Am Bier lag’s nicht!

Bier spots.

Bier Spheres and Posets

In 1992 Thomas Bier presented a strikingly simple method to produce a huge number of simplicial (n− 2)-spheres on 2n vertices as deleted joins of a simplicial complex on n vertices with its combinatorial Alexander dual. Here we interpret his construction as giving the poset of all the intervals in a boolean algebra that “cut across an ideal.” Thus we arrive at a substantial generalization of Bi...

Supplement for BIER

In this document we provide further insights into Boosting Independent Embeddings Robustly (BIER). First, in Section 2 we describe our method for loss functions operating on triplets. Next, in Section 3 we show how our method behaves when we vary the embedding size and the number of groups. In Section 4 we summarize the effect of our boosting based training approach and our initialization appro...

BIER - Boosting Independent Embeddings Robustly

Learning similarity functions between image pairs with deep neural networks yields highly correlated activations of large embeddings. In this work, we show how to improve the robustness of embeddings by exploiting independence in ensembles. We divide the last embedding layer of a deep network into an embedding ensemble and formulate training this ensemble as an online gradient boosting problem....

Kalzium Ist Nicht Alles

Elevation of cerebral Mg2+ with a novel orally delivered ionophore, magnesium threonate, enhances cognition in young and old rats over a 12-24 day treatment interval, as outlined in a paper by Slutsky et al. in this issue of Neuron. Despite both Mg2+ and Zn2+ blocking the NMDA receptor channel, sustained extracellular Mg2+ elevation mimics sustained synaptic Zn2+ concentrations by increasing hi...