“You make what you measure” is a familiar mantra at datadriven companies. Accordingly, companies must be careful to choose North Star metrics that create a better product. Metrics fall into two general categories: direct count metrics such as total revenue and monthly active users, and nuanced quality metrics regarding value or other aspects of the user experience. Count metrics, when used excl...

Let SYM + denote the class of Boolean functions computable by depth-two size-n log O(1) n circuits with a symmetric-function gate at the root and AND gates of fan-in log O(1) n at the next level, or equivalently, the class of Boolean functions f such that f(x1; : : : ; xn) can be expressed as f(x1; : : : ; xn) = hn(pn(x1; : : : ; xn)) for some polynomial pn over Z of degree log O(1) n and norm ...

We give arguments in the support of a relation between M-atrix theory and Maldacena’s conjecture. In the limit when the light-like circle of M-theory decompactifies, M-atrix theory conjecture implies the equivalence of 11-D light-cone supergravity and stronglycoupled (0+1)-D SYM. The large-N version of Maldacena’s conjecture, SUGRA/SYM duality, can be formulated as the validity of supergravity ...

Shephard groups are unitary re ection groups arising as the sym metries of regular complex polytopes For a Shephard group we identify the representation carried by the principal ideal in the coinvariant algebra gener ated by the image of the product of all linear forms de ning re ecting hyper planes This representation turns out to have many equivalent guises making it analogous to the sign rep...

Let κ′, κ ≥ 3 be two odd integers. Let f (resp. g) be a normalized holomorphic modular form of weight 2κ (resp. κ′ + 1) and level one on the upper half plane h. Assume that they are Hecke eigenforms. Let L(s, Sym g×f) be the completed degree six L-function and we normalize so that s = 1 2 is the center of symmetry. Let 〈−,−〉 be the Petersson inner product, defined using the usual measure on h s...