The von Mises-Fisher distribution of the first exit point from the hypersphere of the drifted Brownian motion and the density of the first exit time

A characterization is provided for the von Mises–Fisher random variable, in terms of first exit point from the unit hypersphere of the drifted Wiener process. Laplace transform formulae for the first exit time from the unit hypersphere of the drifted Wiener process are provided. Post representations in terms of Bell polynomials are provided for the densities of the first exit times from the circle and from the sphere.

3D scaffolds co-seeded with human endothelial progenitor and mesenchymal stem cells: evidence of prevascularisation within 7 days

Blood supply is a critical issue in most tissue engineering approaches for large defect healing. As vessel ingrowth from surrounding tissues is proven to be insufficient, current strategies are focusing on the neo-vascularisation process. In the present study, we developed an in vitro pre-vascularised construct using 3D polyurethane (PU) scaffolds, based on the association of human Endothelial Progenitor Cells (EPC, CD34+ and CD133+) with human Mesenchymal Stem Cells (MSC). We showed the formation of luminal tubular structures in the co-seeded scaffolds as early as day 7 in culture. These tubular structures were proven positive for endothelial markers von Willebrand Factor and PECAM-1. Of special significance in our constructs is the presence of CD146-positive cells, as a part of the neovasculature scaffolding. These cells, coming from the mesenchymal stem cells population (MSC or EPC-depleted MSC), also expressed other markers of pericyte cells (NG2 and αSMA) that are known to play a pivotal function in the stabilisation of newly formed pre-vascular networks. In parallel, in co-cultures, osteogenic differentiation of MSCs occurred earlier when compared to MSCs monocultures, suggesting the close cooperation between the two cell populations. The presence of angiogenic factors (from autologous platelet lysates) in association with osteogenic factors seems to be crucial for both cell populations' cooperation. These results are promising for future clinical applications, as all components (cells, growth factors) can be prepared in an autologous way.

"Fascinating Voids: Alexander von Humboldt and the Myth of Chimborazo"

When Alexander von Humboldt reached the village of Calpi in the Andes on 22 June 1802, he was greeted with reverence and enthusiasm. Triumphal arches adorned with cotton, cloth, and silver decorated his path. The natives performed a dance in festive dress. A singer praised the explorer's expedition, which had departed three years earlier from the Spanish port of La Coruña. Like Odysseus on the isle of the Phaeacians, the traveler listened to a local rhapsodist singing about his heroic deeds. Before his adventure ended, it had already spun a popular myth. This episode, which Humboldt recorded in his diary, occurred at a significant moment. One day later, the “Second Discoverer of America” rose to even greater fame on an excursion marking in more ways than one the climax of his enterprise. Humboldt set out to climb Chimborazo (6,310 m/20,702 ft.), the mountain then thought to be the highest in the world. He was accompanied by the French botanist Aimé Bonpland (1773–1858) and the Creole nobleman and future activist Carlos Montúfar (1780–1816), as well as native guides and assistants. They climbed to heights never reached before, setting a new record and catapulting Humboldt to fame on both continents.