A procurement auction format is one in which bidders compete during a live auction event but observe only the rank of their own bid and not the price bids of their competitors. We investigate the performance of auctions with rank feedback in a simple setting for which analytical benchmarks are readily available. We test these benchmarks in the laboratory by comparing the performance of auctions...

In this paper, we give the complete classification of full exceptional collections on smooth toric Fano threefolds and fourfolds with Picard rank two. To be precise, a partial answer to conjecture in \cite{Kuz} \cite{LYY}: provide all maximal length prove that they are fact collections.

We focus on the problem of maximum a posteriori (MAP) inference in Markov random fields with binary variables and pairwise interactions. For this common subclass of inference tasks, we consider low-rank relaxations that interpolate between the discrete problem and its full-rank semidefinite relaxation. We develop new theoretical bounds studying the effect of rank, showing that as the rank grows...

We prove that the filling order is quadratic for a large class of solvable groups and asymptotically quadratic for all Q-rank one lattices in semisimple groups of R-rank at least 3. As a byproduct of auxiliary results we give a shorter proof of the theorem on the nondistorsion of horospheres providing also an estimate of a nondistorsion

Determinantal point processes (DPPs) are an elegant model for encoding probabilities over subsets, such as shopping baskets, of a ground set, such as an item catalog. They are useful for a number of machine learning tasks, including product recommendation. DPPs are parametrized by a positive semi-definite kernel matrix. Recent work has shown that using a low-rank factorization of this kernel pr...