Békési Imre (1936-2021)

Imre Bárány, Lecture 4

Let X ⊂ R d be a set of n points in general position (i.e. no d + 1 points of X lie on the same hyperplane.) For a positive 0 < ε < 1, we define A finite set S ⊂ R d is called a (weak) ε-net of X if S ∩ F = ∅ for any F ∈ F ε. We note that S is called a strong ε-net if, in addition, it also satisfies S ⊂ X. Since we are only going to discuss weak ε-nets, we will simply call these ε-nets. Our goa...

Problems for Imre Bárány’s Birthday

Tverberg’s Theorem states the following: Let x1, x2, . . . , xm be points in R with m ≥ (r − 1)(d + 1) + 1. Then there is a partition S1, S2, . . . , Sr of {1, 2, . . . ,m} such that ∩j=1conv(xi : i ∈ Sj) 6= ∅. This was a conjecture by Birch who also proved the planar case. The bound of (r − 1)(d + 1) + 1 in the theorem is sharp as can easily be seen from configuration of points in sufficiently...

Imre Simon: an exceptional graduate student

This short note reviews the main contributions of the Ph.D. thesis of Imre Simon. His graduate work had major impact on algebraic theory of automata and thirty years later we are in a good position to appreciate how sensitive he was in selecting good problems, and how clever in solving them! Mathematics Subject Classification. 68Q70.

Dev097394 1918..1936

Midbrain dopaminergic (mDA) neuron development has been an intense area of research during recent years. This is due in part to a growing interest in regenerative medicine and the hope that treatment for diseases affecting mDA neurons, such as Parkinson’s disease (PD), might be facilitated by a better understanding of how these neurons are specified, differentiated and maintained in vivo. This ...

EMBL Programme 2017-2021: Digital Biology