Elias M. Stein (1931–2018)

Elias George Hall

3 Elias-bassalygo Theorem

Problem Set 1 is due next Wednesday. 2 Overview Today we will do the following. • Prove the Elias-Bassalygo-Johnson Bound introduced in the previous lecture. Recall that the proof consists of the two lemmas described roughly below – List decodable codes have poor rate. – Good error correcting codes are nicely decodable. • Introduce some algebraic codes along with some helpful idea from algebra....

Dynamic Elias-Fano Representation

We show that it is possible to store a dynamic ordered set S(n, u) of n integers drawn from a bounded universe of size u in space close to the information-theoretic lower bound and yet preserve the asymptotic time optimality of the operations. Our results leverage on the EliasFano representation of S(n, u) which takes EF(S(n, u)) = ndlog u ne+ 2n bits of space and can be shown to be less than h...

μ m SPECTROSCOPY OF ELIAS 1 : ORIGIN OF DIAMONDS IN PROTOPLANETARY DISKS 1

We present spatially resolved 3 μm spectra of Elias 1 obtained with an adaptive optics system. The central part of the disk is almost devoid of PAH emission at 3.3 μm; it shows up only at 30 AU and beyond. The PAH emission extends up to 100 AU, at least to the outer boundary of our observation. The diamond emission, in contrast, is more centrally concentrated, with the column density peaked aro...

Stein E

We present a certain geometrical interpretation of the natural numbers, where these numbers appear as joint products of 5and 3-multiples located at specified positions in a revolving chamber. Numbers without factors 2, 3 or 5 appear at eight such positions, and any prime number larger than 7 manifests at one of these eight positions after a specified amount of rotations of the chamber. Our appr...