Optimal bounds for the colored Tverberg problem

We prove a "Tverberg type" multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of Barany et al. (1980), by adding color constraints. It also provides an improved bound for the (topological) colored Tverberg problem of Barany & Larman (1992) that is tight in the prime case and asymptotically optimal in the general case. The proof is based on relative equivariant obstruction theory.Comment: 17 pages, 3 figures; revised version (February 2013), to appear in J. European Math. Soc. (JEMS

A tight colored Tverberg theorem for maps to manifolds

We prove that any continuous map of an N-dimensional simplex Delta_N with colored vertices to a d-dimensional manifold M must map r points from disjoint rainbow faces of Delta_N to the same point in M: For this we have to assume that N \geq (r-1)(d+1), no r vertices of Delta_N get the same color, and our proof needs that r is a prime. A face of Delta_N is a rainbow face if all vertices have different colors. This result is an extension of our recent "new colored Tverberg theorem", the special case of M=R^d. It is also a generalization of Volovikov's 1996 topological Tverberg theorem for maps to manifolds, which arises when all color classes have size 1 (i.e., without color constraints); for this special case Volovikov's proof, as well as ours, work when r is a prime power.Comment: 9 pages, 2 figure

A tight colored Tverberg theorem for maps to manifolds (extended abstract)

Any continuous map of an $N$-dimensional simplex $Δ _N$ with colored vertices to a $d$-dimensional manifold $M$ must map $r$ points from disjoint rainbow faces of $Δ _N$ to the same point in $M$, assuming that $N≥(r-1)(d+1)$, no $r$ vertices of $Δ _N$ get the same color, and our proof needs that $r$ is a prime. A face of $Δ _N$ is called a rainbow face if all vertices have different colors. This result is an extension of our recent "new colored Tverberg theorem'', the special case of $M=ℝ^d$. It is also a generalization of Volovikov's 1996 topological Tverberg theorem for maps to manifolds, which arises when all color classes have size 1 (i.e., without color constraints); for this special case Volovikov's proofs, as well as ours, work when r is a prime power

Polytopality and Cartesian products of graphs

We study the question of polytopality of graphs: when is a given graph the graph of a polytope? We first review the known necessary conditions for a graph to be polytopal, and we provide several families of graphs which satisfy all these conditions, but which nonetheless are not graphs of polytopes. Our main contribution concerns the polytopality of Cartesian products of non-polytopal graphs. On the one hand, we show that products of simple polytopes are the only simple polytopes whose graph is a product. On the other hand, we provide a general method to construct (non-simple) polytopal products whose factors are not polytopal.Comment: 21 pages, 10 figure

Clonality of circulating tumor cells in breast cancer brain metastasis patients

BACKGROUND: The incidence of brain metastases in breast cancer (BCBM) patients is increasing. These patients have a very poor prognosis, and therefore, identification of blood-based biomarkers, such as circulating tumor cells (CTCs), and understanding the genomic heterogeneity could help to personalize treatment options. METHODS: Both EpCAM-dependent (CellSearch® System) and EpCAM-independent Ficoll-based density centrifugation methods were used to detect CTCs from 57 BCBM patients. DNA from individual CTCs and corresponding primary tumors and brain metastases were analyzed by next-generation sequencing (NGS) in order to evaluate copy number aberrations and single nucleotide variations (SNVs). RESULTS: CTCs were detected after EpCAM-dependent enrichment in 47.7% of the patients (≥ 5 CTCs/7.5 ml blood in 20.5%). The CTC count was associated with ERBB2 status (p = 0.029) of the primary tumor as well as with the prevalence of bone metastases (p = 0.021). EpCAM-independent enrichment revealed CTCs in 32.6% of the patients, especially among triple-negative breast cancer (TNBC) patients (70.0%). A positive CTC status after enrichment of either method was significantly associated with decreased overall survival time (p < 0.05). Combining the results of both enrichment methods, 63.6% of the patients were classified as CTC positive. In three patients, the matched tumor tissue and single CTCs were analyzed by NGS showing chromosomal aberrations with a high genomic clonality and mutations in pathways potentially important in brain metastasis formation. CONCLUSION: The detection of CTCs, regardless of the enrichment method, is of prognostic relevance in BCBM patients and in combination with molecular analysis of CTCs can help defining patients with higher risk of early relapse and suitability for targeted treatment

Non-secreting pituitary tumours characterised by enhanced expression of YAP/TAZ

Tumours of the anterior pituitary can manifest from all endocrine cell types but the mechanisms for determining their specification are not known. The Hippo kinase cascade is a crucial signalling pathway regulating growth and cell fate in numerous organs. There is mounting evidence implicating this in tumour formation, where it is emerging as an anti-cancer target. We previously demonstrated activity of the Hippo kinase cascade in the mouse pituitary and nuclear association of its effectors YAP/TAZ with SOX2-expressing pituitary stem cells. Here we sought to investigate whether these components are expressed in the human pituitary and if they are deregulated in human pituitary tumours. Analysis of pathway components by immunofluorescence reveals pathway activity during normal human pituitary development and in the adult gland. Poorly differentiated pituitary tumours (null cell adenomas, adamantinomatous craniopharyngiomas (ΑCPs) and papillary craniopharyngiomas (PCPs)), displayed enhanced expression of pathway effectors YAP/TAZ. In contrast, differentiated adenomas displayed lower or absent levels. Knock-down of the kinase-encoding Lats1 in GH3 rat mammosomatotropinoma cells suppressed Prl and Gh promoter activity following an increase in YAP/TAZ levels. In conclusion, we have demonstrated activity of the Hippo kinase cascade in the human pituitary and association of high YAP/TAZ with repression of the differentiated state both in vitro and in vivo. Characterisation of this pathway in pituitary tumours is of potential prognostic value, opening up putative avenues for treatments

Educational paper: Abusive Head Trauma Part I. Clinical aspects

Abusive Head Trauma (AHT) refers to the combination of findings formerly described as shaken baby syndrome. Although these findings can be caused by shaking, it has become clear that in many cases there may have been impact trauma as well. Therefore a less specific term has been adopted by the American Academy of Pediatrics. AHT is a relatively common cause of childhood neurotrauma with an estimated incidence of 14–40 cases per 100,000 children under the age of 1 year. About 15–23% of these children die within hours or days after the incident. Studies among AHT survivors demonstrate that approximately one-third of the children are severely disabled, one-third of them are moderately disabled and one-third have no or only mild symptoms. Other publications suggest that neurological problems can occur after a symptom-free interval and that half of these children have IQs below the 10th percentile. Clinical findings are depending on the definitions used, but AHT should be considered in all children with neurological signs and symptoms especially if no or only mild trauma is described. Subdural haematomas are the most reported finding. The only feature that has been identified discriminating AHT from accidental injury is apnoea. Conclusion: AHT should be approached with a structured approach, as in any other (potentially lethal) disease. The clinician can only establish this diagnosis if he/she has knowledge of the signs and symptoms of AHT, risk factors, the differential diagnosis and which additional investigations to perform, the more so since parents seldom will describe the true state of affairs spontaneously

Structural decoding of netrin-4 reveals a regulatory function towards mature basement membranes

Netrins, a family of laminin-related molecules, have been proposed to act as guidance cues either during nervous system development or the establishment of the vascular system. This was clearly demonstrated for netrin-1 via its interaction with the receptors DCC and UNC5s. However, mainly based on shared homologies with netrin-1, netrin-4 was also proposed to play a role in neuronal outgrowth and developmental/pathological angiogenesis via interac- tions with netrin-1 receptors. Here, we present the high-resolution structure of netrin-4, which shows unique features in comparison with netrin-1, and show that it does not bind directly to any of the known netrin-1 receptors. We show that netrin-4 disrupts laminin networks and basement membranes (BMs) through high-affinity binding to the laminin g1 chain. We hypothesize that this laminin-related function is essential for the previously described effects on axon growth promotion and angiogenesis. Our study unveils netrin-4 as a non-enzymatic extracellular matrix protein actively disrupting pre-existing BMs

Current trends in cannulation and neuroprotection during surgery of the aortic arch in Europe†‡

OBJECTIVES To conduct a survey across European cardiac centres to evaluate the methods used for cerebral protection during aortic surgery involving the aortic arch. METHODS All European centres were contacted and surgeons were requested to fill out a short, comprehensive questionnaire on an internet-based platform. One-third of more than 400 contacted centres completed the survey correctly. RESULTS The most preferred site for arterial cannulation is the subclavian-axillary, both in acute and chronic presentation. The femoral artery is still frequently used in the acute condition, while the ascending aorta is a frequent second choice in the case of chronic presentation. Bilateral antegrade brain perfusion is chosen by the majority of centres (2/3 of cases), while retrograde perfusion or circulatory arrest is very seldom used and almost exclusively in acute clinical presentation. The same pumping system of the cardio pulmonary bypass is most of the time used for selective cerebral perfusion, and the perfusate temperature is usually maintained between 22 and 26°C. One-third of the centres use lower temperatures. Perfusate flow and pressure are fairly consistent among centres in the range of 10-15 ml/kg and 60 mmHg, respectively. In 60% of cases, barbiturates are added for cerebral protection, while visceral perfusion still receives little attention. Regarding cerebral monitoring, there is a general tendency to use near-infrared spectroscopy associated with bilateral radial pressure measurement. CONCLUSIONS These data represent a snapshot of the strategies used for cerebral protection during major aortic surgery in current practice, and may serve as a reference for standardization and refinement of different approache