Painter Alex Katz and his son, writer Vincent Katz, discuss their personal experiences in artistic collaboration in a conversation with Derek Bermel, the Institute's Artist-in-Residence. Both Alex and Vincent have been involved in numerous collaborative projects. Alex has collaborated on books with many poets, including John Ashbery, Robert Creeley, and Kenneth Koch, and he has designed sets and costumes for choreographers Paul Taylor and David Parsons. Vincent has collaborated with the artists Rudy Burckhardt, Francesco Clemente, and Wayne Gonzales. He is an art critic who has authored numerous essays and articles on contemporary artists; he is the publisher of the poetry journal Vanitas and of Libellum Books; and he serves as Chair of the Board of the Bowery Poetry Club.
Let η1, . . . , ηn be iid Bernoulli random variables, taking values 1, −1 with probability 1/2. Given a multiset V of n integers v1, . . . , vn, we define the concentration probability as ρ(V ) := supx P(v1η1 + · · · + vnηn = x).
Algorithms spend time on performing arithmetic computations, but often more on moving data, between the levels of a memory hierarchy and between parallel computing entities. Judging by the hardware evolution of the last few decades, the fraction of running time spent on communication is expected to increase, and with it - the demand for communication-avoiding algorithms. We use geometric, combinatorial, and algebraic ideas and techniques, some of which are known in the context of expander graphs, to construct provably communication-optimal algorithms.
We give an algorithmic proof of Forster's Theorem, a fundamental result in communication complexity. Our proof is based on a geometric notion we call radial isotropic position which is related to the well-known isotropic position of a set of vectors. We point out an efficient algorithm to compute the radial isotropic position of a given set of vectors when it exists.