We confront the finite volume and small quark mass behaviour of the scalar condensate, determined numerically in quenched lattice QCD using Neuberger fermions, with predictions of quenched chiral perturbation theory. We find that quenched chiral perturbation theory describes the numerical data well, allowing us to extract the infinite volume, chiral limit scalar condensate, up to a multiplicati...

The polynomial method and the adversary method are the two main techniques to prove lower bounds on quantum query complexity, and they have so far been considered as unrelated approaches. Here, we show an explicit reduction from the polynomial method to the multiplicative adversary method. The proof goes by extending the polynomial method from Boolean functions to quantum state generation probl...

We show that the fluctuation-dissipation relation can be established for a class of stochastic dynamics that lack detailed balance. This class comprises lattice spin models whose time evolution is governed by a master equation with a one-spin-flip transition rate having the up-down symmetry. The relation is obtained by the introduction of a multiplicative perturbation of the transition rate, wh...

A fundamental assumption for most direction nding algorithms is that the background noise is uncorrelated from sensor to sensor, or known to within a multiplicative scalar. In practice this assumption is seldom ful lled, however, the spatial noise covariance may be estimated by measuring the array covariance when no signals are present. This procedure is unavoidably subjected to errors. In this...

A new line of work, started with Dwork et al. [2], studies the task of answering statistical queries using a sample and relates the problem to the concept of differential privacy [4]. By the Hoeffding bound, a sample of size O(log k/α) suffices to answer k non-adaptive queries within error α, where the answers are computed by evaluating the statistical queries on the sample. This argument fails...

We prove a new bound for multiplicative character sums of nonlinear recurring sequences with Rédei functions over a finite field of prime order. This result is motivated by earlier results on nonlinear recurring sequences and their application to the distribution of powers and primitive elements. The new bound is much stronger than the bound known for general nonlinear recurring sequences.