Constructing Simplicial Branched Covers

Branched covers are applied frequently in topology - most prominently in the construction of closed oriented PL d-manifolds. In particular, strong bounds for the number of sheets and the topology of the branching set are known for dimension d<=4. On the other hand, Izmestiev and Joswig described how to obtain a simplicial covering space (the partial unfolding) of a given simplicial complex, thus obtaining a simplicial branched cover [Adv. Geom. 3(2):191-255, 2003]. We present a large class of branched covers which can be constructed via the partial unfolding. In particular, for d<=4 every closed oriented PL d-manifold is the partial unfolding of some polytopal d-sphere.Comment: 15 pages, 8 figures, typos corrected and conjecture adde

Products of Foldable Triangulations

Regular triangulations of products of lattice polytopes are constructed with the additional property that the dual graphs of the triangulations are bipartite. The (weighted) size difference of this bipartition is a lower bound for the number of real roots of certain sparse polynomial systems by recent results of Soprunova and Sottile [Adv. Math. 204(1):116-151, 2006]. Special attention is paid to the cube case.Comment: new title; several paragraphs reformulated; 23 page

Outcome after relapse of myelodysplastic syndrome and secondary acute myeloid leukemia following allogeneic stem cell transplantation : a retrospective registry analysis on 698 patients by the Chronic Malignancies Working Party of the European Society of Blood and Marrow Transplantation

No standard exists for the treatment of myelodysplastic syndrome relapsing after allogeneic stem cell transplantation. We performed a retrospective registry analysis of outcomes and risk factors in 698 patients, treated with different strategies. The median overall survival from relapse was 4.7 months (95% confidence interval: 4.1-5.3) and the 2-year survival rate was 17.7% (95% confidence interval: 14.8-21.2%). Shorter remission after transplantation (PPeer reviewe

Foldable Triangulations

A simplicial d-complex is foldable if it is (d+1)-colorable in the graph theoretic sense. Such a coloring defines a non-degenerated simplicial map to the d-simplex, hence the name "foldable". Foldable simplicial complexes are sometimes referred to as being "balanced". We apply foldable simplicial complexes to obtain the following two results. Any closed oriented PL d-manifold is a branched cover of the d-sphere, but no restrictions on the number of sheets nor the topology of the branching set are known for d>4 in general. As for dimension four, Piergallini [Topology 34(3):497-508, 1995] proved that every closed oriented PL 4-manifold is a 4-fold branched cover of the 4-sphere branched over an immersed PL surface. This generalizes a long standing result by Hilden and Montesinos to dimension four. Izmestiev and Joswig [Adv. Geom. 3(2):191-225, 2003] gave a combinatorial equivalent of the Hilden and Montesinos result, constructing (fairly explicit) closed oriented combinatorial 3-manifolds as unfoldings of combinatorial 3-spheres. The construction of Izmestiev and Joswig is generalized and applied to the result of Piergallini, obtaining closed oriented combinatorial 4-manifolds as unfoldings of combinatorial 4-spheres. Foldable and regular triangulations of products of lattice polytopes are constructed from foldable and regular triangulations of the factors. It is known that foldable triangulations of polytopes have a bipartite dual graph. The (weighted) size difference of this bipartition is a lower bound for the number of real roots of certain sparse polynomial systems by recent results of Soprunova and Sottile [Adv. Math. 204(1):116-151, 2006]. Special attention is paid to the cube case

Prediction of movement for adaptive control of an upper limb exoskeleton

The 9.5th international symposium on Adaptive Motion of Animals and Machines. Ottawa，Canada (Virtual Platform). 2021-06-22/25. Adaptive Motion of Animals and Machines Organizing Committee