remodeling events that disrupt the balance between BAF-mediated gene activation and polycomb-dependent repression. Here, we developed SyS organoids and performed genome-wide epigenomic profiling of these models and mesenchymal precursors to define SyS-specific chromatin remodeling mechanisms and dependencies. We show that SS18-SSX induces broad BAF domains at its binding sites, which oppose polycomb repressor complex (PRC) 2 activity, while facilitating recruitment of a non-canonical (nc)PRC1 variant. Along with the uncoupling of polycomb complexes, we observed H3K27me3 eviction, H2AK119ub deposition and the establishment of de novo active regulatory elements that drive SyS identity. These alterations are completely reversible upon SS18-SSX depletion and are associated with vulnerability to USP7 loss, a core member of ncPRC1.1. Using the power of primary tumor organoids, our work helps define the mechanisms of epigenetic dysregulation on which SyS cells are dependent

Radiotherapy for Soft Tissue Sarcomas after Isolated Limb Perfusion and Surgical Resection: Essential for Local Control in All Patients?

Background: Standard treatment for localized soft tissue sarcoma (STS) is resection plus adjuvant radiotherapy (RTx). In approximately 10% of cases, resection would cause severe loss of function or even require amputation because of the extent of disease. Isolated limb perfusion (ILP) with tumor necrosis factor alpha (TNF-α) and melphalan can achieve regression of the tumor, facilitating limb-saving resection. RTx improves local control but may lead to increased morbidity. Methods: In our database of over 500 ILPs, 122 patients with unifocal STS were treated by ILP followed by limb-sparing surgery. All included patients were candidates for amputation. Results: Surgery resulted in 69 R0 resections (57%), and in 53 specimens (43%) resection margins contained microscopic evidence of tumor (R1). Histopathological examination revealed >50% ILP-induced tumor necrosis in 59 cases (48%). RTx was administered in 73 patients (60%). Local recurrence rate was 21% after median follow-up of 31 months (2-182 months). Recurrence was significantly less in patients with >50% ILP-induced necrosis versus ≤50% necrosis (7% vs. 33%, P = 0.001). A similar significant correlation was observed for R0 versus R1 resections (15% vs. 28%, P = 0.04). In 36 patients with R0 resection and >50% necrosis, of whom 21 were spared RTx, no recurrences were observed during follow-up. Conclusions: In patients with locally advanced primary STS, treated with ILP followed by R0 resection, and with >50% ILP-induced necrosis in the resected specimen, RTx is of no further benefit

The NAD-Booster Nicotinamide Riboside Potently Stimulates Hematopoiesis through Increased Mitochondrial Clearance

It has been recently shown that increased oxidative phosphorylation, as reflected by increased mitochondrial activity, together with impairment of the mitochondrial stress response, can severely compromise hematopoietic stem cell (HSC) regeneration. Here we show that the NAD(+)-boosting agent nicotinamide riboside (NR) reduces mitochondrial activity within HSCs through increased mitochondrial clearance, leading to increased asymmetric HSC divisions. NR dietary supplementation results in a significantly enlarged pool of progenitors, without concurrent HSC exhaustion, improves survival by 80%, and accelerates blood recovery after murine lethal irradiation and limiting-HSC transplantation. In immune-deficient mice, NR increased the production of human leucocytes from hCD34+ progenitors. Our work demonstrates for the first time a positive effect of NAD(+)-boosting strategies on the most primitive blood stem cells, establishing a link between HSC mitochondrial stress, mitophagy, and stem-cell fate decision, and unveiling the potential of NR to improve recovery of patients suffering from hematological failure including post chemo- and radiotherapy.Peer reviewe

Photometric multi-site campaign on the open cluster NGC 884 I. Detection of the variable stars

CONTEXT: Recent progress in the seismic interpretation of field beta Cep stars has resulted in improvements of the physics in the stellar structure and evolution models of massive stars. Further asteroseismic constraints can be obtained from studying ensembles of stars in a young open cluster, which all have similar age, distance and chemical composition. AIMS: To improve our comprehension of the beta Cep stars, we studied the young open cluster NGC 884 to discover new B-type pulsators, besides the two known beta Cep stars, and other variable stars. METHODS: An extensive multi-site campaign was set up to gather accurate CCD photometry time series in four filters (U, B, V, I) of a field of NGC884. Fifteen different instruments collected almost 77500 CCD images in 1286 hours. The images were calibrated and reduced to transform the CCD frames into interpretable differential light curves. Various variability indicators and frequency analyses were applied to detect variable stars in the field. Absolute photometry was taken to deduce some general cluster and stellar properties. RESULTS: We achieved an accuracy for the brightest stars of 5.7 mmag in V, 6.9 mmag in B, 5.0 mmag in I and 5.3 mmag in U. The noise level in the amplitude spectra is 50 micromag in the V band. Our campaign confirms the previously known pulsators, and we report more than one hundred new multi- and mono-periodic B-, A- and F-type stars. Their interpretation in terms of classical instability domains is not straightforward, pointing to imperfections in theoretical instability computations. In addition, we have discovered six new eclipsing binaries and four candidates as well as other irregular variable stars in the observed field.Comment: Accepted for publication in Astronomy and Astrophysics, 21 pages, 14 figures, 4 tables. The full appendix is available at http://www.ster.kuleuven.be/~sophies/Appendix.pdf (74 MB, 169 pages, 343 figures, 1 table