The Winter Wren a Night Singer

Winter wren populations show adaptation to local climate

Most studies of evolutionary responses to climate change have focused on phenological responses to warming, and provide only weak evidence for evolutionary adaptation. This could be because phenological changes are more weakly linked to fitness than more direct mechanisms of climate change impacts, such as selective mortality during extreme weather events which have immediate fitness consequenc...

Song sharing and singing strategies in the winter wren Troglodytes troglodytes.

The winter wren is a common forest bird living in groups of few adjacent neighbours during the breeding season. Inside each group, males vocally interact in the context of both territorial holding and sexual competition, forming a complex communication network. To study this network, we first analysed song type and syllable repertoires within and between distinct groups. We found a limited numb...

Cyclic Orbit Codes with the Normalizer of a Singer Subgroup

An algebraic construction for constant dimension subspace codes is called orbit code. It arises as the orbits under the action of a subgroup of the general linear group on subspaces in an ambient space. In particular orbit codes of a Singer subgroup of the general linear group has investigated recently. In this paper, we consider the normalizer of a Singer subgroup of the general linear group a...

Sir Christopher Wren. A biography

The Kadison-Singer Conjecture

We are given a large integer N , and a fixed basis {ei : 1 ≤ i ≤ N} for the space H = C . We are also given an N -by-N matrix H that has all its diagonal entries zero, and has norm one. If σ ⊆ {1, 2, . . . , N}, let Pσ be the projection onto the space Hσ := ∨{ei : i ∈ σ}. Call such a projection basic, and the range of a basic projection a basic subspace. For each constant 0 < γ < 1, we want to ...