Platelet integrin αIIbβ3 is a key mediator of platelet activation and thrombosis. Upon activation αIIbβ3 undergoes significant conformational rearrangement, inducing complex bidirectional signalling and protein recruitment leading to platelet activation. Reconstituted lipid models of the integrin can enhance our understanding of the structural and mechanistic details of αIIbβ3 behaviour away fr...

Both seismic observations of dense low shear velocity regions and models magma ocean crystallization mantle dynamics support enrichment iron in Earth’s lowermost mantle. Physical properties iron-rich lower heterogeneities the modern Earth depend on distribution between coexisting phases (Mg,Fe)O magnesiowüstite, (Mg,Fe)SiO3 bridgmanite, post-perovskite. The partitioning these was investigated s...

Birch and Tverberg partitions are closely related concepts from discrete geometry. We show two properties for the number of Birch partitions: Evenness, and a lower bound. This implies the first non-trivial lower bound for the number of Tverberg partitions that holds for arbitrary q, where q is the number of partition blocks. The proofs are based on direct arguments, and do not use the equivaria...

If a1, a2, . . . , ak and n are positive integers such that n = a1+a2+· · ·+ak, then the sum a1 + a2 + · · ·+ ak is said to be a partition of n of length k, and a1, a2, . . . , ak are said to be the parts of the partition. Two partitions that differ only in the order of their parts are considered to be the same partition. Let Pn be the set of partitions of n, and let Pn,k be the set of partitio...

In 2009, Blagojević, Matschke & Ziegler established the first tight colored Tverberg theorem. We develop a colored version of our previous results (2008): Evenness and non-trivial lower bounds for the number of colored Tverberg partitions. Both properties follow from similar results on the number of colored Birch partitions.

Recently the authors have proposed tests for the one-sample and the ksample problem, and a test for independence. All three tests are based on sample space partitions, but they were originally developed in different papers. Here we give an overview of the construction of these tests, stressing the common underlying concept of “sample space partitions.”